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L * . 3 ' .

Trends in MuSifactor
Produciwitfg 1948=81

T /y f

U.S. Department of Labor
Bureau of Labor Statistics
September 1983

S£T 2 1 1 9 8 3

.INDUSTRY AND SCIENCE

Bulletin 2178
- 'a y t o n & M o n tg o m e r y r

LABOR PRODUCTIVITY

P u b lic




Co'

Library of Congress Cataloging in Publication Data

Main e n try under t i t l e :

Trends in m u ltif a c to r p r o d u c tiv ity , I 9U8- 8I 0




( B u lle tin / U«S0 D epartm ent o f L abor, Bureau o f
Labor S t a t i s t i c s ; 2178)
"This stu d y was p re p a red by th e B u reau ’s O ffice o f
P r o d u c tiv ity and Technology" — Pref*
In c lu d e s b ib lio g r a p h ic a l r e f e r e n c e s 0
1* I n d u s t r i a l p r o d u c tiv ity - - U n ite d S t a t e s —S t a t i s t i c s *
I . U n ited S t a t e s * Bureau o f Labor S t a t i s t i c s 9 O ffice o f
P r o d u c tiv ity and Technology* II* S e r ie s : B u lle tin
(U nited S ta te s * Bureau o f Labor S t a t i s t i c s ) ; 2178*
HCUO*I52T73 1983
338f *06 f 0973
83- I 8835

Trends in SluSSifaetor
Productivity,1948-81
U.S. Department of Labor
Raymond J. Donovan, Secretary
Bureau of Labor Statistics
Janet L. Norwood, Commissioner
September 1983
Bulletin 2178

For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C. 20402, Stock no. 029-001-02758-3



■




One of the principal functions of the Bureau of Labor
Statistics is to inform policymakers on the utilization of
the Nation’s resources, particularly as this affects the
well-being of U.S. workers. Thus an important part of
the Bureau’s work is the study of productivity, which is
directly related to real income, price stability, employ­
ment, and the competitiveness of U.S. goods and serv­
ices in world markets.
The major purpose of this bulletin is to present new
bls annual indexes of multifactor productivity for pri­
vate business, private nonfarm business, and manufac­
turing for the period 1948 through 1981. These indexes
incorporate capital in addition to labor inputs and are
therefore more inclusive measures of productivity than
the more familiar bls measures of output per hour of all
persons. The indexes, including revisions, will be pub­
lished annually. The bulletin also presents for the first
time bls annual measures of output per unit of capital
service inputs for the three sectors.
In addition, the bulletin presents revised, updated in­
dexes of the bls quarterly measures of output per hour
of all persons in the business, nonfarm business, and
m anufacturing sectors for the period 1947 through
1982. It also includes revised annual indexes of real
product per hour of all persons in the total private
economy beginning in 1909. (Government enterprises
are included in the productivity indexes for the business
sectors but not in those for private business.) The bulle­
tin also includes appendixes describing the methodology
and basic data employed in constructing the bls produc­
tivity measures. Previously, a comprehensive descrip­
tion of the methodology and data sources used to con­
struct the output per hour measures was published in
Trends in Output per M an-hour in the Private
Economy, 1909-1958, Bulletin 1249 (1959).
The bls measurement of multifactor productivity and
output per unit of capital is in keeping with recommen­
dations of the Panel to Review Productivity Statistics set
up by the National Academy of Sciences and chaired by
Professor Albert Rees. The panel’s recommendations,




published in 1979 by the National Academy of Sciences
in Measurement and Interpretation of Productivity,
were:
“ . . . that the Bureau of Labor Statistics experiment with
combining labor and other inputs into alternative measures
of multifactor productivity, (p.14)
“ . . . that government agencies make use of available esti­
mates of real capital stocks to develop ratios of output per
unit of capital in order to determine the savings that have
been achieved over time in physical capital per unit of out­
put.” (p .ll)

The new measures presented in this bulletin are the
first of a series of measures of multifactor productivity
that bls will be producing. Future work will include
multifactor productivity measures by major sector based
on gross output and inputs of energy, materials, and
purchased services as well as capital and labor services.
In addition, bls will be developing measures showing
changes in the composition of the labor force, invest­
ment in research and development, capacity utilization,
economies of scale, and resource allocation in order to
see how these factors have influenced the growth of
multifactor productivity.
This study was prepared by the Bureau’s Office of
Productivity and Technology under the direction of
Jerome A. Mark, Associate Commissioner, and under
the direct supervision of William H. Waldorf, Chief of
the Division of Productivity Research, who also pre­
pared the text. Kent Kunze prepared appendixes A and
F; William Gullickson was responsible for appendix B;
Michael Harper and Steven Rosenthal for appendix C;
Lawrence J. Fulco for appendix D; and Kent Kunze and
Leo Sveikauskas, appendix E. The staff of the Bureau
of Economic Analysis, U.S. Department of Commerce,
provided helpful comments in their review of the
manuscript.
Material in this publication is in the public domain
and, with appropriate credit, may be reproduced without
permission.




©©mtemts

Summary of findings .............................................................................................................................................
Private business sector ...................................................................................................................................
Private nonfarm business sector ...................................................................................................................
Manufacturing sector .....................................................................................................................................
Chapter I.

Page
1
1
2
2

Introduction .......................................................................................................................................

3

Chapter II. Output per hour of all persons in the business sector ..................................................................
Cyclical movements in output per hour .......................................................................................................
Trends in output per hour .............................................................................................................................
Post-1948 growth rates .................................................................................................................................
The long term: 1909-81

5
5
5
9
10

Chapter III. Multifactor productivity in the private business sector .............................................................
Trends in multifactor productivity ...............................................................................................................
Capital per hour of all persons .....................................................................................................................
Relationship between capital per hour and factor prices ...........................................................................

16
16
16
21

Chapter IV. Sources of change in multifactor productivity ............................................................................
Intersectoral shifts .........................................................................................................................................
Changes in labor force composition .............................................................................................................
Capacity utilization.........................................................................................................................................
Research and development ...........................................................................................................................
Hours at work versus hours paid .................................................................................................................
Summary .........................................................................................................................................................

25
25
25
27
29
31
31

Appendix A.

The multifactor productivity model ...........................................................................................

33

Appendix B. Real output measures: Methodsand sources ...............................................................................
Business sector ...............................................................................................................................................
Farm sector .....................................................................................................................................................
Manufacturing sector .....................................................................................................................................

35
35
37
37

Appendix C. Capital input and capital andlabor shares ...................................................................................
Measurement of capital stocks by assettype ...............................................................................................
Aggregation of capital stocks by asset type ...............................................................................................
Capital and labor income shares ...................................................................................................................
Examination of the measures .......................................................................................................................
Sensitivity analysis .........................................................................................................................................
Summary .........................................................................................................................................................

39
40
49
52
53
56
58

Appendix D. Hours of all persons: Methodsand so u rces.................................................................................
Nonmanufacturing .........................................................................................................................................
Manufacturing .................................................................................................................................................
Farm .................................................................................................................................................................
Government enterprises .................................................................................................................................
Nonprofit institutions .....................................................................................................................................

66
67
67
67
68
68




v

0 ® [n ite B itS “

0 © E n 3 in y @ d ]

Page
Appendix E. Comparison of base-year-weighted and Tornquist index numbers of multifactor productivity
Annual percent changes .................................................................................................................................
Average annual rates of growth ...................................................................................................................

69
69
69

Appendix F. Comparison of multifactor measures .........................................................................................
Output .............................................................................................................................................................
Labor input .....................................................................................................................................................
Capital input ...................................................................................................................................................
Aggregation ...........................................................................
Labor and capital shares ...............................................................................................................................

73
73
76
76
79
79

Charts:
1.
2.
3.
4.
5.
6.
7.
8.
9.
C - l.
C-2.

F - l.
F-2.
F-3.
F-4.

Tables:
1.
2.
3.
4.
5.

Real hourly compensation and productivity in the business sector, 1947-82 ................................
Business sector: Output per hour, output, and hours, quarterly, 1948-82 ......................................
Nonfarm business sector: Output per hour, output, and hours, quarterly, 1948-82 ......................
Manufacturing sector: Output per hour, output, and hours, quarterly, 1948-82 ............................
Output per hour, 1909-82 .....................................................................................................................
Private business sector: Output per hour of all persons, output per unit of capital, and multifactor
productivity, 1948-81 .......................................................................................................................
Private nonfarm business sector: Output per hour of all persons, output per unit of capital, and
multifactor productivity, 1948-81 ..................................................................................................
Manufacturing sector: Output per hour of all persons, output per unit of capital, and multifactor
productivity, 1948-81 .......................................................................................................................
Output per unit of capital and rate of capacity utilization in manufacturing, 1948-81 ..................
General forms of an efficiency function ..............................................................................................
Cohort efficiency function for gross stocks with a truncated normally distributed discard
function ...............................................................................................................................................
Output for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick,
1948-81 ...............................................................................................................................................
Labor input for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick,
1948-81 ................................................................................................................
Capital input for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick,
1948-81 ...................................................................................................................................................
Multifactor productivity for the most aggregate sector measured by b l s , Denison, Jorgenson, and
Kendrick, 1948-81 .................................................................................................................................

Rates of growth in output per hour of all persons between business cycle peaks in the business
and nonfarm business sectors, 1948IV to1981 III .........................................................................
Rates of growth in output per hour of all persons, output, and hours by major sector,
1948-81 ....................................................................................................................................................
Output per hour, output, and hours of all persons by major sector, annual and quarterly,
1947-82 ....................................................................................................................................................
Output per hour, output, and hours inthe total private sector, 1909-82 .........................................
Rates of growth in output per hour of all persons, capital per hour, the contribution of capital,
and multifactor productivity by major sector,1948-81




vt

4
6
7
8
11
17
18
19
29
42
43

75

78
78

9
9
12
15

(SooDSents— Continued

Tables— Continued
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.

Page

Labor and capital shares of total income by major sector, 1948-81 ................................................
Relationship between changes in rates of growth in capital services per hour and changes in
relative factor prices in the private business sector, 1948-81 ......................................................
Private business sector: Productivity and related measures, 1948-81 ..............................................
Private nonfarm business sector: Productivity and related measures, 1948-81 ..............................
Manufacturing sector: Productivity and related measures, 1948-81 ................................................
Contribution of intersectoral shifts in labor to rates of growth in multifactor productivity in the
private business sector, 1948-81 ..........................................................................................................
Percent distribution of the labor force by years of school completed, by sex, 1948, 1973, and
1981 ..........................................................................................................................................................
Adjustments to hours measures for changes in composition of labor input ....................................
Rates of growth in multifactor productivity in manufacturing, unadjusted and adjusted for
utilization of physical capital, 1948-81
Rates of growth in the ratio of hours at work to hours paid, private nonfarm business and
manufacturing sectors, selected periods, 1952-81 ..............................................................................

B - l.

Relationship between gross national product and the
product, 1981

C -l.
C-2.
C-3.
C-4.
C-5.

Summary of methods and data sources used to measurecapital andmultifactor productivity . . . .
Illustration of a perpetual inventory calculation for afictional type ofasset ........................................
Types of assets and service life assumptions ...........................................................................................
Weighted sum of differences between hyperbolicefficiencypatterns andsimulated data ....................
Manufacturing sector: Shares in total income used to aggregate labor and capital inputs,
1948- 81 ................................................................................................................................................
Farm sector: Shares in total income used to aggregatelaborand capitalinputs, 1948-81
Nonfarm-nonmanufacturing sector: Shares in total income used to aggregate labor and capital
inputs, 1948-81
Private business sector: Growth rates including and excluding selected assets from published
measures, 1948-81 .................................................................................................................................
Private nonfarm business sector: Growth rates including and excluding selected assets from
published measures, 1948-81 ................................................................................................................
Manufacturing sector: Growth rates including and excluding selected assets from published
measures, 1948-81 .................................................................................................................................
Sensitivity of multifactor productivity measure to relative efficiency assumptions, private
business sector, 1949-81 ......................................................................................
Sensitivity of capital services measure to relative efficiency assumptions, private business sector,
1949- 81 ................................................................................................................................................

C-6.
C -l.
C-8.
C-9.
C-10.
C -ll.
C-12.

bls

vii

21
22
23
24
25
26
26

31

measure of private business sector gross

Private business sector, 1948-81:
C - 13. Real capital input ........................................................................................................................................
C-14. Productive capital stock ..............................................................................................................................
C-15. Shares in current capital cost ....................................................................................................................
C - l 6. Ratio of capital services to productive stock ..........................................................................................
C - l 7.
Gross real investment ..................................................................................................................................
C-18. Price of new capital goods ........................................................................................................................
C-19.
Rate of depreciation ....................................................................................................................................



20

39
41
43
44
54
55

57
57
58

59

60
60
60
61
61
61
61

Contents— Continued

Tables— Continued

Page

Private nonfarm business sector, 1948-81:
C-20. Real capital input ....................................................................................................................................
C-21. Productive capital stock ..........................................................................................................................
C-22. Shares in current capital cost ................................................................................................................
C-23. Ratio of capital services to productive stock ......................................................................................
C-24. Gross real investment ........................................................
C-25. Price of new capital goods ....................................................................................................................
C-26. Rate of depreciation ................................................................................................................................
Manufacturing sector, 1948-81:
C-27. Real capital input ....................................................................................................................................
C-28.
Productive capital stock ...........................................................................................................
C-29. Shares in current capital cost ................................................................................................................
C-30. Ratio of capital services to productive stock ......................................................................................
C-31. Gross real investment ..............................................................................................................................
C-32. Price of new capital goods ....................................................................................................................
C-33. Rate of depreciation ................................................................................................................................
D -l.

E - l.
E-2.
E-3.
E-4.

F - l.
F-2.
F-3.
F-4.
F-5.
F-6.
F-7.
F-8.

Sources of employment and hours data used in labor input measures for bls productivity series,
private business sector .......................................................................................................................
Private business sector: Annual percent change in multifactor productivity under different index
number methods, 1949-81
Private nonfarm business sector: Annual percent change in multifactor productivity under
different index number methods, 1949-81 ..........................................................................................
Manufacturing sector: Annual percent change in multifactor productivity under different index
number methods, 1949-81
Rates of growth of multifactor productivity under different index number methods by major
sector, 1948-81
Computation of output measures by bls, Denison, Jorgenson, and Kendrick .................................
Indexes and rates of growth of output for the most aggregate sector measured by bls, Denison,
Jorgenson, and Kendrick, 1948-81 ......................................................................................................
Indexes and rates of growth of labor input for the most aggregate sector measured by bls,
Denison, Jorgenson, and Kendrick, 1948-81 .................................................................................
Computation of labor input measures by bls, Denison, Jorgenson, and Kendrick .........................
Indexes and rates of growth of capital input for the most aggregate sector measured by bls,
Denison, Jorgenson, and Kendrick, 1948-81 ......................................................................................
Computation of capital input measures by bls, Denison, Jorgenson, and Kendrick .......................
Labor’s share for the most aggregate sector measured by bls, Denison, Jorgenson, and Kendrick,
1948-81 ...................................................................................................................................................
Indexes and rates of growth of multifactor productivity for the most aggregate sector measured by
bls, Denison, Jorgenson, and Kendrick, 1948-81




viii

62
62
62
63
63
63
63

64
64
64
65
65
65
65

66

70
71

73
74
76
77
77
77
79

S u m m a ir f © f F in d in g s

per year. During this period, capital inputs rose by 3.5
percent per year and hours of all persons by 0.9 percent,
so that the rate of growth of capital services per hour
(i.e., capital intensity) was 2.5 percent annually. This
growth in capital per hour, when weighted by capital’s
share of total income, indicates that increased capital in­
tensity contributed 0.9 percentage point—or roughly 40
percent—to the growth in output per hour. Multifactor
productivity—the remainder—grew at an average annu­
al rate of 1.5 percent. This rate of growth in multifactor
productivity means that the U.S. economy produced
about 65 percent more in 1981 than in 1948 from the
same quantity of labor and capital resources.

The American economy experienced a historically
high rate of growth in productivity measured by output
per hour during the quarter century 1948-73; however,
the rate fell sharply in the following decade. There are a
host of factors that could have caused these divergent
trends: Changes in the amount of capital per worker,
changes in technology, shifts in the composition of the
work force, differences in effort per hour worked,
changes in capacity utilization, increases in the cost of
energy, and other factors.
This bulletin presents a recently constructed measure
of productivity—multifactor productivity— which quan­
tifies the effects of changes in the amount of capital per
unit of labor (i.e., capital intensity), one of the most im­
portant sources of growth of output per hour of all per­
sons. The new measure adds to existing bls measures of
productivity; it represents the Bureau’s first step in try­
ing to quantify the contributions of a number of major
factors underlying the movements in productivity.
The index of multifactor productivity measures annu­
al change in output per unit of combined labor and capi­
tal input. This is mathematically equivalent to sub­
tracting the effects of annual rates of change in capital
per hour from the annual rates of change in output per
hour of all persons. Thus, the multifactor productivity
measure differs from the familiar bls measure of output
per hour of all persons in that it excludes the effects of
capital intensity. Comparing the two productivity series
indicates how much of the growth or falloff in the tradi­
tional measure of output per hour was due to changes in
capital per hour and how much was due to a combina­
tion of the other factors— i.e, changes in technology,
shifts in the composition of the labor force, changes in
capacity utilization, and so on.
In addition, the multifactor productivity index can be
interpreted as one of a number of indicators of the eco­
nomic progress of the U.S. economy because it shows
the growth in output that has been obtained from a given
amount of resources (capital and hours of labor), or,
conversely, the reduction over time in the quantity of
these resources used to produce a unit of output.

Output per unit of capital services exhibited marked
fluctuations between 1948 and 1981, but there was little
or no apparent trend over the period as a whole. Thus,
there was no measured saving in the amount of capital
used to produce a unit of output over the more than
three decades. In the latter part of the period, between
1973 and 1981, there was a decrease in output per unit
of capital services, but this represented a change from
the peak of one cycle to the trough of a later one, not a
slowdown in the long-term trend.
The long-term average annual growth rate in output
per hour, however, combines a high rate of growth (3.0
percent) between 1948 and 1973 with a much slackened
one (0.8 percent) from 1973 to 1981. A small part of
this falloff— 0.3 percentage point—was the result of a
slowdown in the annual rate of growth of capital per
hour. The remainder— 1.9 percentage points— came
from a slowdown in multifactor productivity growth:
Between 1973 and 1981, output per unit of combined
capital and labor input rose by only 0.1 percent per year
compared with 2.0 percent during 1948-73.
The slowdown in the rate of growth of capital per
hour after 1973 reflects a decline in the rate of substitu­
tion of capital for labor. From 1948-73 to 1973-81, the
average annual rate of growth of capital inputs in the
private business sector decreased somewhat, whereas
the growth rate of hours of all persons doubled. This de­
cline in the rate of substitution of capital for labor after
1973 was largely associated with a change in relative
factor prices: Historically, the price of capital has de­
clined relative to the price of labor (average hourly
compensation); during 1973-81, the average annual rate
of decline in the price of capital relative to labor com­

Private business sector
From 1948 to 1981, the period mainly covered in this
bulletin, the growth of output per hour of all persons in
the private business sector, which accounts for about 76
percent of gross national product, averaged 2.4 percent



1

pensation was only half as great as in the earlier period,
1948-73.
Comparisons with earlier decades in this century for
which reasonably comparable bls data are available in­
dicate that the average annual rate of growth in output
per hour of all persons during 1948-73 was about the
same as in the two decades 1918-28 and 1938-48. But
the annual growth rate during 1973-81 was the lowest
during any decade since 1909-18, when there was ap­
parently no change in productivity.
Many factors have influenced the movements in the
bls measure of multifactor productivity. Judging from
estimates made by bls and private scholars, about 40
percent of the long-term growth rate can be explained;
the rest remains unexplained. Of the 1.5 percent per
year growth in multifactor productivity from 1948 to
1981, about 0.6 percentage point can be explained by
(1) shifts of labor from the farm to the nonfarm sector
(0.1 percentage point); (2) changes in the composition
of the work force, mainly due to more education per
worker (0.4 percentage point); (3) growth of research
and development ( r & d ) expenditures (perhaps 0 .2 per­
centage point); and (4) a reduction in hours worked rel­
ative to hours paid (—
0.1 percentage point). Changes in
utilization of physical capital appear to have had little or
no effect on the long-term rate of growth of productiv­
ity.
These same underlying factors explain an even
smaller fraction of the 1.9 percent per year falloff in
m ultifactor productivity growth from 1948-73 to
1973-81. About 0.4 percentage point is accounted for
by (1) the virtual end of the shift of labor from the farm
to the nonfarm sector (0.2 percentage point); (2) a slow­
down in the rate of growth of r & d (perhaps 0.1 percent­
age point); and (3) a decrease in hours worked relative
to hours paid (0.1 percentage point). Changes in the
composition of the work force took place at about the
same rate before and after 1973 and therefore did not
contribute to the slowdown. Measures of changes in the
utilization of physical capital are not available for the
private business sector as a whole; but judging from
comparisons for manufacturing, changes in capacity
utilization could have been an im portant factor
contributing to the productivity falloff. However, even
if this additional factor were included, the fraction of
the falloff left unexplained would probably still be
large.

productivity growth was about the same in private nonfarm business as in private business as a whole. This is
not surprising since the private nonfarm business sector
constitutes about 95 percent of the private business sec­
tor. Between 1948 and 1981, output per hour of all per­
sons in private nonfarm business grew at an average an­
nual rate of 2.0 percent. Increases in capital input per
hour contributed about 0.7 percent per year to the
growth of output per hour. M ultifactor productiv­
ity—output per unit of combined labor and capital
input—grew at an average annual rate of 1.3 percent.
The annual rate of growth of output per hour of all
persons dropped from 2.5 percent in 1948-73 to 0.6
percent during 1973-81, a slowdown of 1.9 percent per
year. There was also a slowdown in the rate of growth
of capital intensity, but this only contributed 0.2 per­
centage point to the falloff in output per hour. Multi­
factor productivity grew by 1.7 percent per year before
1973 but did not increase after that. That is, from 1973
to 1981, the growth in output came solely from in­
creases in combined labor and capital inputs; in effect,
the same quantity of resources produced the same
amount of output in 1981 as it did almost a decade
earlier.

Manufacturing sector
Productivity trends in manufacturing were similar to
those in private business and private nonfarm business.
But while the falloff in output per hour in the other two
sectors was associated with slower rates of growth in
capital inputs per hour after 1973, this was not the case
in manufacturing.
From 1948 to 1981, output per hour of all persons in
m anufacturing increased by 2.6 percent per year;
growth in capital intensity contributed about 0.8 per­
centage point; and multifactor productivity contributed
the remainder, 1.8 percentage points. The growth in
multifactor productivity in manufacturing was signifi­
cantly faster than in private business and, particularly,
private nonfarm business.
The average annual rate of growth in output per hour
of all persons decreased from 2.9 percent during
1948-73 to 1.5 percent from 1973 to 1981. The growth
of capital per hour accelerated between the two periods
and, as a result, the falloff in output per hour was less
than if there had been no rise in capital intensity. Con­
sequently, the falloff in multifactor productivity was
also greater than that for output per hour. Specifically,
there was a 1.8 percent per year slowdown in the rate of
growth of multifactor productivity after 1973.

Private noefarm business sector
Although the numbers are different, the pattern of




2

Chapter l„ SrutrodyetoBi

One of the major issues now facing the U.S. economy
is the marked slowdown in productivity during the last
decade. Between 1973 and 1982, the average annual
rate of growth in output per hour of all persons in the
business sector was only one-fourth the rate during the
earlier postwar period, 1948 through 1973. The slow­
down was pervasive: Each of the major sectors—manu­
facturing, farming, and nonfarm-nonmanufacturing—
experienced lower rates of growth in output per personhour during the last decade, bls publishes annual in­
dexes of productivity for 116 industries, and 80 percent
of these showed productivity slowdowns after 1973.1
These slower growth rates are a major source of con­
cern because productivity is important in determining
national economic well-being. Productivity gains ac­
count for most of the increases in real compensation, so
the slowdown means a retarded growth in the American
standard of living. Chart 1 shows that, for the business
sector, changes in hourly compensation adjusted for
movements in consumer prices virtually paralleled those
in output per hour of all persons, including the slow­
down after 1973.
In addition, gains in productivity can contribute to
price stability. Productivity increases help to offset the
effects of increases in hourly compensation on unit la­
bor cost which, in turn, are closely associated with
changes in prices. By moderating price rises, productiv­
ity gains also contribute to the U.S. balance of trade by
making the Nation’s goods and services more competi­
tive in world markets, bls comparisons of productivity
growth in 11 countries (the United States, Canada, 8
Western European countries, and Japan) show that, be­
tween 1960 and 1981, the average annual rate of growth
in U.S. output per employee-hour in manufacturing was
substantially below that of any of the other countries
and only half as large as the combined average for the
10 foreign countries.1 Like the United States, all of the
2
other countries experienced a falloff in productivity
growth in manufacturing after 1973 but, except for Can­
ada, their post-1973 productivity growth rates remained
substantially above that of the United States. The Cana­
dian and U.S. annual productivity growth rates were
virtually the same from 1973 to 1981.
Although the more familiar productivity measures re­
late output to hours of all persons engaged in a sector,

they do not measure the specific contributions of labor,
capital, or any other factor of production. Rather, they
reflect the joint effects of many influences including
changes in capital services, technology, level of output,
utilization of capacity, the organization of production,
managerial skill, and the composition and effort of the
work force.
The new measure of multifactor productivity intro­
duced in this bulletin relates output to inputs of both
capital and labor and, therefore, includes more inputs
than the bls productivity index of output per hour of all
persons. Since it incorporates capital inputs, the multi­
factor productivity measure is intended to reflect all of
the same influences as the labor productivity measure
discussed in the previous paragraph except for changes
in capital services. The bls is currently developing and
reviewing measures of capacity utilization, composition
of the labor force, investment in research and develop­
ment, and other factors in order to determine their influ­
ence on movements in multifactor productivity.
The next chapter discusses the bls quarterly indexes
of output per hour of all persons and reviews trends and
cyclical movements in these series since 1947, the first
year for which the data are available. These quarterly
measures are for the business sector, which includes
government enterprises; the discussions in the succeed­
ing chapters related to multifactor productivity are
based on annual data and cover private business, which
excludes government enterprises. Chapter III discusses
the new b l s index of m ultifactor productivity, its
changes, and how these relate to changes in output per
hour of all persons and output per unit of capital input.
Chapter IV reviews sources of change in multifactor
productivity and their implications for the growth of
productivity and the slowdown since 1973. The bulletin
also includes six technical appendixes. Appendix A
discusses the conceptual framework underlying the
multifactor productivity measures; appendixes B, C,
and D explain the methodology and basic data sources
used in measuring output, capital inputs, and hours of
all persons; appendix E presents a comparison of the re­
sults of using a Tomquist (changing weight) index
versus a fixed weight index; and in appendix F, the new
bls multifactor productivity measures are compared
with those constructed by other researchers.

1Productivity Measures for Selected Industries, 1954-81, Bulle­
tin 2155 (Bureau of Labor Statistics, December 1982).
2Patricia Capdevielle, Donato Alvarez, and Brian Cooper, “ In­
ternational Trends in Productivity and Labor Cost,” Monthly La-

bor Review, December 1982, pp. 3-14. International comparisons
are made in terms of output per employee-hour in manufacturing to
achieve comparability of the series for each country.




3

Chart 1. Real hourly compensation and productivity in the business sector, 1947-82
(Index, 1947 = 100)

1947




1952

1957

1962

4

1967

1972

1977

1982

©Ihaptteir D= O utput per H our o f All [Persons
Q
on tin® B usiness SeeSor

adjusting output, employment, and average weekly
hours in the farm sector for changes in weather and
other conditions. Therefore, the analysis of cyclical
movements focuses on both the business and nonfarm
business sectors.
Output per hour in the nonfarm business sector rose
consistently in all of the eight postwar expansions (chart
3) because output grew significantly faster than hours of
all persons. The business sector exhibited the same pat­
tern during the expansionary phases of the cycles.
During the contractions, however, the movements in
aggregate output per hour were not consistent. In the
nonfarm business sector, output per hour did not decline
during the first five recessions, but it did during the last
two. The percentage decreases in hours were greater
than those in output during the first five recessions
whereas, in the succeeding two contractions, hours de­
clined relatively less than output. This was also the pat­
tern in the business sector.
In sum, during each of the postwar cyclical expan­
sions, hours of all persons showed significantly smaller
relative increases than output, so that output per hour
grew. However, during the contractions, hours some­
times fell relatively more and sometimes relatively less
than output, so that labor productivity rose in some re­
cessions but declined in others.2 This suggests, among
other things, that there is no simple, constant lag be­
tween hours and output at the aggregate level.

There are many determinants of output per hour. Over
time, changes in some of these result in cyclical move­
ments in the series, while others have more gradual ef­
fects and give rise to trends. For exam ple, rapid
changes in output, coupled with lags in hiring or laying
off workers, and changes in the utilization of the ex­
isting capital stock are likely to cause cyclical move­
ments in output per hour. On the other hand, changes in
such factors as capital per unit of labor, labor force
composition, technology and its diffusion, and shifts of
resources among sectors are likely to result in changes
in the long-term trend of output per hour.
This chapter reviews movements since 1947 in the
bls quarterly indexes of output per hour of all persons
in the business, nonfarm business, and manufacturing
sectors and attempts to separate the trends from cyclical
patterns. The trends are then used to date and gauge the
extent of the productivity slowdown. Although cyclical
movements in output per hour help to explain cyclical
changes in unit labor costs, profits, and prices, which
tend to retard both contractions and expansions during
the business cycle, the relationships between output per
hour and costs are not discussed in this bulletin.1

Cyclical movements in output per hour
Charts 2, 3, and 4 show quarterly changes in output
per hour of all persons (seasonally adjusted) for the
business, nonfarm business, and manufacturing sectors
from the first quarter of 1947 (1947 I) through the
fourth quarter of 1982 (1982 IV); the index numbers
charted are given in table 3 at the end of this chapter.
The shaded areas in the charts indicate periods of con­
traction in general business activity; the cyclical peaks
and troughs are those designated by the National Bureau
of Economic Research. Quarterly movements in the
business sector are less clear than movements in the
nonfarm subsector because of difficulties in seasonally

Trends in output per hour
The three charts showing quarterly movements in out­
put per hour of all persons in business, nonfarm busi­
ness, and manufacturing all indicate a definite slow­
down in the rate of growth of productivity since early
1973, a shift now well established. There is, however,
some question about whether the productivity slowdown
actually started earlier, perhaps in 1965 or 1966. In orThor Hultgren based on industry data. He found that “ manhours in
the aggregate usually do not rise and do not fall by as great a per­
centage as output.’’ See Thor Hultgren, “ Changes in Labor Cost
During Cycles in Production and Business,’’ Occasional Paper 74
(New York, National Bureau of Economic Research, 1960), p. 8.
The difference between Hultgren’s conclusions and those offered
here, which are based on broad aggregates, may be due in part to
changes in the product mix during cyclical contractions.

'See Wesley C. Mitchell, Business Cycles and Their Causes
(Berkeley, University of California Press, 1941); and Geoffrey H.
Moore and John Cullity, “ Trends and Cycles in Productivity, Unit
Costs, and Prices: An International Perspective,’’ paper presented
at the Conference on International Comparisons of Productivity and
Causes of the Slowdown held by the American Enterprise Institute,
Washington, Sept. 30, 1982.
2These results are somewhat at variance with those reported by



5

Chart 2. Business sector: Output per hour, output, and hours, quarterly, 1948=82
(Index, 1947 = 100)




6

Chart 3. Nonfarm business sector: Output per hour, output, and hours, quarterly,
1948=82
(Index, 1947 = 100)




7

Chart 4. iHianufactyring sector: Output per hour, output, and hours, quarterly, 1948=82
(Index, 1947 = 100)




8

der to see this, long-term trends have to be separated
from cyclical and random fluctuations.
One method of highlighting the long-term trends is to
compare rates of growth in output per hour of all per­
sons at peaks of business activity. Since these are at the
same stage of the business cycle, there is a presumption
that utilization of capital and labor is also “ roughly”
the same. These peak-to-peak comparisons for the busi­
ness and nonfarm business sectors show that, although
the annual growth rate in productivity differed among
periods, the only clearly evident slowdown occurred af­
ter 1973 (table l) .3 The productivity growth rate in the
business sector during the initial period, 1948 IV—
1953 III, was unusually high (3.7 percent) and reflects a
sharp rise in farming. There was a productivity slow­
down in the subsequent period, 1953 III— 1957 III, but
this was not as large or as prolonged as the one after
1973.
In sum, the peak-to-peak comparisons of growth rates
in output per hour of all persons based on quarterly data
confirm that the slowdown began in early 1973; they do
not reveal any falloff before then.4 For this reason, the
analyses of the slowdown in this bulletin are based only
on a comparison of the periods before and after 1973.

Table 2. Rates of growth in output per hour of all persons,
output, and hours by major sector, 1948-81
(Percent per year, compounded)
1948-81

1948 IV -1953 III .............................
1953 111-1957 III .............................
1957 111-1960 II .............................
1960 11-1969 IV .............................
1969IV -1973 IV ...........................
1973IV -1980 I ...............................
1980 1-1981 III ...............................

(3)

(3)-(2)

2.4
3.3
0.9

2.9
3.7
0.7

0.8
2.2
1.4

-2.1
-1 .5
0.7

2.0
3.4
1.4

2.5
3.8
1.3

0.6
2.1
1.5

-1.9
-1 .7
0.2

Manufacturing:
Output per h o u r ...........
Output ..........................
Hours ..........................

2.6
3.3
0.7

2.9
4.0
1.1

1.5
1.2
-0 .2

-1.4
-2.8
-1 .3

’ Includes government enterprises.
Source : Table 4.

Post-1948 growth rates
During the three decades from 1948 to 1981, output
per hour of all persons in the business sector of the
economy grew at an average annual rate of 2.4 percent.
(Table 2 presents a summary of the quarterly and annu­
al data provided in table 3.) This was significantly
higher than the rate in nonfarm business (2.0 percent)
because of a high rate of growth of output per hour in
farming. During the same three decades, the annual rate
of growth in output per hour in manufacturing (2.6 per­
cent) was slightly higher than in the business sector but
substantially higher than in nonfarm business, apparent­
ly because of slower rates of growth of productivity in
nonfarm-nonmanufacturing activities. Coincidentally,
output grew at virtually the same annual rate in the three
sectors (about 3.3 percent) during the three decades.
The highest rate of growth in hours of all persons oc­
curred in nonfarm business, specifically in nonfarm­
nonmanufacturing .

2.6
1.4
2.8
2.5
2.4
0.6
0.9

1Cyclical peaks are those designated by the National Bureau of Economic
Research.
Source : Table 3.

3Peter Clark also used peak-to-peak growth rates in order to date
the slowdown in labor productivity up to 1973 II, the latest period
for which the data were then available. For the period after that, he
developed an econometric model based on a lagged response of la­
bor inputs (hours) to output. His model assumes that the structure
of the lag is constant throughout the postwar period but, as earlier
analysis in the text shows, there was no constant lag during busi­
ness contractions. Also, about one-half of the slowdown (0.8 per­
cent per year) that Clark found for 1965 II— 1973 II compared with
1955 IV— 1965 II for the business and nonfarm business sectors
based on earlier bls data has “ disappeared” in subsequent statis­
tical revisions. See Peter K. Clark, “ Capital Formation and the Re­
cent Productivity Slowdown,” Journal of Finance, June 1978, pp.
1965-75.
4In addition, comparison of average annual rates of growth in the
index itself, measured between peaks, indicates that, to the extent
that there was a slowdown in the series prior to 1973, it was small.



(2)

Nonfarm business:1
Output per h o u r...........
Output ..........................
Hours ..........................

Nonfarm business

3.7
2.1
2.8
2.9
2.6
0.8
1.1

Slowdown

Business:1
Output per h o u r ...........
Output ..........................
Hours .........................

(Percent per year, compounded)

Business

1973-81

(1)

Table 1. Rates of growth in output per hour of all persons be­
tween business cycle peaks in the business and nonfarm busi­
ness sectors, 1948 IV to 1981 I S
B

Period1

1948-73

Sector and measure

The quarters in which the output per hour series peaked were 1950
IV, 1966 II, and 1973 II. The average yearly growth rate in the
business sector declined from 2.9 percent in 1950 IV— 1966 II to
2.6 percent in 1966 II— 1973 II, only 0.3 percentage point; for the
nonfarm business sector the decline in the rate of growth between
the same two periods was from 2.4 percent to 2.2 percent, only 0.2
percentage point. The results are virtually the same based on
growth rates computed between 3-quarter averages of output per
hour centered on the 3 peak quarters. These growth rate differen­
tials are all well within the range of variation of those shown in ta­
ble 1 for the periods before 1973 IV. The comparisons in this foot­
note begin with 1950 IV because the sharp rise in productivity prior
to that quarter reflects the sharp rise in farming during the Korean
War (see charts 2 and 3). Other analysts, relying on annual data,
have placed the beginning of the productivity slowdown in the
mid- 1960’s.

9

Comparisons of the annual growth rates in the two pe­
riods 1948-73 and 1973-81 show the dimensions of the
productivity slowdown during the last decade. In the
business sector, output per hour of all persons grew at a
yearly rate of only 0.8 percent from 1973 to 1981,
slightly more than one-fourth the 2.9 percent growth
rate between 1948 and 1973. This reflects a sharp drop
in the annual rate of growth of output (1.5 percent) cou­
pled with a significant increase in the rate of growth of
hours (0.7 percent). Part of the productivity slowdown
resulted from shifts of output and employment from in­
dustries with higher to those with lower levels of output
per hour.
Nonfarm business experienced a similar slowdown in
productivity after 1973. The annual rate of growth of
output per hour fell from 2.5 percent during 1948-73 to
0.6 percent during 1973-81. This reflects a somewhat
larger drop in the rate of growth of output (1.7 percent)
and a significantly smaller slowing of the rate of growth
in hours than in the business sector. The annual rate of
growth in hours in nonfarm business (1.3 percent) dur­
ing 1948-73 was substantially larger than in the busi­
ness sector (0.7 percent) because of the large shift of
workers from farm to nonfarm activities. The growth
rates for hours in the two sectors were about the same
during 1973-81, which indicates that the major shift of
labor out of farm ing was essentially com pleted by
1973.5
In manufacturing, the average annual growth rate in
output per hour was 1.5 percent during 1973-81 com­
pared with 2.9 percent in 1948-73, a falloff of 1.4 per­
cent per year. In contrast to the other two sectors, the
slowdown in manufacturing reflects decreases in the an­
nual growth rates of both output (2.8 percent) and hours
(1.3 percent). In fact, hours declined by 0.2 percent per

year from 1973 to 1981 whereas they grew by 1.1 per­
cent in the earlier period, 1948-73.

sThe proportion of all persons in the business sector engaged in
farming was 15.5 percent in 1948, 7.3 percent in 1965, 4.7 percent
in 1973, and 3.5 percent in 1981. Since output per hour is lower in
the farm than in the nonfarm sector, the smaller decrease in the per­
centage after 1965 compared with the period from 1948 to 1965
partially accounts for the small slowdown in labor productivity be­
tween 1965 and 1973 noted earlier.
6The private economy is defined as gross national product ex­

cluding general government. As measured in the National Income
and Product Accounts, the output of the business sector accounts
for between 85 and 90 percent of output of the private economy.
See appendix B for a detailed discussion of the relationship
between gross national product and business output and some of
the problems in using the broader concept for productivity
measurement.




The long term: 1909-81
bls also maintains an annual series on output per
hour of all persons in the private economy for the period
1909-47.6 This series was linked to the bls measure of
output per hour of all persons in the business sector in
order to review long-term movements in productivity
(chart 5 and table 4). This makes it possible to broadly
judge U.S. long-term progress in productivity and to see
whether there was a similar slowdown prior to 1948.
In 1981, output per hour of the average American
worker was about 4V2 times as much as it was in 1909.
This averages out to a long-term yearly rate of growth
of 2.5 percent. The annual rates of growth varied sub­
stantially among the seven decades. The differential
movements largely reflected major events such as the
two World Wars, the Great Depression, and various
recessions.

Comparisons of the pre- and post-1948 experience
show that the average annual rate of growth in output
per hour during 1948-73 was about the same as during
the two decades 1918-28 and 1938-48. Two earlier pe­
riods also were marked by low productivity growth:
1909-18, when there was virtually no change in output
per hour, and 1929-38, when productivity increased
only 1.6 percent per year. However, these two periods
of little or no productivity growth differ from the
1973-81 experience: The post-1973 productivity falloff
was associated with a 3.0 percent annual rate of growth
in output whereas in 1909-18 output grew by only 1.5
percent per year, and in 1929-38 there was virtually no
growth in output.

10

Chart 5. Output p®r hour, 1009=82
(Index, 1 9 09= 100)




11

Table 3. Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82
(Index, 1977=100)
Nonfarm business sector

Business sector

Manufacturing sector

Output

Hours
of all
persons

Output
per hour
of all
persons

Output

Hours
of all
persons

49.9
49.4
49.9
49.9
50.3

34.0
33.6
33.9
33.9
34.5

68.1
68.0
67.9
67.9
68.7

42.4
41.6
42.2
42.6
43.1

33.9
33.5
33.7
33.6
34.7

79.9
80.5
79.9
78.8
80.4

80.7
80.7
80.2
81.1
80.8

52.0
51.0
52.2
51.9
52.8

36.0
35.3
36.1
36.1
36.5

69.2
69.3
69.0
69.6
69.1

45.1
43.7
44.9
45.6
46.0

35.8
35.2
35.7
36.2
36.1

79.4
80.6
79.4
79.5
78.3

36.5
36.8
36.4
36.6
36.1

78.1
79.6
78.8
77.5
76.3

53.1
52.6
52.9
53.7
53.1

35.3
35.8
35.3
35.4
34.9

66.6
67.9
66.7
66.0
65.7

46.9
46.5
46.9
47.4
46.8

33.9
35.0
33.7
34.0
33.1

72.4
75.2
71.9
71.6
70.7

50.4
49.3
50.1
50.9
51.3

39.8
37.7
39.2
40.8
41.4

78.9
76.5
78.3
80.1
80.8

56.3
55.1
56.1
56.8
57.1

38.6
36.4
38.1
39.7
40.3

68.7
66.1
67.8
70.0
70.6

49.4
47.5
49.2
50.5
50.3

38.6
34.6
37.5
40.8
41.7

78.2
72.9
76.2
80.7
82.9

1951 ....................
I ....................
II ..................
Ill ..................
IV ................

51.8
50.8
51.1
52.6
52.7

42.1
41.4
41.8
42.4
42.7

81.3
81.5
81.7
80.8
81.1

57.2
56.5
56.4
57.8
58.3

41.1
40.6
40.9
41.4
41.7

71.9
71.9
72.4
71.6
71.6

51.1
51.0
51.1
50.8
51.4

43.0
43.2
43.6
42.5
42.8

84.2
84.7
85.3
83.6
83.3

1952 ....................
I ....................
II ..................
Ill ..................
IV ................

53.5
52.6
53.6
53.8
53.9

43.5
42.9
43.1
43.4
44.6

81.4
81.6
80.4
80.6
82.7

58.6
58.1
58.6
58.6
58.9

42.5
42.0
42.1
42.3
43.7

72.6
72.2
71.8
72.2
74.3

52.0
51.6
51.4
52.0
53.1

44.5
43.7
43.0
43.9
47.3

85.4
84.6
83.6
84.5
89.1

1953 ....................
I ....................
II ..................
Ill ..................
IV ................

55.2
54.6
55.3
55.5
55.5

45.4
45.4
45.8
45.5
44.8

82.2
83.2
82.8
82.0
80.7

59.5
59.2
59.6
59.8
59.6

44.3
44.4
44.8
44.5
43.6

74.5
75.0
75.2
74.3
73.3

52.9
52.9
52.8
53.3
52.6

47.5
48.1
48.3
48.0
45.6

89.8
91.0
91.6
90.0
86.6

1954 ....................
I ....................
II ..................
Ill ..................
IV ................

56.1
55.0
55.5
56.5
57.3

44.6
44.2
43.9
44.6
45.5

79.5
80.3
79.2
78.9
79.5

60.4
59.6
59.9
60.8
61.2

43.4
43.1
42.9
43.4
44.4

71.9
72.3
71.7
71.3
72.4

53.7
52.5
53.4
54.2
54.8

44.1
44.0
43.8
43.7
45.0

82.1
83.7
81.9
80.8
82.1

1955 ....................
I ....................
II ..................
Ill ..................
IV ................

58.3
58.0
58.6
58.5
58.3

48.1
46.8
47.9
48.6
49.1

82.5
80.8
81.7
83.0
84.2

62.8
62.2
62.9
63.2
62.8

47.0
45.8
46.8
47.5
47.9

75.9
73.5
74.4
75.2
76.3

56.4
56.0
56.6
56.6
56.4

48.9
47.2
49.0
49.2
50.0

86.6
84.3
86.6
87.0
88.6

1956 ....................
I ....................
II ..................
Ill ..................
IV ................

58.9
58.6
58.7
58.7
59.7

49.3
49.0
49.3
49.2
49.8

83.7
83.7
84.0
83.7
83.4

62.9
62.5
63.0
62.9
63.3

48.3
47.9
48.4
48.1
48.8

76.8
76.6
76.8
76.5
77.0

56.0
56.0
56.0
55.5
56.5

49.2
49.5
49.2
48.2
50.0

87.9
88.4
87.9
86.8
88.6

1957 ....................
I ....................
II ..................
Ill ..................
IV ................

60.4
60.1
60.3
60.3
60.8

49.8
50.0
50.0
50.0
49.3

82.5
83.3
82.8
82.9
81.1

64.0
63.7
63.8
64.1
64.4

48.9
49.1
49.0
49.1
48.4

76.4
77.0
76.8
76.6
75.1

57.1
57.2
57.1
57.7
56.5

49.5
50.6
49.9
49.9
47.4

86.5
88.5
87.4
86.4
83.8

1958 ....................
I ....................

62.3
61.1
61.7
62.6
63.8

49.0
48.1
48.0
49.2
50.9

78.8
78.8
77.8
78.6
79.8

65.5
64.1
65.2
65.8
67.1

48.0
47.0
47.0
48.1
49.8

73.2
73.3
72.1
73.1
74.2

56.9
55.3
56.0
57.5
58.9

45.2
44.3
43.5
45.5
47.5

79.4
80.1
77.6
79.1
80.7

Year and
quarter

Output

Hours
of all
persons

Output
per hour
of all
persons

43.7
43.6
43.8
43.6
43.8

35.0
34.9
34.9
34.9
35.5

80.2
80.0
79.6
80.1
81.0

1948 ....................
I ....................
II ..................
Ill ..................
IV ................

46.0
45.0
46.4
45.9
46.7

37.2
36.3
37.3
37.2
37.7

1949 ....................
I ....................
II ..................
Ill ..................
IV ................

46.7
46.3
46.1
47.2
47.3

1950 ....................
I ....................
II ..................
Ill ..................
IV ................

Output
per hour
of all
persons

1947 ....................
I ....................
II ..................
Ill ..................
IV ................

II ................
Ill ..................
IV ................




12

Table 3.

Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82— Continued

(Index, 1977=100)
Manufacturing sector

Nonfarm business sector

Business sector

Output
per hour
of all
persons

Output

Hours
of all
persons

Output

Hours
of all
persons

Output
per hour
of all
persons

Output

Hours
of all
persons

64.3
64.3
64.4
63.9
64.4

52.6
52.0
53.4
52.4
52.7

81.9
80.9
82.8
82.0
81.8

67.7
67.6
68.4
67.3
67.6

51.8
51.0
52.6
51.7
51.8

76.5
75.5
76.9
76.7
76.7

59.6
59.7
60.8
58.9
59.1

50.5
49.9
52.3
49.9
49.8

84.7
83.6
86.0
84.7
84.4

1960 ....................
I ....................
II ..................
Ill ..................
IV ................

65.2
65.9
65.1
64.8
64.9

53.5
54.0
53.7
53.4
52.8

82.0
81.8
82.4
82.4
81.4

68.3
68.7
68.2
68.1
68.1

52.5
53.2
52.8
52.4
51.8

77.0
77.4
77.3
76.9
76.1

60.0
60.9
59.8
59.6
59.7

50.7
52.8
51.1
50.1
48.6

84.4
86.7
85.5
83.9
81.4

1961 ....................
I ....................
II ..................
Ill ..................
IV ................

67.3
65.5
67.4
67.8
68.9

54.4
52.9
53.9
54.6
56.0

80.8
80.8
80.0
80.6
81.3

70.3
68.7
70.1
70.7
71.8

53.5
51.9
53.0
53.8
55.2

76.1
75.6
75.6
76.1
76.9

61.6
59.5
61.1
62.5
63.4

50.7
47.8
49.9
51.6
53.4

82.3
80.4
81.7
82.6
84.2

1962 ..................
I ....................
II ..................
Ill ..................
IV ................

69.9
69.1
69.3
70.3
71.2

57.4
56.7
57.2
57.7
58.0

82.1
82.1
82.5
82.1
81.5

72.8
72.4
72.0
72.9
73.9

56.6
55.9
56.3
56.9
57.3

77.8
77.2
78.2
78.0
77.5

64.3
63.8
63.5
64.3
65.6

55.1
54.1
54.7
55.3
56.1

85.6
84.8
86.1
86.0
85.6

1963 ..................
I ....................
II ..................
Ill ..................
IV ................

72.5
71.4
72.2
73.1
73.5

59.9
58.6
59.6
60.4
61.0

82.6
82.1
82.6
82.6
82.9

75.1
74.1
74.9
75.7
76.0

59.1
57.8
58.8
59.6
60.2

78.7
78.0
78.5
78.7
79.2

68.9
67.0
68.8
69.3
70.4

59.6
57.6
59.5
60.1
61.3

86.5
85.9
86.5
86.8
87.0

1964 ..................
I ....................
II ..................
Ill ..................
IV ................

75.6
75.0
75.2
76.1
76.5

63.5
62.1
63.0
64.0
64.7

83.9
82.9
83.8
84.1
84.7

78.1
77.2
77.8
78.7
78.7

62.8
61.5
62.4
63.3
64.1

80.5
79.7
80.2
80.5
81.4

72.3
71.3
72.1
72.6
73.0

63.9
62.2
63.5
64.5
65.3

88.4
87.2
88.1
88.9
89.4

1965 ..................
I ....................
II ..................
Ill ..................
IV ................

78.3
77.4
77.6
78.7
79.7

67.8
66.3
67.3
68.0
69.6

86.6
85.7
86.7
86.4
87.4

80.5
79.4
80.0
80.7
81.9

67.2
65.6
66.7
67.4
69.1

83.5
82.6
83.4
83.4
84.4

74.5
73.7
74.5
75.1
74.8

69.8
67.8
69.2
70.5
71.6

93.6
92.0
92.8
93.9
95.7

1966 ..................
I ....................
II ..................
Ill ..................
IV ................

80.7
80.5
80.4
80.8
81.2

71.5
71.0
71.2
71.8
72.1

88.6
88.1
88.6
88.8
88.8

82.5
82.4
82.2
82.5
82.9

71.2
70.5
70.8
71.6
71.9

86.3
85.5
86.2
86.7
86.7

75.3
75.3
75.4
75.5
75.4

75.1
73.7
75.1
75.8
76.1

99.8
97.8
99.6
100.4
101.0

1967 ....................
I ....................
II ..................
Ill ..................
IV ................

82.5
81.3
82.5
82.8
83.6

73.1
72.1
72.6
73.4
74.4

88.6
88.6
88.0
88.6
89.0

84.0
82.9
83.9
84.4
85.1

72.7
71.7
72.3
73.0
73.9

86.5
86.5
86.1
86.5
86.9

75.3
74.7
75.0
75.1
76.5

75.0
74.8
74.2
74.5
76.4

99.6
100.1
99.0
99.2
99.9

1968 ....................
I ....................
II ..................
Ill ..................
IV ................

85.3
84.4
85.0
85.8
85.9

76.8
75.3
76.4
77.6
78.1

90.1
89.2
89.8
90.4
91.0

86.8
86.0
86.7
87.2
87.2

76.6

77.8

88.2
87.2
87.9
88.7
89.2

78.0
77.5
78.1
78.0
78.4

79.1

75,0
76.2
77.3

78.9
79.4
80.3

101.4
100.4
101. 0
101 .8
102. 4

1969 ....................
I ....................
II ..................
Ill ..................
IV ................

85.5
85.3
85.5
85.5
85.3

79.0
78.8
79.1
79.4
78.8

92.5
92.4
92.5
92.9
92.4

86.5
87.1
86.7
86.4
86.2

78.8
78.5
78.9
79.1
78.7

91.1
90.2
91.0
91.6
91.3

79.3
79.5
79.1
79.5
79.3

81.7
81.6
81.7
82.3
81.3

103.1
102.7
103.3
103.6
102. 6

1970 ....................
I ....................
II ..................
Ill ..................
IV ................

86.2
85.0
85.8
87.3
86.8

78.4
78.3
78.4
79.0
77.9

91.0
92.2
91.4
90.5
89.7

86.8
85.5
86.6
88.0
87.1

78.0
78.0
78.0
78.7
77.3

89.8
91.2
90.1
89.4
88.8

79.1
77.6
78.6
79.6
80.6

77.0
78.4
77.5
77.0
75.1

97.3
101.0
98.6
96.7
93.2

Output
per hour
of all
persons

1959 ....................
I ....................
II ..................
Ill ..................
IV ................

Year and
quarter




13

77.7

Table 3.

Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82— Continued

(Index, 1977=100)

Manufacturing sector

Nonfarm business sector

Business sector

Output

Hours
of all
persons

Output
per hour
of all
persons

Output

Hours
of all
persons

89.7
88.9
89.2
90.4
90.4

80.3
79.2
79.7
80.6
81.6

89.5
89.1
89.4
89.1
90.2

83.9
82.3
83.6
84.5
85.5

78.7
77.3
78.4
78.7
80.3

93.7
93.9
93.8
93.1
94.0

93.2
92.3
92.7
93.3
94.3

93.0
91.4
92.4
93.6
94.7

85.8
83.4
85.0
86.5
88.5

92.3
91.3
91.9
92.4
93.5

88.2
86.1
87.0
88.7
90.9

86.2
82.5
84.7
86.9
90.9

97.8
95.8
97.4
97.9
100.0

91.8
91.5
91.5
91.6
92.4

96.8
95.6
96.5
97.2
97.7

95.3
96.1
95.3
94.9
94.9

91.7
91.3
91.5
91.8
92.2

96.2
95.0
96.0
96.7
97.2

93.0
92.3
93.3
93.8
92.5

95.9
94.3
96.2
96.8
96.4

103.2
102.1
103.1
103.2
104.1

92.5
92.8
92.8
92.2
92.0

89.9
90.9
90.7
89.8
88.3

97.3
98.0
97.8
97.4
96.0

92.9
93.8
93.0
92.4
92.3

89.8
91.0
90.5
89.7
88.1

96.7
97.0
97.2
97.1
95.4

90.8
90.0
91.0
91.7
90.3

91.9
92.9
92.8
93.3
88.5

101.2
103.2
102.0
101.8
98.1

1975 ....................
I ....................
II ..................
Ill ..................
IV ................

94.5
92.1
94.6
96.0
95.7

88.2
85.7
87.2
89.5
90.3

93.3
93.0
92.1
93.2
94.4

94.7
92.4
94.7
96.2
95.8

89.8
85.4
86.7
89.0
90.0

92.7
92.4
91.5
92.5
94.0

93.4
88.4
92.0
96.6
96.4

85.4
80.9
82.7
88.1
89.9

91.4
91.5
89.8
91.2
93.2

1976 ....................
I ....................
II ..................
Ill ..................
IV ................

97.6
97.2
97.6
97.9
98.0

93.8
92.9
93.5
94.0
94.6

96.0
95.6
95.8
96.1
96.6

97.8
97.1
98.0
98.2
97.9

93.7
92.7
93.5
94.1
94.5

95.8
95.4
95.4
95.8
96.5

97.5
96.2
97.4
97.9
98.3

93.6
92.1
93.2
94.2
94.9

95.9
95.7
95.7
96.1
96.5

1977 ....................
I ....................
II ..................
Ill ..................
IV ................

100.0
99.4
99.6
100.9
100.5

100.0
97.0
99.5
101.5
102.0

100.0
97.6
99.9
100.6
101.5

100.0
99.3
99.9
100.6
100.4

100.0
97.0
99.6
101.4
102.0

100.0
97.7
99.7
100.8
101.6

100.0
99.0
99.9
100.4
100.5

100.0
96.9
99.8
101.2
102.1

100.0
97.9
99.8
100.8
101.6

1978 ....................
I ....................
II ..................
Ill ..................
IV ................

100.6
100.4
100.7
100.6
100.8

105.5
102.7
105.5
106.2
107.4

104.9
102.2
104.8
105.5
106.6

100.6
100.4
100.8
100.6
100.8

105.7
102.7
105.8
106.4
107.8

105.0
102.3
105.0
105.8
106.9

100.8
99.8
100.4
101.2
101.8

105.3
102.0
104.7
106.5
108.1

104.5
102.1
104.3
105.2
106.2

1979 ....................
I ....................
II ..................
Ill ..................
IV ................

99.6
100.4
99.8
99.3
99.1

107.8
108.0
107.5
108.0
107.9

108.2
107.6
107.7
108.7
108.8

99.3
100.3
99.4
98.9
98.8

108.0
108.2
107.6
108.0
108.0

108.7
107.9
108.2
109.2
109.2

101.5
101.5
101.5
101.1
102.0

108.2
108.9
108.0
108.0
107.9

106.6
107.3
106.4
106.9
105.8

1980 ....................
I ....................
II ..................
Ill ..................
IV ................

98.9
99.3
98.2
98.9
99.4

106.2
107.9
104.7
105.3
107.0

107.4
108.7
106.6
106.5
107.7

98.5
98.8
97.6
98.4
99.2

106.3
107.9
104.6
105.3
107.3

107.9
109.3
107.2
107.0
108.2

101.7
102.6
100.5
100.3
103.7

103.6
107.8
101.6
99.9
105.0

101.8
105.1
101.1
99.6
101.3

1981 ....................
I ....................
II ..................
Ill ..................
IV ................

100.7
100.7
100.7
101.0
100.3

108.9
109.1
109.1
109.6
107.8

108.1
108.3
108.3
108.5
107.4

99.9
100.4
100.1
100.0
99.1

108.6
109.2
109.0
109.1
107.1

108.7
108.8
108.9
109.1
108.0

104.6
105.2
105.1
105.1
103.0

105.9
106.7
107.5
107.4
102.0

101.2
101.4
102.3
102.2
99.0

1982 ....................
I ....................
II ..................
Ill
.........
IV ................

101.0
100.1
100.4
101.3
102.0

106.4
106.3
106.4
106.7
105.9

105.4
106.2
106.0
105.3
103.9

99.9
99.3
99.5
100.4
100.4

105.8
106.0
106.1
106.3
104.9

105.9
106.7
106.6
105.9
104.5

103.6
102.4
102.6
104.4
104.7

96.5
98.2
97.0
96.6
94.2

93.2
95.9
94.5
92.5
90.0

Output

Hours
of all
persons

Output
per hour
of all
persons

89.2
88.7
88.6
89.9
90.0

80.7
79.9
80.2
81.0
82.0

90.5
90.0
90.5
90.0
91.1

1972 ....................
I ....................
II ..................
Ill ..................
IV ................

92.4
91.0
92.2
92.6
94.0

86.1
84.0
85.4
86.4
88.6

1973 ....................
I ....................
II ..................
Ill ..................
IV ................

94.7
95.6
94.8
94.3
94.5

1974 ....................
I ....................
II ..................
Ill ..................
IV ................

Output
per hour
of all
persons

1971 ....................
I ....................
II ..................
Ill ..................
IV ................

Year and
quarter




14

Table 4.

Output per hour, output, and hours in the total private sector, 1909-82

(Index, 1977=100)
Output per hour
of all persons

Output

Hours

1909 .............................

22.0

13.4

61.0

1910
1911
1912
1913
1914
1915
1916
1917
1918
1919

.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................

23.2
22.1
22.7
22.7
22.0
21.9
22.2
21.5
22.7
23.6

13.8
14.1
14.9
15.0
14.3
14.1
15.3
15.1
15.9
16.0

59.4
63.8
65.8
66.2
65.1
64.4
69.0
70.4
69.9
67.7

1920
1921
1922
1923
1924
1925
1926
1927
1928
1929

.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................

22.8
23.0
25.1
26.3
26.8
28.1
28.9
29.0
28.8
30.3

15.7
14.2
16.7
18.8
18.7
20.4
21.6
21.5
21.6
23.1

68.6
61.8
66.4
71.5
69.9
72.4
74.8
74.3
75.0
76.4

1930
1931
1932
1933
1934
1935
1936
1937
1938
1939

.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................

28.9
28.8
27.3
26.8
29.6
31.0
32.9
32.9
33.7
35.1

20.6
18.9
15.9
15.5
16.8
18.5
21.0
22.3
20.9
22.9

71.3
65.6
58.3
57.7
56.5
59.6
63.9
67.9
62.1
65.2

1940
1941
1942
1943
1944

.............................
.............................
.............................
.............................
.............................

36.5
38.9
39.2
40.2
42.8

24.9
28.7
31.2
33.1
34.8

68.2
73.8
79.5
82.3
81.2

Year




Year

Output per hour
of all persons

Output

Hours

1945
1946
1947
1948
1949

44.6
43.1
42.9
45.3
46.2

34.2
33.3
33.8
35.8
35.4

76.7
77.3
78.7
79.1
76.6

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................

49.7
51.1
52.9
54.6
55.8
57.9
58.5
60.2
62.2
64.1

38.6
40.8
42.3
44.1
43.6
47.1
48.4
49.1
48.6
52.0

77.7
79.9
79.9
80.8
78.2
81.3
82.7
81.6
78.2
81.2

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................

65.1
67.4
69.9
72.4
75.4
78.0
80.4
82.1
84.7
85.1

53.2
54.2
57.2
59.6
63.1
67.3
71.0
72.8
76.4
78.8

81.6
80.4
81.8
82.4
83.7
86.3
88.4
88.7
90.2
92.5

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................

86.0
89.0
92.0
94.3
92.7
94.8
97.7
100.0
100.7
100.1

78.3
80.7
85.9
91.3
90.0
88.7
94.1
100.0
105.4
108.1

91.1
90.7
93.3
96.8
97.1
93.6
96.3
100.0
104.7
108.0

1980 .............................
1981 .............................
1982 .............................

15

.............................
.............................
.............................
.............................
.............................

99.8
101.5
101.8

107.2
109.8
107.7

107.4
108.2
105.8

Chapter SL Multsfactor Prodyetiwiy
D
in the Prowat© Busines® Seetor

As indicated earlier, the aggregate measure of output
per hour of all persons reflects many influences, such as
the amount of capital per unit of labor, shifts in re­
sources among industries and sectors, composition of
the work force, capacity utilization, and the organiza­
tion of production. This chapter looks at the influence
of one of these— capital per hour of all persons. The
bls index of multifactor productivity, which measures
output per unit of combined labor and capital, is, in
fact, an index of output per hour of all persons adjusted
for the influence of capital per hour. The chapter also
reviews trends in output per unit of capital services,
which indicate the savings realized over time in the use
of physical capital per unit of output. As previously in­
dicated, the analyses in this and the following chapters
are based on the private business and private nonfarm
business sectors, which exclude governm ent
enterprises.1

trends in this measure during the period as a whole.
This means that there were no apparent long-term sav­
ings in the amount of capital services required to pro­
duce a unit of output. The short-term fluctuations in
output per unit of capital are primarily an indication of
changes in capacity utilization, the result of cyclical
movements in aggregate demand.2 Capacity utilization
is discussed in the next chapter as one of the factors af­
fecting movements in multifactor productivity.

Capital per hoar of all persons

Tables 8, 9, and 10 and charts 6, 7, and 8 show the
annual indexes of multifactor productivity in addition to
those for output per hour and output per unit of capital
services for private business, private nonfarm business,
and manufacturing during the period 1948 to 1981. Sev­
eral trends are immediately evident from the charts.
First, in each of the three sectors, output per hour grew
at a faster rate than multifactor productivity. This, as
shown later, reflects the growth of capital per unit of la­
bor. Second, multifactor productivity, like output per
hour, experienced a marked slowdown in the rate of
growth after 1973 in all three sectors. Third, short-term
fluctuations in multifactor productivity generally moved
in the same direction as those in output per hour; for ex­
ample, in 1981, both output per hour and multifactor
productivity rose in all three sectors but multifactor pro­
ductivity indexes rose relatively less.
The charts also show that, although output per unit of
capital exhibited marked short-term fluctuations be­
tween 1948 and 1981, there were no clearly evident

The growth in capital intensity— i.e., the amount of
capital inputs per person-hour— is one of the major
causes of the growth in output per hour during the three
decades as a whole. Between 1948 and 1981, output per
hour of all persons in the private business sector grew at
an average annual rate of 2.4 percent, and this was as­
sociated with a 2.6 percent yearly growth rate in capital
intensity. The growth rate of capital per hour multiplied
by capital’s share of total output measures its contribu­
tion to the growth in output per hour (table 5). (Table 6
shows the capital and labor shares of total income for
1948-81.) Capital’s contribution was 0.9 percent per
year, or nearly 40 percent of the growth rate in output
per hour between 1948 and 1981. Multifactor productiv­
ity, which measures output per combined unit of capital
and labor, grew at a yearly rate of 1.5 percent; this is
the residual obtained by subtracting the contribution of
capital per hour from the growth rate of output per
hour.3
In the private nonfarm sector, capital per hour of all
persons grew at an average annual rate of 2.2 percent
from 1948 to 1981, somewhat less than in the business
sector because of the large rise in capital-intensive pro­
duction in farming. The increase in nonfarm capital in­
tensity contributed 0.8 percent per year, or 40 percent,
to the 2.0 percent annual rate of growth of output per
hour. Multifactor productivity grew at a significantly
slower annual rate in private nonfarm business (1.3 per­
cent) than in business; this, too, reflects the technologi-

'In 1981, output of government enterprises accounted for 2 per­
cent of total business output.
2The index of output per unit of capital input in the manufactur­
ing sector is closely correlated with the Federal Reserve Board in­
dex of capacity utilization for total manufacturing. The correlation

coefficient between the two series was about 0.9 during the years
1948-81.
3See appendix A for a discussion of the multifactor productivity
model and the conceptual relationships among the different
variables.

Trends in nraltifactor productivity




16

Chart 6. Private business sector: Output per hour of all persons, output per unit of
capital, and muitifaotor productivity, 1048=81
(Index, 1498 = 100)




17

Chart 7. Private nonfarm business sector: Output per hour of aiS persons, output per unit
of capital, and multifactor productivity, 1948-81
(Index, 1 948= 100)




18

Chart 8. Manufacturing sector: Output per hour of all persons, output per unit off
capital, and muStiffaetor productivity, 1948-81
(Index, 1 948= 100)




19

Table 5. Rates of growth in output per hour of all persons,
capital per hour, the contribution of capital, and multifactor
productivity by major sector, 1948-81

productivity during 1973-81 was 0.1 percent compared
with 2.0 percent during 1948-73, a falloff of 1.9 percent
per year. In the private nonfarm business sector, there
was no growth in m ultifactor productivity during
1973-81, whereas it grew by 1.7 percent per year dur­
ing 1948-73. The zero growth rate for 1973-81 means
that all of the increase in output during the period came
from increases in capital inputs and hours of labor.
The slowdown experienced in manufacturing was
markedly different than in the other two sectors. In
manufacturing, capital per hour grew at a faster annual
rate (4.2 percent) after 1973 than during the earlier peri­
od (2.4 percent). Consequently, it did not contribute to
the slowdown in output per hour but rather increased
0.4 percent per year, which helped to offset the 1.8 per­
cent falloff in the growth rate for multifactor productiv­
ity after 1973.4
In sum, the growth in capital per hour contributed a

(Percent per year, compounded)
Sector and measure
Private business:1
Output per hour of all per­
sons ...................................
Capital per h o u r....................
Contribution of capital to out­
put per hour2 ......................
Multifactor productivity3 .........
Private nonfarm business:1
Output per hour of all per­
sons ...................................
Capital per h o u r....................
Contribution of capital to out­
put per hour2 ......................
Multifactor productivity3; .......
Manufacturing:
Output per hour of all per­
sons ...................................
Capital per h o u r....................
Contribution of capital to out­
put per hour2 ......................
Multifactor productivity3 .........

1948-81 1948-73 1973-81 Slowdown
(3)-(2)
(2)
(3)
(1)

2.4
2.6

3.0
2.8

0.8
1.8

-2 .2
-1 .0

0.9
1.5

1.0
2.0

0.7
0.1

-0 .3
-1 .9

2.0
2.2

2.5
2.3

0.6
1.2

-1 .9
-0 .6

0.7
1.3

0.8
1.7

0.6
0.0

-0 .2
-1 .7

2.6
2.8

2.9
2.4

1.5
4.2

-1 .4
1.8

0.8
1.8

0.7
2.2

1.1
0.4

0.4
-1 .8

Table 6. Labor and capital shares of total income by major
sector, 1948-81
(Percent)

’ Excludes government enterprises.
2Growth of capital per hour weighted by capital’s share of total output.
3Output per unit of combined labor and capital input.

Private business

Private nonfarm
business
Labor
Capital

Labor

Capital

Manufacturing

Year




62.2
64.2

37.8
35.8

62.7
65.0

37.3
35.0

68.1
67.0

31.9
33.0

1950.........
1951.........
1952.........
1953.........
1954.........
1955.........
1956 .........
1957.........
1958 .........
1959.........

61.3
61.8
64.8
66.4
66.1
63.3
63.9
64.6
64.6
63.5

38.7
38.2
35.2
33.6
33.9
36,7
36.1
35.4
35.4
36.5

62.7
62.3
64.2
65.8
65.8
62.8
63.4
64.2
64.2
63.1

37.3
37.7
35.8
34.2
34.2
37.2
36.6
35.8
35.8
36.9

65.6
66.1
68.3
69.4
69.6
67.1
69.4
69.7
70.6
68.3

34.4
33.9
31.7
30.6
30.4
32.9
30.6
30.3
29.4
31.7

1960.........
1961.........
1962.........
1963 .........
1964.........
1965.........
1966 .........
1967.........
1968 .........
1969.........

63.6
62.9
62.2
61.4
61.6
60.9
61.8
62.5
62.9
64.5

36.4
37.1
37.8
38.6
38.4
39.1
38.2
37.5
37.1
35.5

63.3
62.7
62.2
61.4
61.7
61.2
62.1
62.8
63.1
64.7

36.7
37.3
37.8
38.6
38.3
38.8
37.9
37.2
36.9
35.3

69.6
69.3
68.6
67.5
67.2
65.8
67.1
68.4
68.4
70.4

30.4
30.7
31.4
32.5
32.8
34.2
32.9
31.6
31.6
29.6

1970.........
1971.........
1972.........
1973 .........
1974.........
1975 .........
1976 .........
1977.........
1978 .........
1979.........

65.8
65.0
65.6
65.0
66.4
63.8
63.9
63.3
64.3
65.4

34.2
35.0
34.4
35.0
33.6
36.2
36.1
36.7
35.7
34.6

65.8
65.0
65.8
65.3
66.4
64.2
64.4
63.7
64.9
66.0

34.2
35.0
34.2
34.7
33.6
35.8
35.6
36.3
35.1
34.0

72.3
70.1
70.1
71.2
74.1
71.1
70.1
70.0
71.0
73.2

27.7
29.9
29.9
28.8
25.9
28.9
29.9
30.0
29.0
26.8

1980.........
1981.........

4A small percentage of the post-1973 rise in the bls capital input
measures represents spending for pollution abatement which is not
reflected in the output measures. Based on estimates made by the

Capital

1948.........
1949.........

cal “ revolution” in U.S. agriculture during the postWorld War II years, which both facilitated and resulted
from the reallocation of labor to nonfarm occupations.
Manufacturing experienced the highest average annu­
al rate of growth (2.8 percent) in capital per hour among
the three major sectors between 1948 and 1981. How­
ever, the growth in capital intensity contributed only 0.8
percent per year to the 2.6 percent per year growth in
output per hour. Multifactor productivity grew by 1.8
percent per year during the period.
A slowdown in the growth of capital per hour contrib­
uted somewhat to the slowdown in the growth of output
per hour after 1973 in the private business and private
nonfarm business sectors—but not in manufacturing. In
the private business sector, the average rate of growth
of capital per hour was 1.0 percent per year lower after
1973 than before. This contributed 0.3 percent per year
to the slowdown in output per hour. In the private non­
farm sector, the annual growth rate in capital intensity
was 0.6 percent lower after 1973, and this contributed
0.2 percent per year to the falloff in output per hour in
that sector.
Most of the slowdown in output per hour in the two
sectors was associated with decreases in the annual rates
of growth of multifactor productivity. In the private
business sector, the annual rate of growth in multifactor

Labor

65.5
64.6

34.5
35.4

66.3
65.3

33.7
34.7

75.7
74.8

24.3
25.2

Bureau of Economic Analysis, U.S. Department of Commerce,
capital inputs for pollution abatement in manufacturing, where the
impact was greatest, grew about 0.2 percent per year between 1973
(Continued)

20

sizable fraction—between 30 and 40 percent— to the
longer term growth, from 1948 to 1981, in output per
hour of all persons in private business, private nonfarm
business, and manufacturing. It also accounted for a
small proportion of the post-1973 slowdown in output
per hour in private business and private nonfarm busi­
ness, but not in manufacturing. Thus, most of the long­
term growth— as well as the post-1973 slowdown—in
output per hour in the three major sectors was associ­
ated with movements in multifactor productivity. The
next chapter reviews some of the factors that have influ­
enced the movements in multifactor productivity.

Table 7. Relationship between changes in rates of growth in
capital services per hour and changes in relative factor prices
in the private business sector, 1948-81
(Percent per year, compounded)

Measure

1948-73

1973-81

(1)

(2)

(3)

Factor inputs:
Capital services ...........
Hours of all persons .. .
Capital per hour . ..

3.6
0.7
2.9

3.2
1.4
1.8

-0 .4
0.7
-1.1

3.4
6.4
-3 .0

2.3
5.7
-3 .4

7.2
8.9
-1 .7

4.9
3.2
-1 .7

Ratio: Capital per hour to relative factor prices.............

In a competitive economy, changes in the amount of
capital per unit of labor reflect, among other things, the
behavior of firms trying to minimize their total produc­
tion costs as relative prices of these factors change.
Thus, increases in the price of labor relative to the price
of capital services induce firms to shift production tech­
niques from less to more capital-intensive methods.
Table 7 shows average annual rates of change of capital
per hour (the substitution of capital for labor inputs) and
average annual changes in the relative prices of capital
and labor for the private business sector. During the pe­
riod 1948-81 as a whole, the average annual rate of
growth of inputs of capital services (3.5 percent) was
substantially greater than that for hours of all persons
(0.9 percent). This was probably partly in response to
the slower rise in the price of capital services (3.4 per­
cent) than in labor services (6.4 percent). That is, the
2.6 percent average annual growth in capital per hour
discussed in the previous section may partially reflect a
response to a 3.0 percent per year decline in the price of
capital services relative to the price of labor inputs (av­
erage hourly compensation).5
Comparisons of the subperiods before and after 1973
indicate that the slowdown in the rate of growth of capi­
tal per unit of labor can largely be explained by the
changes in the relative prices of the two factors. As
shown in the previous section, the average annual rate

3.5
0.9
2.6

Factor prices:
Capital services1 .........
Labor2 ...........................
Relative price3 . . . .

Relationship between capital per hour
and factor prices

0.9

0.9

1.1

0.2

11mplicit price of capital services in the private business sector.
2Hourly compensation of all persons in the private business sector.
Numerical (absolute) value of the ratio of the price of capital services rela­
tive to hourly compensation of all persons.

of growth of capital per hour of all persons dropped
from 2.9 percent in 1948-73 to 1.8 percent in 1973-81.
This was the result of a slowdown in the rate of growth
of capital inputs coupled with a doubling in the annual
rate of increase in hours. The falloff in the growth in
capital intensity after 1973 coincided with a slowdown
in the rate of decline in the price of capital services rela­
tive to hourly compensation. Between 1973 and 1981,
the price of capital relative to labor declined 1.7 percent
per year, half as fast as the 3.4 percent annual rate of
decline during the earlier period, 1948-73.
The bottom row of table 7 shows the numerical (abso­
lute) value of the ratio of the average annual rate of
growth of capital per hour (the capital-labor ratio) to the
average annual rate of growth of the price of capital rel­
ative to the price of labor.6 The numerical value of the
ratio was 0.9 for the period 1948-81 as a whole; but,
more interestingly, it appears to have been fairly stable
between the two periods— 0.9 during 1948-73 and 1.1
during 1973-81. This suggests that most of the slow-

(Continued)
and 1981, the same rate as between 1960 and 1973. Thus, the capi­
tal inputs for pollution abatement appear to have had little effect on
the slowdown in productivity; in long-term growth, the overstate­
ment of the contribution of capital inputs to the annual growth rate
of “ measured” output per hour would be less than 0.1 percentage
point. It should also be noted that the equipment can affect produc­
tivity in other ways. For example, the pollution abatement invest­
ment may embody a less or possibly more efficient technology than
the existing one; it may require additional labor inputs, or it may
raise worker efficiency if it results in a cleaner and healthier
workplace.
5The measures of quantity and price of labor services used in this
bulletin are based on hours of all persons and average hourly com­
pensation and, therefore, do not take account of changes in the
composition of the labor force resulting from the growth in the




1948-81

Change,
1948-73
to
1973-81
(3)-(2)

amount of human capital (e.g., education) per worker. However,
this does not affect the broad conclusions in the text because ad­
justing the series for quality changes would lower the annual rate of
growth of capital per unit of labor and the decline in the ratio of the
price of capital to the price of labor by the same percentage.
6The ratio is a crude estimate of the (negative) value of the elas­
ticity of substitution between capital and labor. The estimate is
crude because it ignores technological change, changes in the prod­
uct mix, and other factors that could affect the capital-labor ratio. It
also does not take into account lags between changes in relative
factor prices and the capital-labor ratio. For one of many studies on
the theory and empirical measurement of the elasticity of substitu­
tion, see Murray Brown, On the Theory and Measurement of Tech­
nological Change (Cambridge, Mass., Cambridge University Press,
1966).

21

Table 8. Private business sector: Productivity and related measures, 1948-81
Productivity
Period

Output per
hour of all
persons

Output per
unit of
capital

Inputs
Multifactor
productivity1

Output1
2

Hours of
all persons3

Capital4

Combined units
of labor and
capital inputs5

Capital per
hour of
all persons

Index, 1977=100
1948 ....................
1949 ....................

45.3
46.0

99.2
93.6

60.1
59.4

36.8
36.1

81.3
78.6

37.1
38.6

61.3
60.8

45.6
49.1

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

49.7
51.2
52.9
54.6
55.6
57.8
58.5
60.0
61.8
63.9

98.7
100.2
99.4
100.7
96.3
100.9
100.0
97.9
94.3
99.3

63.6
65.1
66.3
68.0
67.8
70.7
71.0
71.6
72.0
74.9

39.5
41.8
43.2
45.1
44.4
47.9
49.2
49.7
48.9
52.5

79.5
81.8
81.8
82.6
79.8
82.9
84.2
82.9
79.0
82.1

40.0
41.8
43.5
44.9
46.1
47.5
49.2
50.7
51.9
52.9

62.1
64.3
65.2
66.4
65.5
67.8
69.3
69.4
67.8
70.0

50.4
51.1
53.2
54.3
57.7
57.3
58.5
61.2
65.6
64.4

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

64.8
67.0
69.6
72.3
75.4
78.1
80.4
82.3
85.1
85.3

98.4
98.0
101.2
102.6
105.2
107.8
108.0
104.9
105.5
103.7

75.4
76.9
79.7
82.0
84.9
87.6
89.3
89.6
91.7
91.3

53.3
54.2
57.2
59.7
63.3
67.6
71.3
72.9
76.7
78.9

82.2
80.9
82.2
82.7
84.0
86.7
88.7
88.6
90.1
92.5

54.1
55.3
56.6
58.2
60.2
62.8
66.1
69.6
72.7
76.1

70.7
70.5
71.8
72.9
74.6
77.2
79.9
81.4
83.7
86.5

65.8
68.4
68.8
70.4
71.6
72.4
74.5
78.5
80.7
82.3

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

86.1
89.2
92.4
94.7
92.4
94.5
97.6
100.0
100.6
99.6

98.6
98.1
101.0
103.0
96.5
91.9
96.1
100.0
101.8
100.3

90.2
92.2
95.2
97.5
93.8
93.6
97.1
100.0
101.0
99.9

78.3
80.6
86.0
91.8
89.9
88.0
93.7
100.0
105.5
107.8

90.9
90.4
93.2
96.9
97.2
93.1
95.9
100.0
104.9
108.3

79.4
82.2
85.2
89.1
93.1
95.7
97.5
100.0
103.6
107.5

86.8
87.5
90.4
94.1
95.8
94.0
96.5
100.0
104.4
108.0

87.4
91.0
91.5
92.0
95.8
102.8
101.6
100.0
98.8
99.3

1980 ....................
1981 ....................

98.8
100.6

95.3
95.0

97.6
98.6

106.2
108.8

107.4
108.2

111.3
114.5

108.8
110.3

103.6
105.8

Compound annual percent change
1948-73 ...............
1973-81 ...............

3.0
0.8

0.2
-1 .0

2.0
0.1

3.7
2.2

0.7
1.4

3.6
3.2

1.7
2.0

2.9
1.8

1948-81 ...............

2.4

-0.1

1.5

3.3

0.9

3.5

1.8

2.6

10utput per unit of combined labor and capital inputs.
2Gross domestic product originating in the sector, in constant dollars.
3Paid hours of all employees, plus the hours of proprietors and unpaid fam
ily workers engaged in the sector.




4A measure of the flow of capital services used in the sector.
5Hours of all persons combined with capital input, using labor and capital
shares of output as weights.
S ou r c e : See appendixes B, C, and D.

22

;

Table 9. Private nonfarm business sector: Productivity and related measures, 1948-81
Inputs

Productivity
Period

Output per
hour of all
persons

Output per
unit of
capital

Multifactor
productivity1

Output2

Hours of
all persons3

Capital4

Combined units
of labor and
capital inputs5

Capital per
hour of
all persons

Index, 1977=100
1948 ....................
1949 ....................

51.2
52.3

98.1
92.8

64.6
64.2

35.6
34.9

69.6
66.8

36.3
37.7

55.1
54.4

52.2
56.3

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

55.6
56.6
58.0
59.0
59.9
62.3
62.5
63.6
65.1
67.4

98.4
100.6
99.7
100.9
96.2
100.9
100.1
98.0
94.0
99.5

68.2
69.5
70.4
71.5
71.0
74.1
74.0
74.3
74.3
77.5

38.3
40.9
42.2
44.1
43.2
46.8
48.2
48.7
47.8
51.6

69.0
72.2
72.8
74.7
72.1
75.1
77.0
76.6
73.4
76.6

39.0
40.6
42.4
43.7
44.9
46.4
48.1
49.7
50.8
51.9

56.2
58.8
60.0
61.7
60.8
63.2
65.1
65.6
64.3
66.6

56.5
56.3
58.2
58.5
62.3
61.7
62.5
64.9
69.3
67.7

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

67.9
70.0
72.5
74.9
77.8
80.3
82.2
83.8
86.7
86.4

98.4
97.9
101.3
102.6
105.5
108.1
108.7
105.3
106.0
104.1

77.6
78.9
81.7
83.8
86.7
89.2
90.7
90.7
92.9
92.1

52.3
53.3
56.4
58.9
62.7
67.0
71.0
72.5
76.5
78.7

77.0
76.1
77.8
78.6
80.5
83.5
86.4
86.5
88.2
91.1

53.2
54.4
55.7
57.4
59.4
62.0
65.3
68.9
72.1
75.6

67.5
67.5
69.0
70.3
72.3
75.1
78.3
79.9
82.3
85.4

69.1
71.5
71.6
73.0
73.8
74.2
75.7
79.6
81.7
83.0

1970 ....................
1971 ....................
1972 ....................
1973-....................
1974 ....................
1975 ....................
1976 ....................
1977 ....................
1978 ....................
1979 ....................

86.8
89.7
93.0
95.3
92.9
94.7
97.8
100.0
100.6
99.3

98.6
98.0
101.1
103.2
96.5
91.7
96.1
100.0
101.9
100.0

90.7
92.4
95.7
97.9
94.1
93.6
97.2
100.0
101.1
99.6

77.9
80.1
85.8
91.7
89.7
87.6
93.6
100.0
105.7
108.0

89.7
89.3
92.2
96.2
96.6
92.5
95.7
100.0
105.1
108.7

78.9
81.8
84.8
88.8
93.0
95.6
97.4
100.0
103.7
107.9

85.9
86.7
89.7
93.6
95.4
93.6
96.3
100.0
104.6
108.4

88.0
91.5
92.0
92.3
96.3
103.3
101.8
100.0
98.7
99.2

1980 ....................
1981 ....................

98.4
99.8

95.1
94.4

97.3
97.9

106.2
108.5

108.0
108.8

111.7
115.0

109.2
110.9

103.4
105.7

3.6
3.3
3.6

2.1
2.1
2.1

2.3
1.7
2.2

Compound annual percent change
1948-73 ...............
1973-81 ...............
1948-81 ...............

2.5
0.6
2.0

0.2
-1.1
-0.1

1.7
0.0
1.3

3.9
2.1
3.4

See footnotes for table 8.




23

1.3
1.5
1.4

Table 10. Manufacturing sector: Productivity and related measures, 1948-81
Productivity

Period

Output per
hour of all
persons

Output per
unit of
capital

Inputs
Multifactor
productivity1

Output2

Hours of
all persons3

Capital4

Combined units
of labor and
capital inputs5

Capital per
hour of
all persons

Index, 1977=100
1948 ....................
1949 ....................

45.1
46.9

94.4
86.0

56.2
56.0

35.8
33.9

79.4
72.4

37.9
39.5

63.7
60.6

47.8
54.5

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

49.4
51.1
52.0
52.9
53.7
56.4
56.0
57.1
56.9
59.6

94.9
99.6
95.7
98.6
89.2
95.8
92.5
89.6
80.5
89.2

59.9
62.3
62.2
63.5
62.3
65.9
64.8
65.1
62.8
67.0

38.6
43.0
44.5
47.5
44.1
48.9
49.2
49.5
45.2
50.5

78.2
84.2
85.4
89.8
82.1
86.6
87.9
86.5
79.4
84.7

40.7
43.2
46.4
48.2
49.5
51.0
53.2
55.2
56.2
56.6

64.5
69.1
71.4
74.8
70.8
74.2
75.9
76.0
71.9
75.4

52.1
51.3
54.4
53.7
60.2
58.8
60.5
63.8
70.7
66.9

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

60.0
61.6
64.3
68.9
72.3
74.5
75.3
75.3
78.0
79.3

88.0
86.9
92.9
98.3
102.4
107.3
108.7
101.1
101.1
100.5

67.0
68.0
71.5
76.3
79.8
82.8
83.7
81.8
83.7
84.6

50.7
50.7
55.1
59.6
63.9
69.8
75.1
75.0
79.1
81.7

84.4
82.3
85.6
86.5
88.4
93.6
99.8
99.6
101.4
103.1

57.5
58.3
59.2
60.7
62.4
65.1
69.2
74.2
78.2
81.3

75.6
74.6
77.0
78.2
80.0
84.3
89.8
91.7
94.4
96.6

68.2
70.9
69.2
70.1
70.6
69.5
69.3
74.5
77.1
78.9

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

79.1
83.9
88.2
93.0
90.8
93.4
97.5
100.0
100.9
101.6

91.8
92.4
99.9
108.2
99.6
89.4
96.1
100.0
101.5
99.5

82.3
86.0
91.1
96.8
93.0
92.2
97.1
100.0
101.0
101.0

77.0
78.7
86.2
95.9
91.9
85.4
93.6
100.0
105.3
108.2

97.3
93.7
97.8
103.2
101.2
91.4
95.9
100.0
104.4
106.5

83.9
85.2
86.4
88.6
92.2
95.5
97.4
100.0
103.8
108.8

93.6
91.5
94.7
99.1
98.8
92.6
96.4
100.0
104.2
107.2

86.2
90.9
88.3
85.9
91.1
104.4
101.5
100.0
99.4
102.1

1980 ....................
1981 ....................

101.7
104.5

90.0
87.5

98.6
99.9

103.6
105.9

101.8
101.3

115.1
121.1

105.1
106.0

113.1
119.5

Compound annual percent change
1948-73 ...............
1973-81 ..............

2.9
1.5

0.6
-2 .6

2.2
0.4

4.0
1.2

1.1
-0 .2

3.5
4.0

1.8
0.9

2.4
4.2

1948-81 ...............

2.6

-0 .2

1.8

3.3

0.7

3.6

1.6

2.8

See footnotes for table 8.

down in the growth of capital per hour after 1973 was
the result of the change in relative factor prices—the
markedly slower rate of decline in the ratio of the price
of capital to the price of labor. If the ratio (0.9) for the
1948-81 period as a whole was, in fact, the same in

both subperiods, the smaller rate of decline in the price
of capital relative to that of labor (1.7 percent per year)
would alone have accounted for about 80 percent of the
slowdown in the growth of the capital-labor ratio after
1973.7

7Econometric estimates based on a model derived from the
constant-elasticity-of-substitution production function relating the
capital-labor ratio to relative factor prices and including dummy
variables indicates an elasticity of substitution of 0.9 for the period
1948-81 as a whole. There was no statistically significant differ­
ence in the elasticity between 1948-73 and 1973-81. The qualifica­
tions discussed in the previous footnote also apply here. Part of the
slowdown in the rate of substitution of capital for labor after 1973
may also reflect the sharp increases in energy prices that began in
that year. Dale Jorgenson and others have estimated that energy and

physical capital are complementary, whereas energy and labor are
substitutes in production. This implies that the sharp rise in energy
prices in 1973 (and 1979) would have induced firms to decrease
their investment and to increase their employment more than they
otherwise would have done. Such an energy-induced substitution of
capital for labor would be reflected in the figures in table 7 and, to
that extent, the effect of change in relative factor prices on the
slowdown in capital intensity would be overstated. See Dale W.
Jorgenson, “ Energy and the Future of the U .S. Econom y,’’
Wharton Magazine, Vol. 3 (Summer 1979), pp. 15-21.




24

C hapter S . B ourses ©f C hange
W
in M ultifaetor IProduetawity

This chapter reviews several of the statistically ob­
servable sources of change in multifactor productivity to
see how they have influenced long-run growth in pro­
ductivity and the slowdown after 1973. These sources
include (1) intersectoral shifts in resources, (2) selected
changes in labor force composition, (3) changes in ca­
pacity utilization, (4) research and development ( r & d ) ,
and (5) changes in hours at work relative to hours paid.

Tabie 11. Contribution of intersectoral shifts in labor to rates
of growth in multifactor productivity in the private business
sector, 1948-81
(Percent per year, compounded)

Item
Multifactor productivity .........
Contribution of intersectoral
shifts of la b o r......................
Multifactor productivity ad­
justed for intersectoral shifts
of labor ...............................

Intersectoral shifts
Multifactor productivity is increased when labor and
capital shift to sectors where they are more productively
employed. The most dramatic shift of resources during
the period 1948-81 was from the farm to the nonfarm
sector. In 1948, persons engaged in farming accounted
for about 16 percent of the total engaged in the private
business sector; by 1973, the proportion had dropped to
5 percent; and by 1981, to about 4 percent.1 Capital also
moved from the farm to the nonfarm sector during the
post-World War II period. As in the case of labor, the
shift was virtually completed by the mid-1960’s.

1948-73
(2)

1973-81 Slowdown
(3) - (2)
(3)

1.5

2.0

0.1

-1 .9

0.1

0.2

0.0

-0 .2

1.4

1.8

0.1

-1 .7

Changes in labor force composition
The b l s measures of multifactor productivity are
based on hours of all persons engaged in the private
business sector, which assumes that workers are homo­
geneous with respect to skills. As a result, the shifts
from less to more skilled labor because of increased ed­
ucation or on-the-job training are not reflected in the
b l s measure of labor input but instead contribute to
growth in multifactor productivity.3

Table 11 shows the contribution of intersectoral shifts
in labor to the growth rates of multifactor productivity
in the private business sector.2 Because of data limita­
tions, resource reallocation effects reflect only shifts
among the three major sectors— farm, manufacturing,
and nonfarm-nonmanufacturing. Over the total period,
1948-81, the reallocation of labor, mainly from the
farm to the nonfarm sector, contributed 0.1 percent per
year to the average annual growth rate of multifactor
productivity. Intersectoral shifts in labor contributed 0.2
percentage point to the growth rate of multifactor pro­
ductivity betwen 1948 and 1973; but it was not a con­
tributing factor after 1973. Thus, 0.2 percentage point
of the 1.9 percent slowdown in multifactor productivity
growth after 1973 in the private business sector resulted
from the fact that there were no longer large numbers of
workers moving from farm to nonfarm activities.

Historically, the change in the composition of the la­
bor force has been one of the most important sources of
growth in m ultifactor productivity. This includes,
among other things, changes in the amount of formal
education and on-the-job training per worker, in the
age-sex distribution of the labor force, and in the occu­
pational and industry mix of employment. Three of
these compositional changes are discussed in this sec­
tion: The amount of education per worker, which is by
far the most important; the age-sex composition of the
work force; and increases in the efficiency of an hour’s
work resulting from the secular decline in average
weekly hours.
Education is generally viewed as one of the major
factors affecting the productivity of labor. Over the last
three decades, the amount of schooling of U.S. workers

'The shift was largely completed by 1965; in that year, the num­
ber engaged in farming accounted for only 7 percent of all persons
engaged in private business. The importance of farm output also
declined—from about 6 percent of business output in 1948 to 3 per­
cent in 1973.
2The contributions from intersectoral shifts in capital are not in­
cluded in table 11 because they are already reflected in the b l s




1948-81
(1)

m e a su re o f cap ital p e r h o u r a n d ,

hence,

accounted

f o r in th e bls

m e a s u r e o f m u l t i f a c t o r p r o d u c t i v it y s h o w n in th e ta b le .

3For a detailed review of the issues in measuring the effects of
changes in the composition of labor inputs on productivity, see
Kent Kunze, “ Evaluation of Work-Force Composition Adjust­
ment,” in National Academy of Sciences, Measurement and Inter­
pretation of Productivity (Washington, n a s , 1979).

25

has increased dramatically.4 The proportion of the labor
force with at least 1 year of college rose from 12 percent
in 1948 to 36 percent in 1981; the proportion with 1 to 4
years of high school rose from 47 percent to 55 percent;
and the fraction in the lowest education group, those
with only 8 or fewer years of schooling, dropped from
41 percent to 8 percent (table 12). There was also a
marked rise between 1948 and 1981 in the percentage of
students who completed 4 years of high school. The pic­
ture was generally the same for men and women.
Table 13 shows Denison’s estimates of average annu­
al growth rates in the amount of education per worker
during the periods discussed in this bulletin; it also in­
cludes his estimates of the growth in efficiency of an
hour’s work resulting from the decline in the average
workweek, and an index of average annual change in
the age-sex composition of total hours.5 The numbers in
the last three columns of the table show the contribution
of each of these factors to the growth in the bls measure

Table 13. Adjustments to hours measures for changes in
composition of labor input1
Annual growth rate
Item

1948-81 1948-73 1973-81 1948-81 1948-73 1973-81
T otal.........
Amount of education.............
Efficiency of an
hour’s work3 ..
Age-sex composition .............

Elementary
Total

Less
5-8
than
years
5 years

High school

4 years

1-3
years

4 years
or more

Total:
1948 . . . .
1973 . . . .
1981 . . . .

100.0
100.0
100.0

7.5
2.0
1.2

33.5
11.6
6.7

19.8
18.6
14.9

27.2
39.4
40.9

6.9
14.2
17.9

5.2
14.1
18.3

Men:
1948 . . . .
1973 . . . .
1981 . . . .

100.0
100.0
100.0

8.8
2.4
1.5

35.7
13.1
7.9

20.2
18.6
15.4

23.1
35.8
37.5

6.6
14.5
17.4

5.7
15.6
20.3

Women:
1948 . . . .
1973 . . . .
1981 . . . .

100.0
100.0
100.0

4.4
1.4
.8

28.0
9.2
5.1

18.8
18.6
14.2

37.3
45.2
45.5

7.5
13.8
18.6

4.0
12.0
15.7

S ources : Data for 1948 from Edward F. Denison, Accounting for United
States Economic Growth, 1929-69 (Washington, The Brookings Institution,
1974). Data for 1973 and 1981 from Labor Force Statistics Derived from the
Current Population Survey: A Databook, Vol. 1, Bulletin 2096 (Bureau of La­
bor Statistics, September 1982).

—

0.4

0.4

0.4

0.7

0.6

0.7

0.4

0.4

0.5

0.2

0.2

0.1

0.1

0.1

0.1

-0.2

-0.2

-0.3

-0.1

-0.1

-0 .2

He also makes some adjustment for differences in ability and
socioeconomic status.
Similarly, Denison’s annual index showing changes in the agesex composition of the work force is based on a weighted distribu­
tion of total hours worked in the business sector by age and sex.
The weights are relative hourly earnings of the different demo­
graphic groups. For a discussion of the methodology used in
arriving at these estimates, see Denison, Accounting for United
States Economic Growth, 1929-69.
6The b l s measures of m ultifactor productivity employ a
Tornquist index number formula which involves changing weights;
however, labor’s share for the private business sector was fairly
stable between 1948 and 1981—about 65 percent of total output—
so that the use of a fixed weight does not significantly affect the
results.

4The literature on human capital (including education) and its im­
plications for productivity is too extensive to cite here. For a recent
attempt to measure the stock of human capital, see John W.
Kendrick, The Formation and Stocks of Total Capital, National
Bureau of Economic Research (New York, Columbia University
Press, 1976) and the literature cited there; for an earlier review of
the relationship, see Zvi Griliches, “ Notes on the Role of Educa­
tion in Production Functions and Growth Accounting,’’ in W. Lee
Hansen, ed., Education, Income, and Human Capital, Studies in
Income and Wealth No. 35, National Bureau of Economic Research
(New York, Columbia University Press, 1970).
5Edward F. Denison kindly made these estimates available to us.
Denison’s index of the amount of education is based on a weighted
distribution of full-time-equivalent business employment by years
of schooling and sex. The weights are relative earnings for 1959
standardized for age, race, region, and farm-nonfarm employment.




—

of multifactor productivity based on the bls weight for
labor’s share (65 percent).6
The amount of education per worker is, by far, the
most important single source of the measured changes in
the composition of labor input. Denison’s estimates in­
dicate that the amount of education per person in the la­
bor force grew at an average annual rate of 0.7 percent
between 1948 and 1981. This was only 0.2 percentage
point lower than the annual growth rate of hours of all
persons; it means that quality enhancement in the work
force from increased education grew nearly as much as
the quantity of “ raw” labor inputs measured by total
hours of all persons. When weighted by the bls estimate
of labor’s share of total output, Denison’s estimate
shows that the growth in education per worker contrib­
uted about 0.4 percent per year to the annual rate of
growth of the bls measure of multifactor productivity
between 1948 and 1981. Changes in the amount of edu­
cation per worker did not contribute to the falloff in the
growth rate of multifactor productivity after 1973 and,
judging from Denison’s estimates, may even have added
nearly 0.1 percentage point to growth.
Average weekly hours in the private business sector
declined from 42.5 in 1948 to 38.4 in 1973 and to 36.7

College

1-3
years

—

1Based on Edward Denison’s estimates rounded to a tenth of a percentage
point. See Denison, Accounting for United States Economic Growth,
1929-69, and his Accounting for Slower Economic Growth: The United
States in the 1970’s (Washington, The Brookings Institution, 1979).
Contribution to multifactor productivity is equal to the annual growth rate
multipled by the bls estimate of labor’s share (0.65).
efficiency of an hour’s work as affected by changes in hours due to
intragroup changes and specified intergroup shifts.

Table 12. Percent distribution of the labor force by years of
school completed, by sex, 1948,1973, and 1981

Labor force
group
and
years

Contribution to multifactor
productivity2

26

using an index showing changes in the age-sex compo­
sition of the labor force. This index declined about 0.2
percent per year between 1948 and 1981, which implies
that changes in the age-sex composition of the labor
force reduced the annual rate of growth of the bls meas­
ure of multifactor productivity by 0.1 percentage point
during the period. The rate of decline in the age-sex
composition index appeared to be slightly higher after
than before 1973 and thus may have contributed slightly
(less than 0.1 percent per year) to the productivity slow­
down. That is, it offset the equally slight positive effect
from the increased amount of education per worker.
In sum, based on Denison’s estimated growth rates
and bls weights, the total combined changes in the
composition of labor inputs accounted for about 0.4 per­
centage point of the 1.5 percent annual growth rate in
multifactor productivity between 1948 and 1981.8 The
compositional changes in the work force, considered as
a whole, had virtually no effect on the productivity
slowdown after 1973.

in 1981. These declines reflect both decreases in aver­
age hours worked within sectors and the shift of labor
from the farm to the nonfarm sector, where average
weekly hours tend to be shorter. Denison has also esti­
mated changes in the efficiency of an hour’s work re­
sulting from those intrasectoral changes in average
weekly hours and intersectoral shifts in labor. Accord­
ing to his measure, the efficiency of an hour’s work due
to the combination of these two sources rose about 0.2
percent per year between 1948 and 1981. Multiplying
this by the bls estimate of labor’s share indicates that
the contribution of the shorter workweek added 0.1 per­
cent per year to the growth of multifactor productivity
during the period. The contribution was apparently the
same before and after 1973, so that changes in efficien­
cy from the shorter workweek were not a factor in the
productivity slowdown.
Work experience, like schooling, is a major compo­
nent of the composition of the labor force that influ­
ences multifactor productivity. Unfortunately, data are
not available for directly measuring changes in the aver­
age work experience of the total work force, so re­
searchers have had to develop a measure from available
data that is closely associated with the desired one. The
measure generally used is an index showing changes in
the age-sex composition of the labor force.7 For exam­
ple, teenagers entering the labor force for the first time
probably have little or no work experience and, conse­
quently, an increase in their relative importance tends to
reduce the average amount of experience per worker.
The measure is stratified by sex because, in general,
women tend to have less work experience than men of
the same age, either because they enter the labor force
later after raising children or because they temporarily
leave the labor force to raise children.
Between 1948 and 1981, the proportion of the civil­
ian labor force between 16 and 24 years of age in­
creased from 19.5 percent to about 23 percent; over the
same time period, the proportion of women in the civil­
ian labor force rose from about 29 percent to 43 percent.
Both of these shifts tended to have a dampening effect
on the average number of years of work experience of
the labor force during the period.
Denison, like others, has tried to estimate the changes
in the average amount of experience of labor inputs by

Short-term fluctuations in aggregate demand result in
cyclical changes in the utilization of capital and labor,
and these too are reflected in the bls m easures of
multifactor productivity. This is evident from looking at
the cyclical fluctuations in multifactor productivity be­
tween 1948 and 1981 (charts 6, 7, 8), and it is perhaps
most clearly seen in the 1973-75 recession. Multifactor
productivity in each of the three sectors declined from a
peak in 1973, bottomed out in 1975, and recovered in
1976. These changes paralleled those in output per unit
of capital, which also reflects utilization of the capital
stock.
To some extent, the labor inputs are adjusted to cur­
rent production needs by firms hiring and laying off
workers and by changing the number of weekly hours
worked. However, to the extent that labor is a quasifixed factor and there is labor hoarding, firms tend to
underutilize (overutilize) the work force during periods
of recession (expansion), and this is reflected in the bls
measures of multifactor productivity.
In the case of capital, firms mainly adjust their inputs
to meet changes in their short-run production needs by
changing the utilization of existing stocks.9 The magni-

7That is, the index showing changes in the age-sex composition
of the labor force is used as a proxy for changes in the average
amount of work experience per person.
8In the formulation of “ growth accounting,’’ the growth of out­
put is related to the growth of inputs of labor, capital services, and
other factors. Labor inputs are generally measured by combining
hours of all persons and the compositional changes in the labor
force, and the growth rate of this aggregate is then weighted by la­
bor’s share of the total output in order to determine its contribution
to the growth of output. The figures in the text suggest that these
combined labor inputs contributed 1.0 percent per year to the rate

of growth of output in the private business sector between 1948 and
1981; of this, 0.6 percentage point came from hours of all persons
and 0.4—or 40 percent—from the effects of changes in the compo­
sition of the work force.
9The Tornquist index number formula used to construct the b l s
measure of capital stock implicitly adjusts, to some degree, for
changes in the utilization of capital. For a theoretical discussion of
this implicit ex post adjustment, see Charles R. Hulten, “ Produc­
tivity Change, Capacity Utilization, and the Sources of Efficiency
Growth,” b l s Working Paper 137 (Bureau of Labor Statistics,
June 1983).




Capacity utilization

27

tude of the adjustments for the utilization of capital in­
puts is therefore likely to be larger than that for labor.
Unfortunately, there is at present no generally ac­
cepted way to adjust the labor and capital input series in
the private business or nonfarm business sectors for
changes in capacity utilization resulting from fluctua­
tions in aggregate demand. The approach used in this
bulletin has been to calculate growth rates between cy­
clical peaks as designated by the National Bureau of
Economic Research (see chapter II), but it is not clear
that the rates of utilization of the capital stock were the
same at each peak; it is equally problematical for labor
utilization.10*
The Federal Reserve Board ( f r b ) indexes of capacity
utilization for total manufacturing can be used to sug­
gest the effects of changes in resource utilization on the
b l s measures of multifactor productivity in the manu­
facturing sector.11 It is important to stress that the ad­
justments are only suggestive because different pub­
lished measures of capacity utilization yield somewhat
different results and, to some unknown extent, the b l s
multifactor productivity measure implicitly incorporates
adjustments for changes in resource utilization.12
Table 14 compares the growth rates for the b l s multi­
factor productivity measure for total manufacturing un­
adjusted and adjusted for capacity utilization based on
the f r b index. This was done by adjusting the b l s annu­
al measures of capital inputs in manufacturing by the
f r b annual indexes of capacity utilization in that sector.

1From table 3.
2Average annual rates of growth of capacity utilization weighted by capital’s
share of total output.
3Multifactor productivity minus the contribution of utilization of physical
capital.

According to the f r b index, the rate of capacity utiliza­
tion in manufacturing in 1948 was only slightly higher
than in 1981 and, as a consequence, the average annual
rate of change was virtually zero. For 1948-81 as a
whole, the average annual rate of growth in the adjusted
multifactor productivity measure is the same as the
unadjusted one.
The results, however, do suggest that some of the
productivity slowdown after 1973 may be explained by
changes in capacity utilization. The f r b index shows
that the rate of capacity utilization rose from 82.5 per­
cent in 1948 to 87.6 percent in 1973 and then fell to
78.5 percent in 1981. The figures based on the adjusted
capital inputs indicate that the increase in capacity utili­
zation before 1973 added 0.1 percent per year to the an­
nual growth rate in the b l s (unadjusted) measure of
multifactor productivity during 1948-73, and that the
decrease in capacity utilization after 1973 reduced it by
0.3 percent per year during 1973-81. Thus, multifactor
productivity adjusted for changes in capacity utilization
grew at an average annual rate of 0.7 percent in 197381 compared with 2.1 percent in 1948-73. This slow­
down of 1.4 percent per year in the adjusted measure is
0.4 percentage point lower than the 1.8 percent per year
falloff registered by the b l s (unadjusted) series.
In sum, these tentative calculations suggest that
changes in capacity utilization may have accounted for a
significant fraction of the post-1973 falloff in manufac­
turing productivity, but that a large fraction probably
still remains unexplained. The parallel cyclical move­
ments of multifactor productivity in the three major sec­
tors (charts 6, 7, and 8) also suggest that these general
conclusions for manufacturing might be true for the pri­
vate business and private nonfarm business sectors as
well.
Finally, it is interesting to note the virtually parallel
fluctuations in the f r b index of capacity utilization for
total manufacturing and the b l s measure of output per
unit of capital input in the sector (chart 9). During the
period 1948-81 as a whole, the association between the
two indexes was close; about 80 percent of the total var­
iation in output per unit of capital input could be “ ex­
plained” by variations in capacity utilization.13

10Arthur Okun and Robert Solow made relative utilization of la­
bor and capital functions of the unemployment rate and used the
same measure to adjust both inputs simultaneously. Denison pains­
takingly measures the “ effects” of varying intensity of demand on
output per unit of input as a function of the ratio of nonlabor earn­
ings to national income of corporations and he, too, applies the
same measure of utilization rates to labor and capital. See A.M.
Okun, “ Potential GNP: Its Measurement and Significance,” Pro­
ceedings of the Business and Economics Statistics Section of the
American Statistical Association, 1962, pp. 98-104; R.M. Solow,
“ Technical Change and the Aggregate Production Function,” Re­
view of Economics and Statistics, (August 1957), pp. 312-20; and
Denison, Accounting for United States Economic Growth.
u The main reason for using the Federal Reserve Board indexes
rather than other measures of capacity utilization is their availabili-

ty for the total period, 1948-81.
12For a review of the issues, see Frank de Leeuw, Lawrence R.
Forrest, Jr., Richard D. Raddock, and Zoltan E. Kenessey, Meas­
ures of Capacity Utilization: Problems and Tasks (Washington,
Board of Governors of the Federal Reserve System, July 1979).
13The two measures are not wholly independent because the f r b
measure of capacity utilization is at least partially based on meas­
ures of output and capital stock, albeit not the b l s series. Also, the
b l s measures of output per unit of capital input for both the private
business and private nonfarm business sectors exhibit equally high
correlations with the f r b index of capacity utilization in manufac­
turing. On the face of it, this would indicate that the large fluctua­
tions in the b l s series of output per unit of capital largely reflect
changes in capacity utilization and hence fluctuations in aggregate
demand.

Table 14. Rates of growth in multifactor productivity in manu­
facturing, unadjusted and adjusted for utilization of physical
capital, 1948-81
(Percent per year, compounded)

Item
Multifactor productivity1 .......
Contribution of utilization2 ...
Adjusted multifactor productivity3 .................................




1973-81
(3)

Slowdown
(3) - (2)

1948-81
(1)

1948-73
(2)

1.8
0.0

2.2
0.1

0.4
-0.3

-1 .8
-0 .4

1.8

2.1

0.7

-1 .4

28

Chart 9. Output per unit © capita! and rate ©f capacity utilization in manufacturing,
fi
1948=81
(Index, 1948= 100)

Note: Shaded areas indicate recessions.

ured in constant prices as gross investment in the capital
stock of technical knowledge, and this raises a number
of very difficult conceptual and empirical problems.14 It
is, therefore, not surprising that present knowledge
about the contribution of r & d to the long-term growth
of multifactor productivity and its falloff in the 1970’s
is limited.
Total r & d expenditures as a percentage of g n p , a
measure of “ research intensity,” declined from 2.7 per­
cent in 1961 to 2.3 percent in 1973; there was virtually
no change in the rates between 1973 and 1980. The total
figures include r & d expenditures by the U.S. Govern­
ment for defense, the atomic energy program, and space
exploration, and there has been some question about the
degree to which these government r & d outlays affect
measured productivity in the private business sector of
the Economy.15 Private r & d expenditures (which ex-

Research and development
Additions to the stock of knowledge that yield tech­
nological improvements in production are generally
viewed as one of the major sources of growth in multi­
factor productivity. Research and development ( r & d )
expenditures that contribute to this new knowledge have
consequently been a major area of research for ex­
plaining the growth in productivity. In addition, the
slowdown in the rate of growth of r & d during the
1970’s focused attention on its possible role in the pro­
ductivity slowdown.
Unfortunately, the relationship between r & d expend­
itures and multifactor productivity is one of the most
difficult and, perhaps, more intractable areas of produc­
tivity research. The analysis used to relate r & d to
multifactor productivity treats r & d expenditures meas­
14Some of the more obvious problems are: (1) determining the
relevant r & d expenditures that affect multifactor productivity; (2)
r & d expenditures measure the cost of inputs, not the value of the
output of knowledge; (3) there is no appropriate deflator for r & d
presently available and researchers have generally used the g n p de­
flator; (4) the difficulty of measuring the length and structure of the
lag between r & d outlays and their impact on multifactor productiv­
ity; (5) the meaning and measurement of depreciation and obsoles­
cence of the r & d capital stock; (6) determining the spillover effects
(externalities) of r & d among industries using the products of the
industry undertaking the r & d as well as between defense and space



exploration projects and the private business sector; and (7) the
usual quality problems in the price series used to deflate the value
of the products embodying the improved technology. For a review
of these and other conceptual and empirical issues in relating r & d
expenditures to multifactor productivity, see Z. Griliches, “ Issues
in Assessing the Contribution of Research and Development to Eco­
nomic Growth,’’ Bell Journal of Economics. Spring 1979, pp.
92-116.
15Nestor Terleckyj found no correlation between governmentcontract r & d (other than for agriculture) and the productivity of the
industries conducting it. He also found that the indirect effects on
(Continued)

29

elude outlays by the three government agencies) as a
percentage of g n p actually rose from 1 .2 percent in
1961 to 1.4 percent in 1973 and to 1.6 percent in
1980.16 These comparisons suggest that, to the extent
that changes in research intensity contributed to the
post-1973 falloff in productivity, the effect was small.
At present, there is no generally accepted measure of
the r & d stock over time which can be used to evaluate
the impact of research on national multifactor produc­
tivity growth over the 1948-81 period.17 Cross-section
studies based on data for different industries in the
1950’s and 1960’s indicate research intensity had a pos­
itive influence on productivity growth in these periods.
This is true for both the direct effects for the industries
conducting the research and the indirect effects on the
industries that purchased capital and materials with r & d
content. Griliches, for example, estimated that r & d
contributed 0.3 percentage point to the growth of multi­
factor productivity based on a study for the mid-1960’s;
but he also noted that this was probably a maximum.18

The findings based on cross-section analyses for the
1970’s are mixed; they depend upon the particular
sample used and the level of aggregation of the data.19
The estimates made by different researchers on the
contribution of R&D to the slowdown in multifactor
productivity between the 1960’s and 1970’s range from
less than 0.1 percentage point (Denison)20 to about 0.2
percentage point (Kendrick, Clark, and Griliches)21 and
between 0.2 and 0.4 percentage point (Scherer).22 It
might, perhaps, be concluded from these results that the
slowdown in the rate of growth of r & d contributed to
the post-1973 slowdown in multifactor productivity, but
the effect was probably small, perhaps on the order of
0.1 percentage point. This and the earlier cited estimate
of 0.3 percentage point for the 1960’s reported by
Griliches suggest that, over the longer term, r & d ’ s con­
tribution to the annual rate of growth of multifactor pro­
ductivity averaged between 0.2 and 0.3 percentage
point.

(Continued)
productivity of industries purchasing goods from the industries con­
ducting the government-contract r & d were weak or nonexistent.
See Nestor E. Terleckyj, Effects o f r & d on the Productivity
Growth of Industries: An Exploratory Study," Report No. 140
(Washington, National Planning Association, December 1974).
Griliches omits r & d expenditures by the Defense Department, the
Atomic Energy Commission, and the National Aeronautics and
Space Administration, in order to arrive at an estimate of “ expend­
itures with probable effects on measured private productivity.”
Government r & d outlays by these three agencies accounted for half
of the total r & d expenditures in 1970. See Zvi Griliches, “ Re­
search Expenditures and Growth Accounting,” in B.R. Williams,
ed., Science and Technology in Economic Growth (London, 1973)
table 3.1, p. 75.
,6Civilian r & d expenditures accounted for about 70 percent of
total r & d outlays in 1980 compared with 62 percent in 1973 and 44
percent in 1961. However, even this series is not appropriate for
determining the relationship of r & d to multifactor productivity be­
cause it includes research outlays by government, universities,
colleges, other nonprofit institutions, and even consumer product
research by profitmaking firms, that do not affect the amount of in­
puts required to produce a unit of output included in the b l s meas­
ures. See Griliches, “ Research Expenditures,” pp. 74—
77, and
Denison, Accounting for Slower Economic Growth: The United
States in the 1970’s (Washington, The Brookings Institution,
1979), p. 124.
17John Kendrick has developed a time series for the stock of r & d
capital beginning in 1929. Based on this, he estimated that between
1948 and 1978, the growth of R & D capital contributed about 0.8
percentage point per year to the growth of multifactor productivity
(i.e., his total factor productivity). This is about 3 times as large as
estimates made by Griliches and others based on cross-section anal­
ysis. Kendrick obtains this result because his measure of the stock
of R & D capital includes total r & d , both government and privately
financed, and, as pointed out in the text and footnote 15, most
government-financed r & d has little or no effect, directly or indi­
rectly, on measured multifactor productivity. See John W.
Kendrick, “ Why Productivity Growth Rates Change and Differ,”
in Herbert Giersch, ed., Towards an Explanation of Economic
Growth, Symposium 1980 (Tubingen, J.C.B. Mohr (Paul Sieback),
1981), and Edwin Mansfield’s Comment.




18Griliches, “ Research Expenditures,” pp. 59-83; Terleckyj,
Effects of r & d on Productivity Growth; and Leo Sveikauskas,
“ Technological Inputs and Multifactor Productivity Growth,” Re­
view of Economics and Statistics, May 1981, pp. 275-82.
I9For example, Griliches, using more aggregate data, found that
the growth in productivity was much less sensitive to r & d intensity
in manufacturing in the 1970’s than in the 1960’s and that the
1970’s estimate was not significantly different from zero. Taken at
face value, this would imply that developments in r & d were a ma­
jor cause of the slowdown in productivity during the 1970’s. How­
ever, in his later studies with associates using more disaggregated
data, he found that r & d continued to have a positive effect on
multifactor productivity in manufacturing during the 1970’s. See
Zvi Griliches, “ r & d and the Productivity Slowdown,” American
Economic Review, May 1980, pp. 343-48; Kim B. Clark and Zvi
Griliches, “ Productivity Growth and r & d at the Business Level:
Results from the p i m s Data B a se,” Working Paper No. 916
(Cambridge, Mass., National Bureau of Economic Research, June
1982); and Zvi Griliches and F. Lichtenberg, “ r & d Productivity
Growth at the Industry Level: Is There Still a Relationship?”
Working Paper No. 850 (Cambridge, Mass., National Bureau of
Economic Research, February 1982). Clark and Griliches point out
that the p i m s data base is not a representative sample of firms in any
given sector; but, interestingly, their estimate of the direct rate of
return for the firms in the p i m s data base (18-20 percent) is about
the same as the one estimated by Griliches and cited earlier. Clark
and Griliches conclude that about 10 percent of the decline in
multifactor productivity for the firms in the p i m s data base can be
attributed to a reduction in their R&D-to-sales ratio.
20Edward F. Denison, “ Accounting for Slower Economic
Growth: An Update,” paper prepared for the Conference on Inter­
national Comparisons of Productivity and Causes of the Slowdown
held by the American Enterprise Institute, Washington, Sept. 30,
1982, p. 25.
21John W. Kendrick, “ Survey of the Factors Contributing to the
Decline in U.S. Productivity Growth,” in The Decline in Produc­
tivity Growth, Conference Series No. 22 (Boston, Federal Reserve
Bank of Boston, June 1980); and Clark and Griliches, “ Productivi­
ty Growth and r & d at the Business Level.”
22F.M. Scherer, “ r & d and Declining Productivity Growth,”
(Continued)

30

Hours at work versus hours paid

percent per year between 1952 and 1977. Thus, ad­
justing the b l s measure of hours paid to an hours-atwork concept would reduce the average annual rate of
growth of labor inputs by 0.1 percent per year during
that 15-year period and, consequently, raise the annual
rate of growth of multifactor productivity by somewhat
less than 0.1 percent.25 The average annual rate of de­
cline in the ratio was 0.2 percent in 1972-77 compared
with 0.1 percent during 1952-72, which suggests that
the decline in hours at work relative to hours paid con­
tributed to the falloff in the b l s measured productivity
growth, but only minimally.
The estimate for manufacturing suggests that the ef­
fects of the increase in hours paid relative to hours at
work on measured multifactor productivity growth in
that sector are somewhat larger than for private nonfarm
business but still quite small. For all employees in man­
ufacturing, the annual rate of decline between 1952 and
1977 in the ratio of hours at work to hours paid aver­
aged 0.2 percent, so that the annual growth rate of mul­
tifactor productivity in manufacturing would be in­
creased by somewhat more than 0.1 percentage point if
it were adjusted to an hours-at-work concept of labor
inputs.
The evidence on the measured contribution to the
falloff in the productivity growth rate is unclear: The es­
timates for production workers which are based on the
new b l s survey data for 1981 indicate that the rate of
decline in the ratio of hours at work to hours paid re­
mained constant (0.2 percent per year) between 1968
and 1981 and therefore did not affect the measured
falloff in productivity during the 1970’s. The estimates
for all employees, however, show a possible 0.1 per­
centage point difference in the contribution to the fall­
off. In any case, to the extent that the declining ratio of
hours at work to hours paid was a contributing factor to
the measured slowdown, its effects were small.

The b l s series on labor inputs is based on hours paid
for rather than at work and therefore includes paid
vacations and sick leave. Conceptually it would be more
appropriate to use a measure of hours of work but the
necessary data are not now available. In order to help
rectify this problem, b l s started a survey in 1981 which
will make it possible in the future to adjust the hours
measure to a more appropriate one, hours at work.23
Prior to the new survey, the b l s used two sources of
information in order to experiment with possible adjust­
ments of hours paid to obtain an hours-at-work measure.
One source, which was mainly used internally, em­
ployed estimates on leave practices and tenure of em­
ployees to calculate vacation time. These estimates were
used to compute ratios of hours at work to hours paid in
the private nonfarm business and manufacturing sectors
during the years 1952-66. The other source of informa­
tion was a biennial survey conducted by the Bureau of
Labor Statistics between 1968 and 1977.24 In this sur­
vey, annual measures of both hours at work and hours
paid were collected for office and nonoffice workers in
the private nonfarm business and manufacturing sectors.
Table 15 shows average annual rates of growth of the
ratio of hours at work to hours paid for selected years
based on the 1981 survey findings and estimates from
the two earlier sources. The estimates for all employees
in private business show that the ratio decreased by 0.1
Table 15. Rates of growth in the ratio of hours at work to
hours paid, private nonfarm business and manufacturing sec­
tors, selected periods, 1952-81
(Percent per year, compounded)
Employee group
and period

Private nonfarm
business

Manufacturing

All employees:
1952-77 ...................................
1952-72 ...........................
1972-77 ...........................

-0.1
-0.1
-0 .2

-0 .2
-0.1
-0 .3

Production workers:
1968-81 ...................................
1968-72 ...........................
1972-81 ...........................

(1)
(1)
(1)

-0 .2
-0 .2
-0 .2

Summary
This chapter reviewed several of the many factors that
have influenced the movements in the b l s measure of
multifactor productivity since 1948. While these have
helped to explain a part of the longer term annual
growth rate and its fallo ff after 1973, the part left
unexplained remains large.

1Not available.
Sources : 1952-66, unpublished bls study; 1968-77, Employer Expendi­
tures for Employee Compensation Survey; 1981, Hours Worked Survey (cov­
ers production and nonsupervisory workers only).

(Continued)
American Economic Review, May 1983, pp. 215-18.
23The new survey, conducted annually, collects both quarterly
and annual data on hours at work and hours paid for production and
nonsupervisory workers. Approximately 4,000 establishments are
surveyed, representing the private nonagricultural business sector
of the U.S. economy. Adjustments are calculated for the major
groups (1-digit sic) and for the 2-digit industries within the manu­
facturing sector. The data collected refer to the previous year. Most
of the data are tabulated from payroll records. Findings from the
initial survey in 1981 indicate that the measures are reliable and



consistent with prior expectations. Estimates of hours at work will
also be available in the future on a quarterly basis.
24Employer Expenditures for Employee Compensation Survey.
These series have not been published but are discussed in “ Report
of the b l s Task Force on Hours Worked’’ (Bureau of Labor Statis­
tics, March 1976).
25The contribution of the decline in the ratio to multifactor pro­
ductivity growth is measured by multiplying the annual rate of de­
cline by labor’s share of total output (0.65).

31

Between 1948 and 1981, multifactor productivity in
the private business sector grew at an average rate of
1.5 percent per year. During this period, intersectoral
shifts of labor, particularly from the farm to the non­
farm sector, contributed 0.1 percentage point to the pro­
ductivity growth rate. Based on Denison’s estimates,
changes in the composition of the work force, mainly
from increased education per worker, contributed an ad­
ditional 0.4 percentage point. Available information
suggests that there was only a small difference in the
rate of capacity utilization and that it probably had no
significant effect on the long-term growth rate. Judging
from G rilich es’ estim ates for the m id-1960’s and
1970s’s, r & d may have contributed about 0.2 percent­
age point to the annual growth rate in multifactor pro­
ductivity during the period. The sparse data available
relating hours at work to hours paid show that the use of
hours paid rather than the more appropriate hours-atwork concept in the bls measure of hours of all persons
reduced the measured productivity growth rate by 0.1
percentage point. Adding the influences of these five
sources indicates that, together, they explain about 0.6
percentage point of the 1.5 percent annual growth rate
of multifactor productivity in the private business sec­
tor. That is, they explain about 40 percent of the total
long-term growth rate; about 60 percent remains unex­
plained.
The longer term trend was interrupted after 1973: The

average annual rate of growth of multifactor productivi­
ty in the private business sector declined from 2.0 per­
cent in 1948-73 to 0.1 percent in 1973-81, a falloff of
1.9 percent per year. The shift of workers out of farm­
ing into the nonfarm sector had virtually come to an end
by 1965, and this contributed 0.2 percentage point to
the productivity slowdown from the earlier to the later
periods. Changes in the work force occurred at about
the same rate in the two periods and therefore had no ef­
fect on the falloff. The slowdown in the growth of r & d
during the 1970’s contributed only to a small degree to
the productivity falloff, possibly only about 0.1 percent­
age point. Using hours paid rather than hours at work in
measuring total hours of all persons could have contrib­
uted another 0.1 percentage point to the measured pro­
ductivity slowdown. Adding the effects of these four
sources indicates that, together, they contributed about
0.4 percentage point—or about 20 percent—to the 1.9
percent per year slowdown in multifactor productivity in
private business. Unfortunately, data are not available
for measuring changes in capacity utilization for the pri­
vate business sector. However, the analysis of the man­
ufacturing sector strongly suggests that changes in the
rates of capacity utilization could account for a signifi­
cant fraction of the unexplained portion of the produc­
tivity slowdown in private business. But, even with this
additional adjustment, the percentage left unexplained
would probably still be large.26

26For analyses of other possible sources contributing to the pro­
ductivity slowdown besides those discussed in this chapter, see
Edward F. Denison, “ The Interruption of Productivity Growth in

the United States,’’ Economic Journal, Vol. 93, March 1983, pp.
1-22; and Kendrick, “ Survey of the Factors Contributing to the
Decline in U.S. Productivity Growth.”




32

Appendix A, TG MuStiactoir
i®
Prodyetiwiitf Model

puts which are delivered to final demand or, as conven­
tionally stated, the aggregate value added. In accord­
ance with this measure of output, only the primary
inputs, labor and capital, are measured and included in
the framework. Thus both output and input measures are
net of interindustry flows of goods and services. In the
b l s series on multifactor productivity, labor is measured
as total hours, and capital is measured as the value of
services rendered by the stock of capital.1 The general
framework for the measurement of multifactor produc­
tivity comes directly from the economic theory of pro­
duction.2 In this approach, a production function is pos­
tulated as follows:

The new measures of multifactor productivity pre­
sented in this bulletin not only extend the scope of pro­
ductivity analysis by the inclusion of more than one fac­
tor but also incorporate a number of recently developed
measurement techniques. Many theoretical difficulties
in the measurement of aggregate inputs and of produc­
tivity growth have been addressed over the last 20
years. As a result, fewer restrictive assumptions are
needed in order to measure and aggregate inputs. Now
much more general (flexible) functions relating inputs
have been developed. Furthermore, index numbers
based on discrete data on prices and quantities of the in­
puts and output of production have been shown to be
consistent with these more flexible aggregation
functions.
Although econometric methods can be used to identi­
fy the structure of production, index numbers enjoy
several advantages for measuring productivity. Index
numbers avoid the errors inherent in a stochastic speci­
fication on a limited sample size. Estimates of produc­
tivity based on index numbers provide reliable and time­
ly estimates of productivity change.
This appendix describes in detail how the new meas­
ures of multifactor productivity are constructed and how
they relate to the older measures of output per hour. The
appendixes that follow provide detailed descriptions of
the separate factors: Output, capital input, and labor in­
put (hours).
A multifactor productivity measure is similar to a
single-factor productivity measure in that it is computed
as the ratio of output to input. In the case of the
multifactor measure, the input is an index of several
factors. In this bulletin, multifactor productivity is de­
fined as value-added output per unit of combined labor
and capital input. Real output is a function of the quan­
tities of real capital and real labor inputs used and the
technological structure. Output is measured as net of its
intermediate inputs. It is the sum of the industries’ out­

Q (t)= A(t)f[K(t),L(t)]

where:
Q (t) = real output,
K (t) = real capital input,
L (t) = real labor input,
A (t) = index of (neutral)
technological progress or
multifactor productivity.

Taking the logarithmic differential of equation (A .l)
with respect to time yields:
Q/Q = A/A + sk K/K + S L/L.
i

(A.2)

The dot notation refers to the change in the factor over
time; hence, Q/Q represents the growth rate of output.
Similarly, K/K is the growth rate of capital and L/L is
the growth rate of labor. The weights, sk and s1 are the
?
output elasticities of the factor inputs. Assuming com­
petitive factor markets and constant returns to scale, the
weights equal the relative cost shares of the individual
factors in total cost (income):3
o

o

o

will reflect both scale effects and technological change. See Mi­
chael Denny, Melvyn Fuss, and Leonard Waverman, “ The Meas­
urement and Interpretation of Total Factor Productivity in Regu­
lated Industries, with an Application to Canadian Telecommunica­
tions,” in Productivity Measurement in Regulated Industries,
Thomas C. Cowing and Rodney E. Stevenson, eds. (New York,
Academic Press, 1981).

1See appendixes B, C, and D for detailed explanations and meas­
ures of output, capital input, and labor input, respectively
2The methodology described in this appendix can be easily ex­
tended to different measures of output- and to additional factor
inputs.
3If the function does not exhibit constant returns to scale, A/A




(A. 1)

33

PkK(t)

The index I(t) is a Tornquist index, which is consist­
ent with a “ translog” production function.6 The advan­
tage of the general translog form over the more com­
monly used Cobb-Douglas function (which is a special
case of the translog) is that it has fewer restrictive prop­
erties. In particular, the translog function allows the
elasticities of substitution among inputs to vary as input
proportions vary whereas the Cobb-Douglas does not.
This generally is a major improvement over index forms
which use constant-base-year-weighted index numbers.
This improvement amounts to recognizing that input
factor prices and quantities observed in a given year are
most relevant for computing weights in that year. Con­
stant weights mean relative use of inputs is held con­
stant even if there are significant price changes in the
factor inputs. For example, if the price of capital were
to increase sharply relative to labor costs, enterprises
would be likely to begin using relatively more labor
(work more hours, or work more shifts) and relatively
less capital (possibly by reducing investment expansion
plans). In this scenario, two changes take place: The
relative price of capital increases, and the relative quan­
tity used decreases. The two changes have opposite ef­
fects on cost shares or weights. When base-year weights
are used, only the quantity change is reflected; in
Tornquist weights, both changes are included.
Turning to the relationship between the traditional
measure of output per hour and multifactor productivity,
it can be shown that the rate of growth of output per
hour can be separated into the rate of growth of
multifactor productivity and the contribution of changes
in capital services per hour. Subtracting the growth in
labor input (L/L) from both sides of equation (A.2) and
some further algebraic manipulation yields the follow­
ing equation:

S = ------------------k
PkK(t) + PlL(t)

PiL(t)

s, = ------------------PkK(t) + piL(t)

S + sk = 1
i
PkK(t) + piL(t) = current-dollar output
= PqQ(t).

where:
pk = price of capital services (the rental
price)
Pi = price of labor (hourly compensation)
pq = price of output (the value-added de­
flator) .

Equation (A.2) is the basic measurement relationship
for multifactor productivity growth. It expresses the
growth in output as equal to a weighted average of the
growth in capital and labor inputs plus the growth in
o
multifactor productivity (A/A). Or, after rearranging
o
terms, the growth rate of multifactor productivity (A/A)
can be measured as the growth rate of the ratio of output
to inputs.4 Hence A(t), productivity in time (t), is:
A(t) = Q(t)/I(t)

(A.3)

where I(t) is the aggregate index of inputs. This index is
computed using discrete annual estimates of prices and
quantities. It is the weighted average of the growth rates
of the separate inputs. For each time period, the change
in I is calculated as:

o

+ wlt In (L(t)/L(t—1))

(A.4)

o

o

o

t
sk i + sk t-1
2

(A.5)

W -kt

S1 t + Si t-1
2

(A.6)

W =■
it

(A.7)

The left side of equation (A.7) is the rate of change of
the ratio (Q/L), output per hour; the right side of the
equation is the sum of multifactor productivity growth
(A/A) and capital’s share times the rate of change of the
ratio of capital services to hours (i.e., the contribution
of changes in the capital-labor ratio). This is the rela­
tionship that is used to analyze the changes in output per
hour in chapter III.

where the weights are averages of the relative cost
shares of the input factor for the given and previous
year:5

4See Charles R. Hulten, “ Divisia Index Numbers,” Econo­
metrics, Vol. 41, No. 6, 1973, pp. 1017-25; and Marcel K.
Richter, ‘‘Invariance Axioms and Economic Indexes,” Economet­
rics, Vol. 34, No. 4, 1966, pp. 739-55.
s The weights for a Tornquist index are defined as arithmetic av­
erages of the cost shares. The geometric average is used for compu­
tational convenience. Numeric differences between these methods
are slight and considered insignificant.




o

Q/Q - L/L = A/A + sk (K/K - L/L).

In (I(t)/I(t—1)) = wkt In (K(t)/K(t—1))

6This consistency is shown by W.E. Diewert, ‘‘Exact and Super­
lative Index Numbers,” Journal of Econometrics, May 1976, pp.
115-45. The translog production function was formulated by L. R.
Christensen, D. W. Jorgenson, and L.J. Lau, ‘‘Transcendental
Logarithmic Production Frontiers,” Review of Economics and Sta­
tistics, February 1973, pp. 28-45.

34

B. Real Output Measures
Methods and Sources

These components of g n p were excluded from the b l s
measure of output used for productivity measurement

This appendix describes the methodology and data
sources employed in preparing the real output series for
the b l s measures of productivity presented in this bulle­
tin. These include output measures for the business,
nonfarm business, and manufacturing sectors which are
used in the more familiar measures of output per hour of
all persons. The output measures used in the multifactor
productivity indexes are for the private business sector
and exclude the output of government enterprises. Real
output for the farm sector is also measured; it is sub­
tracted from the business output totals in order to obtain
the output measures for the nonfarm business sector.
The measures of real output employed in the b l s pro­
ductivity indexes are derived from data on gross nation­
al product ( g n p ) published in the National Income and
Product Accounts ( n i p a ) by the Bureau of Economic
Analysis ( b e a ) , U.S. Department of Commerce. Several
important components of the gross national product
measures are excluded in order to obtain indexes of out­
put which are appropriate for measuring productivity.
This appendix explains the reasons for these exclusions.
It also describes the concepts and methods underlying
the measures for the farm and manufacturing sectors.

Table B-1. Relationship between gross national product
and the BLS measure of private business sector gross
product, 1981

Item

Percent

Total: Gross national product1 ........................

$1,502.6

100

Excluded from bls private business
gross product: .....................................

349.6

23

Output originating in:
General government2 ......................
Owner-occupied housing3 ................
Rest of the world2 ...........................
Households and institutions2 4 .........
Statistical discrepancy2 ....................
Government enterprises6 ................

156.0
100.2
25.4
52.1
-0 .9
22.0

10
7
2
3
(5)
1

1,147.3

76

1,133.2

75

Equals: BLS private business gross product
Value of output deflated by output price
indexes.................................................
Nonresidential structures1 ................
Services furnished without payment
by financial intermediaries, except
life insurance carriers7 ..................
Other ................................................

The business sector is the largest aggregate for which
productivity measures are presented in this bulletin.
Output of the sector can be briefly described as all ac­
tivities of for-profit business establishments engaged in
production in the United States. It is based on concepts
underlying the n i p a measures of g n p . 1
Table B -l shows the relationship of the b e a measure
of g n p and the b l s measure of private business output in
1981 (1972 prices). The value of output in the private
business sector accounted for 76 percent of g n p . The 24
percent of g n p not included comprised general govern­
ment; output of the “ rest of the world” ; output of
household workers and of nonprofit institutions; output
imputed to the housing services of owner-occupied
housing; and the statistical discrepancy.2

51.6

4

19.6
1,062.0

1
71

Value of output deflated by index of wage
rates and materials prices ..................

Business sector

14.1

1

12.9

1

1.3

(5)

Personal consumption expenditures
(part)8 ..........................................
Producers’ durable equipment
(part)9 ............................................

’ Table 1.2 in Survey of Current Business, July 1982.
2Table 1.6 in Survey of Current Business, July 1982.
3Table 1.21 in Survey of Current Business, July 1982, and unpublished
detail for farms. Comprises $98.9 billion of nonfarm and $1.3 billion of farm
housing.
4Includes unpublished bea measures of nonprofit real estate rental value.
5Less than 0.5 percent.
6Table 6.2 in Survey of Current Business, July 1982.
7Table 2.5 in Survey of Current Business, July 1982.
8Estimate provided by the Bureau of Economic Analysis, U.S. Department
of Commerce, from unpublished detail underlying table 2.5 in Survey of Cur­
rent Business, July 1982. Comprises life insurance and commercial and vo­
cational schools.
9Table 5.7 in Survey of Current Business, July 1982. Comprises ships and
boats.

'For a description of the concepts, methodology, and sources of
data underlying the n i p a , see Carol S. Carson and George Jaszi,
“ The National Income and Product Accounts of the United States:
An Overview,’’ Survey of Current Business, Vol. 61, February
1981, pp. 22-34; “ Revised Estimates of the National Income and
Product Accounts,’’ Survey of Current Business, Vol. 62, July



Amount
(billions of
1972 dollars)

1982, and National Income, 1954 Edition: A Supplement to the
Survey of Current Business.
2The statistical discrepancy is the difference between g n p and
the charges against g n p . It arises because g n p and the charges
against g n p are estimated independently, and each is subject to
measurement errors.

35

because (1) no adequate corresponding labor or capital
input measure can be developed for these components of
the nipa or (2) the gross product measures for the com­
ponent are based on labor inputs, implying constant out­
put per unit of labor input.
The specific reasons for excluding each of these com­
ponents will be discussed in turn. Before doing so, it is
important to note that only about 1 percent of private
business output (measured in 1972 prices)—the remain­
der after the exclusions from gnp—was based on real
output measured by deflating current-dollar output by an
index of labor and materials inputs.3 This clearly does
not represent a serious problem in measuring real output
for the private business or private nonfarm business
sector.
The output of general government has been excluded
since the bls measures of output per hour were first in­
troduced in 1959. This exclusion is due to the manner in
which constant-dollar real output is measured in the
nipa . In the accounts, general government output is de­
rived by moving base-year compensation by changes in
total hours of governm ent employees adjusted for
changes in grade level. This virtually assumes that pro­
ductivity remains constant, since changes in output are
essentially proportional to changes in hours. Although
this is not the only area in the national accounts where,
for lack of data, output change is equated with labor in­
put change, it is by far the largest single sector where
this occurs. In addition, the proportion of employment
accounted for by government (including military) has
increased significantly since 1950.
bls excludes the rest-of-the-world sector because
there are no corresponding labor or capital input data.
The current value of output of the rest-of-the-world sec­
tor is equal to payments to factors (labor and capital)
abroad owned by U.S. residents, less payments to fac­
tors in the United States owned by foreigners. Hence, a
dividend paid to a foreigner is a negative entry and a
wage received by an American employee in a foreign
country is a positive entry. Since it is not possible to
identify domestic labor or capital inputs associated with
this output, the rest-of-the-world sector is excluded.
Output imputed to owner-occupied dwellings is also
excluded from the aggregate productivity measure be­
cause there is no measure available for the labor input
of homeowners. In the nipa , an imputation is made for
the rental value of owner-occupied homes. This imputa­
tion treats homeownership as a business providing hous­
ing services which are sold to the homeowner in his ca­
pacity as tenant. The output of this service is estimated
as the amount for which owner-occupied homes could
be rented, less maintenance, insurance, and like ex­

penses of the homeowner. Since no comparable labor
input data are available for the activity of homeowner­
ship, the product of owner-occupied homes is excluded
from the output estimates for productivity purposes.
The output measure for private households is ex­
cluded because real output in this sector is measured by
labor input. The household industry refers to domestic
employees, and current value of output is measured in
the nipa by the compensation of domestic employees.
Real output is measured by deflating this compensation
by the Consumer Price Index for housekeeping and
home maintenance services, which is essentially an in­
dex of hourly compensation. This assumes that output
per employee is constant over time.
Nonprofit institutions are also excluded because real
output is measured essentially by labor inputs. Current
value of output is measured using employee compensa­
tion. The bea method of deflation used for nonprofit or­
ganizations is somewhat more complex than that used
for private households. Nevertheless, real output of
nonprofit institutions is essentially measured by deflat­
ing the employee compensation series by an index of
compensation per full-time-equivalent employee. These
measures have serious limitations for productivity meas­
urement, and this sector is consequently excluded from
the private business sector.
The “ statistical discrepancy” is the difference be­
tween gnp estimates measured from the product and in­
come ( “ charges against gnp ” ) sides of the accounts.
Government enterprises—the U.S. Postal Service,
other Federal enterprises such as the Tennessee Valley
Authority, and State and local enterprises such as Staterun liquor stores—are excluded for two reasons. First,
it would be especially difficult to measure capital inputs
in this sector because in the nipa , structures and durable
equipment used by these enterprises are treated as final
sales to general government, rather than as investments
of the enterprises. Government enterprises thus show no
capital cost associated with plant and equipment. The
second reason concerns the measurement of income
from capital (i.e., property income). In these enter­
prises, capital and labor are combined in multifactor
productivity measurement, and this requires the use of
labor and capital income shares as weights. Satisfactory
data are available on compensation of employees; how­
ever, the data on income from capital are unsuitable be­
cause these enterprises are subsidized by the govern­
ment and the pricing of output reflects these subsidies.
Thus, estimating property income as the residual of
value of output minus labor compensation would seri­
ously understate capital’s share of output.
measured by labor input.” That is, it accounted for only 1.3 per­
cent of private business output (.01 divided by .76).

3Table B -l shows that, within the 76 percent of GNP used to
calculate the b l s measure of private business output (in 1972
prices), only 1 percentage point was accounted for by “ output




36

Farm sector
The measure of output used in the b l s index of multi­
factor productivity for private nonfarm business is ob­
tained by subtracting real output of the farm sector from
private business real output. The measure for real farm
output is the b e a estimate of “ gross farm product’’ in
constant (1972) prices.4 b e a , in turn, bases its measures
on estimates of farm income and expenses prepared by
the U.S. Department of Agriculture ( u s d a ) employing
data collected by the u s d a and benchmarked periodical­
ly to statistics from the Census of Agriculture.
The b e a measure of gross farm product is derived by
the “ double-deflation” value-added procedure. Using
this method, the current values of output and purchases
of intermediate goods and services by the industry are
first deflated by appropriate price deflators. The de­
flated figures for purchased goods and services are then
subtracted from the deflated value of output; the residu­
al is industry product originating (value added) in con­
stant prices.5
B ea farm output includes cash receipts from farm
marketings, net Commodity Credit Corporation loans,
rental value of farm dwellings, home consumption of
farm products, other farm income, and changes in in­
ventories. Receipts from farm marketing of crops and
livestock are obtained by summing monthly estimates
based on quantities sold and market prices, or, in the
case of poultry and dairy products, directly from pro­
duction reports. Sales of approximately 150 items are
covered, accounting for 90 percent of farm income. All
sales of crops are covered, including seed and feed sold
to other farmers; livestock sold to other farms in the
same State are excluded from both sales and expenses.
Farm sales of forest products are included in the crop
totals.
Constant-dollar estimates of farm output are obtained
by deflating each of the current-dollar components sepa­
rately. Constant-dollar farm marketings are obtained for
the following categories of farm products: Food and
feed grains; oil bearing crops; tobacco; cotton; vegeta­
bles; potatoes, sweet potatoes, and beans; fruit; other
crops; meat animals; dairy products; poultry and eggs;
wool; and other livestock. Deflators are aggregated
from 150 “ prices received by farmers” collected by the
u s d a . Food and fuel consumed on farms are deflated by
the same u s d a prices received by farms or appropriate
n i p a personal consumption expenditure deflators.
Intermediate goods and services purchased include all

M anufacturing sector
The computation of real output in manufacturing fol­
lows the double-deflation method discussed above for
the farm sector.6 In the n i p a , the output measures for
manufacturing are prepared in two steps: (1) A deflator
is obtained by dividing Census current-dollar value
added by constant-dollar value added; and (2) this defla­
tor is applied to the b e a measure of gross product
originating in manufacturing. Current-dollar value
added in the first stage is derived from data from the
Censuses and Annual Surveys of Manufactures on the
value of manufacturing production, less the cost of ma­
terials, less the estimated value of business service in­
puts. Constant-dollar value added is the deflated value
of production, less the deflated value of material inputs,
less an estimate of the deflated value of service inputs.
The b e a gross product data to which the value-added
deflators are applied are the sum of factor and nonfactor
charges, compiled independently for 2-digit Standard
Industrial Classification (sic) industries in the n i p a . The
underlying deflation of the value of output and of mate­
rial inputs is done at the most detailed level of industry
possible.

4For a description of the method and sources used by b e a to
measure gross farm product in the n i p a , see Shelby W. Herman,
“ The Farm Sector,’’ Survey of Current Business, Vol. 58, Novem­
ber 1978, pp. 18-26. The annual figures in current and constant
prices appear in tables 1.18 and 1.19, respectively, in the July is­
sues of the Survey.
Conceptually, the sum of gross product originating (value

added) for all industries is equal to g n p . This is so in both current
and constant dollars. However, in practice, the equality in constant
prices may not hold because of errors of measurement.
6B ls used the same method for manufacturing in the 1950’s. See
Trends in Output per Man-Hour and Man-Hours per Unit o f
Output—Manufacturing, 1939-53, Report 100 (Bureau of Labor
Statistics, 1955).




production costs incurred by the farm operator, such as
feed, seed, fertilizer, contract labor, machine hire, and
rent paid to nonoperator landlords. Estimates of most
expenses are based on information from u s d a surveys
of farm production expenses. Constant-dollar estimates
are prepared by b e a by separately deflating 13 expense
components, using appropriate indexes from among the
“ prices paid by farmers” published by u s d a .
The difference between b e a farm output and interme­
diate purchased goods and services is gross farm prod­
uct in current dollars, the n i p a measure of farm value
added, or the contribution of the farm sector to currentdollar g n p . Equivalently, on the income side, gross
farm product comprises factor incomes (employee com­
pensation, net interest, noncorporate income, corporate
profits) plus nonfactor costs (capital consumption allow­
ances, indirect business taxes), less subsidies to farm­
ers. These components of g n p originating on farms are
estimated concurrently with the farm output and pur­
chases data.
Similarly, the difference between the deflated value
of farm output and the deflated cost of intermediate
goods and services purchased is equal to real farm gross
product, or the contribution of the farm sector to real
GNP.

37

Manufacturing output. Value of shipments and changes
in inventories are prepared for 4-digit sic industries in
manufacturing.7 These data have been collected since
1949 and published in the benchmark Censuses and An­
nual Surveys of Manufactures in generally the same
form. There have been periodic revisions to the sic af­
fecting both product and industry classifications. Large
revisions took place in 1958 and 1972, causing some es­
tablishments in 4-digit Census industries to be moved
across 2-digit lines. In most cases, the effect of these
classification revisions at the 2-digit industry level is
small or even trivial.
The deflation of value of shipments and changes in
inventories is done by b e a using the b l s product class
indexes, which are groupings of highly detailed pro­
ducer price indexes into the “ 5-digit” product catego­
ries reported in the Annual Survey of Manufactures.
This tabulation of prices was published in the late
1950’s as part of the Census of M anufactures for
benchmarking purposes, and it has been maintained ever
since.8 About 54 percent of the product classes in man­
ufacturing are covered by b l s product price indexes.
Another 38 percent are covered by related b l s price in­
dexes. Price series for most of the remainder are con­

The current cost of materials is deflated to obtain the
real quantity of materials inputs for double-deflation
purposes. Deflators are constructed by b e a using b l s
producer prices (mainly the 5-digit product-class defla­
tors) and weights based on the b e a input-output tables
of the U.S. economy for the years 1947, 1958, 1963,
1967, and 1972. The tables provide a complete list of
material inputs for each industry for those years, from
which weights are computed for the aggregation of ma­
terials prices. Weights are interpolated between tables;
for years after the most recent input-output table,
weights remain constant.

7The classification of products and establishments in the b l s pro­
ductivity program follows the scheme established by the Office of
Management and Budget in its Standard Industrial Classification
Manual, 1972 edition. Under this system, related products or serv­
ices are grouped together in categories denoted by a code of up to 7
digits, depending on the breadth of the category. Thus, a 7-digit
code is assigned to a relatively narrowly specified group of prod­
ucts, and a 2-digit code to a broad area such as fabricated metal

products (sic 34). Every establishment reporting data to the Census
Bureau or the b l s is assigned the 4-digit code in which its most im­
portant product, in terms of value of shipments, falls.
8These indexes were constructed jointly by the Board of Gover­
nors of the Federal Reserve System, the Bureau of Labor Statistics,
and the Bureau of the Census. They were published in United
States Census of Manufactures, 1954, Vol. IV: Indexes of Produc­
tion (Bureau of the Census, 1958).




structed as weighted averages of indexes of material in­
put and labor costs.
Cost o f materials, containers, and supplies. The current
cost of materials inputs is collected by the Census Bu­
reau and published in the Annual Survey of Manufac­
tures and the Census of Manufactures. All purchased
materials are included, with the exception of those
bought for resale without further processing. All fuels
and office supplies are included; items treated as capital
investment are excluded.

38

Appendix C. Capfel Input
and Capital and Latoir Slhaires

two stages in developing the aggregate measures are de­
scribed in section II. Section III discusses the method
used to measure capital and labor income shares. Sec­
tion IV examines the capital input measures and capital
and labor shares of income. Section V reports on the
sensitivity of capital input and multifactor productivity
measures to the inclusion of inventories and land and to
alternative “ efficiency” functions. The final section
summarizes the discussion and concludes with the de­
tailed tables of capital input measures by major type of
asset for the private business, private nonfarm business,
and manufacturing sectors. Table C -l provides a con­
venient guide and summary of the procedures used to
generate the b l s capital measures (steps 1-7) as well as
of the additional work needed to measure multifactor
productivity (steps 8-10).

Capital input, defined as the services from physical
assets, is measured for each of three subsectors of the
U.S. private business sector—manufacturing, farm, and
nonfarm-nonmanufacturing. These measures are then
aggregated to the three published sectors: Private busi­
ness, private nonfarm business, and manufacturing.
This appendix presents a detailed discussion of how
capital is measured and of how the capital and labor cost
shares used to weight the respective input measures are
determined.
The capital measures are constructed in three major
stages. First, stocks are estimated for 47 type of assets;
this is discussed in section I. Second, rental prices are
estimated for each type of stock. Third, assets are ag­
gregated using shares based on rental prices. These last

Table C-1. Summary of methods and data sources used to measure capital and multifactor productivity— Continued

1. Obtain real invest­
ment data for depre­
ciable assets

Investment in:
a. equipment
b. structures
c. rental residential capital

2. Allocate investment
data to major sectors

Investment by asset type by sector
(manufacturing, farm, nonfarm­
nonmanufacturing)

3. Determine age/efficiency functions for
each type of asset

4. Perform vintage ag­
gregation

Methods used and detail in
which step is performed

Data item obtained
or constructed

Step

Weights reflecting the declining
services of an asset type cohort as
it ages

Real stocks of depreciable assets by
type by sector

Data source

a. 20 asset types
b. 14 asset types
c. 9 asset types

a.-c. National Income
and Product Ac­
counts (nipa)1

a. asset detail allocated using:
b. sectoral investment totals proportional to
c. historical data cross-classified by asset
detail and sector

a. step 1

A hyperbolic form using:
a. an average service life estimate
b. normal distribution of discards
c. a shape determined using empirical evi­
dence
Perpetual inventory method:
Real historical investments weighted
by age/efficiency functions

b . NIPA
C. NIPA

a.

nipa

b . NIPA

c. Hulten and Wykoff2
a. steps 2 and 3

a. stock of inventories
b. stock of farm land
c. stock of land in manufactur­
ing and nonfarm-nonmanu­
facturing

a. by stage of processing in manufacturing
b. regional services weighted using rental
prices
c. proportional to structures using
benchmark land estimate

a. nipa
b. U.S. Department of
Agriculture
c. Manvel3

6. Construct rental
prices

Implicit rental value of the services
of a unit of each type of asset in
each sector

a. rental price formula estimated using data
on capital stocks and data on payments
to capital

a. Christensen and
Jorgenson4; steps 4
and 5; nipa

7. Aggregate assets

Measure of real capital input in each
sector

Tomquist index of asset capital stocks using rent­
al prices to determine weights

5. Measure nondepreci­
able assets

See footnotes at end of table.



39

a. steps 4, 5, and 6

labile C— Summary of methods and data sources used to measure capital and muitifactor productivity—Continued
1.
Step

8. Constm ct cost shares

Data item obtained
or constructed

Methods used and detail in
which step is performed

Shares of labor and capital inputs in
the value of each sector’s output

Based on:
a. em ployees’ labor compensation
b. corporate capital payments and
c. proprietors’ income allocated to labor and
capital using
d. em ployee com pensation per hour and
e. corporate rate of return to capital

e. based on step 6

Tom quist index of:
a. labor and
b. capital in each sector using
c. cost shares as weights
d. Tom quist index of com bined input across
sectors using factor shares in value of
output

b. step 7
c. step 8
d. shares based on

9. Combine inputs
a .- c . measures of com bined la­
bor and capital input by
sector (manufacturing,
farm, nonfarm -nonm an­
ufacturing)
d. m easures of combined input
for private business,
nonfarm business
10. Compute multifactor
productivity

Reported for private business,
nonfarm business, manufacturing

Ratio of:
a. output to
b. input

Data source

a .- c . NIPA
d . BLS

a . BLS

nipa

a. nipa
b. step 9

’Bureau of Economic Analysis.
2Shares were reconciled to functions reported in Charles R. Hulten and
Frank C. Wykoff, “The Estimation of Economic Depreciation Using
Vintage Asset Prices: An Application of the Box-Cox Power Transforma­
tion,” Journal of Econometrics, 1981, pp. 367- 96; and in C. R. Hulten
and F. C. Wykoff, “The Measurement of Economic Depreciation,” in
C. R. Hulten, ed., Depreciation, Inflation and the Taxation of Income
from Capital (Washington, The Urban Institute Press, 1981), pp.
81-125.

benchmarks based on estimates from Allan D. Manvel, “Trends in
the Value of Real Estate and Land, 1956-1966,” in Three Land Re­
search Studies (Washington, National Commission on Urban Problems,
1966).
4Formula used to measure rental prices derived by Laurits R.
Christensen and Dale W. Jorgenson, “The Measurement of U.S. Real
Capital Input, 1929-1967,” Review of Income and Wealth, Vol. 15,
No. 4, 1969, pp. 293-320.

L ileasuremain! of Capital Stoeks
by Asset Type

Conceptually, the wealth stock represents the present
value of all future services embodied in existing assets.
Unlike the productive stock, the wealth stock does not
directly influence productivity but indicates the current
market value of all new and used capital goods. The
wealth stock is needed to estimate depreciation, which
is used in m easuring the im plicit rental prices for
capital.

This section is concerned with the framework used to
construct the bls capital measures.1 A central concept
in this framework is that of the “ productive” capital
stock, or the stock measured in efficiency units. Con­
ceptually, the productive stock represents the amount of
new investment which would be required to produce the
same capital services actually produced by existing as­
sets of all vintages. Thus, total current services from as­
sets of all vintages are proportional to the productive
stock. It is this measure of capital stock which is direct­
ly associated with productivity. The measurement of the
productive stock involves vintage aggregation, which
requires historical data on real investm ent and an
“ age/efficiency ” function that describes the pattern of
services that capital goods supply as they age.
In addition, this section discusses the measurement of
the “ wealth” stock of physical capital, or the stock
measured in terms of the market price of used assets.

Vintage aggregation
Each type of stock is computed by the perpetual in­
ventory method. The stock at the end of a period is
equal to a weighted sum of all past investment, where
the weights are the asset’s efficiency (defined below) as
of a given age.
Mathematically, the productive stock Kt, at the end
of the period t is given by:
K t = X T= t s T- t l 2 t - T
where It is investment in period t
and st is the efficiency function.
pp. 292-320. An extensive discussion of this topic, together with
references to the literature, may be found in W.E. Diewert, “ Ag­
gregation Problems in the Measurement of Capital,” in Dan Usher,
ed., The Measurement of Capital (Chicago, The University Press,
1980)pp. 433-528.

’The model used to measure capital stock was developed in Rob­
ert E. Hall, “ Technical Change and Capital from the Point of View
of the Dual,” Review of Economic Studies, January 1968, pp.
35-46. The model was used empirically in Laurits R. Christensen
and Dale W. Jorgenson, “ The Measurement of U.S. Real Capital
Input, 1929-1967,” Review of Income and Wealth, Vol. 15, 1969,




(C.l)

40

Table C-2. Illustration of a perpetual inventory calculation for a fictional type of asset

Item
Gross new investment....................................................................
Contribution of goods of a givpn age to year-end stock:
Age 0 ......................................................................................
1 ........................................................................................
2 ........................................................................................
3 ........................................................................................
4 ........................................................................................
5 ........................................................................................
Year-end stock (weighted sum of past investments)....................
Change in stock since previous y e a r............................................
Equals gross investment.........................................................
Minus efficiency losses of all vintages..................................

Age/efficiency
function

The efficiency function is a schedule which indicates
the quantity of services provided by an asset of a given
age relative to a new asset of the same type. This func­
tion is generally assigned a value of 1.00 when the asset
is new and declines as the asset ages, eventually ap­
proaching or reaching zero. Consequently, investments
in the more distant past contribute less to current output.
Illustration of perpetual inventory method. Table C-2
illustrates the perpetual inventory method for a hypo­
thetical asset with a 5-year service life. The cells of the
matrix of contributions to the capital stock are calcula­
ted as the product of two values. The first value is the
age/efficiency function for an asset of the given age
(column 1). The second is the gross investment made
the given number of years ago. The contribution of a
given year’s investment to the stock can be tracked
through the successive years as it ages. This is done by
following a diagonal downward and to the right. One
example is marked with asterisks.
The total stock in a given year is equal to the sum of
contributions from past investments. It changes from
year to year to reflect new gross investments net of
accruing efficiency losses. These losses cannot be cal­
culated without knowing the distribution of past invest­
ments. Only in the case of geometric decay are they
equal to a constant percentage of the stock.
In order to measure the first year’s stocks, it is neces­
sary to collect historical investment data extending back
as long as the life of the asset. The U.S. Commerce De­
partment’s estimates of investment go back as far as
1820 for some types of structures.
The same procedures are used for each of 43 types of
depreciable assets in order to obtain the b l s measures of
capital. Each type of asset has a different efficiency
function depending on its expected life and on whether
it is a structure or a type of equipment. The year-end
stocks are then averaged with the previous year-end
stock to estimate the services contributed by a given
2For a criticism of this approach, see Martin S. Feldstein and Mi­
chael Rothschild, “ Towards an Economic Theory of Replacement



1972

1973

1974

1975

1976

1977

1978

100
1.0
.9
.7
.4
.1
.0

1971

120

150

200

100

200

220

250

100*

120
90*

150
108
70*

200
135
84
40*

100
180
105
48
10*

200
90
140
60
12
0*
502
59
200
141

220
180
70
80
15
0
565
63
220
157

250
198
140
40
20
0
648
83
250
167

443

type of asset during the year. Average stocks of differ­
ent asset types are then aggregated using a Tornquist in­
dex. In this procedure, rental prices are used to con­
struct the weights for assets of different types by
different sectors.
Age/efficiency function
In general, the relationship between the economic ef­
ficiency of an asset and its age is very complex and de­
pends on the particular type of asset as well as on a host
of other factors such as the level of economic activity,
relative input prices, interest rates, and technological
developments. To further complicate matters, it is very
difficult if not impossible to “ observe” or directly
measure quantity of capital services. The standard prac­
tice among economists is to represent the pattern of
services as a capital good ages by using an efficiency
function as defined above. This pattern of services is
proportional to the rental income, in constant prices,
which the good is capable of generating.
Use of an efficiency function involves strong assump­
tions. First, the quantity of capital services from a par­
ticular type of asset is assumed to be a function of its
age.2 Second, the pattern does not respond to any fac­
tors other than age, remaining fixed over time. In view
of these restrictive assumptions, the validity of using an
efficiency function to represent capital services remains
a major issue, particularly as it relates to the applicabil­
ity of microeconomic assumptions to aggregate data.
Several general forms have been employed by re­
searchers. These are illustrated in chart C - l. Use of the
gross stock or “ one hoss shay” form assumes that the
asset exhibits no loss of services until it suddenly ex­
pires. A light bulb is perhaps the best example of this.
The three other forms are “ net” of some loss of serv­
ices during their lives. The straight-line form exhibits
the same loss of services each year. The concave form
exhibits gradual losses early in the life of an asset, and
more rapid losses as it ages. The convex form exhibits
Investment,’’

E c o n o m e tr ic a ,

May 1964, pp. 393-424.

Several attempts have been made to address the effi­
ciency function issue by observing used asset prices.8 A
relationship is postulated between the efficiency of a
used asset and its market price relative to a new asset.
In a dynamic model where the firm minimizes costs
over all time periods, the market price of an asset will
equal the discounted (rental) value of the stream of fu­
ture services that the asset embodies. This duality be­
tween efficiency and price also determines the relation­
ship between the (assum ed) form of the efficiency
function and the pattern of prices as the asset ages.
Thus, observations of used asset prices may be em­
ployed indirectly to infer the form of the efficiency
function.9
The most intensive empirical study of used asset
prices done to date is by Hulten and Wykoff.10 In a
5-year project recently completed for the Treasury De­
partment, Hulten and Wykoff collected extensive data
on prices of used assets and fitted them econometrically
to various mathematical forms. Their published findings
make use of a very general function, the “ Box-Cox”
function. Thus, rather than assume either a convex or
concave form, they employed a function which can be
either convex or concave depending on the sample data.
The gross, straight-line, and geometric shapes are spe­
cial cases of the Box-Cox function so that it can be used
to statistically test each of these cases. Hulten and
Wykoff reject each of these three special forms of the
age/price function. Their results, in particular, rule out
the geometric form and the one hoss shay (gross capital
stock) for most types of assets. They did, however, find
that the typical age/price profile of an asset was convex.
In order to obtain a summary measure of depreciation
for each type of asset, Hulten and Wykoff fitted “ best
geometric approximations” ( b g a ) to their Box-Cox esti­
mated prices. These were determined by regressing the
logarithms of the Box-Cox estimated prices against age
and time. The results indicated no consistent trend in

rapid early service losses followed by more gradual
losses of the remaining efficiency.
Practitioners have adopted a wide variety of solutions
to the problem of selecting an appropriate efficiency
function. John Kendrick prefers a gross stock form.3 A
concave form is used by Edward Denison4 and was used
in the past by b l s . 5 Dale Jorgenson and his associates
have used the convex geometric form.6 Edward Miller
points out that, since obsolescence as well as deteriora­
tion must be removed as an asset ages, a straight-line or
even convex form may be best.7 Both Kendrick’s and
Denison’s work is based on capital stock data computed
by b e a .
Chart C-1.
General forms of an efficiency function

3John W. Kendrick, The Formation and Stocks of Total Capital,
National Bureau of Economic Research (New York, Columbia Uni­
versity Press, 1976).
4Edward F. Denison, Accounting for Slower Economic Growth:
The United States in the 1970’s (Washington, The Brookings Insti­
tution, 1979).
5Capital Stocks for Input-Output Industries: Methods and Data,
Bulletin 2034 (Bureau of Labor Statistics, 1979).
6See, for example, Barbara M. Fraumeni and Dale W. Jorgenson,
“ The Role of Capital in U.S. Economic Growth, 1948-1976,” in
George von Furstenberg, ed., Capital, Efficiency and Growth
(Cambridge, Mass., Ballinger Publishing Co., 1980), pp. 9-250.
7Edward M. Miller, Capital Aggregation for Productivity Meas­
urement and Other Purposes, Working Paper No. 34 (Houston,
Jesse H. Jones Graduate School of Administration, Rice Universi­
ty, May 1983).
8For a discussion of problems in empirically determining the
form of the efficiency function, see Michael J. Harper, “ The Meas­



urement of Productive Capital Stock, Capital Wealth, and Capital
Services,” Working Paper No. 128, (Bureau of Labor Statistics,
1982).
9This is perhaps most simply illustrated in the special case of the
geometric form. If the efficiency function is a geometric form (i.e.,
a convex form in which efficiency declines by the same percent
each year), then the price pattern is also geometric so that deprecia­
tion (i.e., the rate of decline in price) occurs at the same constant
rate as the efficiency loss. This “ self duality” property is pos­
sessed only by the geometric form.
10The work is presented in Charles R. Hulten and Frank C.
Wykoff, “ The Estimation of Economic Depreciation Using Vintage
Asset Prices: An Application of the Box-Cox Power Transforma­
tion,” Journal of Econometrics, 1981, pp. 367-96; and in C.R.
Hulten and F.C. Wykoff, “ The Measurement of Economic Depre­
ciation,” in C.R. Hulten, ed., Depreciation, Inflation and the
Taxation of Income from Capital (Washington, The Urban Institute
Press, 1981), pp. 81-125.

42

Wykoff data using a hyperbolic functional form resulted
in an efficiency function which declines initially at onehalf the straight-line depreciation rate for equipment,
and at one-fourth the straight-line rate for structures.
Since formula (C.2) is applied to broad types of as­
sets, each of which represents a variety of capital
goods, a distribution of lives was assumed. This was
done by constructing a “ cohort” efficiency function
which is a weighted average of efficiency functions cal­
culated using formulas (C.2) and various specific ages.
The weights are determined by a discard density func­
tion. Chart C-2 illustrates a cohort efficiency function
for an assumed average life of L years with a truncated
normally distributed density function of retirement ages
ranging from 0.5 to 1.5 times L.

the age/price profile over time; the age coefficients rep­
resent an estimate of the average rate of depreciation.
After carefully considering the alternatives, b l s de­
cided to use a concave efficiency form (slow decline
during the earlier years), and to determine its shape
using available empirical evidence. The assumption of a
concave form was settled on because of the cursory ob­
servation that many capital assets do not tend to decay
rapidly during their intital years. In addition, members
of the b l s Business Research Advisory Council can­
vassed their organizations and reported similar experi­
ences with the capital assets owned by the firms they
represent.
The mathematical form used for the age/efficiency re­
lationship is the hyperbolic function:
st = (L - t) / (L - j8t)
st = O
where st
L
t
and /3 is
to vary.

0<t<L
t>L

Table C-3. Types of assets and service life assumptions

(C.2)

Type of asset

is the relative efficiency of a t-year-old asset
is the service life
is the age of the asset
the parameter allowing the shape of the curve

Nonresidential equipment
Furniture and fixtures ..........................
Fabricated metal products ..................
Engines and turbines...........................
Tractors ................................................
Agricultural machinery (except tractors)

In this formula, a value of (3 equal to zero corre­
sponds to a straight-line efficiency pattern, while a
value of /3 equal to one is consistent with the one hoss
shay. The mean service lives, L, are the b e a estimates
shown in table C-3. In experiments described shortly, it
was determined that the best statistical fit to the Hulten-

Construction machinery (except tractors) ...............................
Mining and oilfield machinery .................................................
Metalworking machinery...........................................................
Special industry machinery .....................................................
General industrial, including materials handling equipment.. .
Office, computing, and accounting machinery
Service industry machinery ...........................
Electrical machinery........................................
Trucks, buses, and truck trailers....................
Autos ..............................................................
Aircraft ..................
Ships and boats ..
Railroad equipment
Instruments ...........
Other equipment...

Cfoart C-2.
Cohort efficiency function for gross stocks
with a truncated normally distributed discard
function

15
18
21
8

17
9
10

16
16
14
8
10

14
9
10

16
22

25
11
11

Nonresidential structures
Industrial buildings..............................................
Commercial buildings ........................................
Religious buildings..............................................
Educational buildings..........................................
Hospital and institutional buildings ....................

27
36
48
48
48

Other nonfarm nonresidential buildings
Railroad structures...............................
Telephone and telegraph structures . ..
Electric light and power structures
Gas structures .....................................

31
51
27
30
30

Other public utility structures...................................................
Farm nonresidential buildings ..................................................
Petroleum, gas, and other mineral drilling and exploration .. .
All other private nonresidential structures...............................

(Two standard deviations correspond to one-half
of the mean service life, L)




Life (in years)

26
38
16
31

Residential assets
Tenant-occupied nonfarm:
1- to 4-unit structures (additions) .........
1- to 4-unit structures (new)..................
Structures of 5 units or more (new)
Structures of 5 units or more (additions)
Mobile hom es........................................
Residential equipment............................
Tenant-occupied farm:
1- to 4-unit structures (new)..................
1- to 4-unit structures (additions) .........
Mobile hom es........................................

43

80
40
65
32
16
11
80
40
16

b l s selected a somewhat flatter truncated normal dis­
tribution ranging from 0.02 to 1.98 times L. (Two
standard deviations correspond to 0.98 times the mean
service life.) Thus, formula (C.2) was computed repeat­
edly for each asset type, with L varying between 0.02
and 1.98 times the mean service life. The results of
these computations were then added together, weighted
by a discrete approximation to the normal density func­
tion, to produce a cohort efficiency function. The value
0.98 was chosen in order to conform to the empirical
observation by Hulten and Wykoff that assets are occa­
sionally found which are considerably older than the
BEA-estimated average service lives and also to take ac­
count of the fact that a few assets are accidentally de­
stroyed when new.
The final step in estimating the cohort age/efficiency
function was to obtain estimates of (3, the parameter that
determines the shape of the hyperbolic function (C.2).
As previously noted, these were estimated using the
Hulten and Wykoff fitted Box-Cox price functions. Spe­
cifically, the following equation was used to generate
dual price functions for selected values of /3:1
1

Table C-4. Weighted sum of differences between hyperbolic
efficiency patterns and simulated data
Value of /3 parameter1
Type of asset

0.5

0.75

1.00
(one hoss
shay)

S tr u c tu r e s

Retail (prices)2 ................
Offices (prices) ...............
Warehouses (prices) . . . .
Factories (prices) ...........

0.956
.394
.229
1.173

0.803
.324
.203
1.001

0.630 0.432
.217*
.258
.189* .210
.796
.538

0.268*
.421
.483
.139*

.309
.003*
.063

.133*
.155
.359

E q u ip m e n t

Tractors (prices) .............
Light trucks (efficiency)2 .
Heavy trucks (efficiency) .

.523
.224
.023

.467
.139
.008*

.399
.058
.011

*=closest fitting (3 parameter.
1Statistics presented are the weighted sum of squared differences between
the dual to the presumed hyperbolic function and the fitted Box-Cox function.
Weights are the Box-Cox function itself.
2Price comparisons were done between price functions which were dual to
assumed hyperbolic forms and simulated price series using price parameters
based on Hulten and Wykoff's fitted Box-Cox price functions. Efficiency com­
parisons were done directly between efficiency patterns and a miles per year
proxy for truck efficiency. See text for complete descriptions of data and com­
parison statistics.

X ;= t s* (1 - r) T- 1
pt =

0.00
0.25
(straight line)

----------------------------------------------------------

X ;=o s* (1 - r) T

(C.3)
justed for discards (mean service life of 8 years, nor­
mally distributed between 0 and 16 years) and compared
directly to the presumed efficiency pattern using the
same error comparison statistics described in footnote
12. These steps were repeated for light and heavy
trucks.13
The comparison statistics for the seven sets of trials
are shown in table C-4. The lowest value, indicating
the best fit, is marked with an asterisk for each trial. For
structures, one hoss shay was best in two cases, while
relatively high j3 values of 0.50 and 0.75 were best in
one case each. For equipment, one comparison (trac­
tors) was made on the basis of price, while two compar­
isons (trucks) were made directly between efficiency
functions. One hoss shay was best for tractors, while (3
values of 0.75 and 0.25 were best for light and heavy
trucks, respectively.
One of Hulten-Wykoff’s important results is that
structures depreciate very slowly compared to equip­
ment during the initial years, even considering their
longer lifetime. The trial comparisons are consistent
with a somewhat higher (3 value (slower decay) for
structures. Also, as indicated earlier, the Hulten and

where pt is the price of a t-year-old asset relative to a
new one
st * is the cohort efficiency function
and r is real discount rate assumed to be .04.
The values of f3 selected were 0.0 (straight-line effi­
ciency loss), 0.25, 0.5, 0.75, and 1.0 (one hoss shay).
The three intermediate forms correspond to increasing
degrees of concavity for the hyperbolic function (C.2).
The simulated dual price functions for each of the five
values of (3 was compared with the Hulten-Wykoff
fitted Box-Cox function. The estimate of (3 chosen was
the one that resulted in the best fit.12 This same proce­
dure was used to estimate values of (3 for four different
types of structures and one type of equipment (tractors).
In addition, efficiency functions were compared di­
rectly to a proxy for the services provided by trucks.
This proxy was constructed from the Census Bureau’s
Truck Inventory and Use Survey (1977). Estimates of
the total number of trucks and total truck miles were ob­
tained for each of 12 model years. Miles per year were
then computed for each model year as a proxy for the
services provided by the fleet of trucks still in service
by age. Finally, this miles per year variable was ad-

weights are the heights of the Box-Cox function so as to put more
weight on the newer assets which, in fact, constitute a greater
portion of the stock for each type of asset.
13Other factors, particularly maintenance costs and type of driv­
ing, would also affect relative efficiency. However, adjustments for
such factors would be difficult to construct accurately even if data
were available.

n This is simply a discount formula, which assumes that the pur­
chase price of an asset equals the real discounted rental value of the
stream of all future services that the asset will generate.
,2Two statistics were used to determine the best fit between the
simulated dual price functions and the Hulten and Wykoff Box-Cox
prices: (1) the coefficient of determination; and (2) a weighted sum
of squared errors between the dual and Box-Cox prices where the




44

Meal gross investment
Besides an efficiency function, the other element re­
quired to perform vintage aggregation in equation (C .l)
is historical data on real gross investment. This section
discusses the methods and sources of data used to meas­
ure the stocks of depreciable assets and to estimate the
price deflators for new durable goods. It also describes
the sources and methods used to construct stocks of in­
ventories and land.
Estimates of investment are available from bea for a
variety of asset categories, in both historical and con­
stant dollars. Constant-dollar investment is based on
historical-dollar investment deflated by bea in detailed
categories. Equipment is deflated principally by using
bls Producer Price Indexes (ppi). Structures are deflated
by indexes of residential prices, highway construction
prices, and construction cost indexes.15 Historicaldollar investment estimates are developed at bea from
survey data and are assigned to detailed asset categories
using a “ capital flows table” based on U.S. Census Bu­
reau surveys of industry.
Annual investment from bea is available by major
sector, by tenure group, by legal form of organization,
and by asset class. Major sectors include manufactur­
ing, farm, and nonfarm-nonmanufacturing. The calcula­
tions described below are conducted separately for each
of these three sectors. The tenure grouping applies only
to residential capital and refers to whether housing is
owner- or tenant-occupied, bls measures exclude all
owner-occupied housing, but include tenant-occupied
housing, since private business sector output includes
rental housing. Legal form of organization comprises
several subdivisions. The major split is between corpo­

rate and noncorporate. The noncorporate sector, in turn,
can be divided into sole proprietorships, partnerships,
tax-exempt cooperatives, and nonprofit institutions. The
bls measures do not use these detailed subdivisions.
With respect to investment data, the only separate sub­
groups by legal form of organization is nonprofit insti­
tutions, since these are excluded from the business sec­
tor data. How ever, bea net stock figures for the
corporate and noncorporate sectors are used to estimate
corporate factors for the rental price computations.
The final and most detailed breakout available from
bea is by type of asset. The major bea asset types are
equipment and structures. Since residential capital is al­
most entirely structures, aggregates are presented for
three major groups of capital assets: Nonresidential
equipment, nonresidential structures, and total residen­
tial capital. This procedure makes it possible to show
nonresidential fixed capital for those interested in the
effect of excluding residential capital (see tables C-8
and C-9 in the last section of this appendix).
Each major asset category is divided into more spe­
cific types. Table C-3 in the previous section lists the
20 types of equipment, 14 types of structures, and 9
types of residential capital, bls applies the perpetual in­
ventory calculation separately for each type of asset.
Performing the calculation in greater asset detail allows
the stock measures to reflect changes in the distribution
of service lives. Lack of such detail can bias the stock
measures through two mechanisms—through changes in
the asset composition of current-dollar investment and
through differences in the growth rates of the prices of
the various assets. In the present study, such asset detail
is maintained not only during the perpetual inventory
calculation, but also during rental price computation, al­
lowing use of asset-specific estimates of the effects of
tax laws, depreciation, and price inflation.
bea has estimated investment data as far back as pos­
sible (in some cases as early as 1820) to ensure that the
perpetual inventory has been through one full life cycle
by 1948, the initial year for which the bls measures
capital. This is necessary to avoid measurement bias
that would tend to overstate the rate of growth of
capital.
The following subsections specify which nonresiden­
tial and residential investment data are used in the bls
application of the perpetual inventory method. Several
steps are taken to ensure that detailed investment data
are fully consistent with the most recent totals available
from bea .

14It is also important to note that the “ best geometric averages’’
computed by Hulten and Wykoff are equally consistent with
their data. That is, given the current state of knowledge, there is no
empirical basis for choosing between the hyperbolic and geometric
forms. The choice is then up to the researcher, and, clearly, differ­
ent researchers have different preferences. The concluding section

of this appendix reports on a sensitivity analysis based on alterna­
tive assumptions about the form of the age/efficiency function for
the measurement of the growth of both the capital stock and
multifactor productivity.
15A more detailed discussion is presented in the Survey of Cur­
rent Business, August 1974.

Wykoff tests reject the one-hoss-shay specifications. On
the basis of these considerations and the experiments re­
ported above, the estim ate of (3 used in the
age/efficiency functions for structures is 0.75; and the
estimate of (3 used in age/efficiency functions for equip­
ment is 0.50.
To summarize, the age/efficiency function used in the
bls measures of the productive stock of capital by asset
type is the hyperbolic form. The choice of this form is a
“ prior” based on cursory observations and informal
discussions with businessmen. The average lives used
are those estimated by bea . The estimates of the /3 pa­
rameters for structures (0.75) and equipment (0.50) are
consistent with the Hulten-Wykoff evidence on used as­
set prices.14

( b g a ’s )




45

Nonresidential investment, bea has provided historical
data by detailed asset type cross-classified by major sec­
tor. This includes constant-dollar investment by asset
type for residential and nonresidential equipment and
structures in three sectors: Farming, manufacturing, and
nonfarm-nonmanufacturing. This historical detail is re­
vised each time there is a benchmark revision of the Na­
tional Income and Product Accounts (nipa ). Updates
and revisions for more aggregate totals are available
from bea annually. The annual updates include con­
stant-dollar and current-dollar investment data by asset
type and sector. The bea updates also include revisions
to all series used to estimate corporate shares. In gener­
al, the cross-classified data are adjusted at bls to corre­
spond to revisions in the asset type investment totals
using the biproportional matrix model (or “ ras” mod­
el).16 Furthermore, updates of the cross-classified detail
are estimated from asset type and sectoral totals for the
new year by applying the biproportional model to a ma­
trix starting with the cross-classified data for the most
recent year available. Essentially, it is a method of
creating a matrix which is consistent with known row
and column sums and as consistent as possible with
cross-classified data from a second source.
After constant-dollar investment is allocated by asset
type and sector, current-dollar investment is estimated
for each category. This is done by m ultiplying the
constant-dollar figures by price deflators. Separate de­
flators are estimated for each asset type, but are as­
sumed to be the same in all sectors for a given asset
type. In effect, the output deflator for the producing in­
dustry is assumed to apply to all purchasers.
Deflators are estimated in two steps. First, currentdollar investment figures supplied by bea are divided by
corresponding constant-dollar figures for each asset
type. Second, these initial estimates of the deflators are
scaled to equal 1.00 in 1972. This step is necessary be­
cause some adjustments done by bea affect 1972 cur­
rent-dollar investment and constant-dollar investment
differently. These adjustments reflect transfers of prop­
erty, including business purchases of secondhand gov­
ernment assets, sales by business to foreigners, transfer
of residential capital from farm to nonfarm status, pur­
chases of residential capital by government for demoli­
tion, sales of passenger cars to the public by rental
firm s, and conversions of residential capital from
tenant- to owner-occupied status. These adjustments are
reflected in the bls constant-dollar investment series.
Within nonfarm-nonmanufacturing, an adjustment is
made to remove nonprofit institutions from investment
estimates for equipment, structures, and residential cap­
ital. These are removed from capital in order to be con­
sistent with the output and labor data in the private busi­

ness sector; output measures available from the nipa are
based largely on labor inputs.
Specific asset categories likely to contain nonprofit
assets are isolated based on information from bea . For
structures, nonprofit investment is assumed to be a fixed
percentage of investment in four asset categories: Reli­
gious buildings (100 percent), educational buildings (98
percent), hospitals (95 percent), and other nonfarm
nonresidential buildings (30 percent). Since initial bls
estimates of total nonprofit investment based on these
percentages overestimate the bea figure, the difference
is reallocated among educational buildings, hospitals,
and nonfarm nonresidential buildings to ensure consist­
ency with the most recent bea total.
For equipment, total investment by nonprofit institu­
tions reported by bea is allocated to four equipment as­
set types: Furniture and fixtures, office machinery,
trucks, and autos. In this study, the allocation is made
in such a way that, when nonprofit institutions have
been subtracted from these four categories, the relative
proportions of the four asset types are unaffected.

,6The biproportional model is discussed by Michael Bacharach in
“ Estimating Non-Negative Matrices from Marginal Data,’’ Inter­

national Economic Review, 1965, No. 6, pp. 294-310.




Residential investment. Since private business sector
output excludes owner-occupied housing, the only resi­
dential investment series included in bls capital meas­
ures are tenant-occupied farm and nonfarm residential
housing. Tenant-occupied nonfarm investment is as­
signed to the nonfarm-nonmanufacturing sector; farm
investment, to the farm sector.
Constant-dollar residential nonfarm investment in
structures is available for five types of assets (table
C-3). Equipment is available for only a single asset
type. Constant-dollar residential farm investment is
available for structures for three asset types. Since
current-dollar totals were not available for the five types
of tenant-occupied nonfarm structures, deflators are de­
termined for total nonfarm residential investment. These
deflators are then multiplied by each of the five asset
classes to determine estimates of current-dollar invest­
ment for the five categories.
Although stock estimates exist for tenant-occupied
farm structures in recent years, bea has assumed new
investment in this category to be zero since 1967 to en­
sure that their stock estimates decline as quickly as their
benchmark data indicate. Proxies are therefore needed
for bls to calculate deflators for the three asset types in­
cluded in this category. Prices for new and additional
tenant-occupied 1- to 4-unit farm structures are assumed
to equal the ratio of current- to constant-dollar owneroccupied farm structures of this size. Prices for tenantoccupied farm mobile homes are assumed to equal the
ratio of current- to constant-dollar investment in owneroccupied farm mobile homes.

46

annual level. For the manufacturing sector, data are
available from bea on inventories by stage of process­
ing. The stages are materials and supplies, work in
process, and finished goods. Within manufacturing, bls
works with the disaggregate bea inventories to reflect
this detail. The rationale for including all types of in­
ventories in a capital measure is that all represent a cost
and all can contribute to the orderliness of the produc­
tion process.

A number of additional adjustments to residential in­
vestment data are made before the perpetual inventory
method is applied. These include a reallocation involv­
ing nonfarm structures after 1970, an adjustment to
make less detailed updates conform with the categories
for which historical data are maintained, and, finally,
the extraction of nonprofit investment from residential
assets.
First, an adjustment is made by bea to represent the
large number of condominium conversions during the
1970’s. The adjustment—to total constant-dollar invest­
ment for nonfarm residential structures—has the effect
of gradually moving condominiums from new tenantoccupied to new owner-occupied nonfarm structures
during the years after 1970. During the years 1970-74,
this reallocation is not reflected in the data by asset type
cross-classified by major sector. The reallocation for
condominiums is applied entirely to new tenantoccupied nonfarm structures of 5 units or more.
Smaller differences between the bls sum of invest­
ment for the five structure asset types and the structures
total received from bea occur for years where condo­
miniums are not an issue. As in the case of nonresidential capital, these small differences occur because the
more detailed data are obtained from a listing to which
revisions are not frequently made. In the bls measures,
the most recent totals are imposed, and any discrepancy
between totals and detail is distributed proportionally to
the five categories of detail. Also, totals are updated to
include new years before complete detail is available.
Again, totals for updated years are allocated in propor­
tion to detail from the most recent year for which it is
available.
Finally, investment in residential capital by nonprofit
institutions is removed. Total residential nonprofit fig­
ures are available from bea , but asset detail for this sec­
tor is not. Such investment occurs mainly in three asset
types: New 1- to 4-unit structures, new structures of 5
units or more, and nonhousekeeping structures (a resi­
dential asset type not included in the private business
sector). All nonhousekeeping structures are considered
nonprofit institutions. Therefore, they are subtracted
from total residential nonprofit constant-dollar invest­
ment. The amount left over is then removed proportion­
ally from the other two asset types.
Inventories. Estimates of inventories in current and
constant dollars are published in the Survey of Current
Business for the three major sectors. Since the pub­
lished figures are end-of-period estimates, and since the
concept of a productive input would be the average level
during the year, an average of the end-of-quarter figures
is computed in order to better approximate the average

Land. Estimation of the quantity and rental price of
land is important to the measurement of growth in mul­
tifactor productivity for the private business sector, es­
pecially for the farm and nonfarm-nonmanufacturing
sectors. Besides the fact that land is a productive input
in its own right, it is important to assign it a share in
capital income when determining the rates of return and
rental prices for all capital inputs. Unfortunately, the
measurement of land poses several difficulties, the most
serious of which is the scarcity of data for the manufac­
turing and nonfarm-nonmanufacturing sectors. Fortunat­
ely, land represents a smaller share of capital here than
in the farm sector, where data are available.
In the farm sector, data published by the U.S. Depart­
ment of Agriculture include land in farms (acreage), to­
tal current-dollar value of land plus buildings, and total
current-dollar value of buildings alone, bls calculates a
benchmark total value of land by subtracting the total
value of buildings from the total value of land and
buildings in 1972. This benchmark is extrapolated using
an unpublished index of the quantity of land services
provided by V. Eldon Ball of the Department of Agri­
culture. Ball derived this as a Tornquist index of region­
al land estim ates using rental prices to determine
weights. Rental prices are estimated from actual rental
transactions observed in the various regions. These
measures are ideal from a conceptual viewpoint, be­
cause they are aggregated considering the apparent dif­
ferences in efficiency of land in different regions. Also,
the weights used in this aggregation are based on direct
observation of the rental market for land rather than on
the implicit methods used for most rental prices in this
study.
In order to estimate land in manufacturing and non­
farm-nonmanufacturing, structures are multiplied by a
land-structures ratio. The first step toward deriving an
estimate of real land stocks for the manufacturing and
nonfarm-nonmanufacturing sectors is to relate estimates
of structures by Manvel to the bls data on capital effi­
ciency and wealth.17 This is done by using 1966 ratios
of land to structure values based on Manvel’s work and
applying these ratios to the bls estimates of the value of
structures in 1966 results in benchmark land estimates.

17Use was made of data published in Allan D. Manvel, “ Trends
in the Value of Real Estate and Land, 1956-1966,” Three Land

Research Studies (Washington, National Commission on Urban
Problems, 1968).




47

function and is the appropriate concept of capital inputs
to use for productivity measurement.
This section describes the com putation of the
“ wealth” stock, which is based on the age/price func­
tion, equation (C.3). The wealth stock represents the
sum of money (in base-period prices) which could be
generated by selling all vintages of an asset at prevailing
real prices. The wealth stock is used to estimate depre­
ciation, which is used in computing rental prices.
The wealth stock, like the productive stock, is com­
puted by the perpetual inventory method; it too adds
past investments using weights which decline with the
age of the asset. However, in the case of the wealth
stock, the weights are based on the age/price function
rather than the age/efficiency function (C.2). Mathemat­
ically, the vintage aggregation equation used to compute
the wealth stock is:

Manvel’s land estimates are not used directly because
the structures estimate on which they are based does not
conform to bls structures. This is due to differences in
sectoral definitions and in the technique used by Manvel
to arrive at his benchm ark. By employing a ratio,
M anvel’s work is used to extrapolate from the bls
benchmark. The current-dollar stock of structures in
1966 consistent with bls data is calculated by reflating
detailed constant (1972) dollar stocks of structures (in
value or wealth terms) by each asset’s investment price
deflator in 1966. Current- and constant-dollar asset
stocks are then aggregated for each of three categories:
Manufacturing, nonresidential nonfarm-nonmanufactur­
ing, and residential nonfarm-nonmanufacturing. Bench­
marks for 1966 for land are then calculated by multiply­
ing these 1966 structure values by ratios of land to
structures. Each categ o ry ’s stock of structures is
multiplied by a corresponding 1966 ratio. The ratio for
manufacturing is based on Manvel’s estimates of indus­
trial structures and land; for nonresidential nonmanufac­
turing, on his estimates of total commercial and indus­
trial property; and for residential land, on his estimates
of urban residential property.
The linking of current- and constant-dollar land value
growth rates to structures requires selection of an appro­
priate structures concept for extrapolation. Although
stocks net of depreciation (losses in value) are used to
benchmark land quantities, gross stocks of structures
(i.e., based on one-hoss-shay efficiency patterns) are
used to extrapolate them. Also, reflated gross stocks are
used to extrapolate estimates of the current-dollar value
of land. This tends to remove a bias that could be intro­
duced into land quantity and value estimates from the
depreciation of structures. In effect, bls assumes that
the real value of land cannot be a function of the depre­
ciation of the building standing on it. The extrapolation
is done separately for manufacturing and for the resi­
dential and nonresidential business parts of nonfarm­
nonmanufacturing, since separate benchmarks are avail­
able for each. These are then aggregated to represent a
total nonfarm-nonmanufacturing stock of land. Defla­
tors are then calculated by dividing the current-dollar
land stock by the constant-dollar stock for the manufac­
turing and nonfarm-nonmanufacturing sectors.

wt = s ; =tpT i2t_T
_t
where pt is the asset’s age/price function
and It is investment in period t.

The age/price series for pt are obtained from equation
(C.3). The real gross investment data for the It are the
same as those used to construct the productive capital
stock; the sources and methods for these data are de­
scribed above.
Equation (C.4) shows that the wealth stock measures
the value represented by all existing assets. It thus rep­
resents the present value of all future service embodied
in existing capital assets because of the relationship be­
tween efficiency and price discussed earlier.18 The de­
cline in the wealth stock from one period to the next,
before adding in new investment, is a measure of depre­
ciation. Depreciation represents the amount of money in
the current period needed to m aintain the stock of
wealth at its current level. This information is used to
estimate rental prices discussed below.
Timing of investment and output
Both the productive and the wealth stocks are yearend estimates and include all changes occurring during
the year, such as new investment, accruing efficiency
loss, and depreciation. These changes do not, in gener­
al, have their full impact on output during the year in
question. For example, an increment of investment put
in place on January 1 may have an impact on output
during the entire year. Investment put in place July 1
can only affect output during the second half of the
year, and December investment can contribute almost
nothing to current-year output. Since the investment fig­
ures received from bea count investment at the time it is
finished and ready to use, it seems reasonable to count
about half of a given year’s new investment, efficiency
loss, and depreciation towards the annual average meas-

Wealth stock
The discussion up to this point has been mainly con­
cerned with the computation of the “ productive” capi­
tal stock by asset type. The productive stock, as shown
by equation (C .l), is based on the asset’s age/efficiency

18The wealth stock and the productive stock coincide in the spe­
cial case where the age/efficiency function is one of geometric
decay.




(c.4)

48

to be charged in order to cover costs of p dollars’ worth
of an asset. For example, if d = 0.10 and the real inter­
est rate is 0.04, the owner would have to charge $.14 in
rent in order to cover expenses on a $1 asset. At the end
of a year, he could sell what was originally a $1 asset
for $.90 and pay the bank 4 cents interest due, breaking
even.
Inflation in the price of new assets and tax laws com­
plicate the derivation of the rental price. Hall and
Jorgenson19 derived the expression:

ures of stocks. Therefore, a half-year convention is used
in the bls measures. A given year’s output is matched
to the arithmetic mean of the current year-end stock and
the year-end stock for the previous year. Thus, capital
services are assumed proportional to the annual average
productive stock of a given asset. These averages are
used to compute the Tornquist index of real capital in­
put (appendix E) and the index of real factor input in the
multifactor productivity measures. On the other hand,
depreciation during the year is computed from the yearend stocks of wealth in order to reflect the losses of
value from the beginning to the end of the year.
As previously indicated, vintage aggregation is done
separately for each of the 43 depreciable asset types
listed in table C-2. Time series are generated repre­
senting the productive stock, the wealth stock, real de­
preciation, gross new real investment, and the price de­
flator of new capital goods. Each of these is computed
by asset for each of the three major subsectors of the
private business sector.

(1 - utzt - et) (ptrt + ptdt - Apt)
+ Pt*t

ct =

1 - ut

(C.6)
where
Ut
Zt
et
rt
dt

S Aggregation of Capital Stocks
L
by Asset Type

Pt
<1

After the productive capital stock for each type of as­
set is computed, the next major step is to combine these
different stocks in order to obtain the aggregate meas­
ures of capital input for the private business, private
nonfarm business, and manufacturing sectors. The pro­
ductive stocks are aggregated by asset type using im­
plicit rental prices as weights. The method and data
sources used to construct the rental prices are described
below. The Tornquist formula is used for the aggrega­
tion; this is defined in appendix F, where it is compared
with other methods of aggregation.

xt

The data sources for and derivation of these variables
are discussed below. All of the variables on the right
side of expression (C.6) except for the rate of return, rt,
are derived from these sources. Before the rental prices
are computed, expression (C.6) is used to solve for an
implicit rate of return rather than using a market interest
rate.20 Computing the internal rate of return is necessary
to empirically implement (C.6) because the rate of capi­
tal gain is frequently greater than market interest plus
depreciation. The procedure would result in some nega­
tive rental prices if the market interest rate were used.
In order to obtain the implicit rate of return, the rental
price, ct, is multiplied by the capital stock, Kt, and this
product is set equal to capital (i.e., nonlabor) income
reported in the n i p a . The following equation for rt, the
implicit internal rate of return, is derived by substituting
ct from equation (C.6) in the product ct Kt:

Mental price (user cost) off capital
The “ implicit rental price” or “ user cost” of capital
is based on the neoclassical principle that inputs should
be aggregated using weights that reflect their marginal
products. The assumption used to formulate the rental
price expression is that the purchase price of a capital
asset equals the discounted value of the stream of serv­
ices (and, hence, implicitly the rents) that the asset will
provide. Disregarding inflation and taxes, the rental
price, c, would be
c = p (r + d)

IS the corporate income tax rate
is the present value of $ 1 of tax deprecia­
tion allowances
is the effective rate of the investment tax
credit
is the nominal rate of return on capital
is the average rate of economic deprecia­
tion
is the deflator for new capital goods
is revaluation of assets due to inflation in
new goods prices
is the rate of indirect taxes.

Yt -

rt =

- Kt (ptdt - Apt) (1 - utzt —et) / (1 — ut)

----------------------------------------------------------Ktpt (1 - utzt - et) / (1 - Ut)

(C.5)

(C.7)

Where p is the price of the asset, r is a rate of return,
and d is the rate of depreciation. In terms of equation
(C.5), c represents the amount of rent that would have

where Yt is capital income and Kt is productive capital
stock.
Expression (C.6) is computed separately by bls for

19Robert E. Hall and Dale W. Jorgenson, “ Tax Policy and Investment Behavior,’’ American Economic Review, Vol. 57, June
1967, pp. 391-414.

20The method used to obtain the implicit rate of return was derived in Christensen and Jorgenson, “ The Measurement of U.S.
Real Capital Input.”




i

49

each type of asset and rt is computed jointly for all as­
sets. By solving for rt, nipa capital income, Yt is exact­
ly allocated to capital assets. That is, the rental prices,
Ci, are determined by solving for the rate of return such
that:
Y t = Si citK it.

(C.8)

Hence, cit Kit/Kt is the share of capital income allocated
to the i th asset in year t.21
Computation of rental prices for capital requires esti­
mates of capital income and several tax rates. Data on
capital income are available in the nipa. For the corpo­
rate sector, a comprehensive set of categories of capital
income is available for each major sector—profits, net
interest, capital consumption allowances, transfers, in­
direct business taxes, and inventory valuation adjust­
ments. These components are aggregated to obtain a
measure of the current value of corporate capital
income.
Data for measuring capital income for noncorporate
capital are incomplete. This is because proprietors’ in­
come in the nipa is not differentiated between wage and
salary income (labor) and profits (capital income). This
is a difficulty not only for estimating noncorporate rent­
al prices, but also for determining noncorporate capital
and labor income shares, a problem which is addressed
below. Noncorporate rental prices are determined by as­
suming that they are equal to corporate rental prices for
each type of asset. Corporate rental prices are deter­
mined after estimating the corporate portion of each
type of productive capital asset. These percentage esti­
mates are based on ratios of corporate to total net bea
stocks for equipment, structures, and residential capital
in the farm , m anufacturing, and nonfarm ­
nonmanufacturing sectors. The most closely corre­
sponding share is multiplied by the bls estimate of the
total productive stock for an asset type in each year in
order to determine the corporate productive stock of the
asset. This is the estim ate of corporate kt used in
estimating the internal rate of return in equation (C.7).
Deflators are calculated for new investment goods
based on the ratio of current- to constant-dollar invest­
ment for each asset. The rate of depreciation is the ratio
of the real value of depreciation to the real wealth stock.
The real value of depreciation equals real investment

minus the increase in the wealth stock. The effective
rate of indirect taxes is assumed to be equal for all as­
sets, and is defined as total indirect taxes in the sector
divided by the total stock of wealth.
Estimates of the effective rate of the investment tax
credit for each type of capital for each year are also re­
quired. The strategy used by bls to estimate effective
credit rates for each of 21 equipment categories is to
consider historical credit laws and to assume a distribu­
tion of useful tax lives associated with the average serv­
ice lives used.22
In estimating effective tax credit rates, bls attempts
to account for all the special features of the law, except
those related to the profitability tests and carryover
rules. Therefore, the rental price formulation is used in
such a way as to assume that all marginal investment
decisions are made by firms which are operating at a
profit for tax purposes. Although this is restrictive, it is
preferable to the alternative of using actual allowances
claimed, which reflect historical decisions as well as in­
centives in the current period.
The first step in the procedure is to estimate, for each
type of equipment, the percentage of the maximum
allowable rate which is applicable.23 For this purpose,
service lives for tax purposes are assumed to be normal­
ly distributed about the mean service life, with the dis­
tribution cut off before 0.5 times the mean life and after
1.5 times. Although we assume lives are more widely
dispersed for the purpose of vintage aggregation, a more
truncated distribution of service lives is used for tax
purposes. The full amount of the credit is assumed to
have been claimed for that portion of the distribution of
service lives over 8 years, % credit for that between 6
and 8 years, and V credit for lives under 6 years. The
3
procedure is repeated for each asset type for the
post-1970 period, when 5 and 7 years are the appropri­
ate cutoffs. Since the smallest mean service life is 8
years, no portion of any of the distributions falls in the
range where no credit is allowed (less than 3 years).
Next, these initial estimates are multiplied by the rate
of the maximum allowable credit for the year in ques­
tion. In years where the credit was suspended by Con­
gress for part of the year, estimates are multiplied by
the percentage of days in the year in which the credit
was in effect. The result is an asset-specific estimate of
Since the direct data reflect complex rules on profits tests and
carryovers and carrybacks, the volume of credits tends not to re­
spond proportionally to changes in new investment. Thus, the ratio
of the volume of credits taken in a year to nominal new investment
is a poor indicator of marginal incentives. For example, in 1970 the
credit was totally suspended for new investment, and yet substan­
tial credits were claimed against that y ea r’s taxes because of
carryovers from earlier years.
23The procedure used is similar to the methods used by others,
such as Patrick J. Corcoran and Leonard G. Sahling, “ The Cost of
Capital: How High Is It?’’ Federal Reserve Bank of New York
Quarterly Review, 1982, Summer, pp. 23-31.

2‘The farm sector is handled somewhat differently with respect
to determining the asset shares in capital income. This exception
will be discussed together with the handling of farm proprietor’s
capital-labor income shares at the conclusion of this section of the
appendix.
22 Data on investment tax credits actually claimed are available
for corporations by detailed industry group in the U.S. Treasury
Department’s Statistics of Income. The difficulty with this direct
source is that actual credits claimed reflect the complexities of the
tax laws concerning credits.
The rental price expression is meant to represent the price incen­
tives afforded firms on a marginal decision to buy new capital.




50

nipa .

produces estimates of capital costs, by type of cost,
for 2-digit industries. Data collected include capital
consum ption allow ances, profits (before and after
taxes), net interest, business transfer payments, and in­
direct business taxes. Since the work on capital costs is
based on the corporate sector, data specific to that sec­
tor are collected. Each component is obtained separately
for the corporate portions of manufacturing, farm, and
nonfarm-nonmanufacturing. The noncorporate sector is
excluded from this cost work because detailed noncor­
porate income data are unavailable. As discussed
earlier, noncorporate rental prices are assumed to be
equal to corporate rental prices for each specific type of
asset in each major sector.
A majority of the series are obtained from informa­
tion provided by bea containing the “ 14 components”
of income. From this source, bls obtains estimates, by
2-digit industry, of corporate capital consumption al­
lowances, corporate profits, total business transfer pay­
ments, and indirect business taxes. Using this data, in­
direct taxes and transfers are allocated to the corporate
sector in proportion to corporate shares in the stock of
corporate and noncorporate depreciable assets. These
shares are based on bea measures of net capital stock.
Capital consumption allowances exclude adjustments.
Total net corporate interest and corporate profits tax lia­
bility are obtained from table 1.13 in the Survey of Cur­
rent Business. Corporate profits before and after tax by
industry are obtained from tables 6.21 and 6.23 of the
same publication. Net corporate interest by sector is ob­
tained from the bea staff.
As discussed earlier, the bea work on the measure­
ment of capital stock is the source for the gross invest­
ment data for the bls major sector capital measures. Al­
though bls computes stocks by type of asset for each
major sector (manufacturing, farm, and other), it does
not do so separately for corporate and noncorporate
stocks. Estimates of the corporate breakout are needed,
however, to estimate rental prices. Cost data are used as
a basis for rental prices in the corporate sector. Noncor­
porate rental prices are then set equal to corporate rental
prices at a disaggregate level. This equality assumption,
in effect, excludes from the bls measures any capital
composition adjustment based on legal form of organi­
zation., Differences between corporate and noncorporate
rental prices could be used as the basis for a significant
composition adjustment because the relative size of the
noncorporate sector has declined steadily over time.
However, the composition adjustment might mistakenly
imply that capital input is growing faster than it would
if the trend were absent.
Since rental prices must be calculated for the corpo­
rate sector alone, estimates of the corporate stock of

24In this approach, the rental price expression is used to investi­
gate the effects of inflation, working through the tax system, on in­
vestment incentives. See Dale W. Jorgenson, and Martin A.

Sullivan, “ Inflation and Corporate Capital Recovery,” in
Hulten, ed., Depreciation, Inflation and Taxation of Income fr o m
Capital, pp. 171-237.

the marginal incentive associated with the investment
tax credit for that year.
The rental price formulation, equation (C.6), also re­
quires an estimate of the present value of $ 1 of depreci­
ation deductions, zt. This is the portion of investment
expenses which can be recovered in capital consumption
allowances after discounting these allowances for nomi­
nal interest charges. This value is generally less than 1,
since deductions are based on historical purchase prices.
This value is generally lower for longer lived assets be­
cause the deductions must be more severely discounted.
It is assumed that all firms elected straight-line depre­
ciation prior to 1954, double declining balance with
switchover to straight line for 1954-80, and the acceler­
ated capital recovery system (acrs) beginning in 1981.
For each depreciation pattern and for each type of asset,
an allowable stream of deductions for $ 1 of new invest­
ment is calculated. This stream is based on the assumed
average service lives used for computing capital input
and a normally distributed retirement pattern. Then, that
stream is discounted using the average long-term bond
rate in effect during a given year. Therefore, the esti­
mates of the present value of $ 1 of depreciation used by
bls vary not only by type of asset but also from year to
year as a function of changing interest rates.
Finally, equation (C.6) requires an estimate of the
corporate income tax rate, Ui. The traditional way of
estimating this rate is to compute the ratio of total cor­
porate profits tax liability to before-tax total profits.
Such a rate presumably reflects an aggregate of tax rates
actually paid during the year including the effect of
those companies which faced losses. In such an ap­
proach, no attempt is made to differentiate the effective
tax rate by type of asset. The difficulty is that this aver­
age tax rate is not conceptually appropriate for the rental
price expression. In this expression, the tax rate should
reflect the marginal incentives afforded investors in new
capital by current tax laws and it should be specific to
the type of asset.
B ls follows an approach suggested by Jorgenson and
Sullivan.24 They use the statutory tax rate for their esti­
mate of ut in equation (C.6)—the marginal rate faced by
a profitable firm. Using the rental price formulation,
(C.6), they derive an expression for an “ effective” rate
in terms of the statutory tax rate (ut), the effective rate
of investment credits (et), the present value of $1 of de­
preciation (zt), and the other variables in the rental price
expression. Since ut, et, and zt are distinguished by as­
set type, this effective rate reflects the asset-specific ef­
fects of each of these aspects of the tax law.
Capita! costs
The main source of data on capital cost is the




bea

C. R.

51

prietors’ income by assuming either that proprietors and
unpaid family workers earn the same wage as employees
or that corporate and noncorporate capital yield the
same rate of return.
Unfortunately, the two methods of imputation applied
together generally overestimate the nipa measures of
proprietors’ income. Rather than select one imputation
over the other, the two methods are initially employed
simultaneously, and the results are reconciled at a later
stage.
First, an imputation is made for noncorporate income
by assigning proprietors and unpaid family workers the
same average wage received by paid employees, and
then adding to that an imputation of capital income by
assigning noncorporate capital the same rental price as
corporate capital.25 This imputation is compared to
noncorporate income in the nipa . (Noncorporate income
includes proprietors’ income, noncorporate capital con­
sumption allowances, and a portion of indirect business
taxes.) The imputation is adjusted to equal the reported
noncorporate income by multiplying the wages of pro­
prietors and unpaid fam ily workers and the
noncorporate rate of return by a single scalar which
equates the imputed and nipa totals. Thus, noncorporate
wages and the rate of return to capital are scaled back
proportionally to determine proprietors’ capital and la­
bor shares. It should be noted that the scalar is applied
only to the rate of return on capital, not to the entire
rental price. Thus, the noncorporate rates of economic
depreciation, asset revaluation, and indirect taxes are
held equal to the corporate sector.
The rationale for this treatment is that these other ele­
ments are exogenous for the self-employed. The selfemployed can willingly accept lower wages and returns
to their capital in exchange for the greater degree of
independence—or for some other reason. However,
their preference is unlikely to affect factors like eco­
nomic depreciation or inflation. Tables C-5 through
C-7 illustrate the effects of this procedure.
Two exceptions are made to the methods outlined
above for allocating capital income in the farm sector.
During the period studied, farm land prices consistently
increased faster than the deflators for other capital in­
puts. In terms of the rental price equation (C.6), the
capital gains (Ap) on land frequently exceeded the rate
of return, which was presumed equal for all assets. To
maintain the assumption that the rates of return were
equal for all asset types would imply that land frequent­
ly had a negative rental price and a negative income
share. Such a situation makes little sense and would in­
validate a Tornquist index based on these “ shares.”

each asset type in each sector are required, be a net
stocks are used to derive corporate stocks for each asset.
bea provides corporate stocks broken out by sector and
year for equipment, structures, and residential capital.
In each sector and in each major asset category (that is,
equipment, structures, and residential capital), the ratio
of corporate capital stock to total capital stock is com­
puted based on the bea net stock estimates. Using these
ratios, bls proportionally allocates stock estimates for
more detailed asset types to the two legal forms, the
corporate and noncorporate sectors.

Aggregation procedure
As indicated in the introduction to this section, the
Tornquist procedure is used to combine the capital stock
series by asset type described in the previous section
using the rental price described in this section to derive
weights. The resulting indexes are the BLS-derived ag­
gregate measures of capital service inputs. The capital
input index for the private business sector is, in effect, a
weighted sum of the percent changes in capital stocks
by asset type where the weights are averages of the re­
spective rental prices for the current and past year. The
capital input measures for private nonfarm business and
manufacturing are similarly aggregated.
Appendix E contains a discussion of the Tornquist in­
dex number formula. Capital input indexes by broad
class of asset are presented for each of the three major
sectors at the end of this appendix.

@. Capital and Labor Income Shares
1
1
The other major methodological issue addressed in
this appendix concerns the calculation of capital and la­
bor income shares. These shares are used to weight the
labor and capital inputs in order to obtain the combined
input measure.
Data are available in the nipa for employee compen­
sation and for corporate capital income. Corporate capi­
tal income is defined by bls to include unadjusted
before-tax profits, corporate capital consumption allow­
ances, corporate net interest payments, corporate inven­
tory valuation adjustments, and a portion of indirect
business taxes. Corporate capital income is used to de­
termine the corporate rental price for each type of asset
as outlined in the previous section. However, the nipa
report only a single figure for proprietors’ income,
which reflects returns to both labor and capital. Since
data are available on hours of proprietors and unpaid
family workers, and on noncorporate capital stock, it is
possible to develop an implicit capital-labor split of pro­
25For the purposes of this analysis, the income of employees of
proprietors is excluded from noncorporate income. The assumption
made implies that, while proprietors can accept a lower wage and
rate of return than corporations, they do not have the same control
over the wages of their employees. Therefore, employees of propri­




etors are assumed to have the same wage as other employees and no
further adjustment to their wage is made. Adjustment is made only
by changing proprietors’ wages and the rate of return to noncor­
porate capital.

52

This difficulty with high capital gains on farm land is
well known. Doll and Widdows26 point out that farmers
have often made a large portion of their income in the
form of capital gains on land which occur at rates in ex­
cess of the general inflation rate. Sometimes the effect
is so large that farmers with little equity in their land are
forced to take out increasing mortgages against the ever
larger land values to maintain a positive cash flow.
Because of this situation, capital-labor income shares
and asset type income shares cannot be reasonably esti­
mated based on the model described above. Instead,
shares of capital assets in farm capital income are esti­
mated as follows. First, rental prices for each type of
asset are assigned using an assumed real rate of return
(4 percent) plus the asset’s depreciation rate. Then, an
estimate of total farm capital income is computed as a
sum of terms, each term being the productive stock of
an asset type times its assigned rental price. Next, each
asset is assigned a share in total capital income based on
the share of its term in the sum. Finally, these assigned
shares are used to weight the various productive stocks
to compute real capital input as a Tornquist index of the
asset type stocks.
Since these assigned prices are not controlled to any
income or cost estimate, the estimate of capital income
derived in this way is not used in determining farm cap­
ital and labor income shares. Instead, total capital in­
come is assumed to equal corporate capital income in
the n i p a plus an estimate of noncorporate capital in­
come. The noncorporate capital income estimate is as­
sumed equal to the noncorporate productive stock times
the ratio of the corporate capital income to the corporate
productive stock.
Farm proprietors’ wages are initially computed by
equating them with employees’ wages in the same man­
ner as for the nonfarm sectors. Wages are also imputed
to unpaid family workers at the same rate on the as­
sumption that they receive compensation for their serv­
ices in unmeasured forms. This imputation is compared
to total n i p a noncorporate income after noncorporate
capital income is subtracted. The imputation is adjusted
by multiplying the wages of proprietors and unpaid fam­
ily workers by a scalar which equates the imputed and
BEA-reported totals.

Measures of total capital input and multifactor pro­
ductivity were presented in the main body of this bulle­
tin. In this section, capital measures are given in more
detail. The three sectors for which measures are pre­
sented are private business, private nonfarm business,

and manufacturing. These reflect calculations which
were done separately for manufacturing, farm, and
nonfarm-nonmanufacturing. Sets of tables at the end of
this appendix present annual figures for equipment,
structures, rental residential capital, inventories, and
land, as well as the total for all types of assets. The
discussion in this appendix will be directed mainly at
the private business sector, tables C-13 through C-19.
However, much of the discussion applies equally to the
private nonfarm business sector (C-20 through C-26)
and the manufacturing sector (C-27 through C-33).
Referring to table C-13, one can examine the annual
percent changes in the private business capital measure.
With two minor exceptions, every component exhibits
positive growth in every year. Steady growth is not sur­
prising in light of the growth of the economy, but the
uniformity of growth, even during business downturns,
exemplifies the rather static nature of capital as meas­
ured. The main contributor to the measure is a stock es­
timate, which is determined by historical investments
net of efficiency loss (which is assumed to occur at a
small, predetermined rate). New gross investment (table
C-17 ) is added to the stock each year, and accruing ef­
ficiency losses are removed. Gross investment is rela­
tively volatile but has always been great enough to off­
set efficiency losses. Large positive and negative
fluctuations in the growth of investment result in more
modest changes in the rate at which capital inputs in­
crease (C-13). Analogous observations apply to the pri­
vate nonfarm business and manufacturing sectors.
Referring again to table C -1 3 , a clear pattern
emerges when comparing the growth rates of various as­
set types. Equipment consistently grows faster than
structures which, in turn, generally grow faster than res­
idential capital, inventories, or land. In other words,
there has been a long-term shift in the composition of
capital towards depreciable assets, particularly the
shorter lived equipment. This shift in the overall capital
measures is captured by the use of rental prices to
weight capital assets during aggregation. The effect of
the shift on the capital input measures can be judged by
comparing the growth of capital input for all assets (ta­
ble C-13) with that of an index of the direct aggregate
of productive stocks (table C-14). Table C-16 shows
the index of the ratio of capital input to productive
stock, which is sometimes referred to as the capital
“ composition effect.’’ Clearly, the shift toward shorter
lived assets has caused a steady and significant increase
in capital services per unit of stock. This is because
equipment yields its services more quickly than struc­
tures and hence is assigned a larger weight. Also, the
decline in this effect since 1973 reflects in part the low­
er revaluation of equipment. Presumably, investment

26John P. Doll and Richard Widdows, “Imputing Returns to
Production Assets in 10 U.S. Farm Production Regions ’, Eco-

nomic Research Service Staff Report No. ACES820703 (U.S. Department of Agriculture, July 1982).

B
¥.

Examination of the Measures




53

Table C-5.

Manufacturing sector: Shares in total income used to aggregate labor and capital inputs, 1948-81

Year

1948 ............................................................
1949 ............................................................

Ratio adjusting
proprietors’ wages
and rate of return
to noncorporate
capital
(1)

Total
adjusted labor
share
(2)

0.9338
.8215

Breakdown of adjusted
labor share

Breakdown of adjusted
capital share

Employees

Proprietors

Corporate

Noncorporate

(3)

(4)

(5)

(6)

0.681
.670

0.662
.652

0.019
.017

0.307
.317

0.012
.014

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.8745
.9372
.8341
.7492
.6353
.5482
.7744
.6118
.4618
.3043

.656
.661
.683
.694
.696
.671
.694
.697
.706
.683

.640
.645
.668
.681
.685
.662
.681
.686
.698
.678

.016
.016
.014
.013
.011
.009
.013
.010
.008
.005

.329
.326
.304
.293
.290
.315
.295
.291
.280
.302

.014
.013
.014
.014
.014
.015
.010
.012
.014
.015

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.3087
.2207
.2285
.2591
.3340
.3078
.3956
.3595
.3596
.4244

.696
.693
.686
.675
.672
.658
.671
.684
.684
.704

.691
.689
.683
.671
.668
.654
.666
.680
.680
.699

.005
.004
.004
.004
.004
.004
.004
.004
.004
.005

.290
.292
.301
.313
.317
.331
.320
.307
.308
.290

.014
.015
.013
.012
.012
.011
.009
.008
.008
.006

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.4384
.3991
.4232
.4679
.6396
.5130
.3756
.4206
.4756
.5160

.723
.701
.701
.712
.741
.711
.701
.700
.710
.732

.717
.697
.696
.706
.734
.705
.697
.695
.704
.726

.005
.004
.004
.005
.007
.006
.004
.005
.006
.007

.272
.294
.294
.284
.256
.287
.294
.297
.288
.266

.005
.005
.006
.004
.002
.003
.004
.003
.003
.001

1980 ............................................................
1981 ............................................................

.4744
.4423

.757
.748

.750
.742

.007
.006

.243
.250

.000
.002

composition is skewed toward equipment sufficiently so
that $1 of new equipment no longer yields much more
current services than new structures.
A further point can be made about the composition ef­
fect (table C-16). Since each major asset category is ag­
gregated from subcategories of asset types with different
rental prices (i.e., with different depreciation rates and
for different sectors), a composition effect exists within
each major category. The equipment effect is positive
every single year, indicating a pervasive trend toward
the shorter lived types of equipment. In contrast, the
structures effect is often negative, indicating a slow
trend toward longer lived forms of structures. The in­
ventory and land effects reflect mainly intersectoral
shifts. The land effect is persistently positive due to the
relative growth of nonfarm land compared to farm land.
The size of these composition effects demonstrates the
results of measuring capital services as a detailed array
of assets rather than at a more aggregate level.
Table C-5 reports the shares of the major asset cate­



gories in total capital costs. Table C-18 shows the price
index for new investment goods. Table C-19 shows the
depreciation rates used in the rental price formulation.
These are averages for more detailed rates used for indi­
vidual assets.
Capital and labor income shares
In this section, the computation of the capital and la­
bor shares of income is illustrated. As discussed earlier
in this appendix, an estimation procedure is required to
allocate proprietors’ income between labor and capital,
basically a two-step process. The first step is to approx­
imate labor compensation using employee compensation
per hour times proprietors’ hours and to approximate
capital compensation assuming the corporate and non­
corporate rental price of capital to be equal. The second
step is to adjust the capital and labor compensation fig­
ures so that they equal the reported figures for proprie­
tors’ income.
54

farm noncorporate capital earns the same rate of return
as corporate capital; any shortfall or excess in proprie­
tors’ income is attributed as a differential in the wage of
proprietors compared to that of corporate employees.
The farm adjustment is usually, but not always, less
than 1.00. The most notable exceptions are in 1973 and
1974, when new farm subsidies were introduced.
Columns 3 through 6 in each table divide total income
into shares arising from employees’ labor, proprietors’
labor, corporate capital, and noncorporate capital.
These allow the reader to observe the relative impor­
tance of the noncorporate portion of each sector. Non­
corporate enterprises are very important in the farm sec­
tor, but relatively small in manfuacturing.

Tables C-5, C-6, and C-7 refer to the manufactur­
ing, farm, and nonfarm-nonmanufacturing portions of
the private business sector, respectively. In each table,
column 1 illustrates the adjustment made; in manufac­
turing (C-5) and in nonmanufacturing (C-7), this col­
umn indicates the factor by which “ first” estimates of
proprietors’ wages and the rate of return to noncorporate
capital had to be multiplied to “ control” their associ­
ated values to the n i p a proprietors’ income figure. The
most significant observation is that this adjustment is
less than 1.00 and thus involves decreasing the “ first”
estimates in both sectors, more so in manufacturing. For
the farm sector (table C-6), this adjustment is applied
only to the proprietors’ wage rate. It is assumed that

Table C-6.

Farm sector: Shares in total income used to aggregate labor and capital inputs, 1948-81
Ratio adjusting
proprietors’ wages
and rate of return
to noncorporate
capital
(1)

Total
adjusted labor
share
(2)

1948 ............................................................
1949 ............................................................

0.8113
.6410

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

............................................................
............................................................
............................................................
......... ................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

Year

Breakdown of adjusted
labor share

Breakdown of adjusted
capital share

Employees

Proprietors

Corporate

Noncorporate

(3)

(4)

(5)

(6)

0.575
.550

0.134
.157

0.441
.393

0.009
.010

0.416
.440

.5247
.8418
1.0341
1.0148
.8625
1.0482
1.0622
1.0423
1.1399
.9735

.441
.559
.717
.749
.696
.719
.726
.728
.714
.721

.148
.133
.138
.141
.140
.148
.149
.157
.149
.169

.294
.427
.579
.608
.556
.571
.577
.571
.565
.552

.012
.010
.007
.007
.009
.009
.009
.010
.011
.012

.547
.431
.276
.244
.295
.272
.264
.262
.275
.267

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

1.1544
1.0336
.8919
.9097
.7304
.7372
.7176
.7894
.7108
.8283

.694
.662
.626
.608
.581
.536
.528
.549
.551
.580

.165
.170
.174
.179
.197
.176
.169
.176
.181
.173

.529
.492
.452
.429
.385
.360
.358
.372
.370
.407

.014
.016
.019
.021
.023
.026
.027
.027
.031
.033

.293
.322
.355
.371
.396
.438
.445
.425
.418
.388

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.9040
.9965
1.1333
1.7150
1.7130
1.1699
.8853
.7957
.9261
1.1645

.646
.644
.603
.586
.643
.520
.508
.492
.458
.503

.179
.169
.153
.113
.139
.147
.179
.191
.167
.154

.467
.474
.450
.473
.503
.373
.329
.301
.292
.349

.030
.033
.039
.043
.039
.054
.057
.061
.067
.063

.323
.323
.358
.371
.319
.426
.434
.447
.475
.434

1980 ............................................................
1981 ............................................................

.5538
.7343

.401
.425

.190
.175

.211
.250

.077
.074

.522
.501




55

Table G -7.

Wonfarm-nonmanufacturing sector: Shares in total income used to aggregate labor and capital inputs, 1948-81

Year

1948 ............................................................
1949 ............................................................

Ratio adjusting
proprietors’ wages
and rate of return
to noncorporate
capital
(1)

Breakdown of adjusted
labor share
Total
adjusted labor
share
(2)

Breakdown of adjusted
capital share

Employees

Proprietors

Corporate

Noncorporate

(3)

(4)

(5)

(6)

0.6757
.9515

0.595
.639

0.495
.494

0.100
.146

0.230
.226

0.175
.135

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.8382
.7442
.8747
.9272
.9144
.7483
.6493
.7129
.7232
.7061

.610
.599
.617
.635
.635
.600
.597
.609
.606
.600

.488
.497
.502
.510
.508
.500
.508
.509
.503
.503

.122
.101
.115
.125
.127
.101
.089
.100
.103
.098

.237
.233
.230
.227
.231
.243
.240
.240
.243
.248

.153
.168
.154
.138
.134
.157
.162
.152
.151
.151

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.5950
.5620
.5569
.5166
.5824
.5985
.6439
.6848
.7060
.7512

.596
.590
.585
.579
.585
.584
.592
.595
.600
.615

.512
.510
.509
.511
.509
.509
.515
.518
.522
.532

.085
.080
.076
.068
.076
.075
.077
.078
.079
.083

.249
.252
.257
.258
.260
.264
.265
.265
.265
.262

.155
.158
.158
.163
.155
.152
.143
.140
.135
.122

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................
............................................................

.7551
.7715
.8716
.6931
.6910
.6564
.6904
.6548
.7435
.7282

.625
.625
.637
.624
.628
.611
.616
.608
.621
.627

.543
.540
.544
.550
.555
.543
.546
.541
.545
.552

.082
.085
.093
.073
.073
.068
.070
.066
.075
.074

.258
.262
.262
.258
.257
.274
.271
.276
.275
.268

.117
.113
.102
.118
.115
.115
.113
.117
.104
.106

1980 ............................................................
1981 ............................................................

.7196
.7117

.624
.613

.551
.544

.072
.069

.272
.279

.104
.108

¥= Sensitivity AmaSysis

It is apparent that the final measure of multifactor
productivity is only mildly reduced by excluding any of
these assets, with the largest difference being 0.2 per­
cent per year when land, inventories, and residential as­
sets are all excluded. This is due partly to the fact that
capital enters the multifactor measure only after being
multiplied by capital’s income share (roughly 0.35 dur­
ing the two periods). The capital input measures are in­
creased by up to 0.8 percent a year during 1973-81 by
the exclusion of land, inventories, and the residential
component. Thus, exclusion of these components from
a capital measure would lead to attributing more growth
of output per hour of all persons to capital per hour and
less to multifactor productivity. The difference is great­
er in the recent period (1973-81) than in the earlier one
(1948-73). Therefore, failure to include these assets
would result in attributing less of the slowdown in out­
put per hour to capital per hour and more to other
sources. The differences, however, would be small;
about 0.1 percentage point.
The effects on the unweighted productive stock of not

The effects of two major issues concerning the meas­
ures of capital and multifactor productivity are explored
in this section. These are: (1) The choice of assets to in­
clude as capital input, and (2) the mathematical form of
the efficiency function.
Table C-8 shows growth rates during two major peri­
ods for multifactor productivity, capital input, and the
distribution of capital input into the growth in the pro­
ductive stock and the composition effect. The figures
are for the private business sector; similar comparisons
for private nonfarm business and manufacturing are
shown in tables C-9 and C-10, respectively. The first
column shows the actual figures published by b l s . The
succeeding columns indicate what the results would be
for a more restricted list of assets. The alternatives are
computed using the same capital and labor income
shares, and the same rental prices of capital for individ­
ual assets. The other four columns exclude selected as­
set types.



56

stock) efficiency, straight-line efficiency (both with the
same asset lives as the hyperbolic calculation), and with
geometric decay using Hulten and Wykoff’s “ best geo­
metric approximation” ( b g a ) rates of efficiency decline
to construct the efficiency function.
Table C - l l presents annual rates of change and com­
pound growth rates for selected periods for the resulting
private business multifactor productivity measures. It is
evident that the method selected has little effect on the
final measure of multifactor productivity, for year-toyear changes or over a long time period. The largest
variation in the measure for any one year appears to be
0.4 percent (1966), while the largest effect on the long­
er term growth rate is 0.1 percent.
Table C-12 presents the same information for private
business capital input, which is more sensitive to the ef­
ficiency assumption than is multifactor productivity.

Table C-8. Private business sector: Growth rates including
and excluding selected assets from published measures,
1948-81
(Percent per year, compounded)
All assets excluding:
Land, inven­
tories, and
residential

Land

Inven­
tories

Resi­
dential

1.5
2.0
0.1

1.5
1.9
0.1

1.5
2.0
0.1

1.4
1.9
0.1

1.3
1.8
-0.1

Quantity of capital
services:3
1948-81 ...........
1948-73 ...........
1973-81 ...........

3.5
3.6
3.2

3.6
3.7
3.4

3.4
3.5
3.3

3.7
3.8
3.5

4.0
4.1
4.0

Productive capital
stock:4
1948-81 ...........
1948-73 ...........
1973-81 ...........

2.6
2.6
2.7

3.2
3.3
3.2

2.6
2.5
2.8

2.8
2.8
2.9

3.8
3.8
3.7

Composition
effects:5
1948-81 ...........
1948-73 ...........
1973-81 ...........

0.8
1.0
0.5

0.4
0.5
0.2

0.9
1.0
0.5

0.9
1.0
0.6

0.3
0.3
0.2

Measure and
period

All
assets1

Multifactor
productivity:2
1948-81 ...........
1948-73 ...........
1973-81 ...........

Output per unit of
capital input:
1948-81 ...........
1948-73 ...........
1973-81 ...........

Table G-9. Private nonfarm business sector: Growth rates in­
cluding and excluding selected assets from published meas­
ures, 1948-81
(Percent per year, compounded)
All assets excluding:

-0.1
0.2
-1.0

-0.3
0.0
-1 .2

-0.1
-0.2
-1 .0

-0 .4
-0.1
-1 .3




1.3
1.7
0.0

1.2
1.6
0.0

1.3
1.7
0.0

1.2
1.6
-0.1

1.1
1.5
-0 .2

3.6
3.6
3.3

3.7
3.7
3.4

3.5
3.6
3.4

3.8
3.9
3.6

4.0
4.1
4.0

Productive capital
stock:4
1948-81 ...........
1948-73 ...........
1973-81 ...........

3.2
3.2
3.1

3.4
3.4
3.2

3.1
3.1
3.1

3.5
3.6
3.3

3.8
3.9
3.7

Composition
effects:5
1948-81 ...........
1948-73 ...........
1973-81 ...........

0.3
0.4
0.2

0.3
0.3
0.2

0.4
0.4
0.2

0.3
0.3
0.2

0.2
0.2
0.2

Output per unit of
capital input:
1948-81 ...........
1948-73 ...........
1973-81 ...........

including all the assets are even greater than on capital
input; the difference was as much as 1.2 percentage
points in 1948-73. This is because the composition ef­
fect is greater when more assets are included. It is ap­
parent from the tables that much of the composition ef­
fect comes from inclusion of land, a factor which has a
relatively low rental price and slow growth rate.
The second group of comparisons looks at the sensi­
tivity of the multifactor productivity and capital input
measures to the assumption about the form of the effi­
ciency function. In order to do this, all steps in the
measurement process were repeated using alternative as­
sumptions about efficiency, including tracing through
all of the implications for the rates of depreciation, rent­
al prices, rates of return, and so on. Besides the hyper­
bolic form which was selected for the b l s measures,
calculations were made using one-hoss-shay (gross

Land

Inven­
tories

Quantity of capital
services:3
1948-81 ...........
1948-73 ...........
1973-81 ...........

1 Equipment, structures, rental residential capital, inventories, and
land.
2Output per unit of combined labor and capital inputs where the com­
bined input is a weighted average of capital and labor (hours of all per­
sons) inputs. The respective weights are capital’s share (approximately
35 percent during the period) and labor’s share (approximately 65 per­
cent during the period).
Aggregate productive capital stocks by asset type weighted by rental
prices.
4Aggregate productive capital stocks by asset type, unweighted.
5Ratio of weighted to unweighted aggregate productive stocks.

All
assets1

Multifactor
productivity:2
1948-81 ...........
1948-73 ...........
1973-81 ...........

-0 .7
-0.3
-1 .7

Resi­
dential

Land, inven­
tories, and
residential

Measure and
period

-0.1
0.2
-1.1

-0 .2
0.1
-1 .2

-0.1
0.3
-1 .2

-0 .4
-0.1
-1 .4

-0 .6
-0 .2
-1 .8

1Equipment, structures, rental residential capital, inventories, and
land.
2Output per unit of combined labor and capital inputs where the com­
bined input is weighted average of capital and labor (hours of all per­
sons) inputs. The respective weights are capital’s share (approximately
35 percent during the period) and labor’s share (approximately 65 per­
cent during the period.
Aggregate productive capital stocks by asset type weighted by rental
prices.
4Aggregate productive capital stocks by asset type, unweighted.
5Ratio of weighted to unweighted aggregate productive stocks.

57

Table C-10. Manufacturing sector: Growth rates including and
excluding selected assets from published measures, 1948-81

VI. Summary
The b l s measures of capital input have been con­
structed to represent the flow of services attributable to
the stock of physical assets. Stocks are measured by a
perpetual inventory calculation to estimate relative serv­
ice flow, by detailed asset type, from assets of different
vintages. The perpetual inventory method employs a hy­
perbolic efficiency function in which services decline
relatively slowly during the early years of an asset’s life
and more quickly later. A slower hyperbolic form is
used for structures than for equipment, because compar­
isons between the age/price profiles consistent with
various hyperbolic forms and the Hulten-Wykoff re­
search on used asset prices indicated that this distinction
was appropriate. Rental prices are constructed by as­
suming that the value of a new asset equals the dis­
counted stream of services it will provide. Rates of re­
turn in the rental price expression are derived from asset
stocks and from the n i p a data on the components of
income.
Labor and capital income shares used to aggregate the
two inputs are based on employee compensation and
corporate capital income figures from the n i p a and also
on a procedure which allocates proprietors’ income to
labor and capital. In the private nonfarm sector, this al­
location reduces both noncorporate labor’s compensa­
tion per hour and capital’s rate of return after having
initially assumed that these variables are equal to their
corporate sector counterparts. In the farm sector, where
proprietorship is the dominant legal form of organiza­
tion, corporate capital is assumed to earn the noncorpo­
rate rate of return, with the residual of proprietors’ in­
come being attributed to labor.
Extensive detail is presented in the following tables,
C-13 through C-33. For each major asset and in each
sector, there are measures of capital input, productive
capital stock, the asset’s share in capital income, and in­
dexes showing the effects of changes in the composition
of assets over time.
Sensitivity analysis indicates that capital measures are
somewhat sensitive to the inclusion of land, inventories,
and residential capital and to the pattern of efficiency
assumed. However, multifactor productivity measures
are much less sensitive because the capital measures are
weighted by capital’s share (approximately equal to 35
percent). These issues have only relatively small effects
on the conclusions which can be drawn about multifac­
tor productivity growth and the post-1973 slowdown.

(Percent per year, compounded)
All assets excluding:
Land and
Inventories inventories

Measure and
period

All assets1

Land

Multifactor
productivity:2
1948-81 .......
1948-73 .......
1973-81 .......

1.8
2.2
0.4

1.7
2.2
0.3

1.8
2.2
0.3

1.7
2.2
0.2

Quantity of capital
services:3
1948-81 .......
1948-73 .......
1973-81 .......

3.6
3.5
4.0

3.7
3.5
4.1

3.5
3.3
4.3

3.7
3.4
4.5

Productive capital
stock:4
1948-81 .......
1948-73 .......
1973-81 .......

3.3
3.1
3.7

3.4
3.3
3.8

3.2
3.0
3.9

3.4
3.1
4.1

Composition
effect:5
1948-81 .......
1948-73 .......
1973-81 .......

0.3
0.3
0.3

0.3
0.2
0.3

0.4
0.4
0.4

0.3
0.3
0.4

Output per unit of
capital input:
1948-81 .......
1948-73 .......
1973-81 .......

-0 .2
0.6
-2 .6

-0.3
0.5
-2 .8

-0 .2
0.7
2.9

-0 .3
0.6
-3.1

’ Equipment, structures, inventories, and land.
2Output per unit of combined labor and capital inputs where the com­
bined input is a weighted average of capital and labor (hours of all per­
sons) inputs. The respective weights are capital’s share (approximately
35 percent during the period) and labor’s share (approximately 65 per­
cent during the period).
Aggregate productive capital stocks by asset type weighted by rental
prices.
Aggregate productive capital stocks by asset type, unweighted.
5Ratio of weighted to unweighted aggregate productive stocks.

However, the practical difference between efficiency as­
sumptions is again small. The largest annual variation is
1.2 percent (1966), and the largest for a time period is
0.5 percent. It is interesting that the widest differences
are between gross and straight-line methods. A case in
point is 1967, when these two differed by 0.9 percent­
age point, while the hyperbolic and geometric results
differed by only 0.3 percentage point. The close con­
formity of the hyperbolic and the b g a series is due in
large part to the fact that both were selected for their
conformity to the age/price profiles measured by Hulten
and Wykoff.




58

Table C-11. Sensitivity of multifactor productivity measure
to relative efficiency assumptions, private business sector,
1949-81

Table C-12. Sensitivity of capital services measure to rela­
tive efficiency assum ptions, private business sector,
1949-81

(Percent change)

(Percent change)

BLS
(hyperbolic)

Period

Hulten/Wykoff
(best geometric
approximation)

Gross
(one hoss
shay)

Straight
line

BLS
(hyperbolic)

Period

Hulten/Wykoff
(best geometric
approximation)

Gross
(one hoss
shay)

Straight
line

1949 .......

-1.1

-1 .0

-1 .0

-1 .2

1949 .......

4.0

3.5

3.5

4.2

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

7.2
2.4
1.8
2.6
-0 .4
4.4
0.3
0.9
0.7
4.0

7.4
2.5
2.0
2.8
-0 .3
4.4
0.4
1.0
0.8
4.1

7.2
2.5
1.8
2.5
-0 .5
4.3
0.4
0.9
0.5
3.9

7.1
2.2
1.8
2.6
-0 .4
4.3
0.2
0.8
0.7
4.1

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

3.7
4.4
4.2
3.1
2.7
3.1
3.6
3.1
2.2
2.0

3.3
4.0
3.8
2.5
2.3
3.0
3.5
2.9
1.8
1.8

3.6
4.0
4.2
3.3
3.1
3.3
3.5
3.2
2.5
2.4

3.8
4.7
4.3
3.0
2.6
3.2
3.9
3.3
2.1
1.8

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

0.6
2.0
3.6
2.9
3.6
3.1
1.9
0.3
2.4
-0 .5

0.5
1.9
3.6
2.8
3.6
3.1
2.0
0.4
2.5
-0 .4

0.6
1.9
3.6
2.9
3.7
3.3
2.2
0.5
2.5
-0 .4

0.6
1.9
3.6
2.8
3.5
3.0
1.8
0.2
2.3
-0 .5

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

2.4
2.2
2.3
2.9
3.4
4.3
5.3
5.3
4.6
4.7

2.8
2.3
2.4
3.1
3.4
4.2
5.1
5.0
4.3
4.4

2.5
2.3
2.3
2.8
3.1
3.8
4.6
4.8
4.3
4.4

2.5
2.2
2.4
3.2
3.2
4.7
5.8
5.7
4.8
4.8

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

-1 .2
2.2
3.3
2.4
-3 .8
-0 .2
3.8
3.0
1.0
-1.1

-1 .0
2.3
3.4
2.4
-3 .7
-0.1
3.8
3.0
1.0
-1.1

-1.1
2.1
3.2
2.4
-3 .8
-0 .3
3.6
2.9
1.0
-1 .2

-1 .2
2.2
3.3
2.3
-3 .8
-0 .2
3.9
3.1
1.0
-1 .2

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

4.3
3.5
3.6
4.6
4.5
2.7
1.9
2.6
3.6
3.7

3.9
3.1
3.4
4.4
4.3
2.4
1.7
2.5
3.6
3.5

4.3
3.7
3.9
4.6
4.5
3.0
2.2
2.8
3.7
3.8

4.4
3.4
3.6
4.6
4.6
2.5
1.6
2.5
3.7
3.8

1980 .......
1981 .......

-2 .2
1.1

-2 .2
1.1

-2 .3
1.0

-2 .2
1.1

1980 .......
1981 .......

3.6
2.9

3.3
2.6

3.8
3.1

3.5
2.7

1948-65 ..
1965-73 ..

2.2
1.3

2.3
1.4

2.3
1.4

2.2
1.3

1948-65 . .
1965-73 ..

3.1
4.5

3.0
4.2

3.1
4.3

3.3
4.6

1948-73 ..
1973-81 ..

2.0
0.1

2.0
0.2

2.0
0.1

1.9
0.2

1948-73 ..
1973-81 ..

3.6
3.2

3.4
3.0

3.5
3.4

3.7
3.1

1948-81 ..

1.5

1.6

1.5

1.5

1948-81 ..

3.5

3.3

3.5

3.6




59

Table C-13. Private business sector:
Real capita! input, 1948-81
All
assets

Period

Equip­
ment

Struc­
tures

Table C-14. Private business sector:
Productive capital stock, 1948-81

Rental
residential
capital

(Index, 1977=100)
Inven­
tories

Land

All
assets

Period

Index, 1977=100

Equip­
ment

Struc­
tures

47.6
48.7

27.6
30.1

Rental
residential
capital

41.2
42.1

Inven­
tories

Land

68.0
68.1

37.6
37.8

76.8
77.3

1948 .......
1949 .......

37.1
38.6

24.9
27.4

43.8
44.8

61.9
62.2

34.6
34.7

57.0
57.6

1948 .......
1949 .......

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

40.0
41.8
43.5
44.9
46.1
47.5
49.2
50.7
51.9
52.9

29.5
31.5
33.4
35.1
36.5
38.0
39.8
41.5
42.5
43.2

45.6
46.6
47.7
48.9
50.2
51.9
53.8
55.7
57.5
59.1

62.8
63.3
63.5
63.8
64.1
64.6
65.1
65.5
66.0
66.8

35.3
39.5
42.7
43.7
43.3
44.2
46.8
48.2
47.8
48.6

58.1
58.6
59.1
59.7
60.5
61.6
62.8
64.1
65.3
66.4

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

49.7
51.1
52.4
53.4
54.2
55.3
56.7
57.9
58.8
59.7

32.0
34.1
35.9
37.6
39.1
40.5
42.1
43.6
44.6
45.2

43.0
44.0
45.0
46.1
47.4
48.9
50.8
52.7
54.3
55.9

68.5
68.8
68.8
68.9
69.0
69.2
69.5
69.7
70.0
70.6

38.8
42.6
45.5
46.4
46.3
47.2
49.3
50.5
50.4
51.3

77.8
78.1
78.5
79.0
79.6
80.2
80.9
81.2
82.0
82.6

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

54.1
55.3
56.6
58.2
60.2
62.8
66.1
69.6
72.7
76.1

44.1
44.9
45.8
47.1
49.1
51.9
55.8
59.9
63.5
67.5

60.8
62.5
64.2
65.8
67.5
69.7
72.4
75.2
78.0
80.8

67.9
69.0
70.5
72.5
74.8
76.9
78.6
79.9
81.4
83.5

50.9
52.0
53.4
55.9
58.2
61.2
65.8
71.1
75.5
79.3

67.2
68.5
70.0
71.7
73.5
75.6
77.8
79.9
82.0
84.3

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

60.6
61.6
62.9
64.5
66.4
68.7
71.5
74.4
77.1
79.9

46.1
46.9
47.8
49.1
51.0
53.8
57.5
61.4
65.1
69.1

57.5
59.4
61.3
63.2
65.2
67.7
70.7
73.7
76.6
79.7

71.4
72.3
73.7
75.7
77.9
79.9
81.6
82.8
84.1
86.1

53.4
54.5
55.9
58.4
60.6
63.4
67.5
72.2
76.0
79.4

81.7
82.0
82.7
83.5
84.8
85.9
87.2
88.4
89.5
90.9

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

79.4
82.2
85.2
89.1
93.1
95.7
97.5
100.0
103.6
107.5

71.4
74.6
77.9
82.8
88.4
92.6
95.9
100.0
105.7
112.6

83.5
86.0
88.5
91.4
94.4
96.8
98.4
100.0
102.1
104.6

85.7
87.9
91.3
95.0
97.1
98.0
98.8
100.0
101.5
103.2

82.4
84.8
87.6
90.9
94.9
95.6
96.4
100.0
105.3
109.2

86.6
88.8
91.1
93.6
95.7
97.3
98.7
100.0
101.7
102.2

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

82.6
85.0
87.5
90.7
94.1
96.3
97.9
100.0
103.1
105.9

72.9
75.9
79.1
83.8
89.1
93.1
96.1
100.0
105.6
112.3

82.7
85.4
88.0
91.0
93.9
96.3
98.1
100.0
102.2
104.9

88.1
90.0
92.6
95.6
97.5
98.3
99.0
100.0
101.4
103.0

82.2
84.4
87.1
90.8
94.9
96.6
97.2
100.0
104.7
108.4

92.2
93.6
94.9
96.5
98.2
99.3
99.5
100.0
101.0
99.3

1980 .......
1981 .......

111.3
114.5

119.1
124.5

107.4
110.6

104.8
106.1

109.9
110.6

105.8
108.2

1980 .......
1981 .......

109.6
112.5

118.5
123.8

107.7
110.9

104.4
105.6

109.2
110.0

104.0
105.7

Percent change from preceding year
1949 .......

4.0

9.7

2.4

0.6

0.3

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

3.7
4.4
4.2
3.1
2.7
3.1
3.6
3.1
2.2
2.0

7.8
6.9
6.0
5.0
4.0
4.1
4.6
4.3
2.6
1.6

1.8
2.1
2.3
2.5
2.7
3.4
3.7
3.6
3.3
2.8

0.9
0.7
0.3
0.4
0.6
0.7
0.7
0.6
0.8
1.3

1.7
12.0
8.2
2.3
-0.7
1.9
5.8
3.0
-0.7
1.7

0.9
0.8
0.8
1.1
1.3
1.7
2.0
2.0
2.0
1.7

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

2.4
2.2
2.3
2.9
3.4
4.3
5.3
5.3
4.6
4.7

2.1
1.9
2.0
2.9
4.1
5.8
7.4
7.3
6.1
6.3

2.9
2.8
2.6
2.5
2.6
3.3
3.9
3.8
3.7
3.7

1.5
1.7
2.2
2.9
3.1
2.8
2.3
1.7
1.9
2.6

4.7
2.1
2.6
4.8
4.1
5.2
7.5
8.1
6.1
5.0

1.2
1.9
2.3
2.3
2.6
2.8
2.9
2.7
2.6
2.8

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

4.3
3.5
3.6
4.6
4.5
2.7
1.9
2.6
3.6
3.7

5.8
4.4
4.5
6.3
6.7
4.8
3.5
4.3
5.7
6.5

3.4
3.0
2.9
3.2
3.4
2.5
1.6
1.6
2.1
2.5

2.6
2.6
3.8
4.1
2.2
0.9
0.9
1.2
1.5
1.7

3.9
3.0
3.2
3.9
4.4
0.7
0.8
3.7
5.3
3.7

2.7
2.6
2.6
2.7
2.2
1.8
1.4
1.3
1.7
0.5

1980 .......
1981 .......

3.6
2.9

5.8
4.5

2.7
3.0

1.5
1.3

0.6
0.6

Table C-15. Private business sector:
Shares in current capital cost, 1948-81

1.0

3.5
2.3

<
4

Period

1948-81 ..

3.5

5.0

2.8

1.6

3.6

1948-73 ..
1973-81 ..

3.6
3.2

4.9
5.2

3.0
2.4

1.7
1.4

3.9
2.5




1.000
1.000

0.291
.334

0.265
.340

0.220
.099

0.138
.136

0.085
.091

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.379
.345
.345
.443
.417
.364
.312
.400
.328
.442

.350
.219
.296
.301
.347
.333
.232
.271
.356
.294

.125
.180
.132
.103
.089
.135
.191
.142
.120
.110

.030
.197
.156
.088
.061
.070
.174
.108
.076
.082

.116
.059
.072
.065
.086
.098
.090
.080
.120
.073

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.402
.403
.380
.376
.353
.335
.374
.354
.362
.429

.318
.311
.313
.296
.306
.306
.282
.295
.309
.258

.126
.102
.111
.124
.111
.114
.112
.105
.097
.105

.085
.072
.095
.107
.119
.125
.129
.136
.123
.128

.069
.113
.101
.098
.111
.121
.103
.111
.110
.080

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.425
.416
.427
.411
.433
.222
.297
.313
.370
.370

.264
.274
.306
.295
.238
.268
.352
.306
.255
.269

.102
.088
.035
.121
.219
.128
.090
.120
.106
.127

.123
.137
.120
.066
.047
.159
.105
.129
.144
.093

.086
.085
.112
.107
.063
.222
.155
.133
.125
.142

1980 .......
1981 .......

60

Rental
residential
capital

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

2.0
1.8

Struc­
tures

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

2.0

Equip­
ment

1948 .......
1949 .......

Compound annual rate of growth

All
assets

1.000
1.000

.349
.284

.275
.301

.126
.100

.098
.147

.153
.168

Inven­
tories

Land

Table C-16. Private business sector:
Ratio of capital services to productive stock, 1948-81

Table C-18. Private business sector:
Price of new capital goods, 1948-81

(Index, 1977=100)

(Index, 1977=100)

Period

All
assets

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

Period

Land

All
assets

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

Land

33.3
35.0

30.2
30.2

35.8
36.8

45.5
42.3

18.2
19.3

1948 .......
1949 .......

77.9
79.2

90.4
90.9

106.3
106.4

91.0
91.4

91.8
91.6

74.2
74.4

1948 .......
1949 .......

28.8
29.4

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

80.5
81.7
83.0
84.0
84.9
85.9
86.8
87.7
88.2
88.6

92.2
92.5
93.0
93.3
93.4
93.8
94.5
95.1
95.4
95.6

106.2
106.0
106.0
105.9
105.9
106.1
106.0
105.8
105.9
105.9

91.7
92.0
92.2
92.6
93.0
93.3
93.7
94.0
94.3
94.7

90.8
92.6
93.9
94.1
93.7
93.7
94.8
95.4
94.8
94.8

74.7
75.0
75.2
75.6
76.1
76.7
77.7
78.9
79.6
80.5

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

30.4
33.3
34.7
35.2
35.2
35.8
38.2
39.6
40.8
41.1

36.4
39.6
41.8
41.5
41.8
42.7
47.9
49.1
52.2
51.0

30.7
34.7
35.9
36.8
36.2
36.1
40.0
41.9
41.6
41.6

38.0
39.5
40.5
41.4
42.2
42.9
43.3
43.8
44.5
44.5

47.3
48.6
46.1
46.0
45.6
45.3
47.4
48.9
50.2
49.2

19.2
21.8
23.8
24.4
24.4
25.2
26.3
27.7
28.9
30.5

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

89.3
89.7
89.9
90.3
90.7
91.4
92.4
93.5
94.4
95.3

95.6
95.7
95.8
95.9
96.2
96.6
97.0
97.4
97.6
97.7

105.7
105.3
104.8
104.2
103.6
103.0
102.4
102.0
101.8
101.4

95.1
95.4
95.6
95.8
96.0
96.2
96.4
96.6
96.8
97.0

95.4
95.5
95.5
95.7
96.0
96.5
97.4
98.6
99.3
99.8

82.3
83.5
84.7
85.8
86.7
87.9
89.2
90.3
91.6
92.7

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

41.7
41.6
42.0
42.5
43.3
44.5
46.1
47.9
50.0
53.1

51.5
51.5
51.5
51.5
51.9
53.2
53.8
55.8
57.8
59.8

41.6
41.4
41.3
41.8
42.3
43.1
44.9
46.7
48.5
52.6

44.5
44.4
44.4
44.0
44.5
45.3
46.5
48.5
51.1
54.6

49.7
49.6
49.6
49.5
49.6
50.9
51.8
52.4
53.9
56.5

31.6
31.6
32.6
33.6
35.1
36.4
38.7
40.8
43.0
45.8

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

96.1
96.7
97.4
98.2
99.0
99.3
99.6
100.0
100.5
101.5

98.0
98.2
98.5
98.9
99.1
99.5
99.8
100.0
100.1
100.3

101.0
100.7
100.5
100.4
100.5
100.6
100.3
100.0
99.9
99.8

97.3
97.7
98.6
99.4
99.6
99.7
99.8
100.0
100.1
100.3

100.2
100.5
100.5
100.2
100.0
99.0
99.2
100.0
100.6
100.7

93.9
94.9
96.0
97.0
97.4
98.0
99.1
100.0
100.6
103.0

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

56.2
59.6
63.4
68.5
79.2
87.2
92.8
100.0
109.5
122.5

62.9
65.4
67.2
68.8
75.0
87.2
93.5
100.0
105.9
114.5

56.9
61.4
65.1
69.8
82.6
91.5
94.4
100.0
111.4
125.9

58.4
63.4
71.6
76.3
81.2
87.4
94.3
100.0
110.9
122.5

58.2
60.3
64.0
73.1
85.0
90.2
94.6
100.0
109.8
124.5

48.4
51.4
55.2
61.1
75.1
81.3
89.0
100.0
110.5
125.9

1980 .......
1981 .......

101.6
101.8

100.6
100.6

99.7
99.8

100.4
100.5

100.6
100.5

101.7
102.3

1980 .......
1981 .......

136.6
147.4

124.7
134.7

141.5
153.4

135.0
148.4

140.3
146.8

142.8
155.3

Table C-17. Private business sector:
Gross real investment, 1948-81

Table C-19. Private business sector:
Rate of depreciation, 1948-81

(Index, 1977=100)

(Percent per year)

Period

All
assets

Equipment

Structures

Rental
residential
capital

1948 ...............
1949 ................

40.9
34.7

37.2
29.4

51.4
47.1

37.8
38.7

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

................
................
................
.........
................
................
...............
................
................
................

37.8
39.3
38.1
40.7
40.1
45.0
46.7
47.5
42.0
46.1

32.3
34.6
33.0
34.9
33.1
36.5
37.5
38.8
32.5
36.3

48.9
51.9
51.7
56.2
57.7
66.2
71.2
70.3
64.4
66.6

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

................
................
................
................
................
................
................
................
................
................

48.4
48.7
53.2
56.4
61.8
70.9
76.8
74.4
78.6
84.8

37.8
36.6
40.4
43.5
49.6
57.6
66.0
64.2
67.6
73.0

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

................
................
................
................
................
................
................
................
................
................

81.4
80.0
88.9
101.6
97.2
85.2
89.0
100.0
113.9
121.1

1980 ................
1981 ................

119.1
122.9




Period

All
assets

Equipment

Structures

Rental
residential
capital

1948 ................
1949 ...............

3.229
3.463

11.930
12.382

5.772
5.741

2.218
2.247

51.0
37.9
36.3
38.6
40.9
46.7
43.6
45.2
50.3
64.0

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

...............
...............
...............
...............
................
...............
...............
...............
...............
...............

3.529
3.613
3.730
3.803
3.897
3.941
3.954
3.997
4.093
4.108

12.535
12.729
12.955
13.043
13.222
13.245
13.366
13.412
13.651
13.661

5.700
5.660
5.638
5.609
5.587
5.540
5.498
5.474
5.480
5.469

2.264
2.295
2.323
2.348
2.373
2.392
2.416
2.442
2.463
2.475

72.0
73.5
76.8
76.4
82.0
97.4
102.1
99.5
101.9
107.7

63.2
74.6
91.2
109.4
107.4
101.8
86.0
78.1
98.7
115.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

................
................
................
...............
...............
...............
...............
................
...............
...............

4.115
4.136
4.140
4.145
4.167
4.187
4.236
4.333
4.394
4.451

13.716
13.806
13.779
13.753
13.666
13.523
13.376
13.461
13.465
13.451

5.445
5.425
5.399
5.386
5.358
5.302
5.257
5.236
5.215
5.188

2.494
2.502
2.497
2.483
2.476
2.477
2.495
2.516
2.524
2.532

70.6
68.8
77.6
92.5
93.7
81.7
87.3
100.0
116.0
122.6

104.3
100.4
104.3
114.4
109.1
95.7
94.7
100.0
110.1
118.4

100.8
114.5
144.5
143.8
84.9
78.8
83.3
100.0
108.5
116.4

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

...............
................
...............
...............
...............
...............
...............
...............
...............
................

4.537
4.603
4.640
4.691
4.809
4.970
5.041
5.098
5.152
5.259

13.593
13.727
13.726
13.644
13.742
14.042
14.118
14.117
14.075
14.150

5.181
5.184
5.175
5.152
5.150
5.181
5.215
5.241
5.254
5.262

2.558
2.578
2.589
2.616
2.681
2.740
2.784
2.818
2.849
2.879

119.0
121.2

122.6
131.6

105.6
104.2

1980 ................
1981 ................

5.410
5.516

14.339
14.465

5.271
5.277

2.917
2.949

61

Table C-21. Private nonfarm business sector:
Productive capital stock, 1948-81

Table C-20. Private nonfarm business sector:
Real capital input, 1948-81

Index, 1977=100)
All
assets

Period

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

All
assets

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

Land

1948 .......
1949 .......

40.2
41.2

26.6
28.9

41.0
41.9

64.5
64.8

33.7
33.8

49.6
50.1

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

42.2
43.7
45.0
46.0
47.0
48.2
49.8
51.3
52.3
53.4

30.4
32.3
34.1
35.7
37.2
38.7
40.3
42.1
43.1
43.8

42.6
43.6
44.5
45.6
46.9
48.4
50.3
52.3
54.0
55.5

65.2
65.7
65.8
66.0
66.2
66.5
66.8
67.2
67.6
68.3

34.8
38.6
41.4
42.2
42.0
42.8
45.3
46.6
46.3
47.1

50.8
51.5
52.1
52.9
53.8
54.9
56.2
57.6
58.8
60.1

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

54.8
56.1
57.6
59.5
61.6
64.2
67.5
70.7
73.8
77.1

44.8
45.7
46.7
48.1
50.0
52.8
56.6
60.6
64.3
68.5

57.2
59.1
61.0
62.9
65.0
67.6
70.7
73.7
76.7
79.8

69.2
70.2
71.8
73.9
76.2
78.4
80.2
81.5
83.0
85.1

49.4
50.5
51.8
54.3
56.7
59.8
64.4
69.6
73.9
77.7

61.5
63.0
64.7
66.6
68.6
70.8
73.4
75.8
78.2
80.8

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

80.3
83.0
85.9
89.5
93.2
95.7
97.5
100.0
103.5
107.3

72.5
75.6
79.0
83.8
89.2
93.2
96.1
100.0
105.7
112.6

82.9
85.7
88.4
91.3
94.3
96.6
98.3
100.0
102.1
104.6

87.2
89.2
92.0
95.2
97.2
98.1
98.9
100.0
101.5
103.2

80.7
83.0
85.7
89.4
93.8
95.6
96.3
100.0
105.4
109.3

83.5
86.0
88.7
91.6
94.4
96.4
98.2
100.0
102.1
104.5

1980 .......
1981 .......

110.7
114.1

119.1
124.9

107.4
110.6

104.8
106.1

110.2
111.1

107.2
110.0

Land
Period

Index, 1977=100
1948 .......
1949 .......

36.3
37.7

24.7
26.9

43.9
44.9

60.6
61.0

33.8
33.9

49.7
50.4

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

39.0
40.6
42.4
43.7
44.9
46.4
48.1
49.7
50.8
51.9

28.8
30.6
32.5
34.2
35.6
37.1
39.0
40.7
41.9
42.6

45.6
46.6
47.6
48.8
50.1
51.8
53.7
55.7
57.5
59.1

61.7
62.3
62.5
62.9
63.3
63.8
64.3
64.7
65.2
66.1

34.5
39.0
42.2
43.1
42.8
43.6
46.2
47.6
47.3
48.0

51.0
51.7
52.3
53.1
54.0
55.0
56.4
57.7
59.0
60.2

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

53.2
54.4
55.7
57.4
59.4
62.0
65.3
68.9
72.1
75.6

43.5
44.4
45.3
46.7
48.6
51.5
55.4
59.5
63.2
67.2

60.8
62.5
64.2
65.8
67.5
69.7
72.5
75.2
78.0
80.9

67.1
68.3
69.9
71.9
74.2
76.3
78.1
79.5
81.0
83.2

50.4
51.4
52.8
55.3
57.7
60.7
65.3
70.7
75.1
78.9

61.6
63.1
64.8
66.6
68.6
70.9
73.4
75.8
78.2
80.8

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

78.9
81.8
84.8
88.8
93.0
95.6
97.4
100.0
103.7
107.9

71.2
74.4
77.8
82.8
88.4
92.6
95.9
100.0
105.8
112.8

83.6
86.1
88.6
91.5
94.5
96.9
98.4
100.0
102.0
104.5

85.4
87.6
91.0
94.9
97.1
97.9
98.8
100.0
101.5
103.3

82.1
84.5
87.3
90.6
94.8
95.5
96.3
100.0
105.5
109.3

83.6
86.1
88.8
91.8
94.4
96.5
98.2
100.0
102.1
104.6

1980 .......
1981 .......

111.7
115.0

119.5
125.1

107.4
110.5

104.9
106.3

111.0
110.7

107.2
110.1

Percent change from preceding year
1949 .......

3.7

8.8

2.3

0.8

0.2

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

3.5
4.2
4.3
3.2
2.8
3.3
3.7
3.3
2.3
2.0

7.1
6.5
6.1
5.1
4.2
4.3
4.9
4.6
2.8
1.7

1.7
2.1
2.2
2.5
2.7
3.4
3.8
3.6
3.3
2.8

1.2
0.9
0.4
0.5
0.7
0.8
0.8
0.7
0.8
1.3

1.7
13.0
8.3
2.3
-0.8
1.9
6.0
3.1
-0.8
1.7

1.2
1.4
1.3
1.5
1.6
2.0
2.4
2.5
2.2
2.1

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

2.6
2.3
2.4
3.0
3.5
4.4
5.4
5.4
4.7
4.8

2.2
2.0
2.1
3.0
4.2
5.9
7.5
7.4
6.2
6.4

2.9
2.8
2.6
2.5
2.6
3.3
3.9
3.8
3.7
3.7

1.6
1.7
2.3
2.9
3.2
2.9
2.3
1.7
1.9
2.7

4.8
2.1
2.6
4.8
4.2
5.3
7.6
8.3
6.2
5.1

2.2
2.5
2.7
2.8
3.0
3.3
3.5
3.3
3.2
3.4

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

4.5
3.6
3.7
4.7
4.7
2.8
1.9
2.7
3.7
4.0

5.9
4.5
4.6
6.4
6.8
4.9
3.5
4.3
5.8
6.6

3.4
3.0
2.9
3.2
3.4
2.5
1.6
1.6
2.0
2.4

2.7
2.6
3.9
4.2
2.3
0.9
0.9
1.2
1.5
1.7

3.9
3.0
3.3
3.9
4.6
0.7
0.8
3.9
5.5
3.7

3.4
3.1
3.1
3.3
2.9
2.2
1.8
1.8
2.1
2.4

1980 .......
1981 .......

3.5
3.0

5.9
4.7

2.7
3.0

1.6
1.3

0.7
0.6

Table C-22. Private nonfarm business sector:
Shares in current capital cost, 1948-81

1.3

Period

All
assets

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

Land

1948 .......
1949 .......

1.000
1.000

0.285
.328

0.276
.361

0.235
.101

0.141
.142

0.063
.069

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.374
.337
.339
.442
.414
.360
.307
.398
.324
.442

.375
.226
.306
.309
.360
.342
.236
.275
.365
.300

.131
.191
.136
.105
.090
.138
.196
.145
.123
.112

.021
.206
.161
.089
.061
.071
.178
.109
.076
.082

.098
.040
.059
.055
.075
.090
.084
.073
.112
.064

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.401
.402
.379
.375
.352
.333
.374
.353
.361
.431

.326
.318
.321
.302
.312
.313
.288
.301
.315
.262

.129
.104
.114
.127
.114
.117
.115
.108
.099
.108

.085
.072
.096
.108
.121
.127
.132
.139
.125
.130

.059
.104
.091
.087
.101
.110
.090
.100
.099
.068

2.6
2.7

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.427
.418
.430
.416
.438
.218
.297
.314
.374
.374

.268
.278
.312
.303
.242
.274
.361
.313
.261
.275

.105
.090
.035
.126
.227
.134
.093
.123
.110
.132

.124
.139
.122
.064
.045
.163
.107
.131
.147
.094

.076
.076
.102
.091
.048
.211
.142
.118
.108
.125

2.4
2.5
2.3

1980 .......
1981 .......

1.000
1.000

.352
.285

.282
.039

.131
.104

.099
.151

.136
.151

Compound annual rate of growth
1948-81 ..
1948-73 ..
1973-81 ..

3.6
3.6
3.3




5.0
5.0
5.3

2.8
3.0
2.4

1.7
1.8
1.4

3.7
4.0
2.5

62

Table C-23. Private nonfarm business sector:
Ratios of capital services to productive stock, 1948-81

Table C-25. Private nonfarm business sector:
Price of new capital goods, 1948-81

(Index, 1977=100)

(Index, 1977=100)
All
assets

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

Land

1948 .......
1949 .......

33.8
34.1

33.5
35.2

29.9
30.0

35.3
36.5

43.0
40.9

31.8
32.0

100.4
100.4
100.4
100.4
100.3
100.3
100.3
100.3
100.3
100.3

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

35.5
38.4
39.6
40.2
40.2
40.7
43.9
45.2
45.9
45.5

36.7
40.0
42.2
41.9
42.1
43.3
48.6
49.9
53.0
51.7

30.6
34.6
35.9
36.8
36.2
36.1
40.1
41.9
41.7
41.7

37.7
38.9
40.0
41.1
41.9
42.5
43.0
43.5
44.3
44.3

45.2
46.4
45.6
46.0
46.3
47.4
49.3
50.1
50.3
49.8

32.6
35.9
37.1
37.9
37.6
38.1
41.0
42.4
42.3
42.5

101.9
101.8
101.8
101.9
101.6
101.4
101.4
101.6
101.7
101.6

100.1
100.1
100.1
100.1
100.1
100.0
100.0
100.0
100.0
100.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

45.8
45.5
45.4
45.6
46.0
46.9
48.2
50.0
51.9
55.2

52.2
52.1
52.1
52.0
52.4
53.8
54.3
56.3
58.3
60.2

41.8
41.5
41.4
41.8
42.3
43.1
44.8
46.6
48.3
52.4

44.3
44.3
44.3
44.0
44.4
45.2
46.4
48.4
51.0
54.5

49.8
49.7
49.6
49.7
50.0
50.7
51.7
52.5
53.9
56.1

43.3
42.4
42.3
42.5
42.8
43.4
45.1
46.8
48.6
52.6

97.9
98.2
99.0
99.7
99.8
99.8
99.9
100.0
100.1
100.1

101.6
101.8
101.8
101.4
101.1
99.9
99.9
100.0
100.0
100.0

100.1
100.1
100.2
100.2
100.1
100.0
100.0
100.0
100.0
100.0

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

58.8
62.6
66.1
70.5
81.1
89.1
93.9
100.0
109.4
122.0

63.3
66.2
67.6
69.2
75.2
87.4
93.7
100.0
105.7
114.1

56.8
61.2
64.9
69.6
82.3
91.3
94.4
100.0
111.5
125.9

58.4
63.5
71.8
76.5
81.3
87.5
94.4
100.0
110.8
122.4

58.4
60.1
62.3
68.7
83.1
88.9
94.0
100.0
108.1
123.8

56.7
61.4
65.2
70.7
85.5
89.0
93.1
100.0
111.9
126.2

100.1
100.2

99.9
99.7

100.1
100.1

1980 .......
1981 .......

135.4
146.4

124.0
133.8

141.4
153.6

134.9
148.4

139.7
148.4

141.0
153.0

All
assets

Equip­
ment

Struc­
tures

Rental
residential
capital

Inven­
tories

Land

Period

1948 .......
1949 .......

90.3
91.3

92.7
93.1

107.1
107.2

93.9
94.2

100.4
100.2

100.3
100.4

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

92.3
93.0
94.2
94.9
95.7
96.3
96.7
96.9
97.2
97.2

94.5
94.9
95.4
95.7
95.7
96.1
96.6
96.9
97.1
97.2

107.1
107.0
106.9
107.0
106.9
107.0
106.8
106.5
106.5
106.5

94.6
94.9
95.0
95.3
95.6
95.9
96.1
96.3
96.5
96.8

99.1
100.8
102.0
102.2
102.0
102.0
102.0
102.1
102.1
102.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

97.1
96.9
96.7
96.5
96.4
96.5
96.9
97.4
97.7
98.0

97.1
97.0
97.0
97.0
97.2
97.5
97.8
98.2
98.2
98.1

106.3
105.8
105.2
104.6
103.9
103.2
102.5
102.0
101.7
101.3

97.1
97.2
97.4
97.4
97.3
97.4
97.4
97.5
97.6
97.7

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

98.3
98.6
98.8
99.3
99.8
99.9
99.9
100.0
100.2
100.6

98.2
98.3
98.5
98.8
99.0
99.4
99.8
100.0
100.1
100.2

100.8
100.5
100.3
100.1
100.2
100.3
100.1
100.0
100.0
99.9

1980 .......
1981 .......

100.9
100.9

100.3
100.2

99.9
99.9

Period

Table C-24. Private nonfarm business sector:
Gross real investment, 1948-81

Table C-26. Private nonfarm business sector:
Rate of depreciation, 1948-81

(Index, 1977=100)

(Percent per year)

Period

All
assets

Equipment

Structures

Period

Rental
residential
capital

All
assets

Equipment

Structures

Rental
residential
capital

1948
1949

.....................
.....................

39.1
32.4

34.5
26.1

51.3
46.8

37.8
38.7

1948
1949

.....................
.....................

4.183
4.384

11.788
12.258

5.851
5.831

2.206
2.234

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................

35.7
37.7
36.7
39.8
39.4
44.5
46.9
47.8
41.5
45.5

29.1
32.1
30.9
33.1
31.6
35.0
36.9
39.3
30.9
34.9

48.7
52.2
51.8
57.2
59.0
68.5
73.8
73.2
66.7
68.0

51.0
37.9
36.3
38.6
40.9
46.7
43.6
45.2
50.2
64.0

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................

4.453
4.498
4.573
4.639
4.732
4.764
4.798
4.845
4.939
4.930

12.381
12.530
12.732
12.805
12.974
12.999
13.107
13.166
13.451
13.484

5.800
5.766
5.752
5.726
5.705
5.655
5.609
5.582
5.587
5.578

2.251
2.282
2.310
2.335
2.359
2.377
2.401
2.427
2.448
2.459

1960 .....................
1961 .....................
1962 .....................
1963 .....................
1964 .....................
1965 .....................
1966 .....................
1967 .....................
1968 .....................
1969 .....................

48.7
48.8
53.4
56.5
62.3
71.4
77.3
74.5
79.6
86.2

37.2
35.7
39.5
42.4
48.8
56.6
65.1
63.1
67.4
73.2

74.4
75.9
79.1
78.8
85.0
101.6
106.6
103.1
106.1
112.2

63.2
74.6
91.2
109.4
107.4
101.8
86.0
78.0
98.7
115.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................

4.919
4.932
4.909
4.889
4.874
4.866
4.878
4.945
4.977
5.018

13.536
13.653
13.638
13.631
13.548
13.418
13.272
13.366
13.346
13.337

5.553
5.531
5.504
5.489
5.459
5.397
5.347
5.323
5.299
5.269

2.478
2.485
2.479
2.463
2.456
2.456
2.475
2.496
2.504
2.512

.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................

82.4
80.8
90.5
102.6
97.8
84.5
88.4
100.0
114.4
122.2

70.6
68.5
77.8
92.3
93.6
80.5
86.3
100.0
116.3
123.5

108.1
103.8
108.8
118.3
112.0
96.5
95.0
100.0
110.8
120.4

100.8
114.5
144.5
143.8
84.9
78.8
83.3
100.0
108.5
116.4

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................

5.101
5.165
5.184
5.212
5.310
5.459
5.527
5.571
5.628
5.744

13.493
13.643
13.647
13.584
13.693
14.017
14.103
14.096
14.057
14.133

5.261
5.264
5.252
5.228
5.228
5.263
5.304
5.336
5.355
5.365

2.538
2.559
2.571
2.599
2.665
2.726
2.770
2.804
2.837
2.867

1980 .....................
1981 .....................

121.7
126.2

121.4
124.4

126.6
136.6

105.6
104.2

1980 .....................
1981 .....................

5.896
6.006

14.316
14.441

5.372
5.376

2.905
2.937

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979




63

Table C-27. Manufacturing sector:
Real capital input, 1948-81
Period

All assets

Table C-28. Manufacturing sector:
Productive capital stock, 1948-81
(Index, 1977=100)

Equipment

Structures

Inventories

Land
Inventories

Land

1948 ...
1949 ...

41.0
42.4

27.9
30.3

60.0
61.8

35.9
35.4

60.8
62.2

1950
1951
1952
1953
1954
1955
1966
1957
1958
1959

.. .
...
...
...
...
...
...
...
.. .
.. .

43.3
45.9
48.5
50.2
51.1
52.3
54.6
56.6
57.3
57.8

31.9
34.0
36.3
38.4
40.4
42.2
44.2
46.5
47.8
48.1

62.7
63.7
65.0
66.1
67.1
68.7
70.7
72.6
74.3
75.2

35.6
40.8
45.8
47.4
46.7
46.6
49.7
51.4
50.2
50.4

63.0
63.9
65.0
65.9
66.8
68.2
69.9
71.5
73.0
74.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

...
...
. ..
...
...
...
...
...
...
...

58.8
59.7
60.6
62.1
63.7
66.1
69.9
74.6
78.6
81.7

48.5
49.0
49.5
50.4
52.1
55.0
59.3
64.1
68.1
71.3

76.0
77.0
78.0
79.1
80.2
81.8
84.5
87.7
90.5
93.0

52.7
53.8
55.2
57.9
60.0
62.8
67.5
74.0
79.4
83.1

74.8
75.8
76.9
78.0
79.2
80.7
83.1
85.9
88.5
90.7

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

...
...
...
...
...
...
...
...
. ..
...

84.2
85.6
86.6
88.7
92.2
95.5
97.5
100.0
103.4
107.8

74.2
76.2
78.3
81.4
86.0
90.9
95.1
100.0
105.8
113.0

95.1
96.3
97.0
97.6
98.5
99.2
99.5
100.0
100.7
102.1

85.7
86.3
86.3
88.4
93.5
97.7
98.6
100.0
103.4
107.5

92.8
94.3
95.3
96.2
97.4
98.4
99.2
100.0
101.0
102.5

1980 ...
1981 ...

113.0
118.1

122.4
132.7

103.8
105.5

110.9
112.6

104.2
106.0

All assets

Period

Index, 1977=100
1948
1949

....
.......

37.9
39.5

27.0
29.5

62.1
63.9

36.6
36.1

60.8
62.2

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

40.7
43.2
46.4
48.2
49.5
51.0
53.2
55.2
56.2
56.6

31.3
33.4
35.7
37.7
39.6
41.4
43.4
45.8
47.0
47.3

64.9
65.7
66.6
67.8
68.9
70.7
72.0
73.0
74.7
75.6

36.3
41.5
46.6
48.3
47.6
47.5
50.7
52.3
51.2
51.3

63.0
63.9
65.0
65.9
66.8
68.2
69.9
71.5
73.0
74.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

57.5
58.3
59.2
60.7
62.4
65.1
69.2
74.2
78.2
81.3

47.8
48.3
49.0
50.0
51.8
54.9
59.3
64.4
68.3
71.3

76.4
77.6
78.6
79.7
80.6
82.1
84.7
87.9
90.7
93.2

53.7
54.7
56.2
58.9
61.0
63.9
68.7
75.3
80.7
84.4

74.8
75.8
76.9
78.0
79.2
80.7
83.1
85.9
88.5
90.7

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.....
.......
.......
.......

83.9
85.2
86.4
88.6
92.2
95.5
97.4
100.0
103.8
108.8

73.9
75.5
77.3
80.4
84.9
90.0
94.6
100.0
106.0
113.4

95.2
96.4
97.0
97.6
98.5
99.2
99.5
100.0
100.7
102.1

87.1
87.6
87.5
89.6
94.3
97.6
98.6
100.0
103.4
107.5

92.8
94.3
95.3
96.2
97.4
98.4
99.2
100.0
101.0
102.5

1980
1981

.......
.......

115.1
121.1

123.6
135.3

103.8
105.5

111.2
112.9

104.2
106.0

1949

.......

4.0

9.3

3.0

-1 .4

2.4

1950
1952
1953
1954
1955
1956
1957
1958
1959

.......
.......
.......
.......
.......
.......
.......
.......
.......

3.2
7.5
3.7
2.7
3.1
4.3
3.8
1.7
0.8

6.0
7.0
5.6
5.1
4.5
4.9
5.4
2.7
0.5

14.6
1.5
1.7
1.6
2.7
1.9
1.3
2.3
1.3

0.5
12.3
3.6
-1.5
-0 .2
6.6
3.3
-2 .2
0.4

1.3
1.7
1.5
1.4
2.0
2.5
2.4
2.1
1.3

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

1.6
1.4
1.6
2.4
2.9
4.2
6.3
7.2
5.4
3.9

1.1
1.1
1.3
2.1
3.6
5.9
8.2
8.5
6.1
4.3

1.1
1.5
1.4
1.3
1.2
1.9
3.2
3.8
3.2
2.7

4.4
1.9
2.7
4.9
3.6
4.7
7.5
9.6
7.2
4.6

1.1
1.4
1.4
1.4
1.5
2.0
2.9
3.4
3.0
2.6

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......
.......
.......
.......
.......
.......
.......
.......
.......
.......

3.2
1.6
1.4
2.6
4.1
3.5
2.0
2.7
3.8
4.8

3.6
2.2
2.4
3.9
5.6
6.0
5.1
5.7
6.0
7.0

2.2
1.2
0.7
0.6
0.9
0.7
0.3
0.5
0.7
1.3

3.1
0.6
-0.1
2.4
5.2
3.5
1.0
1.5
3.4
4.0

2.3
1.6
1.1
1.0
1.2
1.1
0.8
0.8
1.0
1.5

1980
1981

.......
.......

5.8
5.2

9.0
9.4

1.7
1.7

3.4
1.6

1.7
1.7

Structures

Table C-29. Manufacturing sector:
Shares in current capital cost, 1948-81

Percent change from preceding year

(Index, 1977=100)
All assets

Equipment

Structures

Inventories

Land

1948 ...
1949 ...

Period

1.000
1.000

0.356
.340

0.350
.371

0.248
.248

0.045
.041

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

...
...
...
...
...
...
. ..
...
...
...

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.444
.388
.397
.436
.433
.369
.449
.446
.431
.448

.427
.179
.300
.356
.388
.452
.156
.298
.394
.337

.053
.433
.272
.158
.118
.082
.401
.220
.117
.168

.076
.000
.030
.050
.060
.097
-.006
.036
.057
.048

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

...
...
...
...
...
...
...
...
...
...

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.466
.488
.450
.457
.429
.400
.425
.426
.443
.526

.340
.321
.311
.269
.279
.292
.272
.268
.277
.215

.146
.151
.195
.238
.248
.254
.254
.262
.234
.236

.047
.040
.044
.036
.044
.055
.049
.045
.046
.022

...
...
...
...
...
.. .
. ..
.. .
...
.. .

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

.543
.508
.480
.522
.635
.273
.349
.406
.476
.514

.224
.219
.266
.264
.273
.345
.365
.272
.199
.215

.213
.248
.212
.169
.046
.306
.198
.260
.286
.225

.020
.024
.042
.045
.046
.076
.088
.063
.040
.045

1.000
1.000

.541
.391

.237
.294

.174
.245

.048
.070

1948-81 . ..

3.6

5.0

1.6

3.5

1.7

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

1948-73 . ..
1973-81 . ..

3.5
4.0

4.5
6.7

1.8
1.0

3.5
2.9

1.9
1.2

1980 ...
1981 . . .

Compound annual rate o f growth




Equipment

64

Table C-30. Manufacturing sector:
Ratio of capital services to productive stock, 1948-81

Table C-32. Manufacturing sector:
Price of new capital goods, 1948-81

(Index, 1977=100)

(Index, 1977=100)
Inventories

Land

29.1
28.8

41.6
39.0

29.2
28.8

32.9
36.5
37.7
38.0
38.4
39.9
44.5
46.4
48.3
48.5

29.4
35.7
37.0
37.1
36.0
32.8
39.6
41.3
40.2
39.1

44.4
45.4
44.5
45.2
45.6
47.4
49.4
50.1
50.2
49.1

29.4
35.7
37.0
37.1
36.0
32.9
39.7
41.4
40.2
39.1

44.8
44.7
44.9
45.6
46.6
47.7
49.4
51.2
52.9
56.0

49.4
49.7
50.1
50.4
51.1
52.4
53.9
55.9
57.7
59.6

38.7
38.3
38.5
39.9
41.5
42.7
44.8
47.0
48.9
53.7

49.4
49.2
49.0
48.9
49.2
49.7
50.8
51.5
52.9
55.1

38.7
38.4
38.6
40.0
41.5
42.7
44.9
47.0
49.0
53.7

...
...
...
...
...
...
...
...
...
...

59.6
62.7
65.0
69.2
80.7
90.3
93.9
100.0
107.7
120.3

62.6
65.1
66.4
68.2
74.3
87.6
93.6
100.0
105.4
114.4

58.8
64.1
67.5
73.3
86.6
94.6
94.3
100.0
111.0
126.8

57.7
59.3
61.0
66.1
81.3
89.0
93.8
100.0
107.2
121.4

58.8
64.1
67.5
73.3
86.6
94.6
94.3
100.0
111.0
126.8

1980 . . .
1981 ...

133.6
142.5

123.7
132.8

142.5
150.6

137.8
148.3

142.5
150.6

All assets

Equipment

Structures

Inventories

Land

Period

1948 ...
1949 ...

92.7
93.1

96.9
97.4

103.4
103.4

101.9
101.9

100.0
100.0

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

...
...
...
...
...
...
...
...
...
...

93.9
94.2
95.7
96.0
96.8
97.5
97.4
97.6
98.0
98.0

98.1
98.3
98.4
98.2
98.0
98.1
98.3
98.3
98.4
98.3

103.4
103.1
102.6
102.6
102.6
103.0
101.9
100.5
100.5
100.5

101.9
101.9
101.9
101.9
101.9
101.9
101.9
101.9
101.9
101.9

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

...
...
...
...
...
...
...
...
...
...

97.8
97.8
97.7
97.8
98.0
98.4
98.9
99.4
99.5
99.5

98.5
98.7
98.9
99.1
99.4
99.7
100.1
100.4
100.4
100.0

100.6
100.7
100.8
100.7
100.6
100.4
100.3
100.3
100.3
100.2

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

...
...
...
.. .
...
...
...
...
...
.. .

99.6
99.6
99.7
100.0
100.1
100.0
99.9
100.0
100.3
100.9

99.6
99.1
98.8
98.7
98.8
99.1
99.6
100.0
100.2
100.4

1980 ...
1981 ...

101.8
102.5

101.0
102.0

Period

All assets

Equipment

1948 ...
1949 . . .

32.8
32.2

30.1
31.7

100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

...
...
...
...
.. .
...
...
...
...
...

34.2
38.6
39.4
39.8
39.5
39.0
43.8
45.3
45.3
44.6

101.8
101.7
101.7
101.7
101.7
101.7
101.7
101.7
101.6
101.6

100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

...
...
...
...
...
...
...
. ..
...
...,

100.2
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0

101.5
101.5
101.5
101.4
100.8
99.8
100.0
100.0
100.0
100.0

100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0
100.0

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

100.0
100.0

100.2
100.3

100.0
100.0

Structures

Table C-33. Manufacturing sector:
Rate of depreciation, 1948-81

Table C-31. Manufacturing sector:
Gross real investment, 1948-81

(Percent per year)

(Index, 1977=100)
Structures

Period

All assets

Equipment

Structures

Period

All assets

Equipment

1948 ..........................
1949 ..........................

48.1
36.3

36.1
27.4

102.6
76.8

1949 .........................
1949 .........................

4.961
5.243

11.423
11.916

5.628
5.629

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

..........................
.........................
..........................
..........................
..........................
..........................
..........................
..........................
.........................
.........................

35.2
43.7
42.8
43.3
44.2
47.0
52.5
53.2
42.1
39.5

28.3
35.3
35.1
35.7
37.1
35.2
42.6
43.1
31.5
32.5

66.6
82.0
77.8
77.8
76.6
100.9
97.5
99.6
90.2
71.7

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................

5.374
5.268
5.250
5.328
5.469
5.570
5.535
5.596
5.788
5.830

12.149
12.149
12.295
12.411
12.494
12.651
12.610
12.666
13.041
13.201

5.639
5.608
5.611
5.623
5.639
5.593
5.598
5.599
5.634
5.687

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.........................
..........................
..........................
..........................
.........................
..........................
..........................
.........................
..........................
.........................

44.1
43.6
46.3
49.6
56.4
69.4
81.7
83.7
75.1
77.8

35.5
34.3
37.5
41.0
48.9
59.8
70.0
71.3
64.1
66.8

83.5
86.1
86.5
89.0
90.8
113.4
135.1
140.1
125.1
127.8

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................

5.794
5.822
5.810
5.778
5.765
5.747
5.723
5.736
5.800
5.794

13.299
13.459
13.505
13.527
13.411
13.188
12.975
12.978
13.160
13.099

5.711
5.748
5.788
5.823
5.856
5.842
5.802
5.777
5.796
5.810

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................

73.3
65.5
73.2
79.2
94.6
86.0
89.5
100.0
106.5
126.1

64.0
58.3
68.7
75.3
90.9
84.6
87.6
100.0
105.2
125.6

115.6
98.4
93.6
96.9
111.4
92.6
98.5
100.0
112.0
128.2

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
.........................

5.841
5.926
5.961
5.995
5.959
6.052
6.166
6.255
6.364
6.419

13.140
13.242
13.141
13.072
12.869
12.952
12.992
12.956
13.047
12.968

5.854
5.925
5.988
6.031
6.055
6.118
6.165
6.199
6.208
6.198

1980 .........................
1981 .........................

141.0
147.2

143.7
149.8

128.8
134.9

1980 .........................
1981 .........................

6.566
6.821

12.976
13.174

6.201
6.178




65

Appendix 0= [Ktouirs © All Persons
A
Methods and Sources

sources of data on employment and average weekly
hours by sector and occupation used in the bls produc­
tivity measures are summarized in table D - 1.
Two sources of monthly information are used: The
Current Employment Statistics program survey and the
Current Population Survey. The Current Employment
Statistics survey collects data for the employees of all
nonagricultural establishments; hence it is often called
the “ establishment survey.” The Current Population
Survey obtains its information through household inter­
views and is called the “ household survey.”
Information collected in the establishment survey is
regularly published in the B and C tables of Employ-

The traditional bls measures of output per hour of all
persons and the new multifactor productivity measures
of output per unit of combined labor and capital input
use the same measures of labor input, except that the
new productivity series excludes hours in government
enterprises. Hours of labor represent about two-thirds of
the combined labor and capital inputs in the new
multifactor measures, and are the only input counted in
the traditional productivity series. Using information
gathered in monthly surveys, the Bureau of Labor Sta­
tistics aggregates measures of employment and average
weekly hours at the 2-digit sic level to major sector di­
visions for use in these two productivity series. The

T a b le D-1. Sources o f em ploym ent and hours data used in labor input measures fo r BLS p ro d u c tiv ity series, private

business sector

Employment
Sector
and
occupation

Average weekly hours
Directly collected

Percent of
private
business
hours
(1982)

Estab­
lishment
survey

House­
hold
survey

Estab­
lishment
survey

House­
hold
survey

T o ta l..............................................................

100

N o n m a n u f a c t u r i n g ............................................................

69

Employees:
All employees ..........................................
Production workers .................................
Nonproduction workers .........................

58
NA
NA

Self-employed:
Proprietors and partners .......................
Unpaid family workers ...........................

11
1

M a n u f a c t u r in g ......................................................................

27

Employees:
All employees ..........................................
Production workers .................................
Nonproduction workers .........................

26
18
9

Self-employed:
Proprietors and partners ........................

1

X

X

4
3

X

X

2
(1)

X
X

X
X

Not directly collected

............................................................
Farmers and farm managers ........................
Farm laborers and supervisors:
Paid workers ............................................
Unpaid family workers ...........................

A g r ic u lt u r e

X
X

X
Assumed to be equal to average
weekly hours for production
workers
X
X

X
X

X
Estimates based on data from the
bls survey of employer expenditures for employee compensation, and production-worker average weekly hours.

NA = not available.
1Less than 0.5 percent.
No t e : Detail may not add to totals due to rounding.




X
X

66

total hours in the private business sector. Data are col­
lected for production workers in mining, construction
workers in construction, and for nonsupervisory work­
ers in transportation and public utilities, wholesale and
retail trade, finance, insurance, and real estate, and
business and personal services. Since employment is
collected for all employees and for nonsupervisory
workers, supervisors’ employment can be computed by
subtraction. Average weekly hours are collected for
nonsupervisory workers only. For the purposes of pro­
ductivity measurement, the average weekly hours of su­
pervisory workers are assumed to be equal to those of
nonsupervisory employees in the industry.
Self-employed and unpaid family workers in nonman­
ufacturing occupations contribute an additional 11 per­
cent of private business hours. Information on the em­
ployment and average weekly hours for these workers is
collected directly in the household survey.

merit and Earnings. Measures of employment and aver­
age weekly hours are collected for persons on the
payrolls of approximately 180,000 establishments dur­
ing the pay period which includes the 12th of the
month. Since the hours are payroll hours, the measure
includes paid leave time in addition to time spent at the
work site. Persons who appear on the records of more
than one establishment during the survey week are
counted more than once, whether this results from mul­
tiple jobholding or job changes.
Since several categories of workers are outside the
scope of the establishment survey, additional informa­
tion is obtained from the household survey. These in­
clude self-employed individuals, farmers and farm
workers, employees of private households, and unpaid
family workers. Measures based on this survey are pub­
lished in the A tables of Employment and Earnings.
Monthly interviews are conducted in about 60,000
households to gather information on the labor force sta­
tus and hours at work for the noninstitutional civilian
population during the week including the 12th of the
month. In this survey, multiple jobholders are counted
only once, and all of their hours are assigned to the in­
dustry at which they worked most during the survey pe­
riod. Only hours at work are counted; if a paid holiday
occurs during the survey week, only 32 hours are re­
ported even if 40 hours’ pay is received.
For practical purposes, the hours data used in the bls
productivity measures are hours paid rather than hours
at work. This is so because about 85 percent of total pri­
vate business hours are taken from the establishment
survey, which collects information on hours paid; only
15 percent comes from the household survey, which
collects data on hours at work (table D -l).
In general, hours of all persons are computed by mul­
tiplying employment by average weekly hours at the
2-digit sic level each month. These weekly values are
converted to annual rates by multiplying them by 52.
Seasonal factors are computed using a time span and
method which correspond to the procedure for seasonal­
ly adjusting output used by the Bureau of Economic
Analysis of the U.S. Department of Commerce. This
avoids influencing productivity measures through the
use of different seasonal adjustments to the numerator
and denominator of the productivity ratios.
The seasonally adjusted results are summed to totals
for private business, private nonfarm business, and
manufacturing; quarterly averages are computed from
three monthly levels. Annual averages are computed
based on 12 months of data. Year-to-year changes are
computed by comparing annual averages, rather than
December to December movements.

M anufacturing
The hours of all persons engaged in the manufactur­
ing sector account for about 27 percent of private busi­
ness hours. Employment data are collected for produc­
tion and related w orkers, and for all em ployees.
Average weekly hours are collected only for production
workers; average weekly hours of nonproduction work­
ers are estimated based on information compiled in the
bls survey of employer expenditures for employee com­
pensation and from production-worker average weekly
hours.
The self-employed in manufacturing make up a very
small proportion of the sector. Information on their em­
ployment and average weekly hours is obtained directly
from the household survey.
Farm
Information on labor inputs in the farm sector comes
from the household survey. Data are collected for farm­
ers and farm managers, unpaid family workers, and paid
farm workers. The number of farm proprietors is as­
sumed to be equal to the number of farmers and farm
managers reported in the labor force data; average
weekly hours for self-employed persons in the labor
force “ agriculture” sector, which includes agriculture
services as well as farm, are used to compute hours for
farm proprietors. The number of 14- and 15-year-old
unpaid family workers on farms is assumed equal to the
number of unpaid family workers in this age group in
“ agriculture” ; average weekly hours at work for agri­
cultural unpaid family workers age 16 and over are used
to compute hours of all unpaid family workers.
Employees on farms are represented in the household
data as “ paid workers.” Employment levels of workers
over 16 are available directly; those of 14- and 15-yearolds are estimated by subtracting 14- and 15-year-old
unpaid family workers on farms (estimated as described

Nonmanufacturing
Employees of establishments not engaged in manu­
facturing or agriculture account for about 58 percent of



67

Nonprofit institutions

above) from all farm workers in this age group; average
weekly hours for wage and salary workers at work in
agriculture age 16 and over are used to compute hours
for all employees on farms.

In order to bring employment data drawn from the es­
tablishment survey into conformity with the business
sector concepts, employees of firms owned by nonprofit
institutions are removed. Using b e a compensation data,
factors are obtained by 2-digit sic, representing the frac­
tion of employment associated with nonprofit institu­
tions. Hours of employees in nonprofit institutions are
computed by dividing compensation expenditures of
nonprofit firms by hourly industry compensation; these
hours estimates are then divided by the average weekly
hours appropriate to each industry to obtain employment
in nonprofit institutions. The ratio of nonprofit employ­
ment to employment for the industry as a whole is the
factor used to obtain monthly estimates of employment
for nonprofit institutions from total industry employ­
ment in the monthly establishment survey. The latest
available factor is used until new b e a annual data are
available.

Government enterprises
Hours for government enterprises are measured by
first establishing quarterly employee totals for Federal,
State, and local government enterprises and then ap­
plying these employment levels to average weekly hours
of all government workers, available from the house­
hold survey. The quarterly employee levels are obtained
by extrapolating annual b e a measures of government
enterprise employment using Post Office and State and
local government noneducational employment from the
establishment survey as indicators for Federal and State
and local enterprises. Average weekly hours for govern­
ment workers, from the household survey, are used for
governm ent enterprises. The governm ent class-ofworker category includes all civilian employees.




68

Appendix E„ Com parison of Base-year-weighted
and Tornquist D
enoted IMymlbors
of Multifaotor Productivity

The measures of multifactor productivity introduced
in this bulletin are computed using a Tornquist index
aggregation procedure. Since this is the first time bls
has used this index number formula, a comparison was
made of the results of this method and the more com­
monly used method of base-year weighting. This appen­
dix presents the findings of this comparison .
As shown in appendix A, the index of aggregate in­
puts (labor and capital) is constructed from a weighted
average of the growth rates of the separate inputs. The
weights are an average of the relative cost shares of the
input for the given and previous years. For a base-yearweighted index, the cost shares are held constant over
the period of time. For this comparison, both an index
using one set of weights for the complete series and an
index using different weights for subperiods (hereafter
referred to as a shifted base-year-weighted index) were
constructed. For the constant-base-year-weight series,
the 1972 cost shares were used, as this is the base year
for the output index (gnp). A s with the Tornquist index,
the indexes of inputs for the base-year weighting meth­
od were calculated for the most disaggregated level pos­
sible. The detailed assets were aggregated to the corre­
sponding sector level, and these sectors were then
aggregated to conform to the final indexes. Hence, a
single asset (commercial buildings, for example) within
different sectors has different weights.
Annual percent changes
Tables E - l through E -3 show the annual percent
changes of multifactor productivity for the three pub­
lished sectors (private business, private nonfarm busi­
ness, and m anufacturing) as calculated using the
Tornquist index method, shifted base-year weights, and
the same (1972) base-year weights for the complete
series. Also shown are the differences in the percent
changes for each method.
Tornquist vs. shifted base-year index. With the excep­
tion of a few years (1952 and 1965), there is little dif­
ference between the annual percent changes calculated
using the Tornquist method and the shifted base-year in­
dex for the private business and private nonfarm busi­



ness sectors. For the manufacturing sector, there are
more years where the differences are large, and the
magnitudes are also greater than for the other sectors.
For all three sectors, the differences were virtually all
negative prior to 1958, and almost all were positive and
smaller after 1958. This indicates that, prior to 1958,
multifactor productivity grew faster based on the shifted
base-year-w eighted index, than on the Tornquist
method.
Tornquist vs. base-year index. The differences in the
annual percent changes between the Tornquist index and
the 1972 base-year-weighted indexes follow somewhat
different patterns from the com parisons discussed
above. The differences are greater in value for the pri­
vate business and nonfarm business sectors, but not as
large as for the manufacturing sector.
Average annual rates of growth
Table E -4 presents the average annual growth rates
for the com plete series, 1948-81, and the two
subperiods 1948-73 and 1973-81. For the whole peri­
od, there is a significant difference in results of the dif­
ferent methods for each of the three sectors. The aver­
age annual growth rate based on the Tornquist index is
1.5 percent for private business, 1.3 percent for private
nonfarm business, and 1.8 percent for manufacturing.
Using shifted base-year weights, the annual growth
rates for the sectors are 1.7 percent, 1.5 percent, and
2.0 percent, respectively. And, using 1972 base-year
weights, the annual growth rates are 1.3 percent for pri­
vate business, 1.0 percent for private nonfarm business,
and 1.6 percent for manufacturing. In all sectors, the
annual rate of growth based on the Tornquist index lies
between the shifted base-year index and the 1972 baseyear index.
The average annual growth rates for the two sub­
periods are less affected than those for the total period
by the use of the different index number formulas. For
1973-81, the difference in growth rates is at most 0.1
percent. For the earlier period, differences are still pres­
ent between the Tornquist method and the 1972 baseyear-weighted method, but there is little difference be69

tween the Tornquist and shifted base-year method.
Thus, the measured productivity slowdown after 1973 is

not significantly changed by using shifted base-year
weights rather than the Tornquist method.

1The following base-year weights were used for the subperiods:
1948 weights for 1948-59; 1959 weights, 1959-69; 1969 weights,
1969-73; and 1973 weights, 1973-81.




70

Table E -2 .

Private nonfarm business sector: Annual percent change in m ultifactor productivity under different index

number methods, 1949-81

Shifted
base-year
weights1
(2)

Year
Tornquist
(1)

Difference,
(1)-(2)
(3)

1972 base
year
(4)

Difference,
(1)-(4)
(5)

1949 ........................................................................................

- 0 .6

-0 .3

- 0 .3

-1 .2

0.6

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................

6.2
2.0
1.2
1.5
- 0 .6
4.4
-0.1
0.4

6.5
2.2
1.7
1.8
-0 .3
4.7
0.1
0.7
0.3
4.5

- 0 .3
- 0 .2
- 0 .5
- 0 .3
- 0 .3
- 0 .3
- 0 .2
- 0 .3
-0 .3
-0 .2

5.7
1.4
1.1
1.2
- 1 .0
4.0
- 0 .6
0.0
- 0 .2
4.0

0.5
0.6
0.1
0.3
0.4
0.4
0.5
0.4
0.2
0.3

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
.......................................................................................
.......................................................................................

0.1
1.7
3.5
2.5
3.5
2.9
1.7

0.0

0.1
0.0

2.4
-0 .8

1.7
3.4
2.4
3.3
2.5
1.5
0.1
2.3
- 1 .0

-0 .3
1.2
3.1
2.3
3.1
2.4
1.3
-0 .1
2.2
-1 .1

0.4
0.5
0.4
0.2
0.4
0.5
0.4
0.1
0.2
0.3

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

.......................................................................................
........................................................................................
........................................................................................
.......................................................................................
.......................................................................................
.......................................................................................
........................................................................................
........................................................................................
.......................................................................................
........................................................................................

-1 .6
2.0
3.5
2.3
- 3 .9
- 0 .5
3.8
2.9
1.1
-1 .5

- 1 .7
1.9
3.5
2.3
-3 .9
- 0 .6
3.7
2.8
1.1
- 1 .4

0.2
0.1

-0 .1

- 1 .8
1.9
3.5
2.3
-4 .0
-0 .6
3.2
2.7
1.0
-1 .5

1980 ........................................................................................
1981 ........................................................................................

-2 .3
0.7

-2 .3
0.7

0.0
0.0

- 2 .3
0.7

0.0

0.0

4.3

0.0

1The following base-year weights were used for the subperiods:
1948 weights for 1948-59; 1959 weights, 1959-69; 1969 weights,
1969-73; and 1973 weights, 1973-81.




71

0.1
0.1
0.2
0.4
0.2
-0 .1
0.1
0.2
0.1
0.1
0.1
0.0
0.0

0.1
0.1
0.1
0.0

0.0
0.0

0.1
0.1
0.1
0.2
0.1
0.0

0.0

Table E-3.

Manufacturing sector: Annual percent change in m ultifactor productivity under different index number meth­
ods, 1949-81

Shifted
base-year
weights1
(2)

Year
Tornquist
(1)

Difference,
(1)-(2)
(3)

1972 base
year
(4)

Difference,
(1 )- (4)
(5)

1949

........................................................................................

- 0 .4

0.4

- 0 .8

- 0 .7

0.3

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................

7.1
3.9
-0.1
2.1
-2 .0
5.8
- 1 .6
0.4
- 3 .4
6.6

7.2
4.3
0.9
2.3
- 1 .5
6.1
- 1 .2
0.8
-3 .1
6.5

-0 .1
- 0 .4
- 1 .0
-0 .2
-0 .5
0.3
- 0 .4
- 0 .4
- 0 .3
0.1

6.7
3.6
0.2
1.8
-2 .2
5.6
-1 .8
0.2
- 3 .6
6.5

0.4
0.3
-0 .3
0.3
0.2
0.2
0.2
0.2
0.1
0.1

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970

........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
.................................................................................... ..
........................................................................................
........................................................................................
........................................................................................

0.1
1.5
5.1
6.7
4.6
3.7
1.2
-2 .3
2.4
1.0
-2 .7

0.0
1.5
5.0
6.7
4.5
3.4
0.9
-2 .1
2.4
0.9
-2 .8

0.1
0.0
0.1
0.0
0.1
0.3
0.3
-0 .2
0.0
0.1
0.1

0.0
1.4
5.0
6.7
4.5
3.5
1.0
-2 .3
2.3
0.9
-3 .0

0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.0
0.1
0.1
0.3

1971
1972
1973
1974
1975
1976
1977
1978
1979

........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................
........................................................................................

4.5
6.0
6.3
-3 .9
-0 .9
5.3
3.0
1.0
-0 .1

4.5
5.9
6.2
-4 .0
-1.1
5.2
2.9
1.1
0.0

0.0
0.1
0.1
0.1
0.2
0.1
0.1
-0 .1
-0 .1

4.3
5.9
6.3
-4 .1
-1 .5
5.2
.2.9
1.1
0.0

0.2
0.1
0.0
0.2
0.6
0.1
0.1
-0 .1
-0.1

1980
1981

.......................................................................................
.......................................................................................

- 2 .4
1.4

-2 .5
1.4

0.1
0.0

- 2 .6
1.3

0.2
0.1

1The following base-year weights were used for the subperiods:
1948 weights for 1948-59; 1959 weights, 1959-69; 1969 weights,
1969-73; and 1973 weights, 1973-81.




Table E-4. Rates o f grow th o f m u ltifa c to r p ro d u c tiv ity un­
d e r d iffe r e n t in d e x n u m b e r m e th o d s by m a jo r s e c to r,
1948-81
(Percent per year, compounded)
Sector and method

1948-81

1948-73

1973-81

Private business:
Tornquist............................................
Shifted base-year weights .............
1972 base-year weights ................

1.5
1.7
1.3

2.0
2.0
1.7

0.1
0.2
0.1

Private nonfarm business:
Tornquist............................................
Shifted base-year weights .............
1972 base-year weights ................

1.3
1.5
1.0

1.7
1.8
1.4

0.0
0.0
0.0

Manufacturing:
Tornquist............................................
Shifted base-year weights .............
1972 base-year weights ................

1.8
2.0
1.6

2.2
2.3
2.1

0.4
0.3
0.3

72

Appendix F„ C©mparss©iii
©f iiyltifaet© r Measures

Table F-1. Computation of output measures by BLS, Denison,
Jorgenson, and Kendrick

This appendix compares the b l s m easures of
m ultifactor productivity with those calculated by
Edward Denison, Dale Jorgenson, and John Kendrick.
These authors have been making estimates of productiv­
ity growth for many years and each has contributed sig­
nificantly to the understanding of productivity measure­
ment. The comparisons are drawn from the authors’
latest published studies.1
The comparisons made within each of the following
sections are subject to qualification: First, only the ma­
jor differences in methodology and classification are
discussed; second, the authors’ latest published work
may not incorporate the latest data revisions because of
publication lags.
The comparisons are made on the basis of each of the
separate factors used in the measurement of productiv­
ity—output, capital input, and labor input. Also in­
cluded are the method of aggregation and the allocation
of shares for the input factors. While not all aspects of
productivity measurement fit precisely into these cate­
gories, they capture the major issues.

Measure
GNP ...............................................
Less:
Statistical discrepancy................
Owner-occupied housing ...........
Tenant-occupied housing...........
Rest of the world ........................
General government ..................
Government enterprises.............
Nonprofit institutions ..................
Household sector........................
Capital consumption
allowances...............................
Business transfer
payments.................................
Indirect business ta xe s...............
Federal indirect business
taxes ...................................
State and local indirect
business taxes ..................
Plus:
Services of consumer durables ..
Services of durables held by
institutions...............................
Net rent on institutional real
e sta te ......................................
Capital stock ta x .........................
Business motor vehicle
taxes........................................
Other business taxes ................
Subsidies less surplus of
government enterprises
(Federal, State, and
local)........................................

Output
The various authors include different factors in their
output measures. These are explained below and com­
pared in table F - 1.
The b l s measure of output for multifactor productivi­
ty encom passes the private business sector of the
economy. This definition represents the privately
owned, profit-oriented enterprises in the economy. The
measure for this sector is derived from the gross nation­
al product ( g n p ) measure. Specifically, private business
output is equal to g n p less:
-

X

X

X
X

X
X
X
X
X

X
X
X
X
X

X

Kendrick

X

X
X
X
X
X

X
X

X
X
X
X
X

X
X
X
X
X
X
X
X
X
X
X

X

X

This output measure was 76 percent of g n p in 1972.
(The Bureau of Economic Analysis used 1972 as its
constant-dollar base year for output measurement.)
Denison measures output for the nonresidential busi­
ness sector. While the coverage is similar to the b l s
measures, Denison starts from national income ( n i ) i n ­
stead of GNP.

s ta tis tic a l d iscrep a n cy
o w n e r-o c c u p ie d h o u s in g
rest o f the w o rld
general g o v e rn m e n t
g o v e rn m e n t enterprises
n o n p ro fit in s titu tio n s
h o u seh o ld sector.

counting for Capital,” both in George von Furstenberg, ed., Capi­
tal, Efficiency and Growth (Cambridge, Mass., Ballinger Pub­
lishing Co., 1980); and John Kendrick and Elliot S. Grossman,
Productivity in the United States (Baltimore, The Johns Hopkins
University Press, 1980). Kendrick’s and Grossman’s data are up­
dated quarterly in Multiple Input Productivity Indexes (Houston,
The American Productivity Center).

’Edward F. Denison, Accounting for Slower Economic Growth:
the United States in the 1970’s (Washington, The Brookings Insti­
tution, 1979), and “ Accounting for Slower Economic Growth: An
Update,” paper presented at the Conference on International Com­
parisons of Productivity and Causes of the Slowdown held by the
American Enterprise Institute, Washington, Sept. 30, 1982; Bar­
bara M. Fraumeni and Dale F. Jorgenson, “ The Role of Capital in
U.S. Economic Growth, 1948-1976,” and Dale Jorgenson, “ Ac­



BLS Denison Jorgenson

73

is equal to

ni

-

gnp

less:

statistical discrepancy
capital consumption allowances
business transfer payments
indirect business taxes.

Nonresidential business output is equal to
-

For 1972, Kendrick’s measure was 84 percent of g n p in
current dollars. Table F-2 lists the indexes and long­
term growth rates for each of the output measures de­
scribed above.
The measures are also depicted in chart F - l. As is
evident from the chart, there is little difference over the
postwar period in any of the output measures. Denison’s
measure is the lowest; however, all the growth rates are
about the same. For most of the period, Jorgenson’s
measure is the highest, but his growth rates differ from
Denison’s by only 0.2 percent over the 1948-73 period.

ni

less:

owner-occupied housing
rest of the world
general government
nonprofit institutions
household sector
tenant-occupied housing.

This measure of output was 76 percent of ni and 62 per­
cent of gnp in 1972. The major differences between the
b l s and Denison measures of output are that he includes
government enterprises and excludes capital consump­
tion allowances (depreciation), business taxes and trans­
fers, and tenant-occupied housing.
Jorgenson’s measure of output encompasses the sec­
tor labeled gross private domestic product. In general,
this measure covers all private concerns including
households and nonprofit institutions. In order to calcu­
late output for this sector, services from the capital
stock of households and nonprofit institutions are esti­
mated. The income generated by these services is then
estim ated and added to the basic output measure.
Hence, Jorgenson’s measure of output is larger than any
of the others. For 1972, his output measure was over 92
percent of gnp . It is calculated by subtracting from gnp :
-

Table F-2. Indexes and rates of growth of output for the most
aggregate sector measured by BLS, Denison, Jorgenson, and
Kendrick, 1948-81
Period

Kendrick

44.4
43.0

39.3
39.6

43.2
42.3

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

45.9
48.6
50.3
52.5
51.5
55.7
57.2
57.8
56.8
61.0

47.2
50.1
51.7
54.0
52.5
57.0
58.3
58.7
57.3
61.9

43.5
46.5
48.1
50.4
49.9
53.7
54.9
55.8
55.9
59.2

46.3
49.0
50.6
52.7
51.7
55.9
57.3
57.9
57.0
60.1

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

61.9
63.0
66.5
69.4
73.6
78.6
82.9
84.8
89.2
91.7

62.7
63.6
67.3
70.4
74.8
80.2
84.8
86.2
90.5
92.8

60.4
61.9
65.5
68.1
71.9
76.5
81.3
83.5
87.5
90.5

62.2
63.2
66.7
69.6
73.8
78.8
83.1
84.9
89.2
91.9

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

91.0
93.7
100.0
106.6
104.4
102.3
108.9
116.2
122.6
125.3

91.1
93.7
100.0
107.0
103.8
100.6
107.5
115.1
121.7
124.1

90.5
94.1
100.0
106.4
105.4
104.7
111.0
117.7
123.7
127.1

91.1
93.9
100.0
106.7
104.6
102.7
109.2
116.0
121.5
124.9

1980 ........................
1981 ........................

services of consumer durables
services of durables held by institutions
net rent on institutional real estate
capital stock tax
business motor vehicle licenses
business property taxes
other business taxes.

42.8
42.0

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

rest of the world
general government
Federal indirect business taxes
State and local business taxes;

123.4
126.5

120.8
123.8

126.4
129.3

124.1
126.5

Rate of growth
(annual percent change)
1948-73 ..................
1973-81 ..................

3.7
2.2

3.6
1.8

4.1
2.5

3.7
2.2

1948-81 ..................

statistical discrepancy
owner-occupied housing
rest of the world
general government
government enterprises
nonprofit institutions
household sector.




Jorgenson

1948 ........................
1949 ........................

Kendrick’s measure of output is derived directly from
the industry measures of output computed from the 14
component gross product originating (gpo) measures.
Theoretically, the gpo measures by industry should be
equal to the published gnp . In practice, however the
gpo measure falls short of the gnp by a slight but signif­
icant amount.
This measure is approximately equal to the gnp less
the same factors which b l s subtracts:
-

Denison

Index, 1972=100

and adding:
-

BLS

3.3

3.2

3.7

3.3

Sources: Bureau of Labor Statistics; Edward F. Denison, Accounting for
Slower Economic Growth: The United States in the 1970's (Washington, The
Brookings Institution, 1979); Dale F. Jorgenson, Harvard University,
Cambridge, Mass.; John F. Kendrick, in Multiple Input Productivity Indexes,
Vol. 3, No.1, September 1982 (Houston, The American Productivity Center).

74

Chart F-1. Output for the most aggregate sector measured by B IS , Denison, Jorgenson,
and Kendrick, 1948=01
(Index. 1948= 100)

Chart F-2. Labor input for the most aggregate sector measured by BLS, Denison,
Jorgenson, and Kendrick, 1948=81
(Index. 194 8= 100)




75

Labor input

Table F-3. Indexes and rates of growth of labor input for the
most aggregate sector measured by BLS, Denison, Jorgenson,
and Kendrick, 1948-81

A detailed explanation of b l s ’ s measure of labor in­
put is provided in appendix D. Labor input is a measure
of hours paid derived from the b l s Current Employment
Statistics program (establishment survey) supplemented
with data from the Current Population Survey ( c p s ) . Es­
timates are made for nonproduction and supervisory
workers’ average weekly hours. The hours are measured
to correspond to the output coverage indicated above for
b l s . The only difference between the labor input meas­
ure for the multifactor productivity and output per hour
measures is the exclusion of hours for the government
enterprise sector from the multifactor measures. Table
F-3 shows the indexes and growth rates of labor input
as calculated by b l s , Denison, Jorgenson, and
Kendrick.
Denison computes the level of employment based on
both the c p s estimates and changes from establishment
surveys. This is done to develop a measure based on
persons rather than jobs, unlike the b l s measure of la­
bor input. Employment is then multiplied by average
hours adjusted to an hours-worked rather than an hourspaid concept. Denison further adjusts the labor input
measure for changes in the age, sex, and educational
composition of the work force. Adjustments are also
made for changes in the mix of part-time and full-time
employment. The changes in age, sex, and education
cause this measure of labor input to grow significantly
faster than the b l s measure.
Jorgenson measures labor input starting with the b e a
measures of hours worked, at the 2-digit sic level.
These measures are developed from b l s establishment
surveys, household surveys, and other studies for ad­
justment to an hours-worked measure. For each 2-digit
industry, Jorgenson estimates the proportion of hours
worked disaggregated by age, sex, education, occupa­
tion, and class of worker (self-employed versus employ­
ee). The proportions are estimated from the decennial
census and c p s published data using a multiproportional
assumption for all categories of hours. Changes in the
levels of each category over time are weighted by the
estimated relative compensation to compute a weighted
growth rate of labor input. While the procedure and de­
tail of categories are different from Denison’s approach,
as can be seen in table F-4, the results are quite similar
at the aggregate level.
Kendrick uses the same measure of labor input as
b l s . Chart F-2 clearly shows the distinction between
the various input measures. Denison’s and Jorgenson’s
have much higher levels and much higher rates of
growth due to the adjustment for composition of the la­
bor force. Most of the growth in the adjustment for
composition is the result of the increase in educational

Period

Denison

Jorgenson

Kendrick

Index, 1972=100
1948 ........................
1949 ........................

87.3
84.3

76.7
74.0

70.3
67.7

88.6
83.8

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

85.3
87.8
87.7
88.7
85.7
87.0
90.3
89.0
84.8
88.2

76.2
79.9
81.6
83.2
80.6
83.2
84.3
83.8
80.8
83.8

70.3
73.5
74.2
75.5
73.0
75.6
77.2
76.6
74.5
77.6

84.8
87.3
87.4
88.2
85.3
88.5
89.9
88.5
84.6
87.0

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

88.3
86.8
88.2
88.7
90.2
90.3
95.2
95.1
96.7
99.3

84.0
83.6
85.2
85.9
87.6
90.4
93.1
94.2
96.2
98.5

78.7
78.3
80.5
81.8
83.5
86.7
90.1
91.2
93.5
96.8

88.1
86.7
88.1
88.7
90.1
92.9
95.2
95.1
96.7
99.3

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

97.6
97.0
100.0
104.0
104.3
99.9
103.0
107.3
112.6
116.2

97.4
97.3
100.0
104.5
105.4
102.6
105.6
109.6
115.0
119.3

95.8
96 3
100.0
105.1
105.8
102.7
106.7
111.9
118.4
123.7

97.6
97 1
100.0
103.9
104.3
100.1
102.9
107.1
112.3
116.1

1980 ........................
1981 ........................

115.3
116.1

119.2
120.8

124.8
127.5

115.3
116.2

Rate of growth
(annual percent change)
1948-73 ..................
1973-81 ..................

0.7
1.4

1.2
1.8

1.6
2.4

0.6
1.4

1948-81 ..................

0.9

1.4

1.8

0.8

Sources: See table F-2.

attainment.2 The Kendrick and
gether at the lower level.

bls

measures move to­

Capital input
Appendix C provides a detailed explanation of the
method used for capital measurement by b l s . The meth­
ods of the other authors are also discussed at some
length in that appendix. Briefly, b l s has constructed a
measure of the annual net stock of capital for each ma­
jor sector (farm, manufacturing, nonfarm-nonmanufac­
turing) from data on equipment and structures, using a

2See Denison, Accounting for Slower Economic Growth, pp. 160-169.



BLS

76

Table F-4. Computation of labor input measures by BLS,
Denison, Jorgenson, and Kendrick
Measure

BLS

Denison

Jorgenson

Table F-5. Indexes and rates of growth of capital input for the
most aggregate sector measured by BLS, Denison, Jorgenson,
and Kendrick, 1948-81

Kendrick
Period

Hours paid...........................
Hours w orked......................

X

X
X

Jorgenson

Kendrick

Index, 1972=100
1948 ........................
1949 ........................

X
X
X

X

35.8
38.3

48.5
49.3

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

47.0
49.0
51.1
52.6
54.1
55.8
57.8
59.6
60.9
62.0

44.8
47.5
49.8
51.3
52.5
54.1
56.2
57.9
59.1
60.5

40.0
42.9
95.4
47.1
49.1
50.8
53.7
56.1
58.2
59.2

50.9
52.7
54.0
55.2
56.3
58.4
60.1
61.8
63.0
64.8

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

63.5
64.9
66.4
68.3
70.6
73.7
77.5
81.6
85.4
89.3

62.1
63.7
65.4
67.6
70.0
73.1
77.2
81.5
85.3
89.4

61.3
63.1
64.6
66.8
69.5
72.6
76.7
81.2
85.0
89.0

66.5
68.5
70.1
72.2
74.8
77.8
81.1
84.3
87.5
91.0

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

93.2
96.5
100.0
104.6
109.3
112.3
114.4
117.4
121.6
126.2

93.1
96.4
100.0
104.7
109.8
113.0
115.6
119.4
124.5
129.8

93.2
96.3
100.0
105.3
111.5
115.5
117.6
121.3
126.6
132.7

93.8
96.7
100.0
104.3
107.8
110.2
113.3
117.1
121.0
125.5

1980 ........................
1981 ........................

X

42.1
43.4

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

X

43.6
45.3

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

X
X
X
X
X

variable decay function. Assets are aggregated using a
weighted average of the growth rates of the separate as­
sets. The weights are equal to the relative service
prices, or user prices, of the different assets. The esti­
mates for each of the sectors are aggregated to the pub­
lished measures. Included in the capital input measure
are estimates for the quantities of land and inventories,
which are also weighted by their respective user prices.
The annual flows of services of capital are assumed pro­
portional to the annual stocks of capital; this assumption
is used by the other authors as well.
Denison constructs his estimates of capital input di­
rectly from the b e a estimates of net and gross capital
stock, b e a net capital stock is based on straight-line de­
preciation; gross capital includes no depreciation or de­
cay. Both measures are based on asset prices rather than
rental prices. Denison combines the two measures of
stocks, weighting gross by 0.75 and net by 0.25.
Jorgenson’s construction of capital input begins with
estimates of investment for equipment and structures,
land, and inventories all classified by 46 industry group­
ings and 4 different legal forms of organization. As de­
scribed in appendix D, b l s has generally followed
Jorgenson’s method of capital measurement. The major
difference is in the decay function: Jorgenson uses a
constant decay rate and b l s uses a variable decay rate.
Another major difference is that b l s focuses on asset
detail of capital and Jorgenson concentrates on industry
detail.
Kendrick uses the gross capital stocks of equipment
and structures estimated by b e a for their wealth ac­
counts. He adds measures of land and inventories, as do
the other researchers. Table F-5 displays the different
measures of capital input. Chart F-3 also shows how
the capital measures differ. The Jorgenson measure is
the highest and also has the fastest rate of growth.
Kendrick’s measure, on the other hand, is the lowest.
The Denison and b l s measures move similarly. Table
F-6 summarizes the procedures of the various research­
ers in computing their capital input measures.



Denison

X

Plus adjustments for:
A g e ...................................
S e x ...................................
Education..........................
Occupation ......................
Industry ...........................
Employee versus selfemployed......................
Full- versus part-time
workers ........................

BLS

130.7
134.4

134.1
138.3

138.3
141.6

129.4
133.0

Rate of growth
(annual percent change)
1948-73 ..................
1973-81 ..................

3.6
3.2

3.7
3.5

4.4
3.8

3.1
3.1

1948-81 ..................

3.5

3.7

4.3

3.1

Sources: See table F-2.

Table F-6. Computation of capital input measures by BLS,
Denison, Jorgenson, and Kendrick

Characteristic

Weights:
Asset prices.........
Rental prices.......
Aggregation
of assets:
Fixed weighted ...
Variable
weighted...........

77

BLS
(hyperbolic
decay
function)

Denison
(3 parts
gross;
1 part net)

Jorgenson
(geometric)

X

X
X

X

X

X
X

Kendrick
(gross)

X

Chart F-3. Capita! Input for the most aggregate sector measured by BLS, Denison,
Jorgenson, and Kendrick, 1948=81
(Index, 1948= 100)

400

350

300

250

200

150

100

50

Chart F-4. Muitif actor productivity for the most aggregate sector measured by BLS,
Denison, Jorgenson, and Kendrick, 1948=81
(Index, 1948 = 100)




78

Aggregation

Table F-7. Labor’s share for the most aggregate sector meas­
ured by BLS, Denison, Jorgenson, and Kendrick, 1948-81

The b l s procedure for aggregating the inputs (labor
and capital) to form a combined input is a variable
weighted index method, called a Tornquist index. It is
formed by taking a weighted average of the growth rates
of the individual inputs. The weights are averages of the
given year’s and previous year’s relative cost share for
each of the inputs. Labor’s share is total labor compen­
sation divided by current-dollar output; capital’s share is
property income divided by current-dollar output, or 1
minus labor’s share.
The above procedure is also the one used by Denison
and Jorgenson. Kendrick, on the other hand, computes a
weighted average of the indexes of the various inputs,
not the growth rate. Furthermore, he holds the weights
(the cost shares) constant for different periods: 1948
shares are used for the period 1948-59; 1959 shares for
the period 1959-69; 1969 shares for 1969-73; and 1973
shares for the period 1973 and after. This method is
much more restrictive than the method used by b l s and
the others in that it assumes that the relationship be­
tween output and the different inputs remains constant
with respect to relative changes in the input prices. That
is, increases in the price of one input would not cause a
change in the usage of that input.

(Percent)
Year




62.2
64.2

78.3
78.2

61.9
61.7

63.9
63.9

1950...............................
1951...............................
1952...............................
1953...............................
1954...............................
1955...............................
1956...............................
1957...............................
1958 ...............................
1959...............................

61.3
61.8
64.8
66.4
66.1
63.3
63.9
64.6
64.6
63.5

78.1
78.6
79.4
79.8
80.3
80.9
81.2
81.3
81.7
82.0

60.0
59.3
60.1
61.6
59.9
59.4
60.9
61.4
59.5
59.9

63.9
63.9
63.9
63.9
63.9
63.9
63.9
63.9
64.3
64.3

1960...............................
1961...............................
1962...............................
1963 ...............................
1964...............................
1965 ...............................
1966 ...............................
1967...............................
1968 ...............................
1969 ...............................

63.6
62.9
62.2
61.4
61.6
60.9
61.8
62.5
62.9
64.5

81.9
81.6
81.3
80.6
79.8
79.2
79.1
79.2
79.9
80.7

60.1
59.3
58.9
58.7
58.4
57.1
56.9
57.7
58.3
58.8

64.3
64.3
64.3
64.3
64.3
64.3
64.3
64.3
64.3
65.1

1970...............................
1971...............................
1972...............................
1973...............................
1974...............................
1975...............................
1976...............................
1977...............................
1978...............................
1979...............................

65.8
65.0
65.6
65.0
66.4
63.8
63.9
63.3
64.3
65.4

81.5
82.0
82.3
82.5
82.7
82.7
82.6
82.7
82.8
82.3

60.3
59.1
57.9
57.2
59.6
58.6
58.0
57.0
57.4
58.5

65.1
65.1
65.1
68.8
68.8
68.8
68.8
68.8
68.8
68.8

1980...............................
1981...............................

The major difference, however, among the different
measures of productivity is not the method of aggrega­
tion as much as it is the definition and construction of
the shares (both labor and capital). Table F-7 shows the
annual labor shares used by b l s , Denison, Jorgenson,
and Kendrick. The primary reasons for the differences
are (1) the output measure, (2) the procedure used to al­
locate proprietors’ income (which contains both returns
from labor and capital) between returns to labor and re­
turns to capital, and (3) treatment of capital consump­
tion allowances. Denison measures output net of capital
consumption allowances, b l s , Jorgenson, and Kendrick
include capital consumption allowances in output and
also as part of the cost of capital in the production of
output. Hence, in these measures, income from capital
is a larger share of output than in Denison’s measure.
Jorgenson further estimates the capital services and re­
turns to these services for the household and nonprofit
institutional sectors. These estimates further increase
his measure of capital’s share.
Proprietors’ income is derived from both returns to
capital and returns to labor. In order to compute the la­
bor and capital shares, proprietors’ income has to be al­
located between the two different sources. The method
developed by b l s is described in appendix D. Briefly,
for the manufacturing and nonfarm nonmanufacturing
sectors, b l s assumes the corporate rates of return for
proprietors’ capital and employee compensation per
hour for proprietors’ labor and applies the resulting

Denison

1948...............................
1949 ...............................

Labor aed capital shares

BLS

Jorgenson

Kendrick

65.5
64.6

83.0
83.2

60.1
60.7

68.8
68.8

Sources: See table F-2.

prices to proprietors’ capital and labor services (hours).
Since the sum of these estimates more than exhausts the
reported proprietors’ income, these initially estimated
payments to each factor are proportionately reduced so
that the sum is equal to the n i p a estimates of proprie­
tors’ income. For the farm sector, the corporate rate of
return to capital is imputed to the farm capital. The cap­
ital income is then calculated and subtracted from the
proprietors’ income, the remainder being the labor
income.
Denison allocates proprietors’ income in a similar
manner. The major difference is that business sector
rates of return to capital and compensation per hour are
applied to the farm sector’s hours and capital. The com­
puted income is then reduced by a constant ratio for all
the factors, both labor and tangible assets.
Jorgenson, on the other hand, imputes the corporate
rate of return of capital to proprietors’ capital for each
sector. This imputation is made at a more detailed in­
dustry level than that used by b l s or Denison. Capital
income is then subtracted from proprietors’ income and
the residual is allocated to labor income at the industry
level. This method of allocation further increases capi­
79

tal’s share relative to labor’s because very little is left of
proprietors’ income after subtracting capital income.
Kendrick imputes the employee hourly compensation
to proprietors and the self-employed for the base years
for which he computes weights. The imputed hourly
compensation is multiplied by estimated proprietors’
hours and added to labor compensation to obtain labor’s
share. Capital’s share is obtained by subtracting labor’s
share from unity.
Table F -8 lists the indexes and average annual
growth rates of multifactor productivity calculated by
b l s and other researchers. The implications of the dif­
ferent methods are readily apparent from the table and
from chart F-4. The growth in output for the period
1948-73 is almost the same for each of the different
methods but the growth in productivity is different: The
differences arise because of the definitions of the inputs
and the definition of the factor shares.
Jorgenson’s method attributes most of the growth of
output to the growth of inputs; therefore productivity
growth is the smallest for his measure. Kendrick, on the
other hand, attributes more growth of output to produc­
tivity growth than to input growth. The two major rea­
sons are that he uses a gross rather than a net capital
stock measure and also because he, like b l s , uses an
unweighted hours measure for labor input, which has a
slower rate of growth. Because the level of the gross
capital stock measure is, in general, much higher than
the net measure, the additional increment from annual
investment does not increase the stock relatively as
much. Hence his measure of capital services grows
much more slowly during an expansion than a measure
using net stocks.3
The b l s and Denison measures of multifactor produc­
tivity lie between Jorgenson’s and Kendrick’s measures.
The reasons for this are different, however. As pointed
out above, Denison’s method of output measurement
(net of capital consumption) shifts the weight towards
labor and away from capital. However, even after ad­
justing for changes in composition, labor does not grow
as fast as capital, so the slower growing input has the
much larger weight, b l s does not make the adjustment
for labor force composition, but attributes a larger share
of growth to the faster growing input (capital) and

coincidentially obtains almost the identical total input
growth as Denison.

Table F-8. Indexes and rates of growth of multifactor produc­
tiv ity fo r the m ost aggregate se cto r m easured by BLS,
Denison, Jorgenson, and Kendrick, 1948-81
BLS

Period

Denison

Kendrick

Index, 1972=100
1948 ........................
1949 ........................

63.1
62.3

63.1
62.5

73.2
73.6

57.5
57.8

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

66.8
68.4
69.6
71.4
71.2
74.3
74.5
75.2
75.7
78.7

66.7
67.5
67.9
69.5
69.0
72.7
73.2
73.7
73.8
77.3

77.6
78.6
79.1
80.8
80.4
83.5
82.5
82.8
83.1
85.2

62.0
63.7
65.5
67.4
67.7
70.4
70.8
72.0
73.1
74.4

1960
1961
1962
1963
1964
1965
1966
1967
1968
1969

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

79.2
80.7
83.7
86.1
89.2
92.0
93.8
94.1
96.3
95.8

77.7
78.8
81.9
84.5
88.0
91.4
93.6
93.3
95.6
95.5

85.1
86.5
89.1
90.5
92.9
95.0
96.4
96.0
97.3
96.7

76.2
78.0
80.6
83.2
86.3
89.2
91.5
92.5
95.1
94.8

1970
1971
1972
1973
1974
1975
1976
1977
1978
1979

........................
........................
........................
........................
........................
........................
........................
........................
........................
........................

94.7
96.8
100.0
102.4
98.5
98.3
102.0
105.0
106.1
104.9

94.0
96.3
100.0
102.5
98.2
96.9
100.8
104.2
105.3
103.6

95.5
97.7
100.0
101.2
97.5
97.1
99.9
101.8
101.7
99.9

94.4
96.7
100.0
102.5
99.3
99.5
102.8
105.6
105.6
104.9

1980 ........................
1981 ........................

105.2
103.6

100.4
101.4

97.2
97.2

103.7
104.1

Rate of growth
(annual percent change)
1948-73 ..................

2.0

2.0

1.3

2.3

1973-81 ..................
1948-81 ..................

0.1
1.5

-0.1
1.4

-0 .5
0.9

0.2
1.8

Sources: See table F-2.

3In the short run, gross capital can also grow faster than net capital when the investment rate is declining.




Jorgenson

80

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