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PART II

MAY 1969 / VOLUME 49 NUMBER

SURVEY OF CURRENT BUSINESS

Some Mai or Issues in Productivity Analysis

UNITED
STATES

DEPARTMENT OF COMMERCE /

•/

OFFICE OF BUSINESS ECONOMICS

PART II

MAY 1969 / VOLUME 49 NUMBER

SURVEY OF CURRENT BUSINESS

CONTENTS
U.S. Department of Commerce
SOME MAJOR ISSUES IN PRODUCTIVITY ANALYSIS:
AN EXAMINATION OF ESTIMATES BY JORGENSON
AND GRILICHES
by Edward F. Denison

Maurice H. Stans / Secretary
Rocco C. Siciliano / Under Secretary
William H. Chartener / Assistant Secretary
for Economic Affairs

I. Time Period, Definition of Output,
and Scope of Economy Covered

II. Divisia Indexes

III. The Input Weights: Total Labor vs.
Total Capital and Land

IV. Allocation of the Total Capital-Land
Weight Among Components

V. The Measurement of Capital-Land Inputs

VI. Effect of Price Index Alterations on Output

VII. The Utilization Adjustment for Capital and Land

VIII. Measurement of Labor Input

IX. Summary of Statistical Review

X. Some General Observations

THE EXPLANATION OF PRODUCTIVITY CHANGE
by Dale W. Jorgenson and Zvi Griliches

Office of Business Economics
George Jaszi / Director
Morris R. Goldman / Associate Director
Murray F. Foss / Editor
Leo V. Barry, Jr. / Statistics Editor
Billy Jo Hurley / Graphics

This month's issue of the SURVEY OF
CURRENT BUSINESS appears in two parts.
The usual contents of the SURVEY appear
in Part I.

Reprinted from
The Review of Economic Studies

Single copy of Part //, May 1969 issue, $1.00.
Make checks payable to the Superintendent of Documents and send to U.S. Government Printing Office,
Washington, B.C. 20402, or to any U.S. Department
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By EDWARD F. DENISON

Some Major Issues in Productivity Analysis:
An Examination of Estimates by Jorgenson and Griliches
The Office of Business Economics has been asked by several of the principal users of
its data to supplement its established series on national output and its composition
(GNP) by consistent measures of factor inputs, so as to facilitate the analysis of economic
growth. The OBE is responsive to these requests and considers the preparation of measures
of factor inputs an appropriate extension of its work on the national economic accounts.
The estimates of business capital stocks and some other studies that have been published
in the SURVEY OF CURRENT BUSINESS are important steps leading to the preparation of
factor input measures.
The conceptual and statistical problems that are involved in the measurement of
factor inputs are unusually difficult, however, and OBE believes that some discussion of
these problems is called for before it engages itself to prepare the measures. To elicit such
a discussion is a major purpose of publishing this article.
In this study, Edward F. Denison, one of the outstanding experts in the analysis of
economic growth, provides a searching comparison of the concepts and statistical procedures that he considers appropriate for input measurement with those recently proposed
by the eminent econometricians, Dale W. Jorgenson and Zvi Griliches. The JorgensonGriliches proposals differ sharply from those set forth by Denison, and also by many others
who have done research in this field. For the convenience of the reader, the Review of
Economic Studies article in which the Jorgenson-Griliches proposals appeared is reprinted—
with some corrections by the authors—in this issue of the SURVEY.
These differences in concepts and procedures yield strikingly different conclusions.
According to Denison, a substantial part of the postwar growth of national output has
been due to an increase in productivity; according to Jorgenson-Griliches almost all of
the increase has been due to an increase in factor inputs.
The issues raised by these opposing conclusions are not only important from the standpoint of basic research but are also likely to have far-reaching implications for the formulation of private and public policies directed at the promotion of economic growth. We
believe that the publication of the Denison article and of a reply to it by Jorgenson
and Griliches in a later issue of the SURVEY will be of substantial interest to all those
concerned with economic growth.

N a recent article, "The Explanation
of Productivity Change/' Professors
Dale W. Jorgenson and Zvi Griliches
found that increases in labor and capital
input were responsible for almost all
postwar growth in the United States
[1]. They concluded that output per
unit of input contributed little to the
growth rate of output—only 0.10 percentage points, to be exact. This
estimate contrasts with much larger
amounts obtained in virtually all other
NOTE.—Dr. Denison is Senior Fellow, The Brookings
Institution, Washington, D.C. The views expressed in this
article are those of the author and do not purport to represent
the views of the other staff members, officers, or trustees of
The Brookings Institution.

studies. I arrived at 1.37 percentage
points in Why Growth Rates Differ:
Postwar Experience in Nine Western
Countries (written with the assistance
of Jean-Pierre Poullier) [2].
This review is a response to repeated
requests to comment upon the article
by Jorgenson and Griliches.1 Do their
1. Its preparation was the occasion of rather extended
communication among us, in the course of which Professors
Jorgenson and Griliches clarified certain of their procedures,
provided some unpublished data needed for comparison of
our estimates, and offered suggestions on presentation. This
assistance helped me to isolate the differences between our
procedures and focus my discussion on these differences. It
is acknowledged with gratitude.
I also benefited greatly from discussions of a draft of this
review with George Jaszi, and of certain sections with Murray
F. Foss, Guy V. G. Stevens, and Allan H. Young.

estimates differ so much from mine
because of differences in the time period
analyzed, in the definition of output,
or in the sector of the economy covered?
Does the discrepancy reflect a mere
difference in classifying growth sources
into those regarded as increasing
input and those regarded as raising
output per unit of input? Or is it due
to differences in statistical procedures?
What are the differences in our procedures, what are their quantitative
effects, and whose, in my opinion, are
preferable? In this article, all of these
questions are discussed.
To decompose the discrepancy in
results, it is necessary to examine many
aspects of the estimates. Section I of
this review measures the effects of
differences in time period, definition of
output, and scope of the economy
analyzed, and section II examines a
minor difference in procedure. After
allowance for these differences, most of
the large discrepancy between our
measures of output per unit of input
remains. Our statistical measures of
total output diverge because different
price indexes are used for deflation; the
effect is examined in section VI. Differences between our total input series for
the sector of the economy analyzed by
Jorgenson and Griliches are much
larger. The input series differ because
of (a) differences in the weights we use
to combine individual inputs and (b)
differences in the way we measure each
individual input. In sections III and
IV, I consider the change that would
be introduced in my series, given my
individual input measures, if the
Jorgenson-Griliches weights were used.
In sections V, VII, and VIII, I measure
the effects upon their series, given their
weights, of using their measure for
each input in place of mine. The two
preceding sentences must be qualified
1

SURVEY OF CURRENT BUSINESS
by noting, as I shall at the appropriate
points, that lack of data necessitated
some departures from this plan. In
section IX, I provide a table that
summarizes the results of the preceding
sections and thus reconciles our output
per unit of input series.
An equally important purpose of
this article is to examine the merits of
alternative procedures. In most sections I therefore discuss differences in
procedure that happen not to be important sources of discrepancy in our

series during the particular time period
discussed as well as those that are, and
in sections IX and X offer some general
observations.
The section of most general interest
may well be section VII, in which I
examine the Jorgenson-Griliches capital
utilization adjustment. I try there to
nudge the theory of growth analysis
forward a little. In addition, their
capital utilization adjustment is the
largest single reason that our output
per unit series diverge.

L Time Period, Definition of Output and Scope of Economy Covered
THE Jorgenson-Griliches summary result, that output per unit of input
contributed only 0.10 percentage points
to a 3.59 percent a year increase in
output, refers to the 1945-65 period.
Use of 1945 as a starting point minimizes their figure. From 1948 to 1965
Jorgenson and Griliches obtain a growth
rate of output per unit of input of
0.74.2 Almost all of this increase came
before 1950 and after 1961; the growth
rate of their output per unit of input
series was 0.01 from 1950 to 1961
and 2.01 from 1961 to 1965 [calculated
from 1, table VIII]. Cyclical movements contribute to the difference
between these periods, but even so the
contrast is remarkable.
My summary estimate, that the
increase in output per unit of input
contributed 1.37 points to the growth
rate, refers to the period from 1950 to
1962. For this timespan, Jorgenson
and Griliches obtain 0.30, as against
0.10 for 1945-65. Thus, the difference
in time period is responsible for 0.20
points of the difference between our
summary estimates. Our estimates for
1950-62 and two subperiods are con-

2. National accountants would not draw inferences about
postwar growth trends from an analysis beginning before
1948, at the earliest, because elimination of price controls
distorted the real output measure in 1945-48, and because—
in the case of 1945—of the great difference from later years
in the composition of output. In addition, speciar aspects
of postwar reconversion greatly affected the 1945-48 period.

trasted in the first two rows of the
following table. The third row [from
2, table 21-1] shows my estimates
after adjustment to eliminate, as best
I could, the effects of differences
among terminal years in the intensity
of demand (i.e., short-teim changes in
intensity of utilization of employed
resources).
1950-62

1950-55

1955-62

0.30
1 37

0.42
1.93

0.22
97

1.41

1.54

1.31

Unadjusted:
Jorgenson- Griliches. . .
Denison
Adjusted:
Denison

The Jorgenson-Griliches series refers
to real gross national product per unit
of input in the private domestic
economy; mine, to real national income
(also called net national product valued
at factor cost) per unit of input in the
economy as a whole.
The reason I chose to analyze the
growth of net rather than gross product
is both fundamental and conventional.
"Insofar as a large output is a proper
goal of society and objective of
policy, it is net product that measures
the degree of success in achieving
this goal. Gross product is larger by
the value of capital consumption.
There is no more reason to wish to
maximize capital consumption—the

May ,1969

quantity of capital goods used up in
production—than there is to maximize the quantity of any other
intermediate product used up in
production, such as, say, the metal
used in making television sets. It is
the television sets, not the metal or
machine tools used up in production,
that is the objective of the production
process" [2, pp. 14-15].
Jorgenson and Griliches confine discussion of their choice of gross product
to a single sentence. "Exclusion of
depreciation on capital introduces an
entirely arbitrary distinction between
labour input and capital input, since
the corresponding exclusion of depreciation of the stock of labour services is
not carried out" [1, p. 256]. (They
also cite an article by Domar, but it
contains no reference to depreciation
of labor.) Their statement is too brief
to allow much discussion, particularly
since Jorgenson and Griliches do not
specify how they would depreciate
labor. I am not aware of a definable
labor counterpart to capital depreciation as a component of GNP that there
is no advantage in increasing because
it is not wanted—feeding, clothing,
and housing children surely do not
fall into this category—but if there be
such, the appropriate remedy would
be to change the measures of output
and labor earnings.
I do not wish to pursue this subject
further in this article, but must provide
a statistical reconciliation of our estimates. This is facilitated by the fact
that, sheerly by chance, conversion of
my estimate of output per unit of input
in the 1950-62 period to their concepts
would scarcely change it because the
difference in definition of output happens to be offset by the difference in
the scope of the economy covered. The
explanation is as follows:
(a) My output series refers to national income, or net national product
(NNP) valued at factor cost, measured
in 1958 prices. The Jorgenson-Griliches
output series refers to gross national
product valued at market prices, measured in 1958 prices. The choice between
factor cost and market price weights to
combine the components of product
does not affect comparability of our
results, but that between gross and net

May 1969

product does. The absolute increase in
the value of gross product at 1958
factor cost is equal to the increase in
net product at 1958 factor cost plus the
increase in depreciation valued in 1958
prices. Each year, the change in output
per unit of input (and every other
growth source except depreciable capital) contributes the same absolute
amount to the increase in real GNP at
factor cost as to real NNP at factor
cost. (Depreciable capital contributes
to the increase in real GNP an amount
equal to its contribution to the increase
in real NNP plus the absolute increase
in depreciation at constant prices.) But
the same absolute amount contributed
by output per unit of input yields a
smaller percentage increase in GNP at
factor cost than in NNP because the
value of GNP is bigger than that of
NNP—in 1950 by 11.6 percent, according to my estimates. Hence, output
per unit of input contributed less to
the growth rate of GNP when measured
in percentage points. For 1950-62, my
estimates yield a contribution of output
per unit of input to the growth rate of
GNP of 1.24 percentage points as
against 1.37 to the growth rate of
NNP.3
(b) My output estimates refer to the
economy as a whole; the JorgensonGriliches estimates, to the private
domestic economy. Thus, the latter
exclude the net inflow of property income from abroad and GNP originating
in general government. However, my
estimates imply no increase in output
per unit of input in the sectors they
exclude.4 The absolute contribution of
the increase in output per unit of input
to the increase in output is therefore
the same in the sector covered by the
Jorgenson-Griliches estimates as in the
whole economy. Because the level of
private domestic GNP was smaller than
that of total GNP, the contribution of
3. For consistency with OECD estimates, my GNP
figures include a small amount for government capital consumption. This comes out again when I move to the private
domestic economy in adjustment (b).
4. The entire increase in net property income from abroad
is counted as a contribution of capital. Real GNP in general
government is measured on the assumption that output per
person employed does not change (this statement is only
approximately accurate), and for this reason I used procedures that have the effect of measuring inputs in general
government by employment [2, pp. 187-188]. Hence, no
change in output per unit of input occurs in general government.

SUEVEY OF CURRENT BUSINESS
output per unit of input to its growth
rate is proportionately larger; it is 1.38.5
This is practically the same as my
original figure of 1.37; adjustments (a)
and (b) are almost exactly offsetting.6

Thus, differences in definition and scope
of output together account for none of
the difference between our 1950-62
estimates of the contribution of output
per unit of input.7

II. Divisia Indexes
JORGENSON and Griliches devote ment from 1950 to 1962 of their series
considerable attention in their article to for output, input, and factor productheir use of Divisia indexes (which are tivity is almost unaffected. Indeed, inaverages of growth rates, with frequent troduction of Divisia indexes has no
changes in weights) in their measure- appreciable effect at other dates except
ment of input and output. I shall not at the very beginning of their period,
discuss the alleged theoretical superiority of Divisia indexes, but simply note when price and output patterns were
that their substitution has no effect distorted. Moreover, my own proceupon the comparisons. When Jorgenson dures for combining inputs are suband Griliches introduce them in moving stantially equivalent to the use of
from their table I to table II, the move- Divisia indexes.

III. The Input Weights: Total Lahor vs. Total Capital and Land
TO calculate changes in total input,
weights to combine the various types
of input are required. Our weights,
though different, share two characteristics that distinguish them from those
of some other investigators. First, we
each set the sum of our input weights
equal to 100 percent (or 1). This has
the effect of classifying gains from
economies of scale as a contribution of
output per unit of input to the growth
of output.8 Second, we each use the
shares of labor, and of capital and land,
in total earnings from production as
weights to combine these broad types
of input, and rely upon data from the
national accounts to estimate these
shares.9
Our actual weights differ as a result
of differences in the scope and defini5. As indicated in section IV, my estimates imply that the
contribution to the growth rate of net product at factor cost
in the private domestic sector was 1.51.
6. This implies, of course, that the levels of total national
income and private domestic GNP (both measured in 1958
prices at factor cost) happened to be almost the same at the
start of the period (1950).

tion of our output measures and of
differences in our estimating procedures.
The latter contribute to the discrepancy between our results for growth of
GNP per unit of input. During the
postwar periods analyzed, capital-land
input increased more than labor input
so that the greater the weight attached
to capital-land, the more a measure of

7. In measuring the effects of differences between us in
concepts, scope, or procedures for this review, I often shortcut
the calculations by using average weights or rates for the
period examined even though we each subdivide the periods
in our calculations. The results are accurate enough for the
purpose at hand.
8. Throughout this review, I ignore as of no quantitative
importance the fact that, in presenting the contributions of
the sources to the growth rate, I allocated to output per unit
of input 0.01 percentage points of an interaction term. Jorgenson and Griliches do not present contributions as such and
hence omit this term, but with their estimates nothing would
be allocated to productivity in any case. I also ignore rounding discrepancies that cause their growth rate of output to
exceed the sum of the growth rates of input and output per
unit of input at intermediate points in their analysis by
small amounts varying up to 0.06 (as presented in their
table IX).
9. My reasons for using income shares are stated in 2,
chapter 4.

SUEVEY OF CUEEENT BUSINESS
total input increases and the less output
per unit of input increases.
Differences
related
definition

scope

and

The weights used in my study refer
to the shares of labor and capital-land
in total national income. I measure
labor earnings as the sum of (1) the
compensation of employees and (2)
a portion (about three-fifths) of proprietors' income; this portion is derived
on the assumption that the labor share
of national income originating in proprietorships and partnerships is the
same as the labor share of national
income originating in nonfinancial corporations [2, p. 37]. My estimate of
the total earnings of capital and land
is equal to the sum of the following
items: the remainder (about two-fifths)
of proprietors' net income; corporate
profits (before tax) and inventory
valuation adjustment; the rental income of persons; and net interest.
The labor share plus the capital-land
share equals national income. (Whatever is not earned by labor is counted
as earnings of capital and land despite
the fact that "pure" profit—whether
a return to entrepreneurship or monopoly profit—is included.)10 Depreciation
is revalued at replacement cost in the
computation of corporate and noncorporate earnings and rental income,
and of total national income.11 On the
average in the 1950-62 period, labor
earnings represented 78.6 percent and
capital and land earnings 21.4 percent
of total national income.12 These percentages are shown in line 1 of the
following table. The remainder of the
table will help the reader follow the
rest of this discussion.
The Jorgenson-Griliches analysis is
confined to the private domestic sector.
My results imply that labor earnings
averaged 74.7 percent and capital and
land earnings 25.3 percent of national
10. Since Jorgenson and Griliches do the same, this does
not cause our estimates to diverge.
11. The estimates are based on use of Bulletin F lives and
straight-line depreciation. They were prepared before the
results of the latest OBE capital stock study for nonresidential structures and equipment became available.
12. I do not actually use weights for the period as a whole
in calculations, nor do Jorgenson and Griliches. I use weights
for three subperiods, and they change weights annually.
The averages provide a convenient summary.

Labor
share

Property
share

Denison labor estimates:
1. Whole economy, national income
2. Private domestic economy, national income _ .
.
3. Private domestic economy,
GNP at factor cost

78.6

21.4

74.7

25.3

67.2

32.8

Jorgenson-Griliches labor estimates:
4. Private domestic economy,
GNP at factor cost
5. Private domestic economy,
GNP at market prices
.

70.8

29.2

63.8

36.2

income in this sector. Jorgenson and
Griliches analyze the growth of gross
rather than net output; this obviously
calls for a difference in procedure somewhere in the calculations. One acceptable possibility is to include depreciation with the earnings of capital and
land in the derivation of weights, and
this is what Jorgenson and Griliches
do.13 If depreciation is added to national income and to the capital-land
share, and the percentages are recomputed, my estimates indicate that labor
earnings averaged 67.2 percent of
gross domestic product at factor cost
in 1950-62 and that capital-land earnings together with depreciation
averaged 32.8 percent. (These figures
are unaffected by the method of measuring depreciation.) These shares,
shown in line 3 of the table, differ
from those in line 1 for conceptual
reasons. Their use by Jorgenson and
Griliches to analyze gross private product would have introduced little or no
discrepancy between their estimate of
output per unit of input and that
which I derived in section I after
allowance for differences in the definition and scope of our output measures.
Differences
due
procedures

estimating

The Jorgenson-Griliches weights differ from these for two reasons. First,
although their estimate of labor earnings, like mine, equals compensation
of employees plus a portion of proprietors' income, they obtain the latter
by a different procedure. They assume
13. This procedure is not necessarily exactly equivalent
to that which I used in section I above to adjust my estimates
to a gross product basis, but any difference in the end result
for output per unit of input is probably trivial.

May 1969

that labor earnings of proprietors are
equal to the number of proprietors
(exclusive of unpaid family workers)
times compensation per fulltime equivalent employee in the private domestic
economy [1, p. 278]. This procedure
allocates approximately all of proprietors' income to labor and none to
capital and land. The labor share
obtained by this procedure averages
70.8 percent, and the capital-land
share 29.2 percent, of private domestic
GNP at factor cost instead of 67.2 and
32.8, the percentages at which I arrive.
My allocation of proprietors' income
seems to me the more reasonable,
but admittedly both procedures have
substantial precedent. In the nature
of the case, there is no way to check
the results directly. Their use of a
larger estimate of labor earnings would,
in itself, lead Jorgenson and Griliches
to a higher estimate of the contribution
of output per unit of input to growth
than I obtain. However, it is much
more than offset by what I regard as
an error in their derivation of capitalland earnings.
Jorgenson and Griliches state in their
statistical appendix [1, p. 2781 that
"total income from property is gross
private domestic product in current
prices less private domestic labour income." Gross private domestic product
was valued at market prices in their
calculation. This means that Jorgenson
and Griliches count indirect business
tax liability minus "subsidies less current surplus of government enterprises"
and plus business transfer payments
and the "statistical discrepancy" in the
national accounts as earnings of capital
and land. Jorgenson and Griliches inform me that this inclusion was intentional, not an oversight. Inclusion of
these items in the earnings of capital
and land raises their capital-land share
from 29.2 percent to 36.2 percent, or
by almost one-fourth, and lowers their
labor share from 70.8 to 63.8.14 (These
shares, shown in row 5 of the preceding
text table, were computed from annual
14. It also has the effect of including indirect taxes, and the
other reconciliation items mentioned, in profits after tax in the
numerator of the "implicit rate of return after taxes" that
Jorgenson and Griliches show in table VI, column 4, of their
article. Their article gives no hint of this peculiar definition of
an after tax rate of return. I doubt that many readers of their
article can be aware of it.

May 1969

figures given me by Jorgenson and
Griliches.)
The principal item at issue, quantitatively, is indirect business tax
liability. Jorgenson and Griliches do
not explain why they include indirect
business taxes in their weights or
why, if they are to be included, there
is more reason to add them to capitalland earnings than to labor earnings.
Possible reasons for their procedures
are hard to visualize, and I can only
speculate as to what they may have
had in mind.
The fact that Jorgenson and Griliches
are analyzing the growth of gross
product valued at market prices (which,
viewed from the "income side/' includes
indirect taxes), rather than gross product valued at factor cost, surely necessitates no difference in weights. Share
weights are used as estimates of the
relative response (elasticity) of output
to changes in labor input and to
capital-land input; for example, use
of weights of 30 percent for capital
and land and 70 percent for labor
to analyze gross product growth would
imply that a given percentage increase
in every type of capital-land input
raises gross product by three-sevenths
as large a percentage as does the same
percentage increase in every type of
labor input. There is no systematic
reason for the percentage response of
gross product valued at market prices
to differ from the percentage response
of gross product at factor cost.15
Possibly Jorgenson and Griliches
mean to challenge the classification of
indirect taxes as indirect. The income
division that is appropriate for use as
weights is the distribution of earnings
that would prevail in the absence of
taxes, taking as given the existing
quantities of each input in the sector
and period analyzed. To approximate
this distribution, analysis is required of
what is often called "shortrun" tax
incidence (to distinguish it from analysis
15. The movement over time of gross product at 1958
market prices differs from that of gross product at 1958
factor cost only if the composition of output shifts toward
or away from products that were taxed (or subsidized) at
above- or below-average rates in 1958. Any difference in
movement is not related to share weights in the economy
as a whole. (In 2, pp. 15-16, I suggest that if, in the output
measure whose growth is analyzed, the components of
output are weighted by market prices, such shifts should
themselves be treated as a statistical "source" of growth.)

SUEVEY OF CUKRENT BUSINESS
of incidence when any impact of taxes
on the quantities of factors is taken
into account). My use of the classification of taxes followed in the national
accounts thus implies the following
assumptions. First, that personal income and inheritance taxes (and various
licenses, minor taxes, and nontax recipts
of governments that are classified as
personal) do not alter the distribution
of earnings before taxes; hence, they
need not be deducted from before-tax
shares to achieve the desired distribution. Second, that the "shortrun"
incidence of payroll taxes is on labor
earnings; hence, labor earnings should
be measured inclusive of payroll taxes.
Third, that the "shortrun" incidence of
corporate profit tax accruals is on
corporate profits; hence, corporate
profits should be measured inclusive of
corporate profits taxes. Fourth, that
the incidence of taxes classified as
indirect is on no particular type of
income and their presence does not alter
relative shares measured exclusive of
such taxes. Taxes classified as indirect,
and the average percentage of total
"indirect business tax and nontax
accruals" represented by each type in
1950-62, are: sales and excise taxes and
customs duties, 55 percent; property
taxes, 33 percent; business motor
vehicle licenses, 2 percent; other
business taxes, 7 percent; business nontaxes, 3 percent.
No one supposes this classification
of taxes to be precise. For example, I
have myself suggested that at least
the portion of the corporate income
tax that is levied on regulated utilities
probably is passed on in higher prices,
causing my capital-land share to be
overstated relative to labor. But, with
some allowance for offsets, I have regarded the national accounts classification as acceptable.
If Jorgenson and Griliches count
indirect taxes as earnings of capital
and land because of incidence considerations, this implies that they accept
the first three assumptions listed above
and reject the fourth in favor of an
assumption that the shortrun incidence
of indirect taxes rests on capital and
land.
For one tax classified as indirect,
that on real property, this assumption

may be preferable. 16 Indeed, in the
context of considering the effect of
taxes on the allocation of resources
among sectors of the economy, I have
myself suggested that one should not
consider the impact of the corporate
income tax, which bears only on the
corporate sector, without simultaneously considering the property tax,
which bears most heavily on the principal noncorporate sectors of the private
economy: housing and farming [3,
pp. 186-187]. It is plausible to argue
that neither tax is shifted in the short
run. But I see no possible reason to
suppose that the short-term incidence
of the other components of indirect
tax and nontax liability rests on capital
and land. These represent the bulk of
the category, so I regard addition of
indirect taxes to capital-land earnings
as mainly an error. 17
Although counting the difference
between factor-cost and market prices
as property income raises the Jorgenson-Griliches capital-land share of private domestic GNP by 7.0 percentage
points in. 1950-62, their actual weight
averages only 3.4 percentage points
higher than the weight implied by my
estimates (with depreciation added)
because of their smaller allocation of
proprietors7 income to property income.
My own estimate of output per
unit of input is only moderately
sensitive to differences in weights of
this magnitude. If I were to substitute
their weights for mine, my estimate of
the contribution of output per unit
of input would be lowered by about
0.08 percentage points.18 I shall use
this number to measure the difference
in, our results that is due to differences
in our division of the weights between
labor and capital-land as a whole.
However, it should be noted that the
Jorgenson-Griliches estimates are much
more sensitive than mine to differences
in weights because they estimate the

16. Even if this is so, it is an open question whether addition of property taxes to capital-land earnings would, on
balance, improve the weights in view of the probable overstatement of the capital-land weight in both our estimates
that results from counting "pure profit" and all of the corporate income tax in this share.
17. Inclusion of other, smaller reconciliation items between
GNP at market prices and GNP at factor cost in property
income seems tenable for only one minor subcomponent:
corporate contributions to non-profit organizations.

6
differential between the increase in
capital-land input and labor input
to have been far larger than I do.
Substitution of my weights for theirs
would raise their estimate of output

SURVEY OF CUREENT BUSINESS
per unit of input much more than
0.08. In the reconciliation I attempt,
this extra amount will be reflected in
the difference I identify with differences
in our measures of changes in inputs.

IV. Allocation of the Total Capital-Land Weight Among Components
THE procedures that Jorgenson and
Griliches and I adopt to estimate the
contribution of capital and land to
growth are similar at the most general
level.
The total weight of capital and land
is first divided among types of capital
and land in proportion to the estimated
earnings of each type. In my estimates
five types are distinguished. One of
these, international assets, does not
appear in the portion of the economy
analyzed by Jorgenson and Griliches.
The others are: residential structures
and residential land, nonresidential
structures and equipment, nonresidential land, and inventories. Jorgenson
and Griliches use a different classification. They distinguish among residential
structures, nonresidential structures,
equipment, residential and nonresidential land, and inventories.
Once the weights are assigned, each
component of capital-land is treated as
a separate input. An index measuring
the quantity of each input must be
developed. The weight is then multiplied by the growth rate of the index
to arrive at the contribution of each
component to growth.19 (In my case

contributions of international assets
and, as explained in section V, residential property are calculated by a
different procedure that does not require an input index.) The total
capital-land contribution is the sum of
the contributions of the components.
In this section, I consider the weights.
Later sections will examine the input
indexes.
Because I analyze net product and
my total capital-land weight includes
only net (after-depreciation) earnings,
my total capital-land weight is allocated among types of assets in proportion to their estimated net earnings.
Jorgenson and Griliches allocate earnings in two parts. The portion of their
capital-land weight corresponding to
net (after-depreciation) earnings is allocated by estimates of net earnings, as
in my procedure. To net earnings of
each type of depreciable asset, they
add depreciation (replacement in their
terminology) in order to obtain gross
earnings. This corresponds to their
measurement of gross product and inclusion of depreciation in their total
capital-land weight. This difference in
our weighting procedure is legitimate

18. Substitution of their higher estimates of the labor
content of proprietors' income for mine, and addition of all
the reconciliation items between GNP at factor cost and
GNP at market prices to my estimates of capital-land
earnings, would lower my labor share of total national income
in 1950-62 from 78.6 to 74.1. By my procedures, the difference
of 4.5 percentage points would be allocated among nonresidential structures and equipment, nonresidential land,
and inventories in proportion to their present weight. (The
weight of other capital-land components is independently
derived.) Such a shift in weights would lower my estimate
of the contribution of labor input by 0.06 percentage points,
raise the contribution of capital by 0.14, and hence lower
my estimate of the contribution of output per unit of input
to the growth rate of national income in the whole economy
in 1950-62 by 0.08. The effect on the growth rate of GNP
at factor cost per unit of input hi the private domestic sector
would be the same, for reasons explained in section I.

19. The actual arithmetic of the Jorgenson-Griliches
calculation differs from this description, but it is arithmetically equivalent. Suppose, in a year 1, that in current
prices total income and output are $100 and earnings of
inventories are $5 (equal to 5 percent of the total weight).
Suppose that inventory input is measured by its value in
1958 prices, and this value is $100 in year 1 and $110 (10 percent
more) in year 2. The more usual procedure would multiply
the 10 percent increase in inventory input by its 5 percent
weight, and conclude that the increase in inventories had
raised output by 0.5 percent. The Jorgenson-Griliches
procedure is to divide the $5 of inventory earnings in year 1
by the $100 of constant-price value in year 1 to obtain a
"service price" of 5 cents per unit ($1 of value in 1958 prices)
of inventories. The 100 units of inventory input in year 1
and the 110 units in year 2 are then multiplied by 5 cents,
yielding $5 in year 1 and $5.50 in year 2. The difference of
50 cents is the contribution of the increase in inventories,
and is again equal to 0.5 percent of the year-1 value of output.

May 1969

because we are analyzing the growth
of different output measures.
The preceding description of the
Jorgenson-Griliches methodology pertains to their final estimates, which
incorporate the adjustments introduced
in moving from their table V to table
VI. The weighting structure they
initially use—in their tables I through
V—is a mixture in that the total
capital-land weight includes depreciation but is allocated among components
by net earnings alone.
Use of asset values to allocate net
earnings

The total weight of capital and land
(excluding
depreciation in
the
Jorgenson-Griliches estimates) is, as I
have indicated, divided among components in proportion to their net
earnings. But first the earnings of each
component must be estimated, and this
requires some assumptions.
The earnings of an enterprise can be
measured, but most enterprises use
more than one type of capital and land
and there is no way to observe directly
the earnings of each type. The analyst
has no alternative but to assume that
the individual enterprise earns the
same rate of return on each.20 Given
this assumption, the total net earnings
of capital and land in each enterprise
can be distributed among different
types of assets in proportion to their
value to obtain the earnings of each
type.
Jorgenson and Griliches introduce a
second assumption: that the rate of
return is the same in all enterprises.
The two assumptions together permit
them to allocate the net earnings of
capital-land among types of assets by
current asset values in the private
economy as a whole. Except for a
modification for capital gains and taxes,
which I shall discuss shortly, this is
their procedure.
The second assumption is not required by the nature of the economy.
20. Jorgenson and Griliches and I each assume statistically,
subject to some later qualifications about capital gains and
taxes, that, if the rate of return is the same for all types of
assets, the ratio of net earnings to net value at current prices
is also the same. This is not a wholly satisfactory assumption
[2, p. 143, and 3, pp. 28,112-113, 289-294], but it introduces no
discrepancy between our results because we both use it.

May 1969

If data were available, one could
allocate earnings separately for each
enterprise and add up the results. If it
turned out, for example, that enterprises
having a high proportion of their
assets in inventories had a higher
rate of return, on the average, than
enterprises having a high proportion
of their assets in fixed capital, this
procedure would (I believe appropriately) yield a higher weight for
inventories and a lower weight for
fixed capital than would a summary
allocation of total capital-land earnings
in the economy as a whole by the value
of different types of assets in the
economy as a whole. With the statistics
available, this procedure cannot be
implemented for individual enterprises.
But I have found it possible to introduce
what I regard as major improvements
in the weighting structure by dealing
with groups of enterprises.
(1) The earnings of capital and land
used in the provision of housing
services—called the "services of
dwellings" industry in international
compilations—were isolated [2, p.
40].21 They are almost the same as
total earnings in this industry since
labor earnings are trivial. Since residential capital and residential land
are the only types of capital and land
used by this industry, and since (by
definition) these assets are not used by
any other industry, the earnings of
residential capital and land can be
unambiguously identified. Actual
earnings of residential property are
smaller than the estimate that would
be obtained if total earnings in the
economy as a whole were allocated by
asset values, and hence my procedure
leaves more weight for the remaining
assets.22
(2) The net flow of property income
from abroad, corresponding to the
21. In most Western European countries, the "services of
dwellings" is considered a separate industry, for which the
necessary data are published. In the United States, this
activity is divided between the "real estate" and "farms"
industries and not published separately, but it can be approximated from the details of the national accounts worksheets.
22. My procedures avoid the need to further divide the
earnings of residential property between structures and sites.
If such a breakdown were desired in order to preserve the
Jorgenson-Griliches classification of assets, it could be
obtained by allocating earnings within the housing sector by
asset values.

SUKVEY OF CURRENT BUSINESS
earnings of international assets, was
also isolated; however, once my estimates are adjusted to correspond to the
scope of the economy they cover, this
procedure does not affect the comparison with Jorgenson and Griliches because income from -abroad is outside
their sector.
(3) The remaining earnings of capital
and land—those arising in the domestic
nonhousing sector—were divided between farm and nonfarm components.
Within each sector, the total was
distributed among nonresidential structures and equipment, nonresidential
land, and inventories, in proportion to
their net value. The estimates for the
farm and nonfarm sectors were then
added to obtain total earnings for each
of these three types of assets. Farming
has a lower ratio of earnings to assets
than the nonfarm nonresidential sector,
and a higher proportion of its assets
are in land and a lower proportion in
structures and equipment. Hence, the
separate attention I give to agriculture
results in a lower weight for land and
a higher weight for nonresidential
structures and equipment than would
be obtained if the farm-nonfarm division were not made.
My average weights for the 1950-62
period are shown as percentages of total
national income and of total nonlabor
income in the first two columns of the
following table. The next two columns
give similar data for the private
domestic sector.
The last column gives a percentage
breakdown of the total capital-land
weight that corresponds conceptually to
the percentage distribution of the net
(after-depreciation) portion of the
Jorgenson-Griliches final weights, ex-

cept for an adjustment for capital
gains and taxes that they introduce.
(It also corresponds conceptually to
their division of the total gross capitalland weight, including depreciation,
used in the construction of their
table I.)23
Their distributions differ from this
statistically, however, because they
allocated total net capital-land earnings
among components by values in the
private domestic economy as a whole,
without giving separate attention to
the "services of dwellings" and agricultural industries.24 For this reason,
they presumably assigned a much
higher proportion than I of the total
net capital-land weight to residential
structures and to residential and nonresidential land, and a lower proportion
to nonresidential structures and equipment and (to a lesser extent) inventories.25 On balance, the weighting
structure for net earnings within their
capital-land aggregate probably yielded
a smaller increase in combined capitalland input, and hence tended to produce a larger increase in output per
unit of input, than my weights would
have done. This is chiefly because land,
to which they assign more weight, did
not increase.

23. Note, however, that Jorgenson and Griliches classify
residential land with other land rather than with dwellings.
They also subdivide nonresidential structures and equipment.
24. And possibly also because of differences in data used.
25. In their table I, they presumably also assigned a
lower proportion of their total weight than I to structures
and equipment and a higher proportion to land and inventories because, to arrive at the current value of structures
and equipment, they use the double declining balance
formula which yields lower values for such assets than the
straight-line formula I adopted. In their final gross earnings
weights, this difference is more than offset since depreciation
is added back to the capital component to which it pertains.

Private domestic economy

Whole economy
Percent of
national
income

Percent of
capital-land
earnings*

Percent of
national
income*

Percent of
capital-land
earnings*

International assets

0.6

Residential structures and land..

3.5

4.3

11.2

13.6

2.9

3.5

3.2

3.9

21.4

100

25.3

100

Nonresidential structures and equipment _
Nonresidential land
Inventories
Total capital and land
*Approximate.

8
Capital gains

ratio of current earnings to value may be
lower for land than for capital, and alAnticipated capital gains or losses location of earnings by value may
and taxes on income may bias earnings overweight land and underweight
weights derived in the ways I have capital.
described if their presence causes the
The case of land has no counterpart
percentage distribution of asset values within the reproducible capital aggreto diverge from that of earnings within gate. The values Jorgenson and
a sector of the economy where the Griliches and I use for capital comdistributions have been assumed to be ponents are their current replacement
the same [3, p. 28]. I believe any such costs, estimated by use of price indexes
bias in my estimates to be trivial, but for new equipment, structures, and
must devote extended discussion to the goods held in inventory. These values
topic because Jorgenson and Griliches are firmly anchored to the present price
assign it a central place in theii level and present production costs of
analysis.
capital goods and are not affected by
I shall consider capital gains first. capital gains. (Actually, I doubt that it
Jorgenson and Griliches believe the would matter if the values were true
presence of capital gains or losses market values, since there is no general
affects the validity of the assumption reason foi these to depart fiom reprothat earnings are distributed like asset duction costs.) Therefore I see no reason
values. They state: "Asset prices for to suppose the allocation of weights
different investment goods are not among structures, equipment, and inproportional to service prices because ventories is biased by capital gains.
of differences in ... rates of capital
As indicated, land may be overgain or loss among capital goods" weighted and all the capital components
[1, p. 267]. Their idea is that current correspondingly underweighted because
asset values are proportional to the of capital gains. But if this is true of my
sum of earnings and capital gains so weights, the bias must be slight. My
that allocation of earnings by asset weight for dwellings and dwelling sites
values assigns too much to assets (including vacant lots, which yield no
producing large capital gains and too current income) is completely unlittle to assets producing small capital affected because it is based directly on
gains or capital losses. They do not earnings, excluding capital gains, and
discuss the timespan over which my procedure does not require a divicapital gains and losses must be cumu- sion of this weight between dwellings
lated to secure this proportionality, and their sites. Division of total earnbut I presume it is the discounted ings between farm and nonfarm invalue of the anticipated stream of dustries greatly reduces any possible
earnings and capital gains that would overweighting of private nonresidential
be supposed pertinent.
land. In addition, I used conservative
The relevance of this idea to the estimates of the value of land (Goldactual data we both use must now be smith's earlier, rather than later and
explored. It is necessary, I believe, to higher, estimates). Finally, the weight
distinguish sharply between land and I assigned nonresidential land is so
reproducible capital. The current value small that it could be reduced even
of land is estimated market value; Jor- radically with no great effect. If it were
genson and Griliches and I rely upon cut 40 percent, for example, and this
Eaymond Goldsmith for data. Land weight reassigned to nonresidential
prices may and often do reflect not only structures, equipment, and inventories,
current earnings related to current mar- my estimate of the contribution of
ginal products but also the expectation output per unit of input would fall by
that marginal products will be higher in only 0.04 percentage points in 1950-62.
If capital gains bias weights obtained
the future because of increasing land
from
a distribution by asset values, the
scarcity (relative to other factors).
Jorgenson-Griliches
weights, prior to
Land is also an inflation hedge and may
their
attempted
correction,
are subject
reflect the expectation of a rise in the
to
larger
error
than
mine
because
they
general price level as well. Hence, the

May 1969

SURVEY OF CUEEENT BUSINESS

do not isolate earnings in the "services
of dwellings" and agricultural industries in which land is very important.
Jorgenson and Griliches attempt to
eliminate the bias that they presume
would otherwise enter their weights by
introducing a formula that is based on
the assumption that, each year, values
of types of capital and land are proportional to the sum of the earnings and
capital gains derived from them in that
year.
The formula can best be understood
with the aid of an arithmetic example.
Assume for some year the arbitrarily
selected data for the private domestic
economy shown in the following table.
(The table will be used again, and
includes some numbers not needed as
yet.) For simplicity, I let the data
refer to the base year for deflation so
that asset values are the same in current
and constant prices. The first column
gives data based on "true" depreciation (replacement) as estimated by
Jorgenson and Griliches; the second,
on capital consumption as shown in
the national income estimates. Only
two types of capital—equipment and
inventories—are present, and each has
a value of $50,000. (Eesidential and
nonresidential structures are handled
like equipment in the formula, and
land, like inventories.) During the
year, there is a capital gain (realized
and unrealized) of $1,500 on the stock
of equipment and $500 on inventories.
The problem is to divide the total

Jorgenson- National
Griliches accounts
basis
basis
Income and product account:
Sales (equal GNP at market

Depreciation on equipment- ..
Corporate income taxb
Profit less corporate in-

$60,000
45,000
15,000
7,000
8,000
1,000
7,000
3,333

$60, 000
45,000
15,000
5,000
10,000
1,000
9,000
3,333

3,667

5,667

Addenda:
•

- --

100,000
50,000
50,000
2,000
1,500
500

a Includes indirect business taxes and other reconciliation
items between factor cost and market price valuation for
consistency with the Jorgenson-Griliches classification.
b
Includes tax on capital gains.

SUEVEY OF CUEEENT BUSINESS

May 1969

Jorgenson-Griliches gross capital earnings weight of $15,000 (or 25 percent
of the total input weight of $60,000)
between equipment and inventories
when the Jorgenson-Griliches estimate
of "true" depreciation is accepted.
The usual procedure would assign
to equipment the $7,000 of depreciation on equipment, and divide the
$8,000 of net earnings between equipment and inventories in proportion
to their values—in the example, $4,000
each.26 The total weight of equipment
is then $11,000 and of inventories
$4,000.
In the absence of a corporation
income tax, Jorgenson and Griliches
would compute the weight (they call
it the "service price") for the $50,000
value of each of the two assets by the
following formula [1, p. 256]:

where pk is the price of the kth capital
service, qk is the price of the kth investment good, r is the rate of return, net
of "true" depreciation but inclusive
of capital gains, on all capital, 5k is
the "instantaneous rate of replacement
of the kth investment good" (i.e., the
ratio of depreciation to net value),
and — is the ratio of the capital gain
<Z*
on the kth investment good to the value
of that good.
If there were no capital gains in my
example (g* would then be zero for
both equipment and inventories), this
formula would yield the same weights
as the simple procedure: $11,000 for
equipment and $4,000 for inventories.
The price of $50,000 of equipment would
be calculated as
f 8'000 i

7 000

~ °

or $11,000.
The price of $50,000 of inventories
would be calculated as

or $4,000.
26. I follow here the Jorgenson-Griliches procedure of
counting indirect taxes, etc., as part of the net earnings
component.
348-323 O - 69 - 2

The example actually assumes capital gains of $2,000, of which $1,500 is
on equipment holdings and $500 on
inventory holdings. When these are
introduced, the weights (service prices)
shift toward inventories, which have a
lower rate of capital gain. The estimated price (earnings) of $50,000 of
equipment becomes

not affected (except very indirectly and
irrelevantly) by prospective capital
gains. Consequently, the bias that
Jorgenson and Griliches seek to eliminate is not present in the original data.28
Their capital gains adjustment thus
introduces a bias in the opposite direction—that is, it overweights capital
assets on which capital gains are small.
Even if all three conditions were met,
000 + 2,000 7,000
the
relevance of an annual calculation
$50,000
100,000 +50,000"
would elude me. Since capital gains are
1,500 1
highly erratic from year to year, the
50,OOOJ
weights must also change erratically
or $10,500.
from year to year. It could hardly be
The price of $50,000 of inventories argued that market prices of capital
goods and land fluctuate annually so
becomes
as to maintain proportionality between
000 + 2,000 . 0
capital
values and the sum of earnings
$50,000
1
100,000
50,000
and capital gains each year, nor could
500 I
firms adjust the composition of their
50,000j
real assets annually even if they could
or $4,500.
foresee the pattern of each year's
The assumption of the calculation is capital gains and losses. The supposed
that asset values each year are propor- error in the use of asset values to derive
tional to the sum of net (after-deprecia- weights for a year could have no retion) earnings and capital gains in that lationship at all to the size of capital
year.27 Jorgenson and Griliches base gains in that year.
their weights (service prices) for each Tax on corporate profits
year on such a calculation (or rather a
I turn now from capital gains to taxes
more complicated one to which I shall
on income. Jorgenson. and Griliches
come shortly) for that year.
I find it impossible to believe that the consider only the tax on corporate
procedure adopted by Jorgenson and profits. It is sometimes argued that the
Griliches actually improves the weights. presence of this tax leads to allocation
It might be appropriate to apply the of resources in such a way as to cause
Jorgenson-Griliches assumption that the after-tax rate of return in the corvalues are proportional to the sum of porate sector to be the same as, and
net earnings and capital gains—but hence the before-tax rate of return
only with the use of average capital higher than, that in the noncorporate
gains over long periods of time to sector.
Because earnings from all types of
adjust earlier years—if (1) asset values
used in the calculations were independ- capital and land used by corporations
ently obtained sales values and (2) are taxed alike, it is easy to avoid any
substantially different rates of capital bias from this source in the distribution
gain on different types of capital were of capital-land earnings (which include
forecast by firms and (3) their forecasts this tax) among types of assets if asset
were accurate. But the second condition values are available separately for
is unlikely and the third so restrictive corporations. One need only allocate
that I doubt the procedure would be an earnings of capital and land in the taxed
improvement even if the first condition corporate sector in proportion to asset
were met. Actually, the first condition values in corporations, to allocate
is not met; as already noted, the capital earnings in the untaxed noncorporate
stock values used are not market values sector in proportion to noncorporate
but current reproduction costs that are asset values, and then to add the two

27. The calculation implies net earnings of $3,500 and
capital gain of $1,500 for equipment, and net earnings of
$4,500 and capital gain of $500 for inventories.

28. Except perhaps for the division of the weight between
land, on the one hand, and the four capital components as a
group, on the other.

10
distributions to secure the final earnings
estimates for use as weights. This
procedure avoids any bias from the tax
whether the tax diverts resources from
the corporate to the noncorporate
sector or does not.
My estimates do treat separately two
sectors that are overwhelmingly noncorporate: housing and agriculture.
However, the combined earnings of
corporate and noncorporate firms within the nonfarm nonhousing sector were
allocated by their combined asset
values. This introduces an error into
my weights for nonresidential structures
and equipment, inventories, and nonresidential land if both (1) the rate of
return after tax (rather than before
tax) was the same for corporate and
noncorporate firms, and (2) the percentage distribution of assets among
the three types was different in corporate and noncorporate firms. The first
condition would mean that before-tax
earnings per dollar of value of each type
of capital and land are higher in corporations than in noncorporate firms.
If this is so, and if the second condition
is also met, failure to allocate capitalland earnings of corporate and noncorporate firms (within the nonfarm nonhousing sector) separately would yield
too large an estimate for earnings of
types of assets used most by noncorporate firms and too small an estimate for
types used most by corporations. However, the distribution of assets in noncorporate nonfarm firms could scarcely
differ enough from that in nonfarm
corporations to introduce an error of
appreciable size.
Because Jorgenson and Griliches
make a single allocation for the whole
private domestic economy, without
isolating housing and agriculture, the
potential bias in their estimates is much
larger and extends to residential as well
as nonresidential capital and land. The
direct way for them to remove the
potential bias would be to make
separate allocations of earnings in
corporate and noncorporate sectors. An
indirect way, having no advantage
because it requires the same information, would be to increase the weight
attached to corporate assets by (1)
raising the value of corporate holdings

SUEVEY OF CUEEENT BUSINESS

May 1909

of each type of asset by the ratio of shifts weight from depreciable assets to
after-tax earnings to before-tax earnings land and inventories if (as is the case)
in corporations; (2) adding the resulting "true" depreciation as measured by
adjusted value of corporate holdings to Jorgenson and Griliches exceeds capital
the unadjusted value of noncorporate consumption allowances as measured
holdings of each type of asset; and (3) in the national accounts (which they
allocating combined corporate and non- use as a proxy for depreciation allowcorporate before-tax capital-land earn- able for tax purposes). I presume their
ings among types of capital and land in purpose in doing this is to allow for
proportion to the adjusted asset values supposed effects of taxing depreciable
so obtained. I surmise that Jorgenson assets on amounts that represent reand Griliches may have had this in covery of capital rather than true earnmind when they introduced their for- ings, but defects in their formula and
mula for the determination of service measurements make the amounts
prices in the presence of a direct tax on shifted haphazard.
The formula [1, p. 267, formula 11]
income.
is:
This formula, which is used in their
1—
— uv . l—
actual calculations in place of the
T
simpler formula already discussed, is
quite complex because it tries to deal
The definitions of the terms [as
simultaneously with capital gains and
given
in 1, pp. 256, 267, and 277-279
the corporate income tax, including the
and
in
correspondence from the authors]
effects of differential taxation of capital
and
their
values for equipment and
gains. I believe the formula is intended
for
inventories
in my example above
to allocate earnings among types of
are
as
follows:
capital and land on the assumption that
asset values each year are proportional
pk is the price of the kth capital
to the sum of net (after depreciation)
service. In using the example,
earnings and capital gains in that year
I let it refer for convenience to
when earnings and capital gains from
the price of the service of $50,000
each type of asset are each measured
worth of equipment, and of $50,after deduction of the corporate income
000 worth of inventories.
tax applicable to them.
g> is the price of the kth investment
The formula, which I shall now
good. In the example, it is $50,000
describe, does not actually do this. In
for equipment and $50,000 for
fact, it does nothing at all to remove the
inventories.
bias, just discussed, that allocative
effects of the corporate income tax
u is the ratio of corporate profits
may be presumed to introduce. The
tax liability to profits before taxes
reason is that Jorgenson and Griliches
in
the private domestic sector of
apply the same ratio of before-tax
the
economy.
earnings to after-tax earnings (the
average ratio for the whole private
Corporate profits tax liability is
economy) to both corporate and nontaken from the national accounts.
corporate assets instead of using the
It includes tax liability incurred
corporate ratio for corporate assets
because of inventory profits and
and a ratio of one for noncorporate
other capital gains.
assets.
"Profits before taxes" in the
Introduction of new terms does not
private domestic sector are measimprove the results obtained by the
ured as property income (Jorgsimpler no-tax formula already deenson- Griliches definition) less
scribed but instead compounds the
capital consumption allowances
errors. In particular, it accentuates the
and private domestic net interest,
erroneous shift of the weights from
both
taken from the national
capital-land components on which capiaccounts.
Profits before taxes are
tal gain is high to those on which
therefore
equal to the sum of
capital gain is small. In addition, it

[

SURVEY OF CUEEENT BUSINESS

May 1969

"corporate profits and inventory
valuation adjustment" in the
domestic sector, the proportion
of "proprietors' income" not allocated to labor, the "rental
income of persons," "indirect
business tax and nontax liability,"
"business transfer payments," and
"statistical discrepancy," minus
"subsidies less current surplus of
government enterprises."29
If the reason that Jorgenson and
Griliches count indirect taxes as
capital-land earnings is a belief
that their shortrun incidence is on
this share, one would also expect
indirect taxes to be counted as
taxes on these earnings. This is
not done; indirect taxes are not
counted as taxes on income but as
part of income after tax.
This variable is the same for each
type of asset, regardless of its
distribution between the corporate
and noncorporate sectors. In the
example,
U

= 3,333=

9,000

is the ratio of (a) total income
from property less profits tax liability less the current value of
replacement plus the current
value of capital gain to (b) the
current value of capital stock. It
is the same for all types of capital
and land. In the example,
r = 15,000—3,333—7,000+2,000
= .06667.

100,000

is the ratio of private domestic net
interest to the after-tax rate of
return, r, multiplied by the current value of the capital stock.
It is the same for all types of
capital and land. In the example,

1,000
= .15.
.06667X100,000
29. As originally printed, the Jorgenson-Griliches article
stated that "the variable u, the rate of direct taxation, is the
ratio of profits tax liability to profits before taxes for the
corporate sector. These data are from the U.S. national
accounts" [1, p. 277]. This definition, though logical if u were
to be used only for corporate assets, would make the equation
as it stands wholly inconsistent.

w is the proportion of "true" replacement (depreciation) that is
allowable for tax purposes. Jorgenson and Griliches obtain this
proportion as the ratio of capital
consumption allowances, as measured in the national accounts, to
their estimates of depreciation
(replacement). They use the same
ratio for all types of depreciable
assets (residential structures, nonresidential structures, and equipment). For equipment in the
example,
w=

5,000

11
g*. In the example, the ratio is

1,500 = .03 for equipment,
50,000
and
500 = .01 for inventories.
50,000
When the values derived from the
example are inserted, weights of $10,794
for equipment and $4,206 for inventories are obtained. For equipment pk
equals:
$50,000

=.7143.

7,000

No value is needed for inventories
(or land).
5k is the rate of replacement (depreciation) of the kth investment
good. For equipment in the example,

dk=

7,000

=.14.

50,000

No value is needed for inventories.
x is defined as the proportion of
capital gains included in income
for tax purposes. However, Jorgenson and Griliches inform me
that, in their calculations, x actually was assumed to be zero for
all types of assets.30
— is the rate of capital gain on the
Qk
kth investment good. I defer a
description of the derivation of

30. In then* article this is not really clear. They write only
that "the proportion of capital gains included in income is
zero by the conventions of the U.S. national accounts" [l,
p. 267]. This must be interpreted to mean that "the variable
x, the proportion of capital gains included in income for tax
purposes (but not the value of capital gains as they appear
elsewhere in the formula) is zero." The two statements are
unrelated, and while the first is true, the second is not. Some
capital gains (the inventory valuation adjustment in particular) are fully, and others partly, taxed. Jorgenson and Griliches include these taxes in the numerator of u, which has
the effect of charging them to earnings instead of to capital
gains. With x equal to zero, —ux in the numerator of the last
term of the formula could be omitted without changing the
results.

1-(.3704X.7143)>
1-.3704
1-(.3704X0). .03~|=$10,794.
1-.3704 ^

For inventories, pk equals:
$50,000

[-(.3704X.15)
X-0666 7+.00
1-.3704
1-(.3704XO)>X.0ll = $4,206.
1-.3704

Effects of the formula
It is informative to recapitulate
results from the example, and insert
the results of one additional calculation.
When no account was taken of capital
gains or taxes, weights of $11,000 for
equipment and $4,000 for inventories
were obtained. Use of the no-tax
formula to allow for capital gains
shifted the weights to $10,500 and
$4,500. If tax depreciation had been
the same as true depreciation in the
example, substitution of the formula
with taxes present would have further
shifted the weights to $10,046 and 7
$4,954, this change reflecting the
Jorgenson-Griliches assumption that
capital gains are tax free.31 With
allowance, in addition, for taxation of
part of "true" depreciation on equipment, the weight of equipment is
raised to $10,794 and that of inventories
reduced to $4,206. The particular
numbers reflect only the figures assumed in the example, of course, but
the direction of the changes at each
31. This calculation uses only the column in the example
headed "Jorgenson-Griliches." The values of the variables
are the same as those just given except that u is .4761 instead
of .3704, and w (for equipment) is 1 instead of .7143.

12
step helps to explain just what the
formula does to the weights. I have already pointed out the main consequences.
The Jorgenson-Griliches formula may
have theoretical interest.32 But as they
have applied it, it is hardly to be taken
seriously as a tool for statistical analysis. The alterations in weights, away
from assets with large capital gains, that
would be introduced by their simple
"tax-absent" formula are untenable. If
they were tenable, the additional
changes introduced by their "tax-present" formula would not be. The only
bias potentially introduced by the corporate income tax (except by differential taxation of earnings and capital
gains) is not affected. The overall corporate tax rate, u, as measured, is
meaningless. It also is obviously wrong
to assume that this tax bears as heavily
upon dwellings and land as upon other
assets. How indirect taxes can be
counted as part of before-tax capitalland earnings but not as a tax on these
earnings defies my understanding. Capital gains are not actually taxed at zero,
as is assumed; they are taxed at a wide
range of effective rates, ranging up to
full taxation of the nonfarm inventory
valuation adjustment. The fraction of
depreciation (replacement) as measured
by Jorgenson and Griliches that is
taxable is not the same for all types
of depreciable assets, as is assumed; the
ratio of reproduction cost to original
cost varies greatly between long-lived
structures and short-lived equipment,
and the proportions of these assets on
which fast depreciation is allowed also
varies greatly in the later years of their
period.33 Furthermore, much of the depreciation in the national accounts
(particularly that on most dwellings)
has no tax relevance at all (and farm
depreciation is already on a replacement-cost basis). But these objections
are, of course, largely superfluous if I
am correct in asserting that the capital
gains adjustment is itself a mistake.

32. However, if the formula is viewed as a theoretical
construct rather than a description of their procedures,
u, v, w, and x should all carry the subscript k since they
differ for each asset type.
33. Tax depreciation differs from the Jorgenson-Griliches
estimate of true depreciation chiefly because original cost
is not the same as reproduction cost and because double
declining balance depreciation is not allowed or, if allowed,
is not used by taxpayers because they do not think it to be
to their advantage.

SUEVEY OF CUKRENT BUSINESS
Estimates of capital gains

May 1909

ment and in building up a capital stock
series. It is not met for nonresidential
The estimates of capital gains used
structures or for producers' durables,
by Jorgenson and Griliches that underfor each of which deflation is performed
lie the whole analysis are themselves in considerable detail.34 It is wildly not
subject to considerable criticism. The
met for inventories; the composition of
capital gain on any type of asset in a
inventory change is usually very differyear is properly the difference between
ent from that of the stock of inventories.
(a) the change in the value of holdings
Moreover, the composition of invenof the asset from the beginning to the
tory change varies greatly from year to
end of the year, and (b) the value of
year. As a consequence of this (together
the change in the quantity of the
with the fact that, on a 1958 base, the
asset, measured in current prices. This
levels of price indexes for different infigure can be approximated within an
ventory components diverge greatly as
acceptable error by multiplying the
one moves away from 1958), the imvalue of the asset at the beginning of plicit deflator for the change in inventhe year by the percentage change
tories properly moves very erratically,
during the year in a price index for
especially in years far removed from
the stock of the asset.
1958, even though the deflator for the
Jorgenson and Griliches inform me stock of inventories moves smoothly.
that they used the former of these Jorgenson and Griliches note and dismethods to secure capital gains on like these wild movements. But instead
land, utilizing data from Raymond W. of correcting their method to use the
Goldsmith. For the capital items, deflator for the stock of inventories
however, they use neither of these instead of inventory change, they arbimeasures. They write: "The capital trarily alter the deflator for inventory
gain for each asset is the product of the change by substituting the consumption
rate of growth of the corresponding deflator.
investment deflator and the value of the
asset in constant prices of 1958" Depreciation
[1, p. 279, italics added]. This differs
When an investment yielding a
from proper procedure in two respects. First, they measure changes positive gross return is made, gross
in prices from the average of one year output is increased, depreciation is
to the average of the next, instead of increased, and net output is increased
from the beginning to the end of the by the difference between the two,
year. This is important for their annual which is the net product of the investseries, but probably washes out over ment. If one were interested in analyzing
a period of years. Second, and more the growth of both gross and net
important, they use the implicit de- product, he could proceed in any of
flator for investment instead of the three ways. (1) He could analyze the
implicit deflator for the capital stock. growth of net product using net earnings
This procedure yields an accurate weights (as I did in Why Growth Rates
approximation of the capital gain only Differ), and add constant-price depreciaif the two deflators are the same. They tion to output and to the contribution
are the same if, but only if, the com- of capital in order to analyze gross
position of the stock of an asset is the product (as I did in section I of this
same as the composition of investment paper). When I apply this method to the
in it during each of the years com- private domestic sector covered by
pared—gross investment in the case of Jorgenson and Griliches, my estimates
depreciable assets, net investment in yield the following results:
the case of inventories. Only in this
Contribucase are the weights appropriate for a
Growth rate Contribution of
tion of
of output
output
per
inputs
capital stock price index the same as
unit of input
those that underlie the investment
1.51
3.23
1.72
Net product
price index.
1.38
3.35
1.97
Gross product _ _
In the national accounts framework,
this condition is met only for residential
34. The fact that Jorgenson and Griliches treat each of
structures, which are treated as a single these as a single commodity, with a single service life, in
constructing capital stock series does not suffice to remove
commodity both in deflation of invest- the objection.

SURVEY OF CURRENT BUSINESS

May 1968

(2) He could analyze the growth of
gross product using gross earnings
weights (as Jorgenson and Griliches
do), and subtract constant-price depreciation from output and from the
contribution of capital in order to
analyze net product. (3) He could
analyze the growth of net product using
net earnings weights and the growth of
gross product using gross earnings
weights. The three procedures are
exactly equivalent only in special circumstances, but their results are not
likely, in practice, to diverge very
much. To explore the considerations involved in the choice would take me far
afield, and I content myself with the
assertion that, to measure net product,
it is better to use net product weights
than to follow the second alternative.
Jorgenson and Griliches [1, p. 257]
criticize John W. Kendrick for not
using service prices as his weights.
They are wrong. Kendrick analyzed
growth of net product and appropriately used net earnings weights. To
include depreciation in the weights in
an analysis of the growth of net
product, as Jorgenson and Griliches
insist he should do, would be a plain
error that would lead to overstatement
of the contribution of capital to
growth.35 That the other aspect of
their service prices—their capital gains
and tax adjustment—would have improved his estimates is just not credible
on the basis of my preceding discussion.
Effect

of differences

in weights

When Jorgenson and Griliches adjust
their initial estimates to use what they
call "prices of capital services" in their
calculations, they raise their 1950-62
growth rate of total input, and lower
that of output per unit of input, by
0.35 percentage points [computed from
1, tables V and VI]. This number combines the effects of two changes from
their initial estimates. First, Jorgenson
and Griliches remove an error present
35. Unless the second alternative listed above were to be
adopted, which Jorgenson and Griliches do not suggest.
There have been some studies of gross product that have
included depreciation in the weight of capital and land as
a whole but have allocated it among components by value
of the stock. The Jorgenson-Griliches criticism of this procedure (which corresponds to theirs in construction of their
table 1) is correct.

in their initial weights. Whereas they sure whether it is positive or negative.36
initially allocate the depreciation com- Neither can I calculate the discrepancy
ponent of their gross capital-land earn- between our results (not necessarily
ings weight like net earnings, they now included in the 0.35) that is introduced
allocate it correctly by depreciation. by my according separate treatment to
Second, they introduce the adjustment housing and agriculture. Hence, I canfor capital gains and corporate income not measure the difference in our output
tax that I have described. The portion per unit of input series that resulted
of the 0.35 percentage points that from the difference in our allocation of
results from the reallocation of de- the total capital-land weight among
preciation does not represent a dis- components, and this introduces a gap
crepancy between their estimates and into the reconciliation table I provide
mine of the contribution of output per in section IX.37
unit of input to GNP growth in the
Consideration of the bearing of the
private domestic sector. 1 cannot isolate Jorgenson-Griliches discussion of servthis portion but it is clearly substantial ice prices upon my own estimates
and, like the combined adjustment, suggests only one qualification of my
positive. The portion that results from procedures. This is the possibility,
the adjustment for capital gains and already examined, that I may slightly
taxes does cause a discrepancy, but I bias my results by overweighting noncannot isolate the amount nor even be residential land.

V. The Measurement of Capital-Land Inputs
(Excluding the "Utilization" Adjustment)
I turn now to input series for the land to have been constant over the
various types of capital and land. period.38 Its contribution to growth is
This section compares my estimates therefore zero in both series.39
with those of Jorgenson and Griliches
after their adjustment for what they
call "errors" in investment goods Inventories
prices, but not for changes in "utilizaTo measure inventory input, I use the
tion." Their "utilization" adjustment
OBE
series for the value of farm and
will be discussed separately in section
nonfarm
inventories in 1958 prices; this
VII.
is the series that is consistent with the
annual changes published in the national
Nonresidential land
accounts. The growth rate of this series
Jorgenson and Griliches and I each times the inventory share of national
estimate the input of nonresidential income equals the contribution of
inventories to growth.
Jorgenson and Griliches initially use
a
conceptually
similar, but statistically
36. The percentage division of the Jorgenson-Griliches gross
capital-land earnings weight between net earnings and dedifferent, series obtained by starting
preciation also affects the results. It may or may not differ
with a base-year value and cumulating
appreciably from mine. Their depreciation is presumably
larger because they use the double declining balance instead
annual changes published in the national
of the straight-line formula. But their net earnings are also
accounts. They then introduce a cerlarger because they include indirect taxes.
37. The combined effect of this and certain other differences
tainly erroneous change in the price
is estimated in section IX to be 0.33 percentage points.
deflator; they substitute for the inven38. Their estimates combine residential with nonresidential land. Perhaps they would assume some slight decrease in
tory deflator the deflator for personal
nonresidential land and an increase in residential land if
consumption
expenditures. This error
they were to make the distinction.
39. Because of differences in the weight assigned to this
is apparently a byproduct of their
nongrowing factor, already discussed, this does not mean
faulty procedure for measuring capital
that land does not affect our results.

SUEVEY OF CUKEENT BUSINESS

gains, which I have already discussed. contribute to production typically does
Growth rates of the stock of inven- decline during their service lives but
tories from 1950 to 1962 are 3.00 for my not very much. I suggested [2, pp.
series [2, p. 190], 4.06 for their initial 140-141] that if one weighted the
series, and 4.14 for their series after the growth rate of gross stock about 3, and
price substitution (both computed from that of net stock based on straight-line
1950 and 1962 values in 1958 prices depreciation about 1, he would obtain
provided by Jorgenson and Griliches). a series that might reasonably approxiThe initial Jorgenson-Griliches inven- mate the decline in the ability of
tory series increases by about the same capital goods to contribute to producabsolute number of 1958 dollars as mine. tion as they grow older. To give some
Its much larger percentage change and weight to net stock in this way is meregrowth rate reflect a much lower figure ly a convenient method of introducing
for the base-year value of the stock; a declining pattern.
their series for total inventories runs at
In my actual estimates, I gave equal
a bit lower level than the OBE series for weight to gross stock, based on Bulletin
nonfarm inventories alone. The data F lives, and to net stock, based on
they use for level and change are Bulletin F lives and straight-line deevidently inconsistent.
preciation. (For the 1950-62 period,
The difference of 1.14 points between but not the subperiods, estimates of the
* their final inventory growth rate and contribution of capital to growth with
mine accounts for 0.04 percentage the capital stock data I had were
points of the difference between our actually the same whether gross stock
estimates of output per unit of input or net stock was used, so that the
growth, based on my share weights; weights actually did not matter for the
the amount based on their share whole period.) I did so partly because
weights would probably be about the I feared the gross stock series then
same. Of the divergence, 0.03 is due to available to me was unduly sensitive
the low level of their inventory series; to possible errors in estimated service
this is raised to 0.04 by their price lives as a result of its construction with
adjustment.
but little detail and without a distribution of retirements, and I wished to
Nonresidential structures and equipreduce
this sensitivity; and partly bement: Denison series
cause of the needs of international
One's choice of a capital stock series comparisons [2, pp. 140-141].
to measure input of nonresidential
My estimates were made before the
structures and equipment necessarily latest OBE capital stock study was
depends on his judgment as to whether completed. Before I continue this secor not the ability of a capital good to tion, the change that use of the new
contribute to production declines during OBE data would introduce into my
its actual service life because it per- estimates needs examination. Had the
forms less well, requires more mainte- OBE study been completed, I would
nance, or is installed in a less optimal have used OBE capital stock series
use than it was initially as a result of based on Bulletin F lives, on use of the
demand shifts and the like; and, if it Winfrey distribution for retirements,
does decline, by how much and in what and on use of the OBE "price deflation
time pattern. Gross stock (the value of II."
the stock without deduction for acGrowth rates of the stock of noncumulated depreciation) provides an residential structures and equipment
appropriate measure if there is no from 1950 to 1962 computed from five
decline. Use of a net stock series is measures, and my estimates of the conalways inappropriate on theoretical tribution of structures and equipment
grounds; net value drops as the length to the growth rate based on each, are
of the remaining service life declines, as follows: 40
and this has no relevance to ability to
contribute to production currently.
40. The revised OBE data were provided by letter on
In Why Growth Pates Differ, I assumed December 19, 1967. My average 1950-62 weight for nonresidential structures and equipment is 11.2 percent of total
that the ability of capital goods to input.

May 1969

Nonresidential structures
and equipment capital
stock series

Growth
rate
(percent)

Contribution
to growth rate
of national
income
(percentage
points)

Average of gross and net stock
series, equal weights:
1. Used in Why Growth
Rates Differ
2. OBE revisedDeflation I. _ _
3. OBE revisedDeflation II

3.74

0.43

3.24

.37

3.51

.40

3.40

.39

Average of gross stock
(weighted 3) and net stock
( weighted 1):
4. OBE revisedDeflation II

Row 1 shows the estimates I actually
used. Row 2 shows that the incorporation of revised OBE data, based on
Bulletin F lives, straight line depreciation, and the Winfrey distribution,
but retaining the same deflators (OBE
Deflation I) as the estimates I actually
used, would lower my estimate of the
contribution of capital to growth by
0.06 percentage points. The change is
due mainly to the use of much more
detail in the calculation of stocks.
Row 3 shows that substitution of
OBE's series based on their Deflation II
for nonresidential structures would
yield a contribution of capital 0.03
percentage points higher than does
use of their Deflation I series. (I shall
comment on the difference shortly.)
After this substitution, the contribution of nonresidential structures and
equipment based on revised data remains 0.03 points lower than the
estimate I actually used.
Given estimates incorporating the
Winfrey distribution and the use of
considerable commodity detail, and
in the absence of international comparisons, I would weight gross stock
about three and net stock (based on
straight line depreciation) one, instead
of assigning equal weights. This would
yield a contribution of 0.39 points
(row 4) and would lower the estimates
I actually used for the contribution
of capital by 0.04. My estimate for the
contribution of output per unit of
input is thus 0.04 points too low by
reference to the estimate I would now
secure by use of the data presently
available.

May 1969

Nonresidential structures and equipment: Jorgenson-Griliches series

SURVEY OF CURRENT BUSINESS

double declining balance) apparently are ing, value must decline as remaining
about twice too big to retain the (Bulle- service life diminishes whereas a meastin
F) average service lives that they ure of current services must not do so.
Jorgenson and Griliches treat noninitially
accept and from which they Thus, it is entirely consistent to use
residential structures and producers'
begin
the
calculation [1, p. 277]; that is, net stock values to determine weights,
durables as separate inputs in their
they
greatly
cut their own average and whatever series seems most suitestimates. For each, they use the double
service
lives.
Starting
with a 15.1-year able (including, in particular, gross
declining balance formula to obtain a
average
service
life
for
equipment, for stock) to measure changes in capital
capital stock series. No detail is used
example,
they
estimate
half the stock input (or services) over time. Jorgenson
for either calculation.
has vanished after 5 years, and seven- and Griliches themselves accept this
Capital stock series obtained by the eighths after 15 years.
view when they adjust their capital
double declining balance formula have
Whatever the intent, changing the services for changes in utilization
always heretofore been described as name does not change the data, and I (section VII below) without changing
"net stock" series. Estimates of the shall regard the series constructed by their depreciation.
value of net stock obtained by this Jorgenson and Griliches as measuring
I wish to stress that the choice of
formula assume that net value declines what such series have always been re- depreciation or replacement formula
rapidly—much more rapidly than the garded as measuring—the net stock appropriate for measurement of changes
straight line formula assumes. Justi- based on the double declining balance in capital input has nothing to do with
fication of so rapid a decline in net formula—and what they call "replace- "vintages," that is, with the way one
value has relied on the argument that ment" as an estimate of depreciation. wishes to treat quality differences in
obsolescence is rapid; this justification A series based on this formula makes the capital goods that do not reflect a
seems to require that obsolescence not ability of an individual capital good to difference in costs and that result in
only shortens service lives (this is contribute to current production drop "unmeasured" quality change (or "emreflected in all capital stock series) but much faster than seems to me at all bodied" technical progress) as time
also greatly accelerates the loss of plausible. Whatever can be said to goes on. Use of a fast depreciation
value during the shortened service life. justify its use in measuring net value formula is not a method of making an
Although their method is the same, has no relevance to measurement of allowance for unmeasured quality
Jorgenson and Griliches sometimes ap- changes in ability to contribute to change. This can be readily seen from
pear to regard the series they obtain by current production.
the fact that, with any continuous
the double declining balance formula not
rate
of quality improvement in capital
I have puzzled over the Jorgensonas a net stock series but as a gross stock Griliches discussion of why they use goods, net capital stock based on
series. Thus, in describing the derivation their formula [1, p. 255] but have been double declining balance depreciation
of a capital series, they state [1, p. 255]: unable to discern its relevance to the can rise either more or less than gross
"The quantity of new investment goods choice of a capital stock series to stock or net stock based on straight
reduced by the quantity of old invest- measure changes in capital input.41
line depreciation. From 1950 to 1962,
ment goods replaced must be added to
It may be necessary to note here that for example, data from the OBE capital
accumulated stocks." And, again: "We the choice of a particular formula to stock study show identical percentage
assume that the proportion of an invest- measure capital depreciation (or "re- changes for net stock when straight
ment replaced in a given interval of time placement") in the process of comput- line depreciation is used and when the
declines exponentially over time." [Both ing income share weights, including double declining balance method is
italics mine.] And they usually (though the net capital values used to allocate used.42
not on page 277) refer to the value total net capital-land earnings among
Jorgenson and Griliches employ
eliminated from the stock each year as components, in no way dictates that series they themselves derive by use of
"replacement" rather than as deprecia- the same formula should be used to the double declining balance formula.
tion. If they mean "replacement" to be construct the capital stock series that They assign a single service life to all
construed as equal to discards, they are is used to indicate changes in capital nonresidential structures and to all
indeed trying to construct a gross stock input over time. Different series not producers' durables, whereas OBE asseries. But if this is their intent, their only can be used for the two purposes signs different lives to each of a large
method is certainly odd. I do not know but, conceptually, must be. For weight- number of components. The growth
what evidence they would muster to
rate of their value of nonresidential
support the assumption (which is also
structures and equipment (from the
41. The Jorgenson-Griliches discussion seems to visualize
applied, even more improbably, to dwel- steady growth of replacement investment, and their rational- beginning of 1950 to the beginning of
seems to require, in addition, steady growth of new
lings) that discards decline exponentially ization
1962) is 0.17 higher than that of the
investment. But if gross capital investment grew at a steady
(i.e., are greatest in the first year after rate (and service lives were not changed over tune), it would corresponding OBE series. Even so,
little or no difference whether an index of gross stock
purchase or installation and thereafter make
(in the usual sense of the term) or of net stock computed by
decline each year). But even if it were any of the usual formulas were used to measure capital input.
42. This is the case whether "constant cost I" or "constant
cost II" estimates are compared. Changes are computed
It is only because investment has been irregular—particularly
true that discards decline exponentially, because
from the average of the beginning and end of 1950 to the
of depression and war—that the problem of selection
their exponents (because they use has any importance.
similar figure for 1962.

SUEVEY OF CURRENT BUSINESS

in the period examined, their series is
not radically different from other measures. The 1950-62 growth rates of the
capital stock series they initially obtained (prior to their price substitution) and used in constructing their
table I, are 4.11 for equipment, 3.42
for nonresidential structures, and 3.72
for nonresidential structures and equipment combined (computed from data
for the value of the stock in 1958 prices
provided by Jorgenson and Griliches).
However, in moving from their table
II to table IV, Jorgenson and Griliches
greatly accelerate the rise in the growth
of the equipment stock by deflating
past gross investment in producers'
durables by the price deflator for
consumers' durables instead of that
for producers' durables. This substitution raises the 1950-62 growth rate of
their equipment stock alone by 1.49
points, to 5.60, and the growth rate of
nonresidential structures and equipment combined by 0.62 points, to 4.34
(computed from capital stock data
provided by Jorgenson and Griliches).
To justify the substitution, Jorgenson
and Griliches state that, for items
that appear in both the BLS consumers'
price index and the BLS wholesale
price index, the retail and wholesale
series diverge by roughly the same
amount as the composite indexes.
They further state that the consumers'
price index is better because more
money is spent on it.
It is desirable to deflate common components of consumers' expenditures for
durable goods and producers' purchases
of durable goods by the same deflator,
the best available—at least when they
are sold by the same outlets on similar
terms. But automobiles are the only
important common component (as well
as the only component of the consumer
and wholesale price indexes that is mentioned by Jorgenson and Griliches).43
And OBE already uses the same (consumers') price series to deflate consumer
and business purchases of automobiles.
The sharp divergence between the implicit deflators for all consumers' durables and all producers' durables is
ascribable to commodities not common

to the two series. Production processes
for the two sets of goods are very different. Consumers' durables, which had
the smallest price rise of any sizable
product group, are dominated by massproduced, standardized products. Their
exceptional price behavior was due to
radio and television receivers, "kitchen
and other household appliances," and
automobile "tires, tubes, accessories,
and parts." Producers' durables, in contrast, are dominated by items produced
in small volume, including a large element of individualized, built-to-order
items most akin to custom services. I
do not see how any inference about
changes in prices of producers' durables
can be drawn from prices of consumers'
durables, or that the latter provide a
more relevant comparison with the
former than any other prices.
The OBE deflator for producers'
durables is, to be sure, subject to
substantial error in either direction
because the data entering it are incomplete and their reliability low—
mainly because so many components
are not standardized. But there is no
a priori presumption that the series is
biased upward by reference to the
usual price index criteria. I regard
this substitution as unwarranted.
It must be stressed that this price
substitution cannot be rationalized as
an attempt to allow for quality change
not involving a difference in costs at a
common date ("unmeasured" quality
change). Neither the CPI nor the
WPI makes any such allowance (nor
do any of the GNP deflators).44
In contrast to producers' durables,
there is a presumption that the deflator for the nonresidential structures
portion of GNP is biased upward by
reference to usual price index criteria.
This is because most components are
based on prices of construction materials and labor, rather than on output
prices, and hence do not allow for
changes in output per man-hour in
on-site construction work. This bias
has long been recognized, but its size
has been hard to appraise.
For use in its capital stock study,
OBE developed an alternative non-

43. Some types of office furniture might be regarded as
having a household counterpart, and there are items of
trivial importance.

44. In my view, there is no way to do so. But this is a
controversial matter that need not be discussed here.

May 1969

residential construction price series
that attempts to eliminate this bias,
and used it as an alternative to the
GNP nonresidential construction price
deflator to derive its Deflation II
capital stock estimates that I have
already mentioned. These estimates
differ from OBE's Deflation I estimates
only because of the use of a different
construction deflator. Jorgenson and
Griliches make the same substitution
in moving from their table II to table
IV. This raises the 1950-62 growth
rate of their nonresidential structures
series by 0.50 percentage points, from
3.42 to 3.92, and the growth rate of
nonresidential structures and equipment combined by 0.28 points, from
3.72 to 4.00 (computed from data
provided by Jorgenson and Griliches) ,45
The effect on the combined series is
almost identical to that (0.27 points)
introduced when the similar substitution was made between lines 2 and 3
of the text table above, and the effect
upon the growth rate of total input
when my weights are used is also the
same, 0.03 percentage points.46
The 4.00 growth rate of the stock of
nonresidential structures and equipment obtained by Jorgenson and
Griliches when their construction price
substitution but not their equipment
price substitution is introduced may be
compared with the 3.40 growth rate
I obtain by use of the revised OBE data
with use of Deflation II (text table
above). The 0.60 difference reflects
both a difference in choice of capital
stock series and OBE's greater use of
commodity detail. Based on my
weights, it accounts for 0.07 percentage
points of the difference between us in
output per unit of input.
Residential structures and land

My methodology does not require an
input series for residential structures
45. With both the equipment and construction price substitutions, the 1950-62 growth rate of the Jorgenson-Griliches
series for nonresidential structures and equipment is 4.65.
46. Robert J. Gordon has also attempted to construct a
series for deflation of nonresidential construction from which
the bias has been eliminated. Data he has generously provided
me show that substitution of his series for the OBE nonresidential construction deflator would raise the growth rate
of a series for the stock of nonresidential structures and
equipment (specifically, the gross stock based on Bulletin F
lives) by 0.40 percentage points. A change of this size would
raise the growth rate of a total input series, based on my
weights, by 0.04 percentage points as against the 0.03 indicated by the OBE Deflation II series.

May 1969-

and land. Instead, I isolate the amounts
of national income, measured in constant prices, that originated in the
"services of dwellings" industry in the
same way as the current dollar figures
were obtained in deriving share weights.
The same procedure can be followed
for GNP at factor cost. I find [2, pp.
123-126, 413] that the increase in the
stock of dwellings and residential land
contributed 0.25 percentage points to
the growth rate of national income and
0.32 points to the growth rate of GNP
at factor cost from 1950 to 1962.47 This
method of direct measurement, which I
first used in [2], is, in my opinion, an
important advance in growth analysis.
It provides a measure for the contribution of this very large part of the
capital-land stock to the growth of
output as actually measured that is
entirely accurate, except for some slight
statistical difficulty in the United
States in disentangling the details of
the national product estimates. An
incidental advantage, it may be noted,
is that the figure for the contribution to
GNP makes no use of, and consequently
cannot be affected by, errors in the
price index for residential construction.
Jorgenson and Griliches measure the
contribution of residential structures
as the growth rate of the dwellings
stock times the weight assigned to
dwellings—the procedure I used in an
earlier study [3]. However, instead of
using a gross stock series to measure
changes in the services of dwellings, as
I did then, they use net stock calculated
by the double declining balance formula. It seems to me impossible to
suppose that this pattern remotely
resembles that of the flow of services
of dwellings during their service life.
The 1950-62 growth rate of the dwellings stock computed by this formula,
as they initially estimate it for use
in their table I, is 4.53 (computed
from data provided by Jorgenson and
Griliches).
The deflator for residential construc47. The increase in gross product at factor cost, valued in
1968 prices, was put at $15.7 billion.
348-323 0 - 6 9 - 3

SUEVEY OF CURRENT BUSINESS
tion may be presumed to have an
upward bias for the same reason as the
deflator for nonresidential construction.
Jorgenson and Griliches attempt to
allow for this by deflating residential
construction expenditures by the OBE
Deflation II series for nonresidential
construction in place of the residential
construction deflator. This raises the
1950-62 growth rate of their dwellings
stock by 0.39 points, from 4.53 to 4.92. 48
Residential land is combined with
other land in the Jorgenson-Griliches
procedure. As already indicated, their
combined growth rate (and contribution to growth) is zero.
If I had used the Jorgenson-Griliches
growth rate for the net stock of dwellings, and multiplied it by my share
weights, I would have obtained a much
lower figure than I did for the contribution of dwellings to growth of total
national income: probably around 0.13
percentage points instead of 0.25.49
My output per unit of input series
would then have been raised by about
0.12 points. I am not, unfortunately,
able to quantify the effect upon their
estimates of the difference between us
in the measurement of the contribution
of housing.
Summary comment

The Jorgenson-Griliches estimates of
the contribution of capital and land to
GNP growth differ from mine because
of (1) differences in weights; (2)
differences in the initial method of
measuring capital and land inputs,
including the difference in method of
estimating the contribution of dwellings; (3) their substitutions of price
indexes; and (4) a utilization adjustment they introduce. I have already
examined the weights (1); discussion
of the utilization adjustment (4) is
deferred to section VII.
48. From 1950 to 1962, the Deflation II series rises less than
the residential construction deflator, so the substitution implies that the bias in the deflator is downward in this period.
This accounts for the negative adjustment in the growth rate
of output that the following section shows is introduced by
this price substitution. Over the longer time span reflected
in the capital stock series, the adjustment is in the right
direction.

17
The total effect of all their price
substitutions (3) was to raise their
1950-62 growth rate of total input,
and lower that of output per unit of
input, by 0.23 percentage points [computed from 1, tables II and IV]. This
calculation is based on use of their
weights. Of this amount, in the neighborhood of 0.07 points derives from
adjustment of construction. The remaining 0.16 points are due to substitutions of price series for producers'
durables and inventories (almost entirely the former), which I regard as
illegitimate. (It is partly offset by an
output adjustment described in section
VI below.)
The effect of (2), differences in
measures of input (other than price
substitutions for producers' durables and
inventories), I can calculate only with
the use of my weights—that is, the
numbers refer to the change in my series
that use of their input indexes would
introduce. Of the difference between us
in total input and output per unit of
input, the difference in our measure of
inventory input (excluding their price
substitution) accounts for about 0.03
percentage points, and land indexes for
none. Their nonresidential structures
and equipment series rises enough more
than the revised OBE series I would use
to account for 0.07 points; both are
based on the OBE II construction
deflator. The difference in residential
structures accounts for minus 0.12
points. The difference in capital stock
measures (or their equivalent, in the
case of dwellings) thus accounts for
minus 0.02 points of the difference in
our output per unit of input measures,
based on my weights and apart from
the effects of their price substitutions
for producers' durables and inventories.
My incorporation of revised OBE
data for nonresidential structures and
equipment would add 0.04 points to the
difference between us.
49. This calculation supposes that about one-fourth of the
weight I assign to dwellings pertains to sites, as distinguished
from structures.

SURVEY OF CURRENT BUSINESS

VI Effect of Priee Index Alterations on Output
JORGENSON and Griliches substitute
investment price indexes in deflating
the investment components of GNP
as well as in measuring capital stock.
The 1950-62 growth rate of their private domestic GNP is raised by 0.09
percentage points [calculated from 1,
tables II and IV] and this partially
offsets the deduction from output per
unit of input they introduced by substituting prices in capital stock
measurement.
To isolate the separate effects of
their price substitutions on output, I

duplicated their calculations. The
breakdown of their adjustment is:
producers' durable equipment 0.10;
nonresidential structures 0.03; residential structures, —0.03; and inventories,
0.00.
(The total, 0.10, presumably
differs from their 0.09 because of
rounding.) Thus, their entire output
adjustment stems, on balance, from
the use of consumers' durables prices
to deflate producers' durables; none of
it results from the legitimate attempt
to adjust construction prices.

VII. The Utilization Adjustment for Capital and Land
MORE than half of the difference between our output per unit of input
growth rates in 1950-62 results from
an adjustment that Jorgenson and
Griliches introduce for changes in utilization of capital and land. Their
general idea is that the hours per year
that capital is used have increased
secularly, and that a given percentage
increase in capital hours per dollar of
capital has the same effect on output
as a similar percentage increase in the
quantity of capital. Their capital utilization adjustment raises the contribution of their total input series by 0.60
percentage points in their full 1945-65
period and by about 0.58 points in the
1950-62 period.50 Their method of
60. The 1945-65 figure of 0.60 points was provided by
Jorgenson and Griliches; it can also be approximated from
their published data.
The average growth rate of their capital utilization series
itself was 1.72 in 1945-65 and 1.60 in 1950-62. (See the following text paragraph.) Multiplication of their 1950-62 growth
rate of 1.60 by their average 1950-62 capital-land share of
0.36175 yields an estimated contribution of 0.58 percentage
points.
(In this period, the combined contribution of their capital
utilization adjustment and the labor hours adjustment was
0.52, thus the contribution of the labor adjustment was
apparently about -0.06. I use this figure in section VIII.)

deriving this adjustment is theoretically unsound, and the statistical procedures they followed to obtain their
estimates are altogether untenable. In
my view, their capital utilization adjustment should be discarded.
Series for manufacturing equipment
powered by electric motors

The starting point for the adjustment
was a series contained in a 1963 SURVEY
OF CURRENT BUSINESS article by
Murray F. Foss [4]. Most production
equipment in manufacturing is powered
by electric motors. Foss used Census
data for electric power consumption
and the horsepower of electric motors
to estimate the average number of
hours per year that electric-powerdriven equipment in manufacturing
establishments was utilized. He concluded that its utilization increased
by an amount on the order of onethird to one-half from the 1920's to
the mid-1950;s. The dates for which
he made actual calculations were the
Census years 1929, 1939, and 1954

May 1969

[4, table 2, line 7]. Growth rates of
average equipment hours calculated
from his utilization estimates for these
years are —0.45 from 1929 to 1939,
2.15 from 1939 to 1954, and 1.10 from
1929 to 1954. Jorgenson and Griliches
made a similar comparison of the years
1954 and 1962 [1, table X, line 6].
From 1954 to 1962, the growth rate
was 1.33. Jorgenson and Griliches
used the 1939-54 rate for all annual
changes in the 1945-54 period and the
1954-62 rate for all annual changes
after 1954. They thus obtained average
rates of increase in utilization of about
1.72 for 1945-65 and 1.60 for 1950-62.
These rates almost certainly are much
higher than the trend rate, which is
what Jorgenson and Griliches are seeking, or the rate that would be obtained
if calculations could be made directly
from the terminal years of these periods.
The average rate from the depression
year 1939 to 1954 must have been
greatly raised by the difference in cyclical position; the rate from 1945 or 1950
to 1954 must have been much smaller
than the rate over the 1939-54 period
as a whole.51 The rate from 1954, itself
a recession year, to 1962 or 1965
probably was also raised by cyclical
influences.52 A minimal downward adjustment of their estimates to eliminate
cyclical incomparability in the pre-1954
period could be made by substituting
the 1929-54 rate where they use the
1939-54 rate. This would lower the
1945-65 growth rate of utilization from
1.72 to 1.22, and the 1950-62 rate from
1.60 to 1.25. Probably a better procedure would be to use the 1929-62
rate, which is 1.16, as representative of
the trend throughout the period, hence
for both the 1945-65 and 1950-62 periods; this would cut their 1950-62 rate
by more than one-fourth and their
51. Foss himself wrote: "In fact, some of the illustrations
in this article suggest that the major change in relative
equipment utilization took place during and immediately
after World War II, and that changes since then (aside from
cyclical movements) have been relatively small" [4, p. 8].
52. Because Jorgenson and Griliches interpolate between
far-removed dates rather than use annual estimates, the
capital utilization adjustment obviously cannot purport to
adjust capital input for shortrun variations in utilization.
Jorgenson and Griliches note this and state that it "allows
only for the trend in the relative utilization of capital" [1,
p. 266]. My objection to their procedure is the same whether
one construes their series as representing the trend rate in
1945-65 and 1950-62 or the actual changes from 1945 to 1965
and from 1950 to 1962.

May 1969

1945-65 rate even more. Overstatement
of the increase in this series from the
absence of any procedure to deal with
the cycle is, however, among the least
of my objections to their utilization adjustment, and there is no need to pursue
it further.
A second limitation is that the
weights used to construct the allmanufacturing utilization series are
inappropriate for the use to which
Jorgenson and Griliches put it. "Available kilowatt hours of motors" were
used as weights to combine utilization
ratios for the component industries in
obtaining the all-manufacturing utilization series.63 For use in converting a
series for the value of power-driven
equipment in manufacturing establishments to a capital input series, the
utilization ratios for all manufacturing
should be based on the use of the value
of power-driven equipment in each
industry as that industry's weight.
This was noted by Foss [4, p. 11] but
is not mentioned by Jorgenson and
Griliches. A series so constructed is
not available for comparison, nor are
the value data for power-driven equipment that its construction would require. Perhaps the two sets of weights
would yield tolerably similar results;
at the 2-digit level, Foss finds, with
some exceptions, fair correspondence
between distributions of total fixed capital and installed horsepower. Nevertheless, the possibility of appreciable
error is present in the manufacturing
series.
Equipment values are not available
for mining either, but similar utilization
ratios for the five mineral industries
were published separately by Foss.
Solely as an illustration that weights
may matter, I calculated all-mining
utilization ratios with alternative proxies
for capital values. Use of "available
kilowatt hours" as weights yields a 4
percent increase in utilization from
1929 to 1954, whereas use of "electric
53. Foss confirms this statement, which the reader can
check by use of Foss's ratios for mineral industries [4, table
5], for which the procedure was similar and for which industry data are shown. For minerals industries, Foss shows a
five-industry breakdown. The all-industry utilization ratio
in his column 6 is equal to the ratios for the individual
industry groups weighted by "available kilowatt hours of
motors" as shown in column 2.

SUEVEY OF CUEEENT BUSINESS
power consumed by motors" would
yield a 16 percent decline. Like the
manufacturing series, these calculations
used 1929 weights for 1929 and 1954
weights for 1954. I argue subsequently
that fixed weight indexes would be
more appropriate. I calculated fixed
weight indexes using four alternative
sets of 1929 weights. Use of "value of
machinery and equipment installed
during 1929" yields a 14 percent increase in utilization from 1929 to
1954; "available kilowatt hours of
motors" a 12 percent increase; "national income originating," a 2 percent
increase; and "electric power consumed by motors," a 1 percent decrease.
Probably the first two are better proxies
than the last two for equipment values,
but differences are large and investigation is needed.
In the absence of tests of its effects,
the inappropriate weighting of the
manufacturing equipment series adds
to the reservations about the JorgensonGriliches use of this series that is
created by their failure to allow for
cyclical differences. But there is a
fundamental conceptual objection to
their use of this series to adjust capital
input that would remain if value
weights were used and cyclical adjustments were made. To develop this
point, I shall proceed as if this had
been done.
Conceptual problem of incorporating
utilization data

The trend rate of capital utilization
provides interesting information. But to
integrate this information into the type
of classification of growth sources that
Jorgenson and Griliches or I employ,
one must know the reasons that utilization increased and the amount due to
each reason. Even if one knew exactly
how much utilization had changed, in
the absence of this additional information he still would not know the amount
of the increase in output that (prior to
any utilization adjustment) is included
in the contribution of input (or any
component of input) and the amount
that is included in the contribution of
output per unit of input. This is a
subject that Jorgenson and Griliches do
not discuss at all. However, their procedures imply that, prior to the intro-

19
duction of their capital utilization
adjustment, the effects of an increase in
capital utilization necessarily appear
only in their output per unit of input
series.
The average hours "worked" by
power-driven equipment in manufacturing establishments (adjusted to eliminate short-term fluctuations) may
actually change for quite varied reasons,
and these have altogether different
implications for the analysis.54
1. The effects of some types of
change are fully measured by the
increase in the capital stock, so that
any additional allowance for increased
utilization duplicates the change in the
capital stock measure. These types can
be described as changes in composition
of capital, of which three main categories can be distinguished.
(a) At any point in time, producers
can select among varieties of equipment
with different characteristics that sell
at different prices. One characteristic
that can be purchased at a higher price
is greater reliability: longer use without
downtime for regular maintenance or
to replace worn-out or defective components or the entire machine. If
producers shift to higher priced equipment, average "hours worked" will
increase but so will the capital stock
series. A priori there is reason to
suppose that, as capital has become
more abundant relative to labor, the
use of more expensive equipment has
been one aspect of the rising capitallabor ratio.
(b) At any point in time, different
manufacturing industries vary in the
hours they use capital. On the assumptions that Jorgenson and Griliches and
I accept, the rate of return, as measured
by the ratio of net earnings to net
value, is, nevertheless, the same in each
manufacturing industry. If hours in
each industry are unchanged, but the
weights of the industries alter, the
average hours in manufacturing as a
whole will change but capital input
should not.
Suppose Industry A and Industry B
each have $1 million of equipment, but

54. Not all of these possibilities had occurred to me when 1
discussed capital utilization in Why Growth Rates Differ [2.
pp. 154-155]. I would now word that section somewhat
differently.

20
Industry A operates on three labor
shifts, or 120 hours a week, and
Industry B on one shift of 40 hours,
and capital is used during the same
time periods. Equilibrium requires the
same rate of return in the two industries; otherwise, there would be an
incentive for capital to move from one
industry to the other. If the rate of
return is 10 percent, the product (as
indicated by earnings) of the $1 million
of equipment in each industry is
$100,000. The product of $1 million of
equipment per hour it is used in a
week must then be three times as high
in Industry B as in Industry A ($2,500
against $833.33). This must be the case,
or the rates of return would differ.
If (because of changes in demand
patterns or for other reasons) Industry
B gets bigger relative to Industry A,
average hours worked by equipment in
the two industries combined will decline, whereas if Industry A gets bigger average hours will increase, because
Jorgenson and Griliches use a capital
utilization series that is constructed
with shifting industry weights. They
would therefore measure the former
development as a decline in equipment
input, the latter as an increase. This
is a simple "error of aggregation." It
results from giving an hour worked by
$1 million of equipment in each industry
the same weight.
To illustrate, suppose that in a
second year the total value of equipment is $2,000,000, as before, but
Industry A now has $1,500,000 and
Industry B $500,000. Based on the use
of capital stock to measure input,
without a utilization adjustment, the
contribution of equipment to output
(in first-year values) remains $200,000;
only the division between industries
has changed—to $150,000 in Industry
A and $50,000 in Industry B. This
correct result could also be obtained
by correctly weighting hours: The
value of equipment (in millions) in
each industry is multiplied by average
weekly hours, and the contribution to
output of an hour worked by $1 million
of equipment is counted as $833.33 in
Industry A and $2,500 in Industry B.
In Industry A, equipment value times
hours increased from 120 to 180;
multiplication by $833.33 yields an

SUEVEY OF CUREENT BUSINESS
increase in equipment's contribution
from $100,000 to $150,000. In Industry
B, equipment value times hours dropped
from 40 to 20; multiplication by $2,500
yields a drop in the contribution of
equipment from $100,000 to $50,000.
The total contribution of equipment at
first-year values is again $200,000 in
both years.
In this example, the JorgensonGriliches procedure would erroneously
yield an increase in equipment input
of 25 percent, instead of no change,
because it assigns equal weight to an
hour worked in each industry.
Foss has investigated the effects of
changes in industry weights in selected
periods and concluded that the change
in the all-manufacturing utilization
ratio he observed chiefly reflected
changes in individual industries rather
than in industry mix, although he did
note that there probably was a shift
toward continuous process manufacturing industries, particularly aluminum, refined petroleum, and chemicals.
(c) At any point in time, the number
of hours that different types of equipment are used varies widely within
any establishment, firm, or industry.
If the composition of assets changes,
the average hours worked by all
combined will rise or fall even though
there is no change for any particular
type. The hours for the same type of
equipment may also vary among uses,
and this distribution may change over
time. These cases are identical to that
discussed in (b). Greater use does not
imply larger earnings per dollar of
capital value. Two machines of different
types (or of the same type in different
uses) must be assumed to contribute
equal amounts to production, per dollar
of value, not per dollar of value mutliplied by hours worked. If this assumption is invalid, rates of return vary
and the economic unit is not in equilibrium. The sensitivity of a conglomerate
average-hours-worked series to changes
in weights of different types of machines, and to changes in weights of
different uses of machines, must be
high because the range of hours is
large. Shifts of this type could well
dominate the long-term movement of
"average hours" series for individual
firms, establishments, and industries.

May 1969

Unless a capital utilization series
can. be standardized to eliminate the
effects of all three types of "mix'J
changes, it is useless for the purpose
to which Jorgenson and Griliches put
it. I cannot imagine how such standardization could be achieved. But even if
it could, this would surmount only one
of the difficulties.
2. The amount of downtime of machines depends in part on the number
of workers who operate them (which
affects, among other things, the speed
of machine operation), their skill, and
the care they exercise. It depends also
upon the number and skill of the
workers who repair machines. The skill
of engineers and others employed by
equipment suppliers to service customers is often a crucial determinant of the
amount of time lost from breakdowns.
If machine hours increase because of an
increase in the quantity or an improvement in the quality of labor, this is
already counted in principle, and one
hopes in practice, as a contribution of
labor.
3. The amount of downtime depends
in part on expenditures for maintenance. A firm presumably attempts to
allocate expenditures among maintenance, purchases of new capital goods
for replacement, and production labor
in such a way as to minimize total cost.
Maintenance expenditures may change
because the price of maintenance
changes relative to prices of capital
goods and production workers; in this
case, there is no ascertainable contribution to growth. Maintenance expenditures may also change because management devises a better procedure to
determine the minimum cost combination. If they increase for this reason,
only the net benefit remaining after
deducting the increase in maintenance
costs from the saving in capital and
labor costs contributes to an increase in
output.55 Classification of any net benefit is discussed in case 7 below.
4. Downtime depends in part on the
inventory of spare parts; any change is
already covered as a contribution of

55. Unless output is measured on the Scandinavian "grossgross-product" basis, which double counts maintenance as
well as capital consumption.

May 1969

SURVEY OF CURRENT BUSINESS

inventories. It depends also on the more continuous use of machines. Foss
speed with which parts and servicemen writes:
can be obtained; this, in turn, depends
"Also of importance over the long run
on capital and labor in the transportahas
been the advance in knowledge
tion industries, which are already
acquired
by management in making
56
counted as capital and labor input.
more efficient use of machines. One
5. The hours that machines are used
example of this has been the efforts
may change because of a change in the
by many firms to smooth out within
average hours worked per worker; in
the year the production peaks which
my study I allow, in principle, for this
come from seasonal or other shorteffect in my adjustment of labor input
lived peak loads and which frefor changes in labor hours of full-time
quently entail the use of standby
workers [2, p. 61, n. 11]. (I found no
equipment with relatively low annual
significant change in labor hours of
utilization. . . . Within particular
full-time workers in the economy as a
industries there have undoubtedly
whole over the period analyzed so
been efforts to introduce continuous,
this case did not actually affect my
automatic operations in which maestimates.)
chines tend to be used with a high
6. Machine hours may also change
degree of intensity."
because shift work becomes more or
less prevalent in particular activities.
(c) Improve communications and
In my estimates, such a development speed transportation of parts and of
was regarded as a component source key personnel needed for repairs, notaof the change in output per unit of bly by air.
input [2, pp. 152-154, 173-174], and in
(d) Improve the decisionmaking
my international comparisons, I made
process generally—notably with rea specific estimate for this determinant.
spect to determination of the trade-off
However, I found no evidence of a
among costs incurred for maintenance,
significant change in shift work in the
replacement, downtime, speed of operUnited States in 1950-62, and therefore
ating machines, waste of materials,
estimated the contribution of changes
and quality of product.
in shift work to be zero [2, pp. 152This list of possible reasons for
154, 173-174].
changes in average machine hours may
7. The hours worked by machines
not be exhaustive. But it suffices to
may rise, or in some cases fall, because
make clear that, unless the reasons for
of advances of knowledge and its dischanges in capital utilization are known
persion. These may:
and their effects can be isolated and
(a) Provide more reliable machines
quantified, data on capital utilization
without increasing their cost—a develcannot be integrated into a classificaopment variously described as "untion of growth sources of the type
measured" quality change in capital
Jorgenson and Griliches and I use. It
goods or "embodied" technical progress.
is possible that the entire change indi(In practice, "measured" quality change cated by the Jorgenson-Griliches series
covered in case l(a) above and "un- is already reflected in capital and labor
measured" quality change are often input or counterbalanced by higher
intertwined.)
maintenance costs, and is not a com(b) Enable management to make ponent of the Jorgenson-Griliches output per unit of input series prior to their
utilization adjustment, or of my series.
56. Parts of points 2 to 4 are nicely illustrated by an
Or any or all of it may be a component.
advertising letter that happened to reach me as I was writing
Jorgenson and Griliches never mention,
this section. It states:
"Are you aware that the ... Corporation has for the
and appear unaware of, the range of
past fifteen years been providing preventive and corrective
possibilities.
maintenance to a growing number of manufacturers and
users of electronic and electromechanical devices?
Among the possible reasons for an
"Our experience in performing both scheduled and
increase in capital hours that I have
emergency service (supported by factory-trained personnel, local stocking of replacement parts, and quick response
listed, two would or might contribute
to emergency calls) aims to improve your operation in
to a change in output per unit of input
terms of lower 'down-time' and higher reliability."

21
as I measure it, and as Jorgenson and
Griliches do prior to introduction of
their utilization adjustment. The effects
of one of these, changes in shift work
in particular activities, I estimated [2,
pp. 152-154] to be zero in the economy
as a whole in 1950-62, though admittedly on the basis of inadequate
information; better data may permit
more reliable estimation in future
years. The other is advances in knowledge and their dispersion. There is no
clear presumption that these led to an
increase in the hours that capital goods
are utilized or that, if they did, the net
saving in unit costs bore any systematic
relationship to the change in machine
hours. But if there was such an, effect,
it appears in the "advances of knowledge" component of my output per
unit of input series. I see scant possibility that il will ever be possible to
isolate this effect.
If one could isolate and measure
this effect and the shift-work effect,
one would have a choice of transferring
them to the contribution of capital
(evidently the Jorgenson-Griliches preference) or of classifying them as
component sources of the growth of
output per unit of input. The latter
would be my preference because it is
not the saving-investment process that
governs these income determinants [2,
p. 144], and I shall say a little more
about this at the end of this article.
But it would really make little difference to the sophisticated reader where
they were shown because he could move
them at will.
The Jorgenson-Griliches estimates

The Jorgenson-Griliches estimates
implicitly assume (1) that the utilization series would be unchanged if
weighted by value of power-driven
machinery and (2) that the entire
effect of increased utilization appears
in their productivity measure until
they make their utilization adjustment,
hence that only advances in knowledge
and changes in shift work within industries affected utilization of manufacturing equipment driven by electric
motors. Since they do not diminish the
growth of their capital stock series by

22
shortening service lives as they increase
capital utilization, they also assume
(3) that increased utilization does not
cause equipment to wear out more
rapidly. (If there is such a user cost,
the utilization adjustment duplicates
their original estimate of the contribution of capital for this reason.)
I know of no reason to accept this set
of assumptions. But it is instructive to
calculate what the quantitative importance of the change in utilization of
power-driven equipment in manufacturing would be if by chance all these
assumptions were correct. First, the
weight in total input must be calculated.
All nonresidential structures and equipment represented 13.6 percent of total
input in the private domestic economy
in 1950-62, according to my net earnings weights. All producers' durables in
manufacturing establishments represented about 14 percent of the value of
the total stock of private nonresidential
structures and equipment, hence 1.9
percent of total input. Machinery in
manufacturing establishments driven
by electric motors represented at the
outside 70 percent of the value of the
stock of producers' durables in manufacturing establishments in 1950-62,
hence at most 1.4 percent of total input.
If the utilization of such machinery increased 1.16 percent a year (the figure
I suggested earlier as the trend rate of
the utilization series), and if an increase
in utilization is treated (as Jorgenson
and Griliches do treat it) as equivalent
to the same percentage increase in the
quantity of such equipment, this raises
the growth rate of total input (net
product basis) in the private domestic
economy by 0.016 percentage points
(1.4 percent of 1.16 percent) and lowers
that of output per unit of input by the
same amount. This would be my estimate if I were to accept the JorgensonGriliches utilization estimates and their
three implicit assumptions mentioned
in the preceding paragraph (which, of
course, I do not). Even with the
Jorgenson-Griliches utilization increase
of 1.60 percent a year, the contribution
is only 0.022 percentage points in
1950-62. If, as in the JorgensonGriliches estimates, depreciation is
added to the weights, the calculated

SURVEY OF CURRENT BUSINESS
contribution to gross product growth
would probably come up to 0.03.
How do Jorgenson and Griliches get
from 0.03 to 0.58? By introducing the
"very strong assumption" (their language) that utilization of all types of
capital and land in all activities increased at the same rate as did machinery in manufacturing establishments driven by electric motors! This
assumption is not only "very strong";
it is truly magnificent in its implausibility. Utilization of structures, sites,
furniture, and office equipment in
manufacturing, of office buildings, of
physicians' automobiles, of houses and
their sites, of railroad stations, of
farmland (have the seasons changed?),
of inventories (whatever this may
mean), of literally everything has
increased, and at the same rate as
machinery driven by electric motors in
manufacturing establishments!
If one is willing to assume that the
change in machinery hours in manufacturing was due only to advances in
knowledge and changes in shift work
within industries, he might perhaps, I
suppose, go even further and assume
there was some net increase in machinery
hours outside manufacturing after 1950,
and thus raise the figure derived from
the manufacturing series a little. Foss
found some examples of machinery in
nonmanufacturing industries in which
utilization increased from the 1920's to
the 1950's as well as some where it did
not. For example, in two of five mining
industries, utilization of power-driven
equipment increased from 1929 to 1954
while in three it declined, although it
should be noted again that these years
are not cyclically comparable.67 Locomotive use increased while freight car
use decreased. Utilization in electric
utilities increased from the late 1930's
to 1948, but not from 1948 to 1958. And
so on. But even doubling the manufacturing figure would yield no more than
0.06 points in their gross product growth
rate. Jorgenson and Griliches have
applied the increase in utilization not
57. The Foss series for all mineral industries rises (but its
1929-54 growth rate is only 0.17 as compared with 1.10 for
manufacturing) because of a very sharp increase in nonmetal
mining, which receives a rather heavy weight (20 percent of
the total in 1929 and 27 in 1954) based on available kilowatt
hours of motors.

May CL969

only to all machinery but to all other
types of capital and to land. Since all
capital and land received 36.2 percent
of their total input weight (inclusive of
depreciation as well as indirect taxes),
this raised the contribution of the utilization adjustment from 0.03 to 0.58
(36.2 percent of 1.60).
The conclusion to be drawn from the
preceding discussion—it seems to me
inescapable—is that the JorgensonGriliches utilization adjustment must
be rejected.
After this summation, it may seem
superfluous to mention that the
Jorgenson-Griliches procedures also
contain an important inconsistency.
Houses and sites represent a huge
part of the stock of capital and land,
and much of the capital utilization
adjustment reflects the assumption
that the hours houses are used have
increased. Even if Jorgenson and
Griliches were right to assume that
people have been spending an increasing amount of time in their houses,
per dollar value in constant prices
of house, this would not affect their
output measure because (fortunately)
OBE does not adjust its deflated
consumer expenditure series for housing
to allow for the supposed increased
utilization, and Jorgenson and Griliches
do not adjust the OBE series on this
account. Hence, Jorgenson
and
Griliches are arithmetically wrong to
subtract the utilization adjustment
for residential structures and the residential portion of their land input from
the growth of productivity.58
58. Let me stress that my criticisms of the JorgensonGriliches utilization adjustment do not extend to the article
by Foss, which I have praised in print on several occasions.
Nor do I mean to deny the value and relevance to growth
studies of series of the type that Foss prepared for powerdriven equipment in manufacturing and mining industries
and a few other types of fixed capital and that might be
prepared for additional types. Indeed, like Jorgenson and
Griliches, I should be very glad to see such studies extended.
I believe Foss is correct in suggesting [4, p. 10] their importance for analysis of long-term changes in capital-output
ratios. Studies of shift work would be immediately useful.
More generally, the fact that capital utilization series do not
easily fit into the type of classification discussed in this article
does not imply that one cannot fruitfully explore the relationship between changes in capital utilization and economic
growth. There may be a valid analogy with studies, obviously valuable, of such questions as: "How does transportation affect growth?" or "How did high wages in the United
States affect American as compared'with European growth
in the nineteenth century?" Studies of these questions, too,
do not yield results that fit into the type of classification of
growth sources that is examined here.

SUEVEY OF CUEKENT BUSINESS

May 1069

VIII. The Measurement of Labor Input
JOEGENSON and Griliches and I
measure labor input in ways that are
similar in spirit and general approach.
Both our input series take into account
employment; hours worked, with an
allowance for a productivity offset as
hours change; and the education of
the labor force. My series allows, in
addition, for changes in the distribution
of total hours worked among age-sex
groups whereas theirs does not, but
Jorgenson and Griliches agree that this
should be done [1, p. 269].59 Thus a
comparison does not raise major conceptual issues.
However, the data and procedures
we actually use to measure labor input
differ at almost every step, and it is
necessary to consider whether this
introduces a difference into our estimates of productivity change. My
conclusion is that our labor input series
are in rather close agreement with
respect to the common elements of
our estimates, after allowance for my
inclusion of government employees.60
Their omission of an age-sex measure
contributes to their higher estimate of
the growth of output per unit of input.
Employment, hours, and education

Because of a difference in classification with respect to employment and
hours effects, it is desirable to combine
the two for comparison. It is also necessary to build up a comparison in several
parts.
My employment series is based on
household survey data from the
59. They also say that the labor input series should, in
addition, be standardized by occupation and industry. In
my view, this is a conceptual error, but since they did not do
this, no discrepancy between our estimates is introduced.
60. To adjust for the difference in the scope of our employment estimates, I use OBE data for general government
employment. This is appropriate because these data are
consistent with the government product data used in Section
I above to reconcile productivity estimates. The difference
in the scope of our estimates causes little difficulty in comparing other components of our labor input series because,
with unimportant exceptions, we each assume that changes
are the same for total private employment as for total civilian
employment.

Monthly Report on the Labor Force.
Jorgenson and Griliches rely on the
OBE series for persons engaged in production, which is the sum of its fulltime equivalent employees and active
proprietors of unincorporated enterprises. This series is mainly constructed
from establishment reports.
I have attempted to compare data
from the two sources at the all-civilianemployment level to try to determine
whether movements of the two series
are statistically consistent from 1950 to
1962. My series for civilian employment
has a 1950-62 growth rate of 1.03.61 To
obtain a conceptually similar series for
comparison, I start with OBE series on
persons engaged in production, excluding military employment; substitute the
OBE series for full-time and part-time
employees for full-time equivalent employees; add my estimates for unpaid
family workers; and adjust the 1962
figure to exclude Alaska and Hawaii by
application of a 1960 overlap ratio. The
resulting series has a 1950-62 growth
rate of 1.00. For this timespan, the
statistical difference between MRLF and
OBE data would, by this test, make the
Jorgenson-Griliches employment series
grow 0.03 less than mine. However,
Jorgenson and Griliches omit unpaid
family workers. The 1950-62 growth
rate of their employment series for
private industries would be lowered by
0.06 if my estimates for unpaid family
workers were added to their estimates.
The two differences together would
make their series grow 0.03 more than
mine.
We each estimate the effect of changes
in hours worked by measuring changes
in average hours, and allowing for a
productivity offset as hours of fulltime workers decline. For civilian
workers, my resulting series for the
effect of changes in hours upon the work
61. Computed from 2, tables 5-1A, 5-1C, 5-1D, and C-l.
In my estimates, all series are linked at 1960 to eliminate the
effect of adding Alaska and Hawaii to coverage of the data.

23
done in a year of employment has a
growth rate of —0.25 from 1950 to 1962
[2, table 6-6, and an adjustment to
exclude military personnel]. This figure
includes the effect of a major increase
in part-time employment; in fact, it
mainly reflects the effect on hours of an
increasing part-time component of employment, as distinguished from changes
in hours of full-time workers. Two
figures from the Jorgenson-Griliches
estimates must be combined for comparison. Their series for the effect of
hours on the work done in a year of
Jull-time employment has a growth rate
of about —0.09 from 1950 to 1962.62
The increase in part-time work is reflected in the employment component
of the Jorgenson-Griliches labor input
series because their employment series
is computed on a full-time equivalent
basis. The 1950-62 growth rate of the
OBE persons engaged series for private
industries is lower by 0.23 than that of
an otherwise similar series in which the
OBE series for full-time and part-time
employees is substituted for full-time
equivalent employees. Thus, the combined effect of changes in full-time
hours and increased part-time employment on the Jorgenson-Griliches labor
input series is —0.32 (—0.09 plus
— 0.23), which compares with my
— 0.25. When the difference of —0.07
is added to the 0.03 difference in the
employment growth rates, it appears
that the difference between our employment and hours series makes their
labor input series grow 0.04 points less
than mine. Based on their 1950-62
average labor share, this would make
their estimate of the contribution of
total input 0.03 points lower, and of
output per unit of input 0.03 higher,
than use of my series.63
62. In footnote 50,1 calculated that their hours adjustment
for labor amounted to —0.06 percentage points in the growth
rate of total input. Division of this amount by their average
labor share of 0.638 in 1950-62 yields -0.09.
63. I have not isolated the effect of one of their procedures
in this reconciliation of our estimates. Although unpaid
family workers are excluded from the Jorgenson-Griliches
employment series, they do affect total labor input via
the hours estimates. Jorgenson and Griliches inform me that
they obtained average hours by dividing the BLS establishment-based series for total manhours worked in the private
economy (which includes unpaid family workers) by persons
engaged in production (which excludes unpaid family
workers). Hence, the decline in the ratio of unpaid family
workers to total employment presumably intensifies the decline in their average hours series. This reduces the growth
in labor input insofar as it was not offset by their efficiency
adjustment.

SUEVEY OF CUEEENT BUSINESS

24
We each estimate the effect of the
rise in education upon the quality of
labor. The growth rate of my "education quality" series for civilian employment is 0.75 [2, table 8-5]. Despite
procedural differences, their rate is
also 0.75 [computed from 1, table VII].
No discrepancy in our labor input series
is introduced by education.
Age-sex composition

My "quality index" for changes in

the age and sex composition of hours
worked by civilian employees has a
— 0.15 growth rate from 1950 to 1962
[2, table 7-7, and an adjustment to
exclude military personnel]. Jorgenson
and Griliches omit this labor characteristic from their measure. Based on their
average 1950-62 labor share, the omission causes their total input series to
grow 0.11 points more than mine from
1950 to 1962, and their output per
unit of input series 0.11 points less.

IX. Summary of Statistical Review

May 1969

weights is relevant here; the portion
that is due to inclusion by Jorgenson
and Griliches of depreciation and the
portion that is due to their exclusion
of government and the international
sector are related to the difference in
output measures, and their effects
were previously eliminated in moving
from line 3 to line 6. (There is one
exception: The effect on the capital
utilization adjustment of including depreciation in the weights was not
eliminated and is included in the effect
of the capital utilization adjustment in
line 18.)
The division of the 1.01 points in
lines 13 to 20 is, in principle, that
which results from first measuring the
effect upon my series of substituting
their weights for mine and then measuring the effects of substituting their

AN approximate reconciliation of our types: differences in weights and difoutput per unit of input estimates can ferences in input measures.
now be compiled. It is provided in
Not all of the difference between our
table 1.
The initial difference between our Table 1.—Reconciliation of Denison and Jorgenson-Griliches Estimates of the Growth
estimates is 1.27 percentage points Rate (or Contribution to Growth) of Output per Unit of Input (Percentage points)
(line 3). When my estimates are adReported output per unit of input growth rates:
justed to conform to the definition and
1. Denison, total national income, 1950-62 (p. 1)
1.37
.10
2. Jorgenson-Griliches, phvate domestic GNP, 1945-65 (p. 1).
scope of output used by Jorgenson and
3. Difference 1-2
1.27
Griliches, and their estimates are adRates adjusted for definition and scope of output and time period:
justed to my time period, the dif4. Denison, private domestic GNP, 1950-62 (p. 3)
1.38
5. Jorgenson-Griliches, private domestic GNP, 1950-62 (p. 2)..
.30
ference is reduced to 1.08 (line 6). If my
6. Difference 4-5
1.08
estimates are adjusted to incorporate
Rate adjusted for new data:
revised OBE data for the stock of non.04
7. Adjustment of Denison series to incorporate new "structures and equipment" data (p. 14) _
1.42
residential structures and equipment,
8. Denison, private domestic GNP, 1950-62, adjusted, 4+7
1.12
9. Difference 8-5
including use of the OBE Deflation II
Rate adjusted for difference in classification:
series for nonresidential structures, the
10. Adjustment of Jorgenson-Griliches
series to eliminate effect of changes in "labor quality" due to shift in age-sex
difference between us is widened to
composition of hours worked a,c (p. 24)
—.11
.41
11. Jorgenson-Griliches, private domestic GNP, 1950-62, classification adjusted 5-10
1.12 percentage points (line 9).
1.01
12. Difference 8-11
I found only one significant differ- Breakdown of remaining difference of 1.01:
ence in our classifications of growth
13. Difference in division of input weights between
labor and capital-land *> •« (p. 5)
14. Difference in inventory capital stock series d (p. 14)
sources, as between input and output
.07
15. Difference in nonresidential structures and equipment
capital stock series <* (p. 16)
—.12
16. Difference in residential structures procedure d (p. 17)
per unit of input. My input series is
17. Jorgenson-Griliches substitutions of price indexes for equipment and inventories, net effect e
.07
Effect via output
-0.09 (p. 18)
broader in that it includes the effect on
Effect via input »
. 16 (p. 17)
.58
18. Jorgenson-Griliches capital-land utilization adjustment a (p. 18)
labor "quality" of shifts in the age-sex
-.03
19. Difference in estimates
of
employment
and
hours
(p.
23)
f
20. Other differences
.33
composition of hours worked, whereas
such shifts affect the Jorgensona Amount calculated with Jorgenson-Griliches weights.
b
Reflects the net effect on the Jorgenson-Griliches weights of (1) counting as capital-land earnings all indirect taxes and
Griliches series for output per unit of other reconciliation
items between factor cost and market price measures and (2) allocating to capital-land earnings a smaller
portion
than Denison of proprietors' income.
c
input. This source made a negative
Calculation
based
on Denison input series.
d
Amount calculated with Denison weights.
e
contribution to growth in 1950-62, so
The construction price substitutions had no effect on output. Their effect on input is already taken into account in
and 16.
that adjustment of their output per linesf 7,15,
This estimate was obtained as a residual.
To obtain a full reconciliation it would have been necessary after line 9 to measure (1) the changes in my estimates that
unit of input series to my classification would have been introduced by my use of the Jorgenson-Griliches weights (except for depreciation) and (2) to measure the
on their estimates, based on their weights, of the differences between us in measuring inputs. The first could be done
narrows the difference between us from effect
for the division of weights between labor and capital-land, but not within the capital-land aggregate. The second could be
done for most differences, but lines 14 to 16 were calculated by use of my weights instead of theirs. Line 20 therefore includes:
1.12 to 1.01 percentage points (line 12).
1. The effects of differences in the allocation of the total capital-land weight among components, including the consequences of the Denison division of the economy among sectors and the Jorgenson-Griliches adjustment for capital
The remaining 1.01 points, which
gains and taxes,
e difference between the amounts shown in lines 14,15, and 16 and the amounts that would be obtained in these lines
are divided among components in lines
if Jorgenson-Griliches weights were used in the calculation instead of the Denison weights.
3.
Possible
errors in the calculations of amounts shown in several other lines of this table resulting from my use of average
13 to 20, result from differences in
1950-62 weights instead of annual weights (in the case of Jorgenson-Griliches estimates) or 1950-54, 1955-59, and 196062
weights
(in the case of the Denison estimates) to calculate differences.
statistical procedures. These are of two
4. Rounding discrepancies.

SURVEY OF CURRENT BUSINESS

May 1969

input measures for mine when their
weights are used; the breakdown would
be different if the order were reversed.
Two departures from this principle
should be noted. The effect of a different allocation of total net capital-land
earnings among components, the principal subject of section IV, was not
measured and is included in "other
differences" in line 20. Also, the effect
of using different capital stock series
(or a different method in the case of
dwellings) could be measured only with
the use of my weights (lines 14, 15, 16),
and the difference between these results and those that would be obtained
with their weights is also included in
"other differences" in line 20.
The difference between us of 1.01
points shown in line 12 would be 1.04
were it not for a small offset (line 19)
flowing from a difference in our estimates of employment and hours, which
I did not evaluate. I have presented
what I regard as compelling reasons to
consider each of their procedures that
contributes to this discrepancy as

inferior. Nothing in their article suggests to me a change in my estimates.
Well over half of the entire statistical
difference stems from the JorgensonGriliches utilization adjustment for
capital and land (line 18). If increased
utilization of capital and land resulting
from advances in knowledge had really
contributed 0.58 percentage points to
the growth rate, then this amount would
be regarded as due to classification
rather than to statistical procedure. I
have stressed my reasons for concluding
that this is not the case. Although the
portion of the total gains from advances
in knowledge that is transmitted to
higher productivity by the mechanism
of lengthening capital hours simply
cannot be estimated from available
information, an amount larger than,
say, 0.02 or 0.03 points in the 1950-62
growth rate seems improbable. I therefore classify the Jorgenson-Griliches
utilization adjustment of 0.58 as resulting from differences in statistical procedure rather than in classification.

X. Some General Observations
JORGENSON and Griliches draw vances in knowledge, whether transcertain conclusions from their results mitted through improvements in capital
that I believe to be unsupported and goods or not, may result from expensive
unsupportable.
research at one extreme or from com, To introduce this discussion, let me pletely cost-free accidental discoveries
first recall that, in the framework of at the other.
my estimates, output per unit of input
2. Knowledge may become more
in the private domestic economy may quickly or widely dispersed.
rise, or fall if changes are adverse, for
3. Expansion of markets may permit
any of a large number of reasons. economies of scale.
Seven are perhaps worth listing. Having
4. The allocation of resources may
concluded that Jorgenson and Griliches move closer to the allocation that
do not have a broad'er classification of would maximize output. Allocation has
inputs than mine, I consider that all a myriad of aspects ranging from the
apply equally to their estimates.
distribution of total resources among
1. Advances in technical, managerial, industries, products, and firms of differand organizational knowledge permit ent size to the placement of each
more output to be obtained with a individual worker in the particular job
given quantity of inputs. The gains in which his contribution is greatest.
may take the form of making possible
5. Obstacles deliberately imposed by
production of more efficient capital governments, business, or labor unions
goods at the same cost (resulting in against the most efficient utilization of
"embodied" technological progress) or resources in the use to which they are
they may take any other form. Ad- put may weaken.

348-323 O - 69 - 4

25
6. The adequacy of government services (roads, police, courts, etc.) that
affect private productivity may change.
7. The intensity of utilization of
resources may change cyclically with
variations in the pressure of demand
[2, pp. 273-277, 441-442]. (I try to
eliminate the effects in presenting "adjusted" growth rates of output per
unit of input.)
My statistical estimates of output
per unit of input may also rise or fall
because my measures of input are
incomplete (for example, I could not
measure how hard people work) or
inexact. In presenting my estimates, I
have always tried to stress the limitations of information and technique,
and the fact that one cannot proceed
with growth analysis without introducing some assumptions. He can only try
to adopt assumptions that are as realistic as he can make them. In this
article, I have considered only differences between the Jorgenson-Griliches
techniques, data, and assumptions and
my own. I have not considered the
limitations of techniques and assumptions that we share.
Interpretation of Jorgenson^Griliches
results

Jorgenson and Griliches introduce
their article by stating that its purpose
is to test the hypothesis that "if real
product and real factor input are accurately accounted for, the observed
growth in total factor productivity is
negligible." [1, p. 249] Their small estimate of the rise in total output per
unit of input leads them to "conclude
that our hypothesis is consistent with
the facts." From this conclusion, they
draw sweeping inferences. My conclusion is that they obtain their strikingly
low estimate of productivity growth not
by eliminating errors made in other
research but by introducing new errors
of their own. If so, the inferences they
draw from this finding are also wrong.
I have stressed that the determinants
of changes in output per unit of input
are the same for the Jorgenson-Griliches
series as for mine.641 am unable to find
anything in their procedures that would
have the effect of reclassifying a growth
64. Except that they also include changes in labor quality
due to changes in age-sex composition.

26
source that I consider to be a component of output per unit of input into a
component of input except their wholly
unwarranted capital utilization adjustment. Nevertheless, their theoretical
discussion suggests that Jorgenson and
Griliches would like to reclassify growth
sources from productivity to input.
Some readers of their article have supposed that they have actually done so;
this is understandable because Jorgenson and Griliches are not very clear on
this matter.
Their discussion [1, p. 260] of "vintages" of capital goods is likely to
mislead the unwary reader. This discussion is concerned with the fact that
the design of capital goods improves as
time passes. For this reason, an investment of a given sum this year buys a
bundle of capital goods that is more
productive than the bundle that could
have been purchased this year with the
same sum of money if capital goods of
designs known 10 or 20 years ago were
now being produced and were the only
types known and available.
Jorgenson and Griliches indicate that,
to aggregate capital goods in the capital
stock, they would like to treat capital
goods of different vintages as different
commodities and weight them by their
marginal products at a common date,
rather than weight them by their costs
at a common date as is the general
practice in existing capital stock series.
This procedure would be equivalent
to adjusting existing capital stock
65. Jorgenson and Griliches would like to allow for "unmeasured quality change" of capital goods in computing the
fixed investment components of GNP at constant prices as
well as in constructing capital stock series. This would not
affect the amount transferred from "GNP per unit of input"
to input as "embodied technical progress," but by raising the
growth rate of gross product, it would offset to some degree
the reduction of the productivity series. However, three
points should be noted. (1) The addition to growth of GNP
per unit of input would tend to be much smaller, on the
average, than the deduction because the ratio of gross fixed
investment to GNP is much smaller than the fixed
investment share of gross earnings, especially when the latter
includes indirect taxes. [See 1, p. 262.] (2) In an analysis of
net product growth, most of the addition to productivity
(but not of the subtraction) would disappear because the
increase in the growth rate of gross output in constant prices
would be accompanied by a corresponding increase in the
growth rate of depreciation in constant prices. (3) The relative
size of the positive and negative adjustments to GNP per
unit of input would change from time to time unless (a) the
rate of "unmeasured quality improvement" were constant
over a long period (from the installation date of the oldest
capital in the stock when output is first measured to the
last date that output is measured) and (b) chaages in the
share of fixed investment in output synchronized with
changes in the share of fixed investment in earnings in some
very special way.

SURVEY OF CUEEENT BUSINESS
series to reflect "unmeasured" quality
change; "unmeasured" quality change
in the capital stock is defined as the
difference in movement between a
capital stock series constructed by
weighting components by marginal
products and a series in which costs are
used as weights [2, pp. 134-135,
144-145]. The contribution of "unmeasured" quality change to growth
is "embodied technical progress." Thus,
the procedure Jorgenson and Griliches
recommend would have the effect of
transferring "embodied technical progress" from the productivity to the
input measure.65
It is difficult to read their article
without supposing that they actually
do make such a transfer.66 But they
stop short of making this claim explicit.
In actual fact, I find nothing in their
procedures that has the effect of adjusting capital input for the type of
quality change that is not reflected in
cost differences at a common date, and
thus of "embodying" technical progress
(nor am I aware of any statistical
procedure that could be introduced to
do this). I have taken pains to point
out that neither their price substitutions
nor their use of a fast depreciation
(replacement) formula in measuring
capital stock has any such effect.
It should also be noted that a distinction they introduce between costly
and "costless" advances in "applied
technology, managerial efficiency, and
industrial organization" [1, p. 250]
plays no role in their estimating procedure. They do not capitalize the
costs or benefits of research and development, of reallocation of labor, or of
any other action that would contribute
to an increase in output per unit. Thus,
they have transferred none of the gains
from costly research or from other
expenditures or costly actions out of
their estimates of output per unit of
input.
Given the characteristics of their productivity estimates that I have
described, how is one to interpret the
66. Their footnote 1 on p. 254, does not contradict this. It
merely states that they do not measure embodied technical
progress in such a way as to make the change in output per
unit of input zero by definition. Their footnote 1, p. 274,
refers to errors in capital goods prices, which they try to
correct, as "analogous to embodied technical change."

May 1969

following passage, which appears after
their empirical results are presented?
"Our results suggest that the residual
change in total factor productivity,
which Denison attributes to Advance
in knowledge, is small.67 Our conclusion is not that advances in knowledge
are negligible, but that the accumulation of knowledge is governed by
the same economic laws as any other
process of capital accumulation. Costs
must be incurred if benefits are to be
achieved. Although we have made no
attempt to isolate the effects of expenditures on research and development from expenditures on other types
of current inputs or investment goods,
our results suggest that social rates of
return to this type of investment are
comparable to rates of return on other
types of investment. Another implication of our results is that discrepancies
between private and social returns to
investment in physical capital may
play a relatively minor role in explaining economic growth." [1, p.
274]
This quotation seems to contain four
statements. Even if the JorgensonGriliches statistical results were accurate, they would not, I believe, support
all of these statements. Indeed, the
interpretation of their residual productivity estimate that is required for it
to support the first statement seems
directly contrary to the interpretation that would be required for it to
lend any support to the other three
statements.
The first statement is that the small
Jorgenson-Griliches residual does not
imply a small contribution to growth
from advances in knowledge. This
statement could be correct only if their
procedures have the effect of reclassifying
much of what I regard as the contribution of output per unit of input to an
input contribution. In the absence of
such a reclassification, a tiny figure for
growth of output per unit of input
would in fact leave little room for a
contribution from advances in knowledge—or from economics of scale, reallocation of resources, or any of the
67. Footnote by Denison: Actually, I have attributed to
advances in knowledge only part of my estimate of the
contribution of output per unit of input.

May 1969

SURVEY OF CUREENT BUSINESS

other sources I have listed as contribut- too, does not follow from their results. inconvenient classification of growth
ing to changes in output per unit of As just indicated, they provide neither sources, and this leads me to a final
input.
measures of the costs of research and comment on this topic. I believe there
The second statement is that, to development for comparison with costs is an advantage in matching growth
obtain important advances in knowl- of tangible investment, nor measures of sources with the reasons that income
edge, commensurate costs must be the benefits of research and develop- changes, and I have tried to adhere to
incurred; costs must be incurred if ment and of tangible investment.
this principle in my own work. In
benefits are to be achieved. This
As to their fourth point, I do not particular, confusion and misinterpreimplies that a comparison of costs and understand how their results could tation are avoided if the contribution
gains has been made. Actually, possibly show that discrepancies of capital is identified with changes in
Jorgenson and Griliches provide no between private and social returns to income that result from investment,
estimates at all of the costs of obtaining investment in physical capital are small. and that can be altered by changing
knowledge—e.g., costs of research or Jorgenson and Griliches must some- the amount of investment, and the
exploration. The fact that their residual how have drawn this inference from contribution of advances in knowledge
productivity estimate is small can the size of their residual. But their in- is identified with changes in income
indicate that gains from advances in troduction of a capital utilization ad- that result from advances in technical
knowledge—whether costly or cost- justment renders use of their residual and managerial knowledge, and that
less—are small only if Jorgenson and for inferences about social rates of can be altered by changing the state of
Griliches have not transferred gains return conceptually invalid, just as it knowledge. Confusion is hard to avoid
from advances in knowledge from does for inferences about returns to if the consequences of advances in
productivity to input. I would regard research. And even their small residual knowledge are classified as contribuas implausible a finding that advances would be big enough to add greatly to tions of capital. This is why I believe
in knowledge have contributed to the private rate of return on investment it would be unwise, even if they
growth an amount as small as their if (improbably) it arose entirely from could be isolated, to count as contriburesidual.68 I have tried to show that the discrepancy between public and pri- tions of capital the gains made possible
their estimate actually results from vate returns to investment.
because someone has devised improved
procedural and statistical errors. But,
Part of the difficulty with the designs of capital goods, or found ways
although I have argued that Jorgenson quotation I have just analyzed stems to make possible more continuous use
and Griliches have made no valid from the preference of Jorgenson and of capital goods. Such a classification
transfers of growth sources from pro- Griliches for what I regard as an is an invitation to misinterpretation.
ductivity to input, the actual reason
their residual is so very small is their
introduction of the capital utilization
adjustment. If this adjustment were
really accurate and appropriate, they
would have counted gains (their estimate implies most of the gains) resulting
from advances in knowledge as a contribution of capital. If they had succeeded
in adjusting capital stock series for
1. Dale W. Jorgenson and Zvi Griliches, "The Explanation of Prounmeasured quality change by their
ductivity Change," The Review of Economic Studies, Vol. XXXIV (3),
"vintage" approach, this too would
No. 99, July 1967. pp 249-283.
have counted gains resulting from
advances in knowledge as a contribution
2. Edward F. Denison assisted by Jean-Pierre Poullier, Why Growth
of capital.69
Rates Differ: Postwar Experience in Nine Western Countries. Washington:
The third statement is that social
The Brookings Institution, 1967.
rates of return on research and develop3. Edward F. Denison, The Sources of Economic Growth in the United
ment are comparable to those on other
States and the Alternatives Before Us. New Tork: Committee for Economic
types of investment. This statement,
Development, 1962.
4. Murray F. Foss, "The Utilization of Capital Equipment: Postwar
68. It may be noted that Jorgenson and Griliches have
estimated that the increase in output per unit of input was
Compared with Prewar," Survey of Current Business, Vol. 43, No. 6, June
negligible over the whole 1929-64 period as well as during the
1963. pp. 8-16.
postwar period [5, p. 61]. They clearly believe this to be the
typical situation.
5. Dale W. Jorgenson and Zvi Griliches, "Sources of Measured Pro69. If the superiority of later "vintages" of capital goods
ductivity Change," American Economic Review, Vol. LVI, No. 2, May 1966.
was that they could be used longer hours, the same gains
would actually be transferred twice—once by the capital
pp. 50-61.
utilization adjustment, and once by the adjustment of the

References

quality of capital.

The Explanation of
Productivity Change
By D. W. JORGENSON
and

Z. GRILICHES

Reprinted with corrections from
The Review of
Economic Studies
Vol. XXXIV (3), No. 99
(July 1967)

May 1969

SUEVEY OF CURRENT BUSINESS

The Explanation of Productivity
Change'
But part of the job of economics is weeding out errors.
That is much harder than making them, but also
more fun.—R. M. SOLOW
1. INTRODUCTION
Measurement of total factor productivity is based on the economic theory of production. For this purpose the theory consists of a production function with constant
returns to scale together with the necessary conditions for producer equilibrium. Quantities
of output and input entering the production function are identified with real product and
real factor input as measured for social accounting purposes. Marginal rates of substitution are identified with the corresponding price ratios. Employing data on both
quantities and prices, movements along the production function may be separated from
shifts in the production function. Shifts in the production function are identified with
changes in total factor productivity.
Our point of departure is that the economic theory underlying the measurement of
real product and real factor input has not been fully exploited. As a result a number of
significant errors of measurement have been made in compiling data on the growth of
real product and the growth of real factor input. The result of these errors is to introduce
serious biases in the measurement of total factor productivity. The allocation of changes
in real product and real factor input between movements along a given production function
and shifts of the production function must be corrected for bias due to errors of concept
and measurement.
The purpose of this paper is to examine a hypothesis concerning the explanation of
changes in total factor productivity. This hypothesis may be stated in two alternative and
equivalent ways. In the terminology of the theory of production, if quantities of output
and input are measured accurately, growth in total output is largely explained by growth
in total input. Associated with the theory of production is a system of social accounts
for real product and real factor input. The rate of growth of total factor productivity is
the difference between the rate of growth of real product and the rate of growth of real
factor input. Within the framework of social accounting the hypothesis is that if real
product and real factor input are accurately accounted for, the observed growth in total
factor productivity is negligible.
We must emphasize that our hypothesis concerning the explanation of real output
is testable. By far the largest portion of the literature on total factor productivity is
devoted to problems of measurement rather than to problems of explanation. In recognition of this fact changes in total factor productivity have been given such labels as The
Residual or The Measure of Our Ignorance. Identification of measured growth in total
factor productivity with embodied or disembodied technical change provides methods
for measuring technical change, but provides no genuine explanation of the underlying
changes in real output and input.2 Simply relabelling these changes as Technical Progress
or Advance of Knowledge leaves the problem of explaining growth in total output unsolved.
1
2

The authors' work has been supported by grants from the National Science and Ford Foundations.
See Jorgenson [35] for details.
249

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250

REVIEW OF ECONOMIC STUDIES

The plan of this paper is as follows: We first discuss the definition of changes in
total factor productivity from the point of view of the economic theory of production.
Second, we provide operational definitions for the measurement of prices and quantities
that enter into the economic theory of production. These definitions generate a system
Of social accounts for real product and real factor input and for the measurement of total
factor productivity. Within this system we provide an operational definition of total
factor productivity. This definition is fundamental to an empirical test of the hypothesis
that if real product and real factor input are accurately accounted for, the observed rate
of growth of total factor productivity is negligible.
Within our system of social accounts for real product and real factor input we can
assess the consequences of errors of measurement that arise from conceptual errors in the
separation of the value of transactions into price and quantity. Errors in making this
separation may affect real product, real factor input, or both; for example, an error in
the measurement of the price of investment goods results in a bias in total output and a
bias in the capital accounts that underlie the measurement of total input. Within this
system of social accounts we can suggest principles for correct aggregation of inputs and
outputs and indicate the consequences of incorrect aggregation. Many of the most
important errors of measurement in previous compilations of data on real product and
real factor input arise from incorrect aggregation.
Given a system of social accounts for the measurement of total factor productivity
we attempt to correct a number of common errors of measurement of real product and
real factor input by introducing data that correspond more accurately to the concepts of
output and input of the economic theory of production. After correcting for errors of
measurement we examine the validity of our hypothesis concerning changes in total
factor productivity. We conclude with an evaluation of past research and a discussion
of implications of our findings for further research.
2. THEORY
Our definition of changes in total factor productivity is the conventional one. The
rate of growth of total factor productivity is defined as the difference between the rate of
growth of real product and the rate of growth of real factor input. The rates of growth
of real product and real factor input are defined, in turn, as weighted averages of the
rates of growth of individual products and factors. The weights are relative shares of
each product in the value of total output and of each factor in the value of total input.
If a production function has constant returns to scale and if all marginal rates of substitution are equal to the corresponding price ratios, a change in total factor productivity
may be identified with a shift in the production function. Changes in real product and
real factor input not accompanied by a change in total factor productivity may be identified
with movements along a production function.
Our definition of change in total factor productivity is the same as that suggested by
Abramovitz (1), namely, " . . . the effect of * costless' advances in applied technology
managerial efficiency, and industrial organization (cost—the employment of scarce
resources with alternative uses—is, after all, the touchstone of an ' i n p u t ' ) . . . " *
Of course, changes in total factor productivity or shifts in a given production function
may be accompanied by movements along a production function. For example, changes
in applied technology may be associated with the construction of new types of capital
equipment. The alteration in patterns of productive activity must be separated into the
part which is " costless", representing a shift in the production function, and the part
which represents the employment of scarce resources with alternative uses, representing
movements along the production function.
i Abramovitz [1, p. 764].

^ 1969

SURVEY OF CURRENT BUSINESS

May 1909

THE EXPLANATION OF PRODUCTIVITY CHANGE

33
251

On the output side the quantitites that enter into the economic theory of production
correspond to real product as measured for the purposes of social accounting. Similarly,
on the input side these quantities correspond to real factor input, also as measured for
the purposes of social accounting. The prices that enter the economic theory of production are identified with the implicit deflators that underlie conversion of the value of total
output and total input into real terms. The notion of real product is a familiar one to
social accountants and has been adopted by most Western countries as the appropriate
measure of the level of aggregate economic activity. The notion of real factor input is
somewhat less familiar, since social accounting for factor input is usually carried out
only in value terms or current prices. However, it is obvious that income streams recorded
in value terms correspond to transactions in the services of productive factors. The value
of these transactions may be separated into price and quantity and the resulting data may
be employed to construct social accounts for factor input in constant prices. This type
of social accounting is implicit in all attempts to measure total factor productivity.
The prices and quantities that enter into the economic theory of production will
be given in terms of social accounts for total output and total input in current and constant
prices. We observe that our measurement of total factor productivity is subject to all the
well-known limitations of social accounting. Only the results of economic activities with
some counterpart in market transactions are included in the accounts. No attempt is
made to measure social benefits or social costs if these diverge from the corresponding
private benefits or private costs. Throughout this study we adhere to the basic framework
of social accounting. The measurement of both output and input is based entirely on
market transactions; all prices reflect private benefits and private costs. That part of
any alteration in the pattern of productive activity that is " costless " from the point of
view of market transactions is attributed to change in total factor productivity. Thus
the social accounting framework provides a definition of total factor productivity as the
ratio of real product to real factor input.
To represent the system of social accounts that provides the basis for measuring total
factor productivity, we introduce the following notation:
Yt—quantity of the ith output,
A}—quantity of theyth input,
# f —price of the /th output,
Pj—price of theyth input.
Where there are m outputs and n inputs, the fundamental identity for each accounting
period is that the value of output is equal to the value of input:
9iYl+q2Y2 + ...+qmYm=plXi+p2X2 + ...+pnXn.
...(1)
This accounting identity is important in defining an appropriate method for measuring
total factor productivity; it also provides a useful check on the consistency of any proposed definitions of total output and total input.
To define total factor productivity we first differentiate (1) totally with respect to time
and divide both sides by the corresponding total value. The result is an identity between
a weighted average of the sum of rates of growth of output prices and quantities and a
weighted average of the sum of rates of growth of input prices and quantities:

with weights {w{} and {Vj} given by the relative shares of the value of the ith output in
the value of total output and the value of jth input in the value of total input:

SURVEY OF CURRENT BUSINESS
252

May i960

REVIEW OF ECONOMIC STUDIES

To verify that both sides of (2) are weighted averages, we observe that:
MI ^ 0, i = l...m;

A useful index of the quantity of total output may be defined in terms of the weighted
average of the rates of growth of the individual outputs from (2); denoting this index of
output by y, the rate of growth of this index is

an analogous index of the quantity of total input, say X, has rate of growth

These quantity indexes are familiar as Divisia quantity indexes ; the corresponding Divisia
price indexes for total output and total input, say q and /?, have rates of growth:

P _
—
— T«
2J)j — ,
P
Pj
respectively.1
In terms of Divisia index numbers a natural definition of total factor productivity,
say P, is the ratio of the quantity of total output to the quantity of total input:
P = -.
X

...(3)

Using the definitions of Divisia quantity indexes, Y and X, the rate of growth of total factor
productivity may be expressed as :

Y --- x = E_w —yf — ItVj
_ —Xj-.
Y

...(4)

or, alternatively, as:
P

-S--4-Sw*
--— xv
LAJ f ^
J - — jLWil — .

— —

These two definitions of total factor productivity are dual to each other and are equivalent
by (2). In general, any index of total factor productivity can be computed either from
indexes of the quantity of total output and total input or from the corresponding price
indexes.2
Up to this point we have defined total factor productivity as the ratio of certain index
numbers of total output and total input. An economic interpretation of this definition
may be obtained from the theory of production. The theory includes a production function
1
Divisia [17, 19]. Application of these indexes to the measurement of total factor productivity is
suggested by Divisia in a later publication [18, pp. 53-54]. The economic interpretation of Divisia indexes
of total
factor productivity has been discussed by Solow [61] and Richter [52].
2
The basic duality relationship for indexes of total factor productivity has been discussed by Siegel,
57, 58].

May 1969

SURVEY OF CURRENT BUSINESS
THE EXPLANATION OF PRODUCTIVITY CHANGE

35
253

characterized by constant returns to scale; writing this function in implicit form, we have:
t,

Y2 ..... Ym; Xlt X2, ..., Xn) = 0.

Shifts in the production function may be defined in terms of appropriate weighted average
rates of growth of outputs and inputs,
...(5)
where Ft = —, F,J = — and:

Changes in total factor productivity may be identified with shifts of the production
function as opposed to movements along the production function by adding the necessary
conditions for producer equilibrium—all marginal rates of transformation between pairs
of inputs and outputs are equal to the corresponding price ratios—
dYt
dXj

Fj
pJ9 8Yt
= —;
— =
F,
qt dYk

Fk
qim BXj
= —;
=
Ft
q,' 8X,

= Pl
—; u. /c = l...m; 7, / = I...TI).
'
Pj

Combining these conditions with the definition (5) of shifts in the production function,
we obtain the definition (4) of total factor productivity:

et.t.
F.

The rate of growth of total factor productivity is zero if and only if the shift in the production function is zero.
The complete theory of production consists of a production function with constant
returns to scale together with the necessary conditions for producer equilibrium. This
theory of production implies the existence of a factor price frontier relating the prices of
output to the prices of input. The dual to the definition (4) of total factor productivity
may be identified with shifts in the factor price frontier.1
The economic interpretation of the index of total factor productivity is essential in
measuring changes in total factor productivity by means of Divisia index numbers. As is
well known,2 the Divisia index of total factor productivity is a line integral so that its
value normally depends on the path of integration; even if the path returns to its initial
value the index of total factor productivity may increase or decrease. However, if price
ratios are identified with marginal rates of transformation of a production function with
constant returns to scale, the index will remain constant if the shift in the production
function is zero.3
From either of the two definitions of the index of total factor productivity we have
given it is obvious that the rate of growth of this index is not zero by definition. Even for
a production function characterized by constant returns to scale with all factors paid
the value of their marginal products, the rate of growth of real product may exceed or
fall short of the rate of growth of real factor input; similarly, the rate of growth of the
1
The notion of a factor price frontier has been discussed by Samuelson [54]; the factor price frontier
is employed in defining changes in total factor productivity by Diamond [16] and by Phelps and Phelps
[51].
2 See, for example, Wold [64].
3 See Richter [52], We are indebted to W. M. Gorman for bringing this fact to our attention.

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price of real factor input may exceed or fall short of the rate of growth of the price of
real product.1
The economic theory of production on which our interpretation of changes in total
factor productivity rests is not the only possible theory of production. From the definition
of shifts in the production function (5) it is clear that the production function may be
considered in isolation from the necessary conditions for producer equilibrium, provided
that alternative operational definitions of the marginal rates of transformation are introduced. Such a production function may incorporate the effects of increasing returns to
scale, externalities, and disequilibrium. Changes in total factor productivity in our sense
could then be interpreted as movements along the production function in this more general
sense.
To provide a basis for assessing the role of errors of measurement in explaining
observed changes in total factor productivity, we first set out principles for measuring
total output and total input. The measurement of flows of output and labour services is,
at least conceptually, straightforward. Beginning with data on the value of transactions
in each type of output and each type of labour service, this value is separated into a price
and a quantity. A quantity index of total output is constructed from the quantities of
each output, using the relative shares of the value of each output in the value of total output
as weights. Similarly, a quantity index of total labour input is constructed from the
quantities of each labour service, using the relative shares of the value of each labour
service in the value of all labour services as weights.
If capital services were bought and sold by distinct economic units in the same way
as labour services, there would be no conceptual or empirical difference between the
construction of a quantity index of total capital input and the construction of the corresponding index of total labour input. Beginning with data on the value of transactions in
each type of capital service, this value could be separated into a price of capital service or
rental and a quantity of capital service in, say, machine hours. These data would correspond to the value of transactions in each type of labour service which could be separated
into a price of labour service or wage and a quantity of labour service in, say, man hours.
A quantity index of total capital input would be constructed from the quantities of each
type of capital service, using the relative shares of the rental value of each capital service
in the rental value of all capital services as weights.
The measurement of capital services is less straightforward than the measurement of
labour services because the consumer of a capital service is usually also the supplier of the
1
It is essential to distinguish our basic hypothesis from a misinterpretation of it recently advanced
by Denison:
Since advances in knowledge cannot increase national product without raising the marginal
product of one or more factors of production, they of course disappear as a source of growth if an
increase in a factor's marginal product resulting from the advance of knowledge is counted as an
increase in the quantity of factor input [14, p. 76].
In terms of our social accounting framework Denison suggests that we measure factor input as the sum
of the increase in both prices and quantities; denoting the index of input implied by Denison's interpretation by XD, gives:
£- *,&+*, 4;

the corresponding index of output, say YD9 would then be defined as :

The resulting index of total factor productivity, say PD, is constant by definition:
D
^D = Zf-^
=o
YD
XD

By comparing this definition with our definition (4), the error in Denison's interpretation of our hypothesis
is easily seen.

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service; the whole transaction is recorded only in the internal accounts of individual
economic units. The obstacles to extracting this information for purposes of social
accounting are almost insuperable; the information must be obtained by a relatively
lengthy chain of indirect inference. The data with which the calculation begins are the
values of transactions in new investment goods. These values must be separated into a
price and quantity of investment goods. Second, the quantity of new investment goods
reduced by the quantity of old investment goods replaced must be added to accumulated
stocks. Third, the quantity of capital services corresponding to each stock must be
calculated.1
Paralleling the calculation of quantities of capital services beginning with the quantities
of new investment goods, the prices of capital services must be calculated beginning with
the prices of new investment goods. Finally, a quantity index of total capital input must
be constructed from the quantities of each type of capital service, using the relative shares
of the implicit rental value of each capital service in the implicit rental value of all capital
services as weights. The implicit rental value of each capital service is obtained by simply
multiplying the quantity of that service by the corresponding price. At this final stage the
construction of a quantity index of total capital input is formally identical to the construction of a quantity index of total labour input or total output. The chief difference between
the construction of price and quantity indexes of total capital input and any other aggregation problem is in the circuitous route by which the necessary data are obtained.
The details of the calculation of a price and quantity of capital services from data on
the values of transactions in new investment goods depend on empirical hypotheses about
the rate of replacement of old investment goods and the quantity of capital services corresponding to a given stock of capital. In studies of total factor productivity it is conventional
to assume that capital services are proportional to capital stock. Where independent
data on rates of utilization of capital are available, this assumption can be dispensed with.
A number of hypotheses about the rate of replacement of old investment goods have been
used in the literature: (1) Accounting depreciation measured by the straight-line method
is set equal to replacement, possibly with a correction for changes in prices. (2) Gross
investment in some earlier period is set equal to replacement. (3) A weighted average of
past investment with weights derived from studies of the " survival curves " of individual
pieces of equipment 2 is set equal to replacement. From a formal point of view, the last
of these hypotheses includes the first two as special cases.
We assume that the proportion of an investment replaced in a given interval of time
declines exponentially over time. A theoretical justification for this assumption is that
replacement of investment goods is a recurrent event. An initial investment generates a
series of replacement investments over time; each replacement generates a new series of
replacements, and so on; this process repeats itself indefinitely. The appropriate model
for replacement of investment goods is not the distribution over time of replacements for
a given investment, but rather the distribution over time of the infinite stream of replacements generated by a given investment. The distribution of replacements for such an
infinite stream approaches a constant fraction of the accumulated stock of investment
goods for any " survival curve " of individual pieces of equipment and for any initial
age distribution of the accumulated stock, whether the stock is constant or growing. But
this is precisely the relationship between replacement and accumulated stock if an exponentially declining proportion of any given investment is replaced in a given interval of time.
The quantity of capital services corresponding to each stock could be measured
directly, at least in principle. The stock of equipment would be measured in numbers of
1
Here we assume that the " quantity " of a particular type of capital as an asset is proportional to
its " quantity " as a service, whatever the age of the capital. If this condition is not satisfied, capital of
each distinct age must be treated as a distinct asset and service. Output at each point of time consists of
the usual
output plus " aged " capital stock.
2
Studies in which these three methods have been employed are (1) Jaszi, Wasson, and Grose [33],
Goldsmith [25], and Kuznets [39]; (2) Meyer and Kuh [44] and Denison [15]; (3) Terborgh [63].

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machines while the service flow would be measured in machine hours, just as the stock of
labour is measured in numbers of men while the flow of labour services is measured in
man hours. While the stock of equipment may be calculated by cumulating the net flow
of investment goods, the relative utilization of this equipment must be estimated in order
to convert stocks into flows of equipment services. For the purposes of this study we
assume that the relative utilization of all capital goods is the same; we estimate the relative
utilization of capital from the relative utilization of power sources. An adjustment for
the relative utilization of equipment is essential in order to preserve comparability among
our measurements of output, labour input, and capital input.
To represent the capital accounts which provide the basis for measuring total capital
input, we introduce the following notation:
Ik—quantity of output of the Ath investment good,
Kk—quantity of input of the kth capital service.
As before, we use the notation:
qk—price of the Ath investment good,
Pk—price of the kth capital service.
Under the assumption that the proportion of an investment replaced in a given interval
of time declines exponentially, the cumulated stock of past investments in the Ath capital
good, net of replacements, satisfies the well-known relationship:
4 = Kk+6kKk9

...(6)

where 5k is the instantaneous rate of replacement of the kth investment good. Similarly,
in the absence of direct taxation the price of the Ath capital service satisfies the relationship:
...(7)
where r is the rate of return on all capital, dk is the rate of replacement of the Ath investment
good, and qk/qk is the rate of capital gain on that good. Given these relationships between
the price and quantity of investment goods and the price and quantity of the corresponding
capital services, the only data beyond values of transactions in new investment goods
required for the construction of price and quantity indexes of total capital input are rates
of replacement for each distinct investment good and the rate of return on all capital.
We turn now to the problem of measuring the rate of return.
First, to measure the values of output and input it is customary to exclude the value
of capital gains from the value of input rather than to include the value of such gains in
the value of output. This convention has the virtue that the value of output may be
calculated directly from the values of transactions. Second, to measure total factor
productivity, depreciation is frequently excluded from both input and output; this
convention is adopted, for example, by Kendrick [37]. Exclusion of depreciation on
capital introduces an entirely arbitrary distinction between labour input and capital
input, since the corresponding exclusion of depreciation of the stock of labour services is
not carried out.1 To calculate the rate of return on all capital, our procedure is to subtract
from the value of output plus capital gains the value of labour input and of replacement.
This results in the rate of return multiplied by the value of accumulated stocks. The
rate of return is calculated by dividing this quantity by the value of the stock.2 The
1
2

This point is made by Domar [21].
Domar's procedure [21, p. 717, fn. 3] fails to correct for capital gains. Implicitly, Domar is assuming
either no capital gains or that all capital gains are included in the value of output, whether realized or not.

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implicit rental value of the A:th capital good is :

To calculate price and quantity indexes for total capital input, the prices and quantities of
each type of capital service are aggregated, using the relative shares of the implicit rental
value of each capital service in the implicit rental value of all capital services as weights.
An almost universal conceptual error in the measurement of capital input is to confuse
the aggregation of capital stock with the aggregation of capital service. This error may be
exemplified by the following passage from a recent paper by Kendrick [38] devoted to
theoretical aspects of capital measurement:
. . . the prices of the underlying capital goods, as established in markets or imputed
by owners, can be appropriately combined (with variable quantity weights) to provide
a deflator to convert capital values into physical volumes of the various types of
underlying capital goods at base-period prices. Or, the result can be achieved directly
by weighting quantities by constant prices.
As I view it, this is the most meaningful way to measure " real capital stock,"
since the weighted aggregate measures the physical complex of capital goods in terms
of its estimated ability to contribute to production as of the base period.1
The " ability to contribute to production " is, of course, measured by the price of capital
services, not the price of investment goods.2
We have already noted that direct observations are usually available only for values
of transactions; the separation of these values into prices and quantities is based on
much less complete information and usually involves indirect inferences; the presence of
systematic errors in this separation is widely recognized. For output of consumption goods
or input of labour services an error in separating the value of transactions into price
and quantity results in an error in measurement of the price and quantity of total output
or total labour input and in the measurement of total factor productivity. For example,
suppose that the rate of growth of the price of a particular type of labour service is measured
with an error; since all relative value shares remain the same, the resulting error in the
price of total labour input has a rate of growth equal to the rate of growth of the error
multiplied by the relative share of the labour service. The quantity of total labour input
is measured with an error which is equal in magnitude but opposite in sign. The error in
measurement of the rate of growth of total factor productivity is equal to the negative
of the rate of growth of the error in the quantity of total labour input multiplied by the
relative share of labour. The effects of an error in the rate of growth of the price of a
particular type of consumption good are entirely analogous; of course, an upward bias
in the rate of growth of output increases the measured rate of growth of total factor
productivity, while an upward bias in the rate of growth of input decreases the measured
rate of growth.
An error in the separation of the value of transactions in new investment goods into
the price and quantity of investment goods will result in errors in measurement of the price
and quantity of investment goods, of the price and quantity of capital services and of total
1
Kendrick [38, p. 106]; see the comments by Griliches [27, p. 129]. Kendrick takes a similar position
in a more recent paper [36]; see the comments by Jorgenson [35]. The treatment of capital input outlined
above is based on our earlier paper [31]. The data have been revised to reflect recent revisions in the
U.S. 2national accounts.
The answer to Mrs. Robinson's [53] rhetorical question, " what units is capital measured in? " is
dual to the measurement of the price of capital services. Given either an appropriate measure of the flow
of capital services or a measure of its price, the other measure may be obtained from the value of income
from capital. Since this procedure is valid only if the necessary conditions for producer equilibrium are
satisfied, the resulting quantity of capital may not be employed to test the marginal productivity theory of
distribution, as Mrs. Robinson and others have pointed out.

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factor productivity. To measure the bias in the rate of growth of the quantity of investment goods, we let g* be the relative error in the measurement of the price of investment
goods, 7* the " quantity " of investment goods output, calculated using the erroneous
" price " of investment goods, and /the actual quantity of investment goods output. The
bias in the rate of growth of investment goods output is then:

/**-'—£.
/ e*

...TO

The rate of growth of this bias is negative if the rate of growth of the error in measurement
of the price of investment goods is positive, and vice-versa. If we let K* be the " quantity "
of capital calculated using the erroneous " price " of investment goods and K the actual
quantity of capital:
*= P

e-*«-*I*(s)ds= P

G*(*)

J-

J-oo

The bias in the rate of growth of the quantity of capital services is then:

K
K

£*
K*

I
<2*K*

I
p

g-3(.-.)6!(0/(s)ds

J-oo

...(9)

G*«

J-o

which is negative if the rate of growth of the error in measurement of the price of investment
goods is positive, and vice-versa.
To calculate the error of measurement in total factor productivity, we let C represent
the quantity of consumption goods and L the quantity of labour input; second, we let
Wj represent the relative share of the value of investment goods in the value of total output
and wc the relative share of consumption goods; finally, we let VK represent the relative
share of the value of capital input in the value of total input and vL the relative share of
labour. The rate of growth of total factor productivity may be represented as:
P
I
C
K
L1
h WCC
VK
Vr —.
P
*I
C
K
L
If we let P* represent the measured index of total factor productivity using the erroneous
" price " of investment goods:
— = Wr

P*
P*

= Wr — + VVC

K*
K*

Vr —.

Subtracting the first of these expressions from the second we obtain the bias in the rate
of growth of total factor productivity:
P* P
[> /I V [£* K]
—
= Wj
\— K\
•
P* P
[I* JJ
L^* KJ
Substituting expressions (9) and (8) for the biases in the measured rates of growth of
capital input and the output of investment goods, we have :
P*

If investment and the error in measurement are growing at constant rates, the biases in
the rates of growth of the quantity of investment goods produced and the quantity of
capital services are equal, so that the net effect is equal to the rate of growth in the error

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in measurement of the price of investment goods multiplied by the difference between the
capital share in total input and the investment share in total output.1
A second source of errors in measurement arises from limitations on the number of
separate inputs that may be distinguished empirically. The choice of commodity groups
to serve as distinct " inputs " and " outputs " involves aggregation within each group by
simply adding together the quantities of all commodities within the group and aggregation
among groups by computation of the usual Divisia quantity index. The resulting price
and quantity indexes are Divisia price and quantity indexes of the individual commodities
only if the rates of growth either of prices or of quantities within each group are identical.
Errors of aggregation in studies of total factor productivity have not gone unnoticed;
however, these errors are frequently mislabelled as "quality change". Quality change
in this sense occurs whenever the rates of growth of quantities within each separate group
are not identical. For example, if high quality items grow faster than items of low quality,
the rate of growth of the group is biased downward relative to an index treating high and
low quality items as separate commodities. To eliminate this bias it is necessary to construct
the index of input or output for the group as a Divisia index of the individual items within
the group. Elimination of " quality change " in the sense of aggregation bias is essential
to accurate social accounting and to measurement of changes in total factor productivity.
Separate accounts should be maintained for as many product and factor input categories
as possible. An attempt should be made to exploit available detail in any empirical
measurement of real product, real factor input, and total factor productivity.
In some contexts the choice of an appropriate unit for the measurement of quantities
of real product or real factor input is not obvious. For example, fuel may be measured
in tons or in B.T.U. equivalents, tractor services may be measured in tractor hours or in
horsepower hours, and so on. Measures of real product and real factor input may be
adjusted for " quality change " by converting one unit of measurement to another. This
procedure conforms to the principles of social accounting we have outlined and their
interpretation in terms of the economic theory of production if the adjustment for quality
change corrects errors of aggregation. In the examples we have given, if the marginal
products of different types of fuel always move in proportion when fuel is measured in
B.T.U. equivalents but fail to do so when fuel is measured in tons, the appropriate unit
for the measurement of fuel is the B.T.U. Similarly, if the marginal products of tractor
services measured in horsepower hours always move in proportion, but when measured
in tractor hours fail to do so, tractor services should be measured in horsepower hours.
The appropriateness of any proposed adjustment for quality change may be confronted with empirical evidence on the marginal products of individual items within a
commodity group. Under the assumption that these products are equal to the corresponding price ratios this evidence takes the form of data on relative price movements
for the individual items. Under a more general set of assumptions the marginal products
might be calculated from an econometric production function. The latter treatment
would be especially useful for " linking in " new factors and products since the relevant
prices cannot be observed until the new factors and products appear in the market. Any
change in measured total factor productivity resulting from adjustments for quality change
is explained by evidence on the movement of marginal products and is not the result of
an arbitrary choice of definitions. The choice of appropriate units for measurement of
1
Domar [22, p. 587, formula (5)] considers a special case of this problem in which capital" is imported
from the outside". This specialization is unnecessary, as suggested in the text. A more detailed discussion
of this issue is presented by Jorgenson [35].
For constant rates of growth of the relative error in the investment goods price index and the level
of investment, formula (10) may be expressed in closed form:

*-t=&+v &,
P Wt Q* K Q*

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real product and real factor input may go beyond selection among alternative scalar measured
such as B.T.U. equivalents or tons; a commodity may be regarded as multi-dimensional
and an appropriate unit of measurement may be defined implicitly by taking prices as
given by so-called " hedonic " price indexes. The critical property of such price indexes
is that when prices are given by a " hedonic " price index for the commodities within a
group, all such commodities have marginal rates of transformation vis-a-vis commodities
outside the group that move in proportion to each other. Insofar as this property is substantiated by empirical evidence, adjustment of the commodity group for "quality change"
by means of such a price index is entirely legitimate and amounts to correcting an error
of aggregation.1 This is not to say that any proposed adjustment for quality change is legitimate. The appropriateness of each adjustment must be judged on the basis of the evidence.
If no fresh evidence is employed, the choice of appropriate units is entirely arbitrary and any
change in measured total factor productivity resulting from adjustment for "quality
change" is simply definitional.
" Quality change " is sometimes used to describe a special type of aggregation error,
namely, the error that arises in aggregating investment goods of different vintages by
simply adding together quantities of investment goods of each vintage. If the quality of
investment goods, as measured by the marginal productivity of capital, is not constant over
all vintages, this procedure results in aggregation errors. An appropriate index of capital
services may be constructed by treating each vintage of investment goods as a separate
commodity. To construct such an index empirically, data on the marginal productivity
of capital of each vintage at each point of time are required. If independent data on relative
prices of capital services of different vintages are used in the construction of such a capital
services index, any resulting reduction in measured productivity growth is not tautological.
Only where the change in quality is measured indirectly from the resulting increase in
total factor productivity, as suggested by Solow [60], does such a procedure result in the
elimination of productivity change by definition.2
3. MEASUREMENT
3.1. Initial estimates
We can now investigate the extent to which measured changes in total factor productivity are due to errors of measurement. We begin by constructing indexes of total
output and total input for the United States for the twenty-year period following World
War II, 1945-65, without correcting for errors of measurement. As an initial index of
total output we take U.S. private domestic product in constant prices as measured in the
U.S. national product accounts [48], As an index of total input we take the sum of labour
and capital services in constant prices. Labour and capital services are assumed to be
proportional to stocks of labour and capital, respectively. The stock of labour is taken
to be the number of persons engaged in the private domestic sector of the U.S. economy.
The stock of capital is the sum of land, plant, equipment, and inventories employed in
this sector.3 The rate of growth of total factor productivity is equal to the difference in
the rates of growth of total output and total input.
Indexes of total output, total input, and total factor productivity are given in Table I.
The average annual rate of growth of total output over the period 1945-65 is 3-49 per cent.
The average rate of growth of total input is 1-83 per cent. The average rate of growth of
total factor productivity is 1-60 per cent. The rate of growth of total input explains 524
1
2

See Griliches [28] and the references given there.
Jorgenson [35].
3 To make stocks of labour and capital precisely analogous, it would be necessary to go even further.
Unemployed workers should be included in the stock of labour since unemployed machines are included
in the stock of capital. Workers should be aggregated by means of discounted lifetime incomes since
capital goods are aggregated by means of asset prices.

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TABLE I
Total output, input, and factor productivity, U.S. private
domestic economy, 1945-65, initial estimates

1945
1946
1947
1948
1949

0-699
0-680
0-695
0-729
0*726

0-786
0-817
0-854
0-876
0*867

0-891
0-836
0-818
0-836
0-841

1950
1951
1952
1953
1954

0*801
0-852
0-873
0-917
0-904

0-891
0-928
0*947
0-966
0-954

0-901
0-919
0-924
0-951
0-949

1955
1956
1957
1958
1959

0-981
0-999
1-013
1-000
1-069

0-976
1-001
1-012
1-000
1-019

1-005
0-998
1-000
1-000
1-048

1960
1961
1962
1963
1964
1965

•096
•115
•189
•240
•307
1-387

1*036
1-039
1-057
1-074
1-097
1-129

1-057
1-072
1-123
1-152
1-188
1-224

1. Output.

2. Input.

3. Productivity.

per cent of the growth in output; the remainder is explained by changes in total factor
productivity.
3.2. Errors of aggregation
The first error of measurement to be eliminated is an error of aggregation. This error
results from aggregating labour and capital services by summing quantities in constant
prices. To eliminate the error, we replace our initial index of total input by a Divisia
index of labour and capital input, as suggested by Solow [61 ]. A similar error results from
aggregating consumption and investment goods output by adding together quantities in
constant prices. This error may be eliminated by replacing our initial index of total
output by a Divisia index of consumption and investment goods output. Indexes of
total output, total input, and total factor productivity with these errors of aggregation
eliminated are presented in Table II.
The average annual rate of growth of total output over the period 1945-65 with the
error in aggregation of consumption and investment goods output eliminated is 3-39 per
cent. The average rate of growth of total input with the error in aggregation of labour
and capital services eliminated is 1-84 per cent. The resulting rate of growth of total
factor productivity is 1-49 per cent. We conclude that these errors in aggregation result
in an overstatement of the initial rate of growth of total factor productivity. With these
errors eliminated total input explains 54-3 per cent of the growth in total output. This
result may be compared with the 52-4 per cent of the growth in total output explained
initially.
3.3. Investment goods prices
We have demonstrated that an error in the measurement of investment goods prices
results in errors in the measurement of total output, total input, and total factor productivity.

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Roughly speaking, a positive bias in the rate of growth of the investment goods price
index results in a positive bias in the rate of growth of total factor productivity, provided
that the share of capital in the value of input exceeds the share of investment in the value
of output. This condition is fulfilled for the U.S. private domestic sector throughout the
period, 1945-65. Hence, we must examine the indexes of investment goods prices that
underlie our measurement for possible sources of bias.
Except for the price index for road construction the price indexes for structures that
underlie the U.S. national accounts are indexes of the cost of input rather than the price
of output. In the absence of changes in total factor productivity properly constructed
TABLE II
Total output, input, and factor productivity, U.S. private domestic
economy, 1945-65, errors of aggregation eliminated

1945
1946
1947
1948
1949

0-713
0-679
0-694
0-727
0-727

0-783
0-810
0-847
0-870
0-864

0-912
0-841
0-824
0-840
0-845

1950
1951
1952
1953
1954

O'SOO
0-851
0-873
0-918
0-905

0-888
0-925
0-945
0-964
0-954

0-903
0-921
0-926
0-953
0-950

1955
1956
1957
1958
1959

0-981
0-999
1-013
1-000
1-070

0-976
1-001
1-012
1-000
1-019

1-005
0-998
1-000
1-000
1-049

1960
1961
1962
1963
1964
1965

1-096
1-115
1-189
1-240
1-307
1-387

1-036
1-038
1-057
1-073
1-096
1-128

1-057
1-073
1-124
1-153
1-189
1-225

1. Output.

2. Input.

3. Productivity.

price indexes for construction input would parallel the movements of price indexes for
output. This is assured by the dual to the usual definition of total factor productivity (3).
Dacy [12] has shown that the rate of growth of the price of inputs in highway construction
is considerably greater than that of the price of construction output. Dacy's output
price index grows from 0-805 to 0-982 from 1947 through 1959, while the input price
index grows from 0-615 to 1-024 in the same period, both on a base 1-000 in 1958.1 This
empirical finding is simply another way of looking at the positive residual between rates
of growth of total output and total input where total factor productivity is measured with
error. Input price indexes are subject to the same errors of aggregation as the corresponding quantity indexes. Since input quantity indexes grow too slowly, input price indexes
grow too rapidly.
1
The growth of the output price index may be compared with that for personal consumption
expenditures, which grows from 76-5 to 108'6 from 1947 through 1959. The close parallel between the
output price index for construction and the price of consumption goods suggests an explanation for the
difference in rates of growth of prices of consumption and investment goods described by Gordon [26].
This difference results from the error of measurement in using an input price index in place of an output
price index for investment goods. If this error is corrected, the difference vanishes.

May 1969

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263

The use of input prices in place of output prices for structures results in an important
error of measurement. To eliminate this error it is necessary to use an output price index
in measuring prices of both investment goods output and capital services input. An index
of this type has been constructed for the QBE 1966 Capital Stock Study [49]. Components
of this index include the Bureau of Public Roads price index for highway structures, the
Bell System price index for telephone buildings, and the Bureau of Reclamation price
indexes for pumping plants and power plants. The resulting composite index may be
compared with the implicit deflator for new construction from the U.S. national accounts
[48]. The implicit deflator grows from 0-686 to 1-029 during the period 1947 through
1959 while the OBE Capital Goods Study price index for new construction output grows
TABLE III
Alternative investment deflators
1

1945
1946
1947
1948
1949

0-544
0-594
0-721
0-749
0-743

0-510
0-570
0-686
0-770
0-755

0-759
0-768
0-827
0-863
0-868

0-517
0-575
0-646
0-703
0-736

0-633
0-705
0-786
0-827
0-818

0-357
0-638
2-310
1-023
0-788

1950
1951
1952
1953
1954

0-763
0-836
0-881
0-895
0-897

0-791
0-847
0-876
0-889
0-886

0-878
0-942
0-954
0-943
0-929

0-752
0-809
0-822
0-835
0-840

0-823
0-879
0-896
0-903
0-914

0-818
0-945
0-949
0-497
0-772

1955
1956
1957
1958
1959

0-902
0-959
1-001
1-000
1-006

0-910
0-956
0-992
1-000
1-029

0-919
0-949
0-984
1-000
1-014

0-859
0-918
0-975
1-000
1-020

0-921
0-945
0-978
1-000
1-012

0-931
0-978
1-113
0-994
0-991

1960
1961
1962
1963
1964
1965

1-005
1-008
1-024
1-038
1-059
1-089

1-042
1-053
1-069
1-089
1-119
1-149

1-009
1-006
1-008
1-004
1-004
0-995

1-022
1-021
1-023
1-023
1-031
1-038

1-026
1-037
1-048
1-059
1-071
1-089

1-020
1-011
1-001
1-011
1-014
1-032

1. Structures II.
2. Structures I.
3. Equipment II.

4. Equipment I.
5. Inventories II.
6. Inventories I.

from 0-762 to 0-958 during the same period. Thus the relative bias in the input price
index for all new construction as a measure of the price of construction output is roughly
comparable to the relative bias in Dacy's input price index for highway construction as a
measure of the price of highway construction output. The input price index, labelled
Structures I, and the output price index, labelled Structures II, are given in Table III.
The price indexes for equipment that underlie the U.S. national accounts are based
primarily on data from the wholesale price index of the Bureau of Labour Statistics [6],
Since expenditures on the wholesale price index are less than those on the consumers'
price index [4], adjustments for quality change are less frequent and less detailed. A
direct comparison of the durables components of the wholesale and consumers' price
indexes gives some notion of the relative bias. The wholesale price index increases from
0-646 to 1-023 and the consumers' price index increases from 0-858 to 1-022 over the
period 1947 to 1959, both on a base of 1-000 in 1958. A direct comparison of components
common to both indexes reveals essentially the same relationship. To correct for bias

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in the implicit deflator for producers' durables, we substitute for this deflator the implicit
deflator for consumers' durables. The deflator for producers' durables increased from
0-646 in 1947 to 1-020 in 1959. Over this same period the deflator for consumers' durables
increased from 0-827 to 1-014, both on a base of 1-000 in 1958. Thus the relative bias in
the producers' durables price index as revealed by a comparison with components common
to the wholesale and consumers' price indexes may be corrected by simply substituting the
implicit deflator for consumers' durables for the producers' durables deflator. Both
indexes are given in Table III; the producers' durables index is labelled Equipment I while
the consumers' durables index is labelled Equipment II.
The durables component of the consumers' price index was itself subject to considerable upward bias in recent years. The consumers' price index for new automobiles
increased 62 per cent from 1947 to 1959. It has'been estimated that correcting this index
for quality change would reduce this increase to only 31 per cent in the same period.1
In view of the upward bias in the consumers' price index our adjustment for bias in the
producers' durables price index is conservative. In order to reduce the error of measurement further, detailed research like that already carried out for automobiles is required
for each class of producers' durable equipment.
The price indexes for change in business inventories from the U.S. national accounts
contain year-to-year fluctuations that result from changes in the composition of investment
in inventories; these changes are much more substantial than the corresponding changes
in the composition of inventory stocks. The implicit deflator for change in inventories
is not published; however, it may be computed from data on change in inventories in
current and constant dollars. Changes that amount to nearly doubling or halving the
index occur from 1946 to 1947, 1947 to 1948, and 1951 to 1952. The value of the index is
0-357 in 1945, 0-638 in 1946 and 2-310 in 1947, all on a base of 1-000 (or, to be exact, 0-994)
in 1958. The index drops to 1-023 in 1948 and 0-788 in 1949. A less extreme but equally
substantial movement in the index occurs from 1952 through 1957. Changes in the
implicit deflator of this magnitude cannot represent movements in the price of all stocks
of inventories considered as investment goods. To represent these movements more
accurately, we replace the implicit deflator for change in inventories by the deflator for
private domestic consumption expenditures. The level of this index generally coincides
with that of the implicit deflator for change in business inventories; however, the fluctuations are much less. Both indexes are given in Table III; the implicit deflator for change
in business inventories is labelled Inventories I while the implicit deflator for private
domestic consumption expenditures is labelled Inventories II.
Indexes of total input, total output, and total factor productivity with errors in the
measurement of prices of investment goods eliminated are presented in Table IV. The
average rate of growth of total output over the period 1945-65 with these errors of measurement removed is 3-59 per cent. This rate of growth may be compared with the original
rate of growth of total output of 3-49 per cent or with the rate of growth of 3-39 per cent
for total output with errors of aggregation removed. The average rate of growth of total
input over this period is 2-19 per cent. The original rate of growth of total input is 1-83
per cent; with errors of aggregation removed the rate of growth of total input is 1-84 per
cent. The rate of growth of total factor productivity is 1-41 per cent. With errors in
measurement of the prices of investment goods eliminated the rate of growth of total
input explains 61-0 per cent of the rate of growth of total output.
3.4. Measurement of services

Up to this point we have assumed that labour and capital services are proportional
to stocks of labour and capital. This assumption is obviously incorrect. In principle
flows of capital and Jabour services could be measured directly. In fact it is necessary to
i Griliches [28, Table 8, last column, p. 397].

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265

infer the relative utilization of stocks of capital and labour from somewhat fragmentary
data. Okun [50] has attempted to circumvent the problem of direct observation of labour
and capital services by assuming that the relative utilization of both labour and capital is
a function of the unemployment rate for labour so that the gap between actual and
" potential" output, that is, output at full utilization of both factors, may be expressed
in terms of the unemployment rate. A similar notion has been used by Solow [62] to
adjust stocks of labour and capital for relative utilization. Most of the available capacity
utilization measures are based on the relationship of actual output to output at full utilization of both labour and capital, so that these measures also attempt to adjust both labour
and capital simultaneously.
TABLE IV
Total output, input, and factor productivity, U.S. private domestic economy, 1945-65,
errors in investment goods prices eliminated

1945
1946
1947
1948
1949

0-692
0-662
0-679
0-718
0-717

0-759
0-786
0-822
0-845
0-842

0-913
0-846
0-829
0-853
0-854

1950
1951
1952
1953
1954

0-798
0-839
0-858
0-905
0-900

0-867
0-908
0-930
0-950
0-942

0-922
0-925
0-925
0-954
0-957

1955
1956
1957
1958
1959

0-982
0-995
•009

1-016
0-999

•076

0-966
0-996
1-010
1-000
1-022

1960
1961
1962
1963
1964
1965

•107
•127
•199
•249
•319
•400

1-042
1-049
1-071
1-091
1-117
1-153

•061
•073
•117
•142
•177
•209

1. Output.

•ooo

2. Input.

•ooo
•ooo

•052

3. Productivity.

Our approach to the problem of relative utilization is somewhat more direct in that
we attempt to adjust capital and labour for relative utilization separately. Of course,
this adjustment gives rise to a new concept of " potential " or capacity output, but we do
not pursue this notion further in this paper. Our first assumption is that the relative
utilization of capital is the same for all capital goods; while this is a very strong assumption
it is weaker than the assumption underlying the Okun-Solow approach in which the
relative utilization of capital and labour depends on that of labour. We estimate the
relative utilization of capital from the relative utilization of power sources.1 Data on
the relative utilization of electric motors provides an indicator of the relative utilization of
capital in manufacturing, since electric motors are the predominant source of power there.
We assume that relative utilization of capital goods in the manufacturing and nonmanufacturing sectors is the same. When more complete data become available, this
assumption can be replaced by less restrictive assumptions. Unfortunately, this adjustment

Foss [24]. See the Statistical Appendix for further details.

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allows only for the trend in the relative utilization of capital; it does not adjust for shortterm cyclical variations in capacity utilization. Thus we are unable to attain the objective
of complete comparability between measures of labour and capital input.
The assumption that labour services are proportional to the stock of labour is obviously
incorrect. On the other hand, the assumption that labour services can be measured
directly from data on man-hours is equally incorrect, as Denison [14] has pointed out.
The intensity of effort varies with the number of hours worked per week, so that labour
input can be measured accurately only if data on man-hours are corrected for the effects
of variations in the number of hours per man on labour intensity. Denison [15] suggests
that the stock of labour provides an upper bound for labour services while the number
of man-hours provides a lower bound. He estimates labour input by correcting manhours for variations in labour intensity. We employ Denison's correction for intensity,
TABLE V
Total input and factor productivity, U.S. private domestic economy, 1945-65,
errors in relative utilization eliminated

1945
1946
1947
1948
1949

0-716
0-742
0-777
0-801
0-802

0-968
0-895
0-877
0-899
0-897

1950
1951
1952
1953
1954

0-830
0-873
0-899
0-924
0-923

0-963
0-963
0-956
0-980
0-976

1955
1956
1957
1958
1959

0-959
0-994
1-009
1-000
1-035

1-023
1-001
1-000
1-000
1-038

1960
1961
1962
1963
1964
1965

1-057
1-067
1-089
1-114
1-146
1-189

1-046
1-054
1-098
1-118
1-147
1-172

1. Input.

2. Productivity.

but we apply this correction to actual hours per man rather than potential hours per man.
Thus, our measure of labour input reflects short-run variations in labour intensity.
The assumption that labour and capital services are proportional to stocks of labour
and capital results in an error in separating a given value of transactions into a price
and a quantity. To correct this error we multiply the number of persons engaged by hours
per man. The resulting index of man-hours is then corrected for variations in labour
intensity. The corresponding error for capital is corrected by multiplying the stock of
capital by the relative utilization of capital. Indexes of total input and total factor productivity after these errors have been eliminated are presented for the period 1945-65 in
Table V. The average annual rate of growth of total output is the same as before these
corrections, 3-59 per cent per year. The average rate of growth of total input is 2-57 per
cent. The resulting average rate of growth of total factor productivity is 0-96 per cent.
Total input now explains 71-6 per cent of the rate of growth in total output.

May 1969

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49
267

3.5. Capital services
In converting estimates of capital stock into estimates of capital services we have
disregarded an important conceptual error in the aggregation of capital services. While
investment goods output must be aggregated by means of investment goods or asset prices,
capital services must be aggregated by means of service prices.
The prices of capital services are related to the prices of the corresponding investment
goods; in fact, the asset price is simply the discounted value of all future capital services.
Asset prices for different investment goods are not proportional to service prices because
of differences in rates of replacement and rates of capital gain or loss among capital goods.
Implicitly, we have assumed that these prices are proportional; to eliminate the resulting
error in measurement, it is necessary to compute service prices and to use these prices in
aggregating capital services.
We have already outlined a method for computing the price of capital services in the
absence of direct taxation of business income. In the presence of direct taxes we may
distinguish between the price of capital services before and after taxes. The expression (7)
given above for the price of capital services is the price after taxes. The price of capital
services before taxes is:
1 — uv
1 — uw - 1 — uxqJ]
,ii^
r+dk- 2»
...(11)
1—u
l—u
1 — u qk_\
where u is the rate of direct taxation, v the proportion of return to capital allowable as a
charge against income for tax purposes, w the proportion of replacement allowable for
tax purposes, and x the proportion of capital gains included in income for tax purposes
We estimate the variables describing the tax structure as follows: The rate of direct
taxation is the ratio of profits tax liability to profits before taxes. The proportion of the
return to capital allowable for tax purposes is the ratio of net interest to the total return
to capital. Total return to capital is the after tax rate of return, r, multiplied by the current
value of capital stock. The proportion of replacement allowable for tax purposes is the
ratio of capital consumption allowances to the current value of replacement. The proportion of capital gains included in income is zero by the conventions of the U.S. national
accounts. Given the value of direct taxes we estimate the after tax rate of return by
subtracting from the value of output plus capital gains the value of labour input, replacement, and direct taxes. This results in the total return to capital. The rate of return is
calculated by dividing this quantity by the current value of the stock of capital. Given
data on the rate of return and the variables describing the tax structure, we calculate the
price of capital services before taxes for each investment good.1 These prices of capital
services are used in the calculation of indexes of capital input, total input, and total factor
productivity.
For the U.S. private domestic economy it is possible to distinguish five classes of
investment goods—land, residential and non-residential structures, equipment, and
inventories. Although it is also possible to distinguish a number of sub-classes within
each of these groupings, we will employ only the five major groups in calculating an index
of total capital input. For each group we first compute a before tax service price analogous
to (11). We then compute an index of capital input as a Divisia index of the services of
land, structures, equipment and inventories. In constructing this index we eliminate the
conceptual error that arises from the implicit assumption that service prices are proportional
to asset prices for different investment goods. In eliminating this conceptual error we
also eliminate the error of aggregation that results from adding together capital services
in constant prices to obtain an index of total capital input. To eliminate the corresponding
error in our index of investment goods output we replace our initial index by a Divisia
index of investment in structures, equipment, and inventories. Indexes of total output,
total input and total factor productivity resulting from the elimination of these errors are

[

Further details are given in the Statistical Appendix.

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REVIEW OF ECONOMIC STUDIES

presented in Table VI. The after tax rate of return implicit in the new index of capital
input is also given in Table VI.
The average rate of growth of total output over the period 1945-65 with the error in
aggregation of investment goods eliminated is 3-59. This rate of growth is essentially the
same as for total output with errors in the aggregation of consumption and investment
goods and errors in the measurement of investment goods prices eliminated. The average
rate of growth of total input with errors in aggregation of capital services eliminated is
2-97 per cent. This rate of growth may be compared with the initial rate of growth of
1-83 per cent.
TABLE VI
Total input and factor productivity, U.S. private domestic economy, 1945-65,
errors in aggregation of capital input eliminated; implicit rate of return after taxes

1945
1946
1947
1948
1949

0-692
0-661
0-678
0-717
0-716

0-671
0-698
0-735
0-765
0-773

1-030
0-950
0-926
0-940
0-930

0-158
0-198
0-237
0-223
0-126

1950
1951
1952
1953
1954

0-797
0-837
0-857
0-905
0-900

0-804
0-850
0-880
0-908
0-911

0-992
0-986
0-976
0-997
0-988

0-095
0-242
0-143
0-091
0-078

1955
1956
1957
1958
1959

0-982
0-995
•009
•000
•077

0-951
0-987
1-005
1-000
1-039

1-032
1-008
1-004
1-000
1-035

0-113
0-175
0-138
0-107
0-097

1960
1961
1962
1963
1964
1965

•107
•127
•199
•250
•320
•401

1-063
1-076
1-099
1-126
1-160
1-206

1-040
1-046
1-089
1-107
1-134
1-157

0-105
0-118
0-138
0-131
0-127
0-141

1. Output.

2. Input.

3. Productivity.

4. Rate of return.

The resulting rate of growth of total factor productivity is 0-58 per cent. The index of
total factor productivity with these errors eliminated is presented in Table VI. With these
errors eliminated total input explains 82-7 per cent of the growth in total output. The
original index of total input explains 52-4 per cent of this growth.
3.6. Labour services
We have eliminated errors of aggregation that arise in combining capital services
into an index of total capital input. Similar errors arise in combining different categories
of labour services into an index of total labour input. Implicitly, we have assumed that
the price per man-hour for each category of labour services is the same; to eliminate the
resulting error of measurement it is necessary to use prices per man-hour for each category
in computing an index of total labour input. Second, to eliminate the error of aggregation
that results from adding together labour services in constant prices, we replace our initial
index of labour input by a Divisia index of the individual categories of labour services.
The Divisia index of total labour input is based on a weighted average of the rates

May 1969

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51
269

of growth of different categories of labour, using the relative shares in total labour compensation as weights. To represent our index of total labour input, we let Ll represent
the quantity of input of the /th labour service, measured in man-hours. The rate of growth
of the index of total labour input, say L, is :

where vl is the relative share of the /th category of labour in the total value of labour
input. The number of man-hours for each labour service is the product of the number
of men, say nh and hours per man, say h^ using this notation the index of total labour
input may be rewritten:

L
^-a
For comparison with our initial indexes of labour input we separate the rate of growth
of the index of labour input into three components—change in the total number of men,
change in hours per man, and change in labour input per man-hour. We have assumed
that the number of hours per man is the same for all categories of labour services, say H.
Letting JV represent the total number of men and el the proportion of the workers in the
/th category of labour serivces, we may write the index of total labour input in the form:
.1
L

...(12)

Our initial index of labour input was simply N9 the number of persons engaged; we corrected this index by taking into account the number of hours per man, H. To eliminate
the remaining errors of aggregation we must correct the rate of growth of man-hours
by adding to it an index of labour input per man-hour. The third term in the expression
(12) for total labour input given above provides such an index. We will let E represent
this index, so that :
*=Si,A
E
et

...(13)

For computational purposes it is convenient to note that the index may be rewitten in the
form:
E

"Lpft

where pl is the price of the /th category of labour services and pi is the relative price. The
relative price is the ratio of the price of the /th category of labour services to the average
price of labour services, Ep^.
In principle it would be desirable to distinguish among categories of labour services
classified by age, sex, occupation, number of years schooling completed, industry of
employment, and so on. An index of labour input per man-hour based on such a breakdown requires detailed research far beyond the scope of this study. We will compute such
an index only for males and only for categories of labour broken down by the number of
school years completed. The basic computation is presented in Table VII. Data on
relative prices for labour services are available for the years 1939, 1949, 1956, 1958, 1959
and 1963.1 Combining these prices with changes in the distribution of the labour force
provides a measure of the change in labour input per man-hour.2
1
Additional details on relative prices for labour services are presented in the Statistical Appendix,
Table2 XII.
Additional details on the distribution of the labour force are presented in the Statistical Appendix,
Table XI.

to
-<i
o

TABLE VII
Relative prices * changes in distribution of the labour force9 and indexes of labour-input per man-hourp,
U.S. males, the civilian labour force, 1940-64

/
Pi

A*i

/
Pi

A*i

**i

1952-57

1958

1957-59

1959

1959-62

1963

1962-65

0-452

-1-3

0-409

-0-8

0-498

-0-8

0-407

-0-8

-0-5

0-624

-0-2

0-565

-1-0

0-688

-0-9

0-562

-1-5

o
o
hrj
hcj

0-813

-1-8

0-796

-3-3

0-753

-1-2

0-801

-1-9

0-731

-1-2

2-4

0-974

-1-3

0-955

0-7

0-923

0-6

0-912

-0-6

0-886

-0-3

1-241

7-0

1-143

1-0

1-159

2-6

1-113

0-9

1-039

1-6

1-087

3-2

College 1-3

1-442

1-4

1-336

1-2

1-356

0-2

1-392

0-7

1-255

1-3

1-269

0-0

4+ or 4

1-947

1-3

1-866

1-6

1-810

1-3

1-840

0-9

1-569

1-0

1-571

0-2

0
GO

w
d
CO

...

1-888

0-3

1-730

0-4
CO

/
Pi

A*i

/
Pi

A*i

/
Pi

1939

1940-48

1949

1948-52

1956

Elementary 0-4

0-497

-2-3

0-521

-0-3

5-6 or 5-7

0-672

-3-1

0-685

7-8 or 8

0-887

-6-8

High School 1-3

1-030

School year
completed

...

Percentage change in labour
input per man-hour

6-45

2-50

2-97

2-39

2-36

2-13

Annual percentage change

0-78

0-62

0-59

1-20

0-79

0-72

SOURCE: Derived from Tables 11 and 12, Statistical Appendix.
* The relative prices are computed using the appropriate beginning period distribution of the labour force as weights.

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53
271

Indexes of total input and total factor productivity with errors in the aggregation of
labour services eliminated are presented in Table VIII. The average rate of growth of
total input over the period 1945-65 with the error in aggregation of labour services eliminated
is 3-47. This rate of growth may be compared with the initial rate of growth of total input
of 1*83 per cent. The resulting rate of growth of total factor productivity is 0-10 per cent.
With these errors eliminated total input explains 96-7 per cent of the growth in total output.
TABLE VIII
Total input and factor productivity, U.S. private domestic economy 1945-65,
errors in aggregation of labour input eliminated

0-634

1-090
1-001
0-971
0-981

1945
1946
1947
1948
1949

0-700
0-732
0-743

1950
1951
1952
1953
1954

0-776
0-823
0-857
0-887
0-894

1-026
1-017
1-002
1-020
1-007

1955
1956
1957
1958
1959

0-936
0-976
0-997

1-000
1-047

1-048
1-019
1-012
1-000
1-027

1960
1961
19(52
1963
1964
1965

1-077
1-096
1-125
1-158
1-200
1-255

1-027
1-027
1-064
1-076
1-096
1-112

1. Input.

0-661

0-966

2. Productivity.

4. SUMMARY AND CONCLUSION
4.1. Summary
The purpose of this paper has been to examine the hypothesis that if quantities of
output and input are measured accurately, growth in total output may be largely explained
by growth in total input. The results are given in Table IX and Charts 1, 2 and 3. We
first present our initial estimates of rates of growth of output, input, and total factor
productivity. These estimates include many of the errors made in attempts to measure
total factor productivity without fully exploiting the economic theory underlying the social
accounting concepts of real product and real factor input. We begin by eliminating errors
of aggregation in combining investment and consumption goods and labour and capital
services. We then eliminate errors of measurement in the prices of investment goods
arising from the use of prices for inputs into the investment goods sector rather than
outputs from this sector. We remove errors arising from the assumption that the flow of
services is proportional to stocks of labour and capital by introducing direct observations
on the rates of utilization of labour and capital stock. We present rates of growth that
result from correct aggregation of investment goods and capital services. Finally, we give
rates of growth that result from correcting the aggregation of labour services.

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REVIEW OF ECONOMIC STUDIES

The rate of growth of input initially explains 52-4 per cent of the rate of growth of
output. After elimination of aggregation errors and correction for changes in rates of
utilization of labour and capital stock the rate of growth of input explains 96-7 per cent
of the rate of growth of output; change in total factor productivity explains the rest.
In the terminology of the theory of production, movements along a given production
function explain 96-7 per cent of the observed changes in the pattern of productivity
activity; shifts in the production function explain what remains.
This computation is based on the 1945-65 period, measuring total factor productivity
peak to peak. If one were to choose a different set of years, the numerical results would
be slightly different, but their main thrust would be the same. For example, starting with
the Post-Korean peak year of 1953, the rate of growth of input initially explains only
37-3 per cent of the rate of growth of output. After all the corrections the rate of growth
of input explains 79-2 per cent of the growth in output between 1953 and 1965, reducing
the estimated rate of change in total factor productivity from 2-12 per cent per year to
TABLE IX
Total output, input, and factor productivity, U.S. private domestic economy, 1945-65,
average annual rates of growth

1. Initial estimates
Estimates after correction for:
2. Errors of aggregation
3. Errors in investment goods prices
4. Errors in relative utilization
5. Errors in aggregation of capital services
6. Errors in aggregation of labour services

Output

Input

Productivity

3-49

1-83

1-60

3-39
3-59
3-59
3'59
3-59

1-84
2-12
2-57
2-97
3-47

1-49
1-41
0-96
0-58

o-io

0-72. We conclude that our hypothesis is consistent with the facts. If the economic theory
underlying the measurement of real product and real factor input is properly exploited,
the role to be assigned to growth in total factor productivity is small.
4.2. Evaluation of past research
Our conclusion that most of the growth in total output may be explained by growth
in total input is just the reverse of the conclusion drawn from the great body of past
research on total factor productivity, the research of Schmookler [55], Mills [46], Fabricant
[23], Abramovitz [2], Solow [61], and Kendrick [37]. These conclusions, stated by
Abramovitz, are " . . . that to explain a very large part of the growth of total output
and the great bulk of output per capita, we must explain the increase in output per unit
of conventionally measured inputs. . . " *. This conclusion results from inadequacies
in the basic economic theory underlying the social accounts employed in productivity
measurements. The increase in output per unit of conventionally measured inputs is
characterized by very substantial errors of measurement, equal in magnitude to the
alleged increase in productivity. We have given a concrete and detailed list of errors of
this type.
Our results differ from those of Denison [15] in that we correct changes in total
factor productivity for errors in the measurement of output, capital services, and labour
services, while Denison corrects only for errors in the measurement of labour services.
1

Abramovitz [1, p. 776].

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THE EXPLANATION OF PRODUCTIVITY CHANGE

273

To get some idea of the relative importance of errors in the measurement of labour and
errors in the measurement of output and capital, we may observe that the rate of growth
of total factor productivity is reduced from 1-60 per cent per year to 0-10 per cent per
year. Of the total reduction of 1-50 per cent per year errors in the measurement of output
and capital account for 1-17 per cent per year while errors in the measurement of labour

INDEXES OF TOTAL OUTPUT, TOTAL INPUT AND TOTAL FACTOR
PRODUCTIVITY (1958 = 1-0), U.S. PRIVATE DOMESTIC ECONOMY,
1945-1965
1-500 1945

1950

1955

1960

1965

1950

1955

1960

1965

1. TOTAL
OUTPUT

fe
W

™
g
O

fe
w

0-600
1-300

2. TOTAL
INPUT

H
O
Q

0-600
1-300

3. TOTAL
FACTOR i [
PRODUCTIVITY

0-600

1945

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REVIEW OF ECONOMIC STUDIES

account for 0-33 per cent per year. We conclude that errors of measurement of the type
left uncorrected by Denison are far more important than the type of errors he corrects.1
Our results suggest that the residual change in total factor productivity, which Denison
attributes to Advance in Knowledge, is small. Our conclusion is not that advances in
knowledge are negligible, but that the accumulation of knowledge is governed by the same
economic laws as any other process of capital accumulation. Costs must be incurred if
benefits are to be achieved. Although we have made no attempt to isolate the effects of
expenditures on research and development from expenditures on other types of current
inputs or investment goods, our results suggest that social rates of return to this type of
investment are comparable to rates of return on other types of investment. Of course,
our inference is indirect and a better test of this proposition could be provided by direct
observation of private and social rates of return to investment in scientific research and
development activities. Unfortunately, many of the direct observations on these rates of
return available in the literature attribute all or part of the measured increase in total
factor productivity to investment in research and development; 2 since these measured
increases are subject to all the errors of measurement we have enumerated, satisfactory
direct tests of the hypothesis that private and social rates of return to research and development investment are equal to private rates of return to other types of investment are not
yet available.
Another implication of our results is that discrepancies between private and social
returns to investment in physical capital may play a relatively minor role in explaining
economic growth. Under the operational definitions of total factor productivity we have
adopted, a positive discrepancy between social and private rates of return would appear
as a downward bias in the rate of growth of input, hence an upward bias in the rate of
growth of total factor productivity. The effects of such discrepancies are lumped together
with the effects of other sources of growth in total factor productivity we have measured.
The fact that the growth of the resulting index is small indicates that the contribution
of investment to economic growth is largely compensated by the private returns to investment. This implication of our findings is inconsistent with explanations of economic
growth such as Arrow's model of learning by doing [3], which are based on a higher social
than private rate of return to physical capital.3
Of course, ours is not the first explanation of productivity change that does not rely
primarily on discrepancies between private and social rates of return. An explanation
of this type has been proposed by Solow [60], namely, embodied technical change. As
Solow [59] points out, explanation of measured changes in total factor productivity as
embodied technical change does not require discrepancies between private and social rates
of return: " . . . the fact of expectable obsolescence reduces the private rate of return
on saving below the marginal product of capital as one might ordinarily calculate it. But
this discrepancy is fully reflected in a parallel difference between the marginal product of
1
Errors in the aggregation of labour services account for 0*48 per cent per year, but this is offset by
errors of measurement in the relative utilization of labour of —0*15 per cent per year so that the net
correction for errors of measurement of labour is 0*33 per cent per year.
An alternative interpretation of our results may be provided by analogy with the conceptual framework for technical change discussed by Diamond [16]. Errors of measurement in the growth of labour
services may be denoted labour-diminishing errors of measurement; capital-diminishing errors of measurement may be separated into embodied and disembodied errors. Errors in capital due to errors in the
measurement of prices of investment goods are analogous to embodied technical change. Finally, some
of the errors in measurement affect levels of output; these errors may be denoted output-diminishing errors
of measurement.
A decomposition of total errors of measurement into labour-diminishing, capital-diminishing, embodied
and disembodied, and output-diminishing is as follows: Labour-diminishing errors of measurement
contribute 0*33 per cent per year to the initial measured rate of growth of total factor productivity. Embodied
capital-diminishing errors contribute 0*28 per cent per year and disembodied capital-diminishing errors
contribute 0'99 per cent per year. Finally, output-diminishing errors of measurement of (MO per cent
per year
must be set off against the input-diminishing errors totalling 1*60 per cent per year.
2
See, for example, the studies of Minasian [47] and Mansfield [42].
3
See Levhari [40, 41] for an elaboration of this point.

May 1969

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THE EXPLANATION OF PRODUCTIVITY CHANGE

57
275

capital and the social rate of return on saving. So ... the private and social rates of
return coincide"1. In referring to " capital as one might ordinarily calculate it ", Solow
explicitly does not identify quality-corrected or " surrogate " capital with capital input
and " surrogate " investment with investment goods output. In Solow's framework the
marginal product of " surrogate " capital is precisely equal to the private and social rate
of return on saving. The difference between Solow's point of view and ours is that the
private and social rates of return are equal by definition in his framework, where the
equality between private and social rates of return is a testable hypothesis within our
framework.2
4.3. Implications for future research
The problem of measuring total factor productivity is, at bottom, the same as the
estimation of national product and national factor input in constant prices. The implication of our findings is that the predominant part of economic growth may be explained
within a conventional social accounting framework. Of course, precise measurement of
productivity change requires attention to reliability as well as accuracy. Our catalogue of
errors of measurement could serve as an agenda for correction of errors in the measurement
of output and for incorporation of the measurement of input into a unified social accounting
framework. Given time and resources we could attempt to raise all of our measurements
to the high standards of the U.S. National Product Accounts in current prices. This
could be done with some difficulty for rates of relative utilization of labour and capital
stock and the prices of investment goods, which require the introduction of new data
into the social accounts. The elimination of aggregation errors in measuring capital
services and investment goods requires a conceptual change to bring these concepts into
closer correspondence with the economic theory of production. The measurement of
appropriate indexes of labour input, corrected for errors of aggregation, necessitates fuller
exploitation of existing data on wage differentials by education, occupation, sex, and so on.
The most serious weakness of the present study is in the use of long-term trends in the
relative utilization of capital and labour to adjust capital input and labour input to concepts
appropriate to the underlying theory of production. As a result of discrepancies between
these trends and year-to-year variations in relative utilization of capital and labour,
substantial errors of measurement have remained in the resulting index of total factor
productivity. Examination of any of the alternative indexes we have presented reveals
substantial unexplained cyclical variation in total factor productivity. An item of highest
priority in future research is to incorporate more accurate data on annual variations in
relative utilization. Hopefully, elimination of these remaining errors will make it possible
to explain cyclical changes in total factor productivity along the same lines as our present
explanation of secular changes. Cyclical changes are very substantial so that even our
secular measurements could be improved with better data. For example, the use of the
period 1945-58, a peak in total factor productivity to a trough, reveals a drop in total factor
productivity of nine per cent; the use of the period 1949-65, a trough to a peak, yields an
increase in total factor productivity of eleven and a half per cent.
In compiling data on labour input we have relied upon observed prices of different
types of labour services. Given a broader accounting framework it would be possible to
treat human capital in a manner that is symmetric with our measurement of physical
capital. Investment in human capital could be cumulated into stocks along the lines
suggested by Schultz [56]. The flow of investment could be treated as part of total output.
The rate of return to this investment could then be measured and compared with the rate
of return to physical capital. Similarly, investment in scientific research and development
could be separated from expenditures on current account and cumulated into stocks.

1 Solow [59, p. 58-59].
For further discussion of this point, see Jorgenson [35],

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EEVIEW OF ECONOMIC STUDIES

The rate of return to research activity could then be computed. In both of these calculations
it would be important not to rely on erroneously measured residual growth in total output
for measurement of the social return to investment.
It is obvious that further disaggregation of our measurements would be valuable in
order to provide a more stringent test of the basic hypothesis that growth in output may
be explained by growth in input. The most important disaggregation of this type is to
estimate levels of output and input by individual industries. The statistical raw material
for disaggregation by industry is already available for stocks of labour and capital and
levels of output. However, data for relative utilization of labour and capital and for
disaggregation of different types of labour and capital within industry groups would have
to be developed. Once these data are available, it will be possible to estimate rates of
return to capital for individual industries and to study the effects of the distribution of
productive factors among industries along the lines suggested by Massell [43]. The
fact that past observations do not reveal significant changes in productivity does not imply
that the existing allocation of productive resources is efficient relative to allocations that
could be brought about by policy changes. In such a study it might be useful to extend
the scope of productivity measurements to include the government sector. This would
be particularly desirable if educational investment, which is largely produced in that
sector, is to be incorporated into total output.
Finally, our results suggest a new point of departure for econometric studies of
production function at every level of aggregation. While some existing studies [29, 30]
employ data on output, labour, and capital corrected for errors of measurement along the
lines we have suggested, most estimates of production functions are based on substantial
errors of measurement. Econometric production functions are not an alternative to our
methods for measuring total factor productivity, but rather supplement these methods in a
number of important respects. Such production functions provide one means of testing
the assumptions of constant returns to scale and equality between price ratios and marginal
rates of transformation that underlie our measurement. A complete test of the hypothesis
that growth in total output may be explained by growth in total input requires the measurement of input within a unified social accounting framework, the measurement of rates of
return to both human and physical capital, further disaggregation, and new econometric
studies of production functions. A start has been made on this task, but much interesting
and potentially fruitful research remains to be done.
University of California, Berkeley
University of Chicago

D. W. JORGENSON
Z. GRILICHES.

STATISTICAL APPENDIX
1. As our initial estimate of output we employ gross private domestic product which
is defined as gross national product less gross product, general government, and gross
product, rest of the world, all in constant prices of 1958. These data are obtained from the
U.S. national accounts. Our second estimate of output requires data on gross private
domestic investment and gross private domestic consumption, defined as gross private
domestic product less gross private domestic investment, in both current and constant
prices of 1958. These data are also obtained from the U.S. national accounts.
As our initial estimate of labour input we employ private domestic persons engaged,
defined as persons engaged for the national economy less persons engaged, general government, and persons engaged, rest of the world. These data are obtained from the U.S.
national accounts [48]. Our initial estimate of capital input is obtained by the perpetual
inventory method based on double declining balance estimates of replacement. For
structures and equipment the lifetimes of individual assets are based on the " Bulletin F
lives " employed by Jaszi, Wasson and Grose [33]. Data for gross private domestic

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THE EXPLANATION OF PRODUCTIVITY CHANGE

277

investment prior to 1929 are unpublished estimates that underlie the capital stock estimates
of Jaszi, Wasson and Grose [33]. For inventories and land, the initial values of capital
stock in constant prices of 1958 are derived from Goldsmith [25]. The stock of land in
constant prices is assumed to be unchanged throughout the period we consider. Estimates
of the value of land in current prices are obtained from Goldsmith [25].
The estimates of gross private domestic investment are subsequently revised by introducing alternative deflators to those employed in the U.S. national accounts. These
deflators are given in Table III of the text. Gross private domestic consumption is left
unchanged in this calculation. We compute stocks of land, structures, residential and
non-residential, equipment, and inventories separately for each set of deflators. The basic
formula is:
*,+1 =/,+(!-«)*„
...(14)
where It is the value of gross private domestic investment for each category in constant
prices. The initial (1929) value of capital stock in constant prices of 1958 and the depreciation rates are as follows:
National accounts
deflators

Alternative deflators

Ki929

Land

254,700

Structures
Residential
Non-residential

183,234
163,205

0-0386
0-0513

162,708
142,670

0-0384
0-0509

74,851
48,504

0-1325
0

51,701
48,504

0-1226
0

Equipment
Inventories

2. In dropping the assumption that services are proportional to stock for both labour
and capital, we require data on hours/man and hours/machine. The data on hours/man
are derived from Kendrick's data on man-hours in the U.S. private domestic economy,
extended through 1965.
To estimate hours/machine we first estimate the relative utilization of electric motors
in manufacturing. Estimates have been given by Foss [24] for 1929, 1939 and 1954. We
have updated these estimates to 1962. The basic computation is given in Table X. The
1954 data and the basic method of computation are taken from Foss [24, Table II, p. 11].
The 1954 data differ from the figures given by Foss due to a revision of the 1954 horsepower data by the Bureau of the Census and omission of the " fractional horsepower
motors " adjustment. The latter, applied to both 1954 and 1962, would not have affected
the estimated change in relative utilization. The horsepower data for 1962 and 1954 are
from the 1963 Census of Manufactures [7], " Power Equipment in Manufacturing Industries," MC63(l)-6. Consumption of electric energy is taken from the 1962 Survey of
Manufactures [11], Chapter 6. The 1962 total (388-2) is reduced by the consumption of
electric power for nuclear energy (51.5) as shown in Series S81-93 of Bureau of the Census,
Continuation to 1962 of Historical Statistics of the U.S. [9].
3. To estimate service prices for capital from the formula (11) given in the text
we require data on the tax structure and on the rate of return. The variable u, the rate of
direct taxation, is the ratio of corporate profits tax liability to total net private property
income. These data are from the U.S. national accounts. The variable v, the proportion
of return to capital allowable as a charge against income for tax purposes, is the ratio of

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REVIEW OF ECONOMIC STUDIES

private domestic net interest to the after tax rate of return, r, multiplied by the current
value of capital stock. Private domestic net interest is net interest less net interest for
the rest of the world sector. These data are taken from the U.S. national accounts. We
discuss estimation of the after tax rate of return below. The current value of capital stock
is the sum of stock in land, structures, equipment, and inventories. Each of the four
components is the product of the corresponding stock in constant prices of 1958, multiplied
by the investment deflator for the component. Finally, the variable w, the proportion of
replacement allowable for tax purposes, is the ratio of capital consumption allowances to
the current value of replacement. Capital consumption allowances are taken from the
U.S. national accounts. The current value of replacement is the sum of replacement in
TABLE X

Relative utilization of electric motors, manufacturing, 1954 and 1962

1. Horsepower of electric motors, total
2. Available kilowatt-hours of motors (line 1 X7261)
3. Electric power actually consumed, all purposes
4. Per cent power used for electric motors
5. Power consumed by motors (line 3 x line 4)
6. Per cent utilization (line 5/line 2x 100)
7. Number of equivalent 40 hour weeks (line 6 x 4*2/1 00
8. Index

Unit

1954

1962

Thousand
horsepower
Billions of
kilowatt-hours
Billions of
kilowatt-hours

91,505

126,783

664-4

920-6

222-1

336-7

64-6
143-5

65-6
220-9

21-6
0-907
lOO'O

24-0
1-008
111-1

Billions of
killowatt-hours
...
1954= 100

Line 2: The adjustment is derived as follows: It is assumed " that each electric motor could work
continuously throughout the year . . ., 8760 . . . . Horsepower hours are converted to kilowatt-hours;
. . . 1 horsepower-hour = 0'746 kilowatt hours. The result [is] . . . adjusted upward by dividing through
0*9, since modern electric motors have an efficiency of approximately 90 per cent. . . . " Foss [23, p. 11].
8760x0-746/0-9 = 7261.
Line 4: Per cent power used for electric motors in 1962 computed using the industry distribution in
1945 given by Foss [24] in his Table I, and the 1962 consumption of total electric power by industries from
the 1962 Survey of Manufacturers [11, Chapter 6].
Line 7: There are 4*2 forty-hour shifts in a full week of 168 hours.

current prices for structures and equipment. Replacement in current prices is the product
of replacement in constant prices of 1958 and the investment deflator for the corresponding
component. Replacement in constant prices is a by-product of the calculation of capital
stock by formula (14) given above. Replacement is simply 5Kt, where Kt is capital stock
in constant prices.
To estimate the rate of return we define the value of capital services for land, structures, equipment and inventories as the product of the service price (11) and the corresponding stock in constant prices. Setting this equal to total income from property, we
solve for the rate of return. Total income from property is gross private domestic product
in current prices less private domestic labour income. Private domestic labour income is
private domestic compensation of employees from the U.S. national accounts multiplied
by the ratio of private domestic persons engaged in production to private domestic fulltime equivalent employees, both from The National Income and Product Accounts of the
United States, 1929-1965 [49]. This amounts to assuming that self-employed individuals
have the same average labour income as employees.
The final formula for the rate of return is then the ratio of total income from property
less profits tax liability less the current value of replacement plus the current value of
capital gain to the current value of capital stock. The current value of capital gain is the

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279

THE EXPLANATION OF PRODUCTIVITY CHANGE

sum of capital gains for all assets; the capital gain for each asset is the product of the rate
of growth of the corresponding investment deflator and the value of the asset in constant
prices of 1958.
4. The basic sources of data underlying Table VII of the text are summarized in
Tables XI and XII. Table XI presents estimates of the distribution of the male labour
force by school years completed for 1940, 1948, 1952, 1957, 1959, 1962 and 1964. These
data are taken from various issues of the Special Labor Force Reports [5] and Current
TABLE XI
Civilian labour force, males 18 to 64 years old, by educational attainment
per cent distribution by years of school completed
School year
completed
Elementary 0-4
5-6 or 5-7*
7-8 or 8*
High School 1-3
4
College 1-3
4+ or 4
5+

1940

1948

1952

1957

1959

1959f

1962f

1965t

10-2
10-2
33'7
18-3
16-6
5-7
5'4

7.9
7'1
26'9
20-7
23-6
7-1
6'7
...

7-6
6'6 11-6
25-1 20-1
19-4
24-6
8-3
8-3

6-3
11-4
16-8
20-1
27-2
8-5
9'6
...

5-5
10-4
15-6
20-7
28-1
9-2
10-5

5-9
10-7
15-8
19*8
27-5
9.4
6-3
4'7

5-1
9'8
13-9
19*2
29-1
10-6
7-3
5-0

4'3
8-3
12-7
18-9
32-3
10-6
7-5
5'4

SOURCE: The basic data for columns 1, 3, 4, 5 and 6 are taken from U.S. Department of Labor,
Special Labor Force Report [5], No. 1, " Educational Attainment of Workers, 1959 ". The 5-8 years class
is broken down into the 5-7 and 8 (5-6 and 7-8 for 1940, 1948, and 1952) on the basis of data provided
in Current Population Report [10], Series P-50, Nos. 14, 49 and 78. The 1940 data were broken down using
the 1940 Census of Population [8], Vol. Ill, Part 1, Table 13. The 1952 breakdown for translating the
5-7 class into 5-6 and 7-8 was done using the information on the educational attainment of all males by
single years of school completed from the 1950 Census of Population [8], Detailed Characteristics, U.S.
Summary. The 1962 data are from Special Labor Force Report [5], No. 30, and the 1965 figures are from
Special Labor Force Report [11], No. 65, " Educational Attainment of Workers, March 1965 ".
* 5-6 and 7-8 for 1940, 1948 and the first part of 1952, 5-7 and 8 thereafter.
t Employed, 18 years and over.
TABLE XII
Mean annual earnings of males, 25 years and over by school years completed,
selected years
School year
completed
Elementary 0-4
5-6 or 5-7
7-8 or 8
High School 1-3
4
College 1-3
4+ or 4
5+

1939

1949

1956

1958

1959

1963

665
900
1188
1379
1661
1931
2607

1724
2268
2693 2829
3226
3784
4423
6179

2127
2927
3732
4480
5439
6363
8490

2046
2829
3769
4618
5567
6966
9206

2935
4058
4725
5379
6132
7401
9255
11,136

2465
3409
4432
5370
6588
7693
9523
10,487

SOURCE: Columns 1, 2, 3, 4, H. P. Miller [45, Table 1, p. 966], Column 5 from 1960 Census of
Population [8], PC(2)-7B, " Occupation by Earnings and Education ". Column 6 computed from Current
Population Reports [10], Series P-60, No. 43, Table 22, using midpoints of class intervals and $44,000 for
the over $25,000 class. The total elementary figure in 1940 broken down on the basis of data from the
1940 Census of Population [8]. The " less than 8 years " figure in 1949 split on the basis of data given in
H. S. Houtha'kker [32]. In 1956, 1958, 1959 and 1963, split on the basis of data on earnings of males
25-64 from the 1959 l-in-a-1000 Census sample. We are indebted to G. Hanoch for providing us with
this tabulation.
Earnings in 1939 and 1959; total income in 1949, 1958 and 1963.

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REVIEW OF ECONOMIC STUDIES

Population Reports [10], with some additional data from the 1940, 1950 and 1960 Census
of Population [8] used to break down several classes into sub-classes. We could have used
data from the 1950 and 1960 Censuses on educational attainment. The increase in the
number of links did not seem to offset the decrease in comparability that would be introduced by the use of different sources of data. Table II presents estimates of the mean
incomes of males (25 years and over) for these classes. These data are largely taken from
Miller [45], supplemented by Censu' and Current Population Reports [10] data. Table VF
of the text presents the relative incomes, the first differences of the educational distribution,
and the computation of an appropriate index of the change in the average education per
man.

REFERENCES
[1] Abramovitz, Moses, " Economic Growth in the United States ", American Economic
Review, 52, No. 4 (September 1962), pp. 762-782.
[2] Abramovitz, Moses, Resource and Output Trends in the United States since 1870,
Occasional Paper 63, New York, National Bureau of Economic Research, 1950.
[3] Arrow, K. J. "The Economic Implications of Learning by Doing", Review of
Economic Studies, 29 (3) No. 80 (June 1962), 155-173.
[4] Bureau of Labor Statistics, Consumers9 Price Index, Washington, U.S. Department
of Labor, various monthly issues.
[5] Bureau of Labor Statistics, Special Labor Force Reports, U.S. Government Printing
Office, Washington, D.C.
[6] Bureau of Labor Statistics, Wholesale Prices and Price Indexes, Washington, U.S.
Department of Labor, various monthly issues.
[7] Bureau of the Census, Census of Manufactures, U.S. Government Printing Office,
Washington, D.C.
[8] Bureau of the Census, Census of Population, U.S. Government Printing Office,
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May 1969

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THE EXPLANATION OF PRODUCTIVITY CHANGE

63
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[38]

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U.S. GOVERNMENT PRINTING OFFICE : 1969 O - 348-323

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