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862d o ° n? reSS J
oj
Session 1

JOINT COMMITTEE PRINT

STUDY PAPER NO. 20

THE POTENTIAL ECONOMIC GROWTH
IN THE UNITED STATES
BY

James W. K nowles
WITH THE ASSISTANCE OF

Charles B. W arden, Jr.

MATERIALS PREPARED IN CONNECTION WITH THE

STUDY OF EMPLOYMENT, GROWTH, AND
PRICE LEVELS
FOR CONSIDERATION BY THE

JOINT ECONOMIC COMMITTEE
CONGRESS OF THE UNITED STATES

JANUARY 30, 1960

Printed for the use of the Joint Economic Committee

UNITED STATES
GOVERNMENT PRINTING OFFICE
50506

WASHINGTON : 1960

For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington 25, D.C. - Price 20 cents




JOINT ECONOMIC COMMITTEE
(Created pursuant to sec. 5(a) of Public Law 304, 79th Cong.)
PAUL H. DOUGLAS, Illinois, Chairman
WRIGHT PATMAN, Texas, Vice Chairman
SENATE
JOHN SPARKMAN, Alabama
J. WILLIAM FULBRIGHT, Arkansas
JOSEPH C. O’MAHONEY, Wyoming
JOHN F. KENNEDY, Massachusetts
PRESCOTT BUSH, Connecticut
JOHN MARSHALL BUTLER, Maryland
JACOB K. JAVITS, New York

HOUSE OF REPRESENTATIVES
RICHARD BOLLING, Missouri
HALE BOGGS, Louisiana
HENRY S. REUSS, Wisconsin
FRANK M. COFFIN, Maine
THOMAS B. CURTIS, Missouri
CLARENCE E. KILBURN, New York
WILLIAM B. WIDNALL, New Jersey

St u d y of E m p l o y m e n t , G r o w t h , a n d P rice L e v e l s
(Pursuant to S. Con. Res. 13, 80th Cong., 1st sess.)
Otto Eckstein, Technical Director
John W. Lehman, Administrative Officer
James W. Knowles, Special Economic Counsel
II




This is one of a series of papers being prepared for consider­
ation by the Joint Economic Committee in connection with
its Study of Employment, Growth, and Price Levels. The
committee and the committee staff neither approve nor dis­
approve of the findings of the individual authors.




iii




LETTERS OF TRANSMITTAL
J a n u a r y 12, 1960.

To Members oj the Joint Economic Committee:

Submitted herewith for the consideration of the members of the
Joint Economic Committee and others is a paper on “ The Potential
Economic Growth in the United States.”
This is one of a number of subjects which the Joint Economic Com­
mittee requested individual scholars to examine and report on in
connection with the committee’s study of “ Employment, Growth, and
Price Levels.”
The findings are entirely those of the author, and the committee and
the committee staff indicate neither approval nor disapproval of this
publication.
P a u l H. D o u g l a s ,
Chairman, Joint Economic Committee.

J an u ary

Hon.

P aul

H.

D

10, I960*

o u g las,

Chairman, Joint Economic Committee,
U.S. Senate, Washington, D.C.
D e a r S e n a t o r D o u g l a s : Transmitted herewith is one of a series
of papers prepared for the study of “Employment, Growth, and Price
Levels” by outside consultants and members of the staff. The
author of this paper is James W. Knowles, Special Economic Counsel
of the Study.
All papers are presented as prepared by the authors.




O tto E

c k s t e in ,

Technical Director,
Study oj Employment, Growth, and Price Levels.

▼




C O N T E N T S

PART I
Page.

1
Chapter I. The nature and significance of potential economic growth___ _
The Employment Act goals.................... .......... .....................................
2
A dynamic economy______________________________________________
4
Economic growth------------------------------------------------------------------------4
Current economic performance____________________________________
5
Potential output versus capacity__________________________________
6
The rate of employment-------- --------------------------------------------------- 8
The measurement of potential growth_____________________________
9
Chapter II. The determinants of potential economic growth_____________
11
Supply, demand, growth, and output_____________________________11
Capacity and growth-------------------------------------------------------------------12
The production function__________________________________________
13
Production in the individual plant versus the total economy________
13
The design of an aggregate production function-----------------------------16
Chapter III. The statistical analysis of output_________________________
19
The variables and their measurement_____________________________
19
Three transformations____________________________________________
22
Fitting the production function to the historical data_______________
28
31
The final equation_______________________________________________
Interpreting the production function in economic terms____________
33
Potential output: 1909-60_______________________________________
35
Chapter IV. Potential growth: Prospects and problems______________ —
38
Alternative assumptions: 1959-75_________________________________
38
The alternative projections_______________________________________
40
Implications of the projections____________________________________
43
PART II
Technical materials----------------------- ----------------------------------- -------------- - -

45

CHARTS
Chart I. Capacity, output, and potential—an explanatory sketch-----------Chart II. Computed gross stocks of business plant and equipment at con­
stant (1959) prices (ratio scale)_____________________________________
Chart III. Estimated percentages of original installations of plant and
equipment surviving after the periods indicated------------------------------Chart IV. Gross national product in constant dollars and related variables,
1909-58....................................................... ................. .............. - .................
Chart V. Gross national product in constant dollars, 1909-58, actual versus
predicted__________________________________________________________
Chart VI. Potential gross national product compared to actual 1909-59,
and projected for 1975------------ --------------------------------------------------------

6
21
22
24
32
36

TABLES
Table 1. The variables used in the anslysis, and their components, 1909-58Table 2. Actual, predicted, and potential gross national product in 1954
dollars for the United States, 1909-60.......................... ......... ................. ..
Table 3. Selected indicators of economic growth potentials---------------------




V II

26
37
40

S T U D Y P A P E R N O . 20
TH E

P O T E N T IA L

E C O N O M IC

U N IT E D

G R O W TH

IN

TH E

ST A T E S1

PART I

C h a p t e r I. T h e N a t u r e a n d S ig n if ic a n c e o f P o t e n t i a l E c o n o m ic
G ro w th 2

Confidence in the Nation’s potential for future economic growth
has been the fundamental assumption upon which public and private
economic policies have been based in the United States since its
founding. Though occasionally challenged during unexpected re­
verses, as during the 1930’s when concepts of economic maturity and
stagnation were brought into the debates over economic policies for a
time, this basic belief in the possibilities or opportunities for future
increases in employment, output, and in per capita, real purchasing
power for a rising population, has survived all vicissitudes of public
debate to provide the foundation for public and private economic
policies.
Hamilton’s “ Report on the Subject of Manufactures,” 1791; en­
couragement to canal building; public lands policies; land grants to
encourage railroad building beyond the limits of settlement ; “ Mani­
fest Destiny;” aid to agricultural and mechanical education, including
colleges; the “ New Era;” the patent system—any student of American
economic history could compile a long list of examples of growthoriented policies and programs in both the public and private sectors
of the economy. In 1812, when the population was less than 10 mil­
lion, a sketch of the Nation’s destiny pointed to an economy of 100
million, stretching from Atlantic to Pacific, possessed of large cities,
magnificent canals and roads, seminaries of learning, vast domestic
manufacturing industries, and other advantages of division of labor.
(1) In 1872, when the population was hardly 40 million, another writer
foresaw a population of 300 million, mail delivery from coast to coast
in 24 hours, artificial fibers, and expansion of steel production by over
50 times (incidentally a drastic underestimation) (2).
11 wish to express my deep appreciation to my research associate in this study, Mr. Charles B. Warden,
Jr., who carried the burden of preparing the various time series for use in the study and brought together the
material on potential labor force and hours of work. Without his careful and unstinting efforts, the study
could not have been brought to completion.
Mr. Thomas Wilson of the special study staff gave invaluable assistance in carrying out the complex com­
putations on the IBM 660 computer. We are especially grateful to the Bureau of Labor Statistics and the
Board of Governors of the Federal Reserve System, who made time available on their IBM 650 computers
so that we could carry out these computations.
2Numbered references in parentheses in text are to numbered sections of “Technical Materials,"
beginning on p. 45.

50506— 60------ 2




1

2

PO
TEN
TIAL ECO O IC GROW
N M
TH IN THE UNITED STATES

The Employment Act goals

When the Employment Act of 1946 incorporated economic growth
as an objective of national economic policy, therefore, the action was
in line with a long American tradition. The emphasis on maximum
or full employment in the early history of the act, both before and
after enactment into law, occasionally has led to the comment that
recent stress on economic growth and price stability as objectives of
policy constitutes a change in interpretation of the act's stated goals
of “ maximum employment, production, and purchasing power” (3).
The act's language and history yield a different view. Section 2
declared it is to be “ * * * the continuing policy and responsibility
of the Federal Government to use all practicable means * * * to
promote maximum employment, production, and purchasing power,”
with maximum employment clearly stated to involve “ * * * creating
and maintaining * * * conditions under which there will be afforded
useful employment opportunities, including self-employment, for those
able, willing, and seeking to work,” and, further, these objectives
should be accomplished through programs which would “ * * * foster
and promote free competitive enterprise and the general welfare” (4).
The Employment Act, it should be noted, does not purport to
guarantee or assure full employment, an adequate rate of growth, and
a stable level of prices. It does commit the Federal Government, in
cooperation with other public and private agencies, to “ * * * utilize
all its plans, functions, and resources” to promote the accomplishment
of these objectives.
The Employment Act, as basic enduring statutory law, is general
in its statement of these goals or objectives, but it seems clear from
the legislative history that supporters of the act did not intend its
generalized expression of ultimate or ideal aspirations of a free people
to be empty phrases or mere timeless expressions of vague hopes. In
fact, under the act, the President is required to submit to the Congress
at the beginning of each of its regular sessions an Economic Report
which shall set forth “ * * * the levels of employment, production,
and purchasing power obtaining in the United States and such levels
needed to carry out the policy [sec. 2] * * *.” Prediction of the
future course of the economy in specific quantitative terms was not
required, according to one interpretation of section 3(a), though the
act does direct that the Economic Report contain a statement of
“ * * * current and foreseeable trends in the levels of employment,
production, and purchasing power * *
There is an unmistak­
able mandate, however, for the regular, annual administrative deter­
mination of the levels of activity which will give definite and timely
meaning to the ideals expressed in section 2 of the act (5).
This annual determination of the specific employment, output, and
price levels which would constitute, in the judgment of the President
and his advisers, the optimum achievement of the economy for the
particular year requires the development of estimates of the economy's
potentials for employment, growth, and price performance. Such
quantitative economic potentials provide guidelines with which the
actual performance of the economy can be compared, revealing
directions and magnitudes of improvements needed if national
economic objectives are to be achieved.
When estimates of the economy's potential employment and output
are computed, however, the result necessarily constitutes measures of



PO
TEN
TIAL ECO O IC GROW
N M
TH IN THE UNITED STATES

3

potential growth of the United States. In a country with an increas­
ing population, sufficient savings, and a significant rate of techno­
logical advance, maximum employment and output, if achieved year
after year, will be accompanied by growth— the increase in population
makes possible a rising supply of labor; saving makes possible a rising
stock of capital; and technological progress results in labor and capital
becoming more efficient so output rises even faster than population.
Obviously this is not an inevitable set of relations at all times in all
countries but the combination has been true in this country.
The connection between maximum employment and production,
on the one hand, and potential growth on the other, was recognized
even during the debates preceding passage of the Employment Act.
A number of projections were prepared providing estimates of the
growth of employment and output which might reasonably be expected
in the immediate postwar years in view of past trends ancl then known
conditions (6). The early Economic Reports contained similar esti­
mates of the possible employment and output which could be achieved
if recession were avoided (7). Beginning in 1950, its staff has pre­
pared similar estimates for the use of the Joint Economic Committee,
estimates to which the label “ potential” growth has been applied since
publication of a staff study in 1954, entitled “ Potential Economic
Growth of the United States During the Next Decade” (8).
In the same way that economic growth possibilities have been an
inseparable part of the Employment Act’s history and of the goals set
forth in section 2, the ideal of a stable level of prices has always been
a basic part of the act. It is easy to understand why this point should
be the subject of controversy since the act treats of price stability
solely through its reference to maximum purchasing power. This
term has generally been taken to imply a stable level of prices since
advancing prices clearly erode the purchasing power of both current
incomes and past savings (9). But the failure of Congress to delineate
clearly the kind of price behavior to be sought under the act provided
a basis for controversy.
From the beginning, the President's Economic Reports, statements
of his Council of Economic Advisers, and the activities and reports of
the Joint Economic Committee have reflected deep concern about the
inflationary tendencies of the postwar period. President Truman’s
first Economic Report under the act (January 1947) pointed to the
rise in prices in the latter half of 1946 as an impediment to the maxi­
mum purchasing power goal of the act. The Joint Economic Com­
mittee in June and July 1947 devoted its first major inquiry to price
developments. Whatever may be one’s view as to the desirability of
changes in the language of the act, one point is indisputable—those in
the Federal Government charged with the responsibility for policy
under the act have always operated on the belief that reasonable
price stability is one of the objectives it sets for national economic
policies (10).
This study of the potential economic growth of the United States,
therefore, is the latest in a series of quantitative analyses of economic
growth possibilities which have originated in connection with the
Employment Act. It differs in some respects from its predecessors,
however, and succeeding chapters can be more easily followed if the
concept of economic growth, its relationship to policy analysis under




4

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

the Employment Act, and the analytical framework used in developing
the estimates of potential growth are sketched briefly at the outset.
In line with the preceding discussion, this study looks at the goals
of maximum employment, production, and purchasing power as direct­
ing attention of public and private policymakers to the ideal of a
dynamic, growing economy, exhibiting a minimum of fluctuation in
actual rates of use of labor and capital around the maximum average
rate of utilization feasible under existing institutional conditions,
which, at the same time, is consistent with reasonable stability of
the general average level of prices of goods and services.
A dynamic economy

The “dynamic” aspect of this ideal seems to have been reflected in
the act, though not perhaps in the exact language an economist might
suggest if it were being drafted today. The goal of a free, private,
competitive economy, listed in section 2, calls for a dynamic economy,
i.e., one free from those public and private restraints which would
impede adjustment to changes—
(а) in individual tastes and preferences;
(б) in effective demand for different goods and services as a
result of (a) above combined with changes in the level and distri­
bution of purchasing power, and changes in relative prices;
(c) in techniques for combining resources in production;
(d) in characteristics of products and services;
(e) in the geographic distribution of population and industries;
and
(f) in international economic relationships.
“Dynamic” thus describes the more outstanding characteristics of
American economic life. The frequency and magnitude of these
changes have a profound effect on the potential rate of economic
growth, on the magnitude of the frictions in the economy and hence
on the proportion of resources which are unavoidably idle at any given
time, and on the ease or difficulty faced in minimizing economic
fluctuations.
Economic growth

Economic growth is an increase in the Nation’s capacity to produce
goods, services, and leisure (11). It is not, therefore, synonymous
with the idea of progress or with the more conventional concept of
economic growth as an expansion of real per capita gross national
product, or with other definitions of growth that have been used from
time to time. The distinction between progress and economic growth
is the familiar distinction economists make between means and ends.
Progress relates to an increase in the welfare of the people of the
Nation while economic growth is an increase in the economy’s produc­
tive capacity, i.e., an increase in the Nation’s ability to provide the
material means to satisfy individual or collective desires for different
kinds of goods and services, and thus, in the end, contribute to an
increase in welfare. Much of the increase in well-being—progress—
comes about in ways unrelated, or only indirectly related, to economic
growth, per se, such as: a decline in the death rate; a rise in the per­
centage of children of school age in school and of youths going on to
higher education; the growth of leisure; the growth of the creative
arts; the circulation of books; a rise in political and religious freedom
for the individual; improvements in moral standards and behavior.



POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

5

Economic growth as an objective of national ecoDomic policy,
therefore, is an intermediate objective—it is a goal which the Nation
can seek in order to provide a material basis for progress or an increase
in welfare. If the output of goods and services that results from the
increased productive capacity of the economy is used wise!}7 and in
,
accordance with the desires of individuals and of the community as
expressed through community and political channels, it can contribute
to welfare and progress. Professor Galbraith has produced perhaps
the most familiar recent example of an economic analysis resting on
the distinction between progress and growth in capacity to provide
material goods and services (12).
Distinction between economic growth and a mere increase in output,
either in the aggregate or per capita, is of both practical and theoretical
significance. The distinction is between the performance of the
economy in any given period of time (output, or increase in output, for
example) and its capability. Economic growth refers, of course, to
an increase in the capability or productive capacity of the economy
while the current performance of the economy is measured by output,
employment, the increase in output, output per capita, real income per
capita, the amount of leisure (individual), and the stability or in­
stability of output, employment, and prices.
C u r r e n t e c o n o m i c 'p e r fo r m a n c e

Performance of the economy is reflected in the Employment Act's
description of the other aspects of its ideal of how the economy should
operate. As stated above, this means at least the following: (1)
a minimum of fluctuations in actual rates of use of labor and capital
around the maximum average rate of utilization feasible under existing
institutional conditions, managerial skill, and economic knowledge;
and (2) reasonable stability of the general level of prices of goods and
services.
The first part of this definition of economic performance is generally
called economic stability for it means that there is a limited range of
fluctuations in the rate at which the Nation uses its economic capacity,
human and material. It therefore implies a constantly rising level
of employment and of total production of goods and services as the
Nation’s supply of labor and capital goods increases. In the Em­
ployment Act this stability objective, in part, is described as maximum
employment and production, referring to that aspect of economic
stability which I have just described.
It also includes, of course, the second aspect already noted, stability
in the general level of prices of goods and services. In respect to this
goal, it is necessary to refer to the fact that the economy should be
dynamic, adjusting readily, rapidly, to changing conditions. In such
an economy, relative prices must remain free to change, that is each
individual price, or the prices of individual goods and services, must
be free to change rapidly and in such magnitude as will call forth those
changes in outputs, demands, and resource allocations required by
changing preferences, incomes, and technological feasibilities. Price
stability implies that while the general average of prices is reasonably
stable, with no upward or downward drift, each individual price
remains free to change relative to the general level so long as the
various changes offset each other and leave the general average
unchanged.




6

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

P o te n tia l o u tp u t versu s c a p a city

At the outset of this chapter, the term “potential” was used and
reference was made to the Nation’s potential for economic growth.
Now we refer to economic growth in terms of an increase in the
Nation’s capacity to produce goods and services as well as leisure.
In the analysis that follows, the distinction between capacity and
the output potential for which a measure is developed, is of critical
importance. To make the relationship clear, chart I was developed.
Chart I
CAPACITY, OUTPUT, AND POTENTIAL
an EXPLANATORY SKETCH

It will be noted that the topmost line, labeled “capacity,” is above
the “potential” by some unspecified percentage, though the two lines
are snown parallel. The potential is a measure of the optimum or
best practice which it is believed the economy is capable of sustaining
on the average, year after year, without running into serious insta­
bility of employment, output, or prices. It is, in a word, a measure
of what would be reasonably good performance of the economy, main­
taining a stable relationship between output and capacity. Around
this line of potential, lines have been dotted which represent what
may be termed tolerance zones. Within these limits, the economy
is fluctuating by so little that it cannot be regarded as being a serious
challenge to the objectives of the Employment Act though certainly
a matter of concern. Over time, it might be possible to reduce this
type of variation. In fact, one of the objectives of economic research,
both pure and applied, should be to determine what these limits of
variation are and how much they can be narrowed in practice.
No attempt to determine them quantitatively has been made in
this study.




POTENTIAL ECONOMIC GROWTH

IN THE

UNITED STATES

7

Actual output is shown varying part of the time within this ac­
ceptable zone on either side of the potential, sometimes above and
sometimes below. Occasionally, output may move completely out­
side of this tolerance zone. Either it rises too close to capacity,
hence, into a seriously inflationary and probably unstable position, or,
on the other hand, falls far below the potential as recession and wide­
spread unemployment develop. In terms of the objectives of the
Employment Act, the stability goal would be achieved if the economy
could remain inside the zone of acceptable variations, as close as
practical to the potential line. Over time, to the extent possible, an
increase in the ratio of potential output to capacity would be desirable
so long as this does not involve either inflation or drastic instability
of output and employment. As a practical matter, therefore, the
measurement of the potential output of the economy can be an
important instrument for analyzing the relation of current economic
performance to the objectives of the Employment Act, that is, as to
whether or not output and employment are staying as close as reason­
able men might require to the standard set up by the Employment Act.
It also may be used as a convenient technique for anatyzing the
current situation of the economy a use to which, in fact, the staff of
the Joint Economic Committee has been putting earlier versions.
If an index of capacity for the total economy was available, the
problem would reduce to two steps: (1) Analysis of causes of growth of
capacity; and (2) analysis of operating characteristics of the economy
to discover the optimum operating rates, or ratio of output to capacity.
But, economic analysts have debated at length whether or not it is
possible to develop an unambiguous concept of capacity for the
economy (or even a single industry), much less measure it. To illus­
trate the point, it may be possible to operate a given plant 24 hours a
day, yet under ordinary circumstances the usual practice may be to
operate only one or two 8-hour shifts a day. Suppose the plant
ordinarily operates on one 8-hour shift per day, what is the practical
capacity of the plant? By this standard, capacity would be the
amount produced in one 8-hour shift. Obviously, if demands were
strong enough it would be possible to operate the plant three shifts, or
24 hours a day— tripling its capacity. Many plants that normally
operated one shift or two shifts added shifts during World War II,
and plants that normally operated on an around-the-clock, continuousprocess basis were run during these war emergency years at increased
rates of output through such devices as lengthening the period between
maintenance or repair, thus reducing downtime.
In a host of ways, therefore, the maximum output of the economy
is flexible over a considerable range, even when each industry or trade
is operating at what managements ordinarily would call full capacity
rates. No attempt was made, therefore, to measure the ultimate
capacity of the economy. It is clear only that it must be much higher
than the measure of potential output arrived at in this study. F o r
e a c h y e a r , th e p o t e n t i a l o u t p u t l e v e l r e p r e s e n t s th e a m o u n t th e e c o n o m y
c o u l d p r o d u c e a t s o m e s t i p u l a t e d r a t e o f u s e o f th e l a b o r f o r c e a n d o f
c a p ita l, a n d
at

s o m e th in g

u n d e r th e a s s u m p t i o n
a p p ro a ch in g

th e

th a t p r o d u c tiv e

e c o n o m y ’s

n o tio n

oj

resou rces a re
a

le a s t-c o s t,

u sed
com ­

b in a tio n o f in p u ts .
That is, capacity, however conceived, is being
operated so as to produce output at the least cost per unit of output, in




8

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

accordance with the best practices possible with existing management,
capital, and training and knowledge of the labor force. It is, in a word,
a measure of what practical man can do under the usual operating
conditions maintainable over long periods of time without excess
strain or breakdown, on the one hand, or, on the other, excessive,
wasteful slack in the system, particularly prolonged, involuntary un­
employment of labor.
T h e ra te o f e m p lo y m e n t

A key element in the measurement of the potential output is the
ratio of employment to the labor force, or, in more familiar form, the
percentage of the labor force unemployed. This ratio, the key to
debate about Employment Act policies, never has been defined
officially, either by the executive branch, the Congress, or any of its
committees. Indeed, no such definition could be stated which would
be valid for all time, because of two bas e facts.
First, measures of employment, labor force, and unemployment,
undergo improvements from time to time, with a consequent change
in the level of unemployment revealed by the surveys and in the ratio
to the labor force. The same degree of tightness in labor markets, for
example, might be measured at one time by, let us say, 3){ percent of
unemployment, whereas later under a different system of measurement,
perhaps using an improved interviewing technique, an enlargement of
sample, or other change in the statistical program, the same degree of
tightness might be measured by a figure which averaged 4 percent.
Does this mean the percentage of unemployment has increased or our
objectives have changed? Obviously not. The same degree of tight­
ness or slack in the labor force is revealed each time. It is simply that
the measuring device has changed and, presumably, is more efficient
than formerly. There is need to be aware constantly of changes or im­
provements in the system of economic measurement, and, from time
to time, redefine, in terms of the changing system of measurements,
maximum employment, production, and purchasing power within the
meaning of the Employment Act (13).
The second point is that the Nation ought to, and does, strive con­
tinually to make improvements in the efficiency with which labor
markets operate and in the efficiency with which labor is used. If
the efficiency with which shifts of labor from job to job and from
industry to industry, is raised and the stability of the economy in­
creased, then we should be able to operate with, let us say, only 3
percent unemployment on the average compared to about 4 to 5
percent unemployment, which seemed to have been achieved, in fact,
on the average of the better years, simply because policies could not
be designed to do better consistently (14). One path of progress is
through learning how to operate with less slack in the labor force—
less time spent between jobs, unemployed because labor markets do
not operate smoothly in transferring labor from places and industries
experiencing declining demand to places and industries with increasing
demand.
Even if the efficiency of the economy increases, and the flexibility
and speed of operation of labor markets improves, the Nation may be
willing to tolerate or even seek a higher level of unemployment than




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

9

the minimum technically possible. This might happen if the unem­
ployment was exceedingly short-range— that is, only a few days or
a week or two at a time for each person affected—and constituted
a necessary condition for achieving a desired speed of movement of
labor between industries, occupations, and jobs; in the process, pro­
ducing a much-enlarged scope of opportunity for each individual to
improve himself, and a wider range of choice. In a word, although
there could be a net gain in welfare or progress from a higher rate
turnover of the labor force, this higher turnover itself— though
desirable—would generate a higher level of unemployment on the
average (15).
While there has been no official statement or determination of the
percentage of the labor force unemployed which shall be regarded as
consistent with the objectives of the Employment Act, nevertheless,
various figures have been widely used in discussions of policy under
the act. These figures range between 2 percent on the low side to
5 or 6 percent unemployed in the upper end of the range. The staff
of the Joint Economic Committee has from time to time computed
the output of the economy at an assumed rate of maximum employ­
ment, or a potential growth trend, basing this computation on the
assumption that unemployment would average about 4 percent of
the civilian labor force (16). In periods of high prosperity, with
modest fluctuations in output and employment, unemployment has
averaged about 4 percent of the labor force.
In view of the historical record, and the past use of the 4 percent
figure by the staff, it is again used in this current study. In the
discussion below, chapter IV, it will be shown that the choice of an
assumed rate of unemployment does have implications both for
public and private policies, and for the rate of growth. For the
historical analysis in chapter III, however, the choice of any average
that would seem reasonable for the past probably would result in a
potential output close to that calculated on the assumption of 4
percent actually used. While a lower rate than this could be achieved
in the future if private and public policies were designed to do the
job, in the past the economy has not achieved a lower unemployment
on the average. It seems useless to measure past performance
against a standard the economy seems to have been unable to achieve
in view of its institutions and technical possibilities.
T h e m e a s u r e m e n t o f p o te n tia l g r o w th

How can economic growth, in terms of the potential output as
described above, be measured?
In the first place, the output measure to be used is the total of
goods and services in constant prices, that is, real gross national
product. Potential output, then, is the real GNP that the economy
would be capable of producing under stipulated assumptions, the
principal one being that 96 percent of the labor force is employed.
This is merely the indicator or measure.
How can the level of this indicator and its rate of growth be
calculated? The potential output and growth of the economy de­
pends on the amount and rate of growth of available resources and
their productivities; in short, upon the size of the labor force, its
50506—60—




3

10

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

skills and know-how, on the accumulated stock of capital, 011 the
availability of natural resources, and upon the current technology
and the rate at which new techniques are introduced.
These factors are familiar. Output and growth also are influenced
by the rate and character of scientific research; the proportion of out­
put which is plowed back into intangible capital assets; the extent to
which the current capital stock embodies the most up-to-date tech­
nology or still reflects that of some past period; rising levels of educa­
tional attainment and health; the ratio of the labor force to population;
changes in the average number of hours worked per year per person
employed; changes in the average degree of managerial skill; the degree
of stimulation of advancement of efficiency from competition at home
and abroad; and a wide variety of influences arising out of the social
and political environment in which the economy operates. Some of
these factors cannot be measured directly at the present time, some of
them are not measured though perhaps they could be, and some may
not- be measurable at all.
Economists, however, cannot put off attempts at the solution of
practical problems until final, perfect solutions to the problems of
concept and measurement can be found. Progress comes from the
continual interplay of theory, measurement, and empirical analysis
so that theorists develop better analytical tools out of the challenge
of practical research attempts, while measurement and empirical anal­
ysis progress by using to the utmost whatever tools are available to
do the best job possible at the moment, recognizing always that even­
tually some better solution will be possible when improved tools and
improved measurements are developed out of experience.
In this spirit, the present study is an attempt at development of a
simple model or description of the economic process of production,
using available measurements of the various inputs and outputs, and
at development of a way of determining from these data the quan­
titative relationships between the various inputs and outputs.
In chapter II, the technical argument is outlined, including the
measures of the various factors and the aggregate function, expressing
the relation between inputs of productive factors and outputs of goods
and services. Further, the structure of the model of the growth of
the economy will be related to preceding work.
In chapter III, the actual fit of the model to the histor cal data is
given, showing the way in which the actual relationships were de­
veloped by processing various measures of inputs and outputs. Some
of the implications of this analysis for interpreting past economic
growth are developed.
I 11 chapter IV, the measures of potential economic growth developed
in chapter III are utilized to develop a picture of the possibilities for
future potential economic growth of the United States to the year
1975, with some discussion of their implications for public policy.
Notes referring to sources or expanding on particular technical
points in the analysis are given in part II of this paper, entitled
“Technical Materials.” Numbered references throughout part I
are to these numbered “Technical Materials.”




C h a p t e r II. T

he

D

e t e r m in a n t s of

P o t e n t ia l E

c o n o m ic

G

row th

The calculated growth potentials of the American economy pre­
sented in chapters III and IV rest upon an analysis of the historical
record of the performance of the economy and of the major outputdetermining factors. Fortunately today the analysis of the factors
which determine the output of the economy at any particular time
and which determine the rate at which the economy’s capabilities for
producing goods and services increases over time, can draw upon
a much larger and richer body of theoretical and empirical research
than formerly.
Almost two decades ago, when, during World War II, analysts in
and out of Government developed models of the economic growth
of the economy as a basis for making projections of a postwar full
employment economy, the data available and the analytical tools
were more primitive than at present. These models, or projections
were used to study the problems of reconversion and unemployment
which would arise when World War II came to an end, and a return to
more peaceful conditions was possible. In the intervening years, both
economic theory and empirical research have turned increasingly to the
study of economic growth and progress under various pressures of
practical problems, on the one hand, and of increased theoretical
interest on the other. This increased interest in, and devotion of
intellectual and research resources to, the study of economic growth is
all to the good.
Professor Domar has stated the past position of growth in economic
theory quite aptly:
In economic theory, growth has occupied an odd place: always seen around but
seldom invited in. It has been either taken for granted or treated as an after­
thought (17).

The turn of economic research toward mathematical and empirical
studies, finding its ultimate expression in rationally designed econ­
ometric studies and input and output tables, has produced a whole
new body of analytical tools for taclding the problems of analyzing and
measuring the potential growth of the economy. The pioneering work
is found in the studies of the production function and its empirical
measurement, by Prof. Paul H. Douglas and his colleagues, first at
Amherst and later at the University of Chicago, which found expres­
sion in the Cobb-Douglas production function (18).
This work has been carried forward in a number of studies including
those by Tintner, Hildreth, Nichols, Verhaulst, Heady, Solow, and
Leontief (19). Closely related developments have occurred in linear
programing (20) and the development of input-output models asso­
ciated principally with the work of Leontief (21). The critical
literature on the statistical derivation of production functions is ex­
tensive, especiall}7 on the economic interpretation of the results (22).
S u p p l y , d e m a n d , g r o w th , a n d o u tp u t

The previous chapter stated that the growth in the economy’s
capabilities for producing goods and services, that is, its capacity, and,



11

12

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

hence, by implication its potential output, is a function of a large
variety of factors affecting the supply of productive resources—labor,
capital, natural resources—as well as the efficiency with which those
resources can be used in production. Actual output is a result of a
wide variety of factors affecting both demand and supply. The rate
of increase in output will be determined by the growth of demand, on
the one hand, or the growth of supply, or potential output, on the
other, according to which is the smaller, and hence the limiting factor
in each period of time. If the potential growth is growing at 4 percent
per year, and aggregate demand is growing at 3 percent, then, output
obviously will tend to be limited to a rate of rise of 3 percent rather
than rising in line with the potential supply at 4 percent per year.
The reverse situation, of course, will be true if aggregate demand is
growing at, say 5 percent, while the growth of potential output is only
3 percent. In this case an inflationary excess of demand will develop
and the excess of aggregate money demand over potential output will
find expression in inflation—a familiar development during war periods
or periods of monetary inflation.
In making an analysis of the historical record in search of a measure
of potential output and growth, allowance must be made for the fact
that two sets of forces have been operating—a set of demand factors
and a set of supply factors that tend to make available output in line
with demand. In the analysis, therefore, measures of cyclical varia­
tions in demand and other short-term influences have been introduced
and by taking account of these, the output of the economy at some
rate of operation, which we shall specify as the potential, was deter­
mined for each year, defining this potential in terms of a rate of use
of resources. The historical data analyzed below cover the years 1909
to 1958 in detail.
C a p a c it y a n d g r o w th

The preliminary sketch presented in chapter I (p. 6) indicated one
possible approach to analyzing and measuring the potential output of
the American economy and its rate of growth. If, in addition to the
series on GNP in constant prices, a measure of capacity was available, it
would be possible to calculate the ratio between actual output and
capacity for each year, or month, or quarter, over a series of years.
Then the performance of the economy in each of these time periods
could be studied and compared with the ratio of output to capacity.
From this process, it would be possible to arrive at an average ratio of
output to capacity corresponding to criteria for desirable perform­
ance, including perhaps ratio of employment to the available labor
supply, use of capital to availability of capital, stability of prices, and
rate of growth of capacit}^. This average ratio applied to the
measure of capacity each year would give a time series representing
the desired potential output of the economy.
This would be a suitable process if a reasonably unambiguous
measure of the capacity of the economy was available. As noted
above, no such measure for the capacity of the economy as a whole
is available and, indeed, there is much dispute over whether or not
one can be produced, or even designed in theory (23). The problem
of computing the measure of potential economic growth arises in part
because the development of a concept and measure of the capacity
of the economy has proved impossible up to the present.



POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

13

T h e p r o d u c tio n ju n c t io n

If the problem cannot be approached via a measure of capacity,
how can the definition and measurement of the potential output be
arrived at more directly from an analysis of the historical record of
the performance of the economy?
The technique used involves a variation on the economists' device
of “the production function.” By this is meant a set of functional
relationships between each of the productive factors and the output
of the economy. As noted above, output is the aggregate of the
economy—including government, agriculture, all of the various other
private industries, nonprofit organizations, individual households,
distribution, finance, and services—in a word, all that is covered in
the now conventional measure of output, the gross national product.
This measure is used here in real terms adjusted to constant 1954
dollars.
In the past, production functions have been developed covering
manufacturing (24), agriculture (25), and for somewhat larger aggre­
gates (26). An extensive literature has developed on the theory of
production functions and the interpretation of the results of fitting
them to statistical data for individual industries, sectors or the econ­
omy as a whole (27). Since the economy is made up of literally
hundreds, if not thousands, of industries or separate economic sectors,
of several million business firms, at least a minimum of 100,000
governmental units, and somewhere in the neighborhood of 55 to
60 million household units, as well as numerous foreign entities
having an impact on our economy, the process of deriving a mean­
ingful aggregate production function involves heroic simplifica­
tions. Any attempt at aggregate or national economic analysis in­
evitably faces this problem, which, in the literature, has led to elabo­
rate investigations of theories of aggregation and the construction of
index numbers.
While these problems in aggregation and index number construc­
tion are not discussed here at length, it must be recognized at the
outset that existing measures of total output and inputs are com­
promises arrived at in the search for the best measures possible at
the present time. The question to be answered is whether or not
the utility of such devices of aggregate analysis is sufficiently great
to offset any lack of precision such compromises entail. This study
is founded on the conviction that the price is not too great—that
useful analyses of the economy as a whole can be made if the qualifi­
cations arising from aggregation are kept constantly in mind.
P r o d u c t i o n i n th e i n d i v i d u a l p l a n t v e r s u s th e t o t a l e c o n o m y

The characteristics of the aggregate production function for the
economy developed below will be clearer if its relationship to the
productive process in an individual plant is outlined briefly. In such
a small unit—small compared to the total economy—production
consists of a series of processes of combining and coordinating ma­
terials, forces, services in the creation of valuable goods or services.
These valuable goods or services are called output, while the materials,
forces, and services used up in their creation are called inputs. These
terms have different meaning in the case of the individual establish­
ment than when used with reference to the economy as a whole. In the
individual case, a good or service can be an output of one establish­
ment but an input to another. In aggregate output, measured by



14

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

GNP, only the value added in each establishment or firm is counted,
costs of purchased materials being deducted, so that total output is as
free as possible of double counting. The total of the incomes paid to
productive factors will equal total output for the economy as a whole
but will fall short for the individual productive unit by the value of
purchased materials and components.
A second distinction exists between the flows per unit of time—year,
month, etc.— of inputs and outputs, on the one hand, and stocks of
goods or productive resources on the other. Generally, inputs and
outputs are time flows, such as hours of labor or of machine time on
the input side of the productive process, and tons of steel per year
or months of rent of dwellings on the output side. Stocks are sources
of flows of productive services—capital and labor—and are results of
past output flows, being the sums (integrals) of those parts of past
output flows which were not used up, consumed, in the time period
in which they were produced.
The production function relates the flow of outputs per unit of time
to the various flows of inputs per unit of time in such fashion that if
the coefficients of the function are known, and the volumes of the
various inputs are known, the resulting volume of output can be pre­
dicted from the function.
The third important distinction is between production under sta­
tionary or static and under dynamic conditions. A static situation
may be thought of as one in which productive capacity is unchanging
and technical knowledge always remains the same. Under these con­
ditions, met with occasionally in an individual unit, but rarely, if ever,
in an entire economy, the volume of production can vary only between
zero and the fixed capacity volume, and the constant knowledge of
technical possibilities readily yield the best combination of productive
resources to yield any required output volume between these limits.
In a dynamic situation, capacity can be expanded to meet demands
as they push beyond present capabilities, present inputs may increase
either current output, as in the static case or future outputs, and tech­
nical knowledge can change, making possible combinations of produc­
tive services or types of outputs not previously feasible. In a djmamic
world, current output possibilities and the spectrum of input combina­
tions reflect the cumulative effects of an endless stream of past deci­
sions allocating resources between consumption and investment, and
between investment in tangible productive resources and in intangibles
such as education, research, health, institutional arrangements (pro­
tection of competition, economic and political rights at law, etc.) and
promotion of moral standards.
To bring out the implications of these distinctions for the later
analysis, let us assume a productive unit with a fixed stock of plant
and equipment, operating in competitive markets for both inputs and
outputs, and during a time period in which technical knowledge is
unchanged. At low rates of production, output will tend to rise faster
than inputs, productivity will rise as volume rises and the firm will
experience increasing returns. At higher operating ranges, output and
inputs will rise together, the rise in productivity will slow down and
finally halt so that constant returns appear. If very high rates of
production are attempted, productivity may fall and decreasing re­
turns set in as inputs rise faster than output.




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

15

What happens if dynamic conditions replace the static assumptions
used above? First, capacity can now change as a result of investment
in new plant and equipment called forth by high rates of production
and high profits. The same type of relationship between inputs and
outputs will prevail as in the static case at each point of time but at
the larger volumes corresponding to rates of utilization of productive
resources experienced at the former lower capacity.
Changes in techniques are also possible and these have a somewhat
different range of possible effects. One possibility is that changes
will be neutral as between inputs so that production relations retain
the same shapes but the efficiency of each combination of inputs is
increased—that is, a doubling of capital and labor inputs which would
double output under one set of production relations, might, through
simultaneous changes in techniques, be accompanied by a tripling of
output.
It will be noted that under both static and dynamic conditions
some combination of inputs is feasible which, given existing tech­
niques, relative prices and stocks of productive resources, yields a
minimum total cost per unit—that is, a least-cost combination. A
rational entrepreneur would prefer to maintain this rate of output at
all times if this were possible. Little is known about the rates of
production corresponding to these least cost combinations, but such
information as is available suggests that this rate is below what man­
agement generally regards as the practical capacity of their firms,
particularly in manufacturing.
The McGraw-Hill surveys of business plans for investment in new
plant and equipment provide estimates of actual operating rates and of
preferred operating rates in various manufacturing industries. This
survey measures capacity in terms of plant and equipment without
adjustment for availability of manpower or materials. Each company
reports changes in capacity and rates of operation in accordance with
their own definition though most companies in each industry appear
to follow similar practices in defining capacity. In two surveys (1955
and 1957) companies reported their preferred operating rates. For
all manufacturing, the preferred rate is reported to be about 90 per­
cent of capacity and the rates for individual industries range from
85 percent in transportation equipment to 95 percent in paper and 96
percent in steel.
If, in general, managements tend to report as preferred operating
rates, those corresponding to their least-cost combination of resources,
as seems reasonable, then it could be concluded that the optimum
operating rate, at least in manufacturing, is significantly below man­
agement’s estimate of practical capacity and even further below any
conceivable measure of absolute capacity since this must be well above
rated capacity. Higher rates of operation for prolonged periods (as
during and immediately after World War II) amply sustain this point.
When attention turns from the individual plant, firm, or industry to
an aggregate production process for the total economy these points
become clear:
(1)
The optimum or best operating rate for the economy may not
be a simple average of the preferred or optimum rates of the individual
production units—firms, plants, etc., weighted by their individual
capacities. The optimum rate for the total economy will reflect both
the individual preferred rates and the composition or mix of demand



16

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

which may not call for operations to be at the optimum or preferred
rates in each individual producing unit. Under dynamic conditions,
some misjudgment of markets by firms is unavoidable and cannot
quickly be corrected by shifting resources to other outputs.
(2) The optimum rate of operation for a dynamic economy such as
ours will be affected also by the proportion of labor and capital which
must be shifted annually to new uses or retired in order to adjust to
changing demands and techniques. The higher the rate of turnover
or shifting of resources in response to dynamic changes in the economy
the low the optimum rate of use productive resources which it is
~er
practical to aim for and vice versa.
(3) As a corollary to point (2), the more mobile resources are, the
more rapidly and efficiently they respond to changes, the higher the
preferred operating rate for the economy can be; while slow adjust­
ments or shifts will lower the operating rate which can be on a sustained
basis without inflation.
(4) For the total economy, it will be difficult to detect statistically
valid evidence of increasing or decreasing returns under dynamic condi­
tions, except those associated with wide cyclical swings in the rates of
operation—recession or deep contraction and subsequent recovery, on
the one hand, and periods of over-full demand, such as World War II,
on the other. During other periods, the influence of technological
progress on productivity of resources, and inevitable errors in esti­
mating inputs and outputs, seem likely to conceal or gloss over any
tendencies to increasing or decreasing returns between periods of
similar rates of operation but different all-out output capabilities.
This tendency will be reinforced by the offsetting occurring in putting
together the aggregates from data on a myriad of individual units
except in the unlikely event that all, or almost all units, experienced
simultaneously either strongly increasing or decreasing returns.
(5) Measures of total inputs and output for a dynamic growing
economy like ours are likely to exhibit, as a common characteristic,
highly correlated growth trends. These correlated growth trends in
output and inputs will be accompanied by a persistent, rapid time
trend in total productivity of all inputs combined reflecting changes
in the intangible contributions to production already mentioned in­
cluding research, education, technological change, improved health,
etc. These common time trends complicate the statistical problem of
determining quantitatively the functional relationships between inputs
and output that constitute the desired aggregate production function.
T h e d e s i g n o f a n a g g r e g a t e 'p r o d u c t i o n f u n c t i o n

In light of the preceding sketch, the required design of a production
function incorporating relationships between inputs and outputs can
be laid out in a way that make possible a statistical determination of
the production coefficients relating each input to aggregate output for
the economy. At this point, and in the following chapter, the over­
riding objective of this study must be kept constantly in view since it
vitally affects the design and its implementation in chapter III.
The production function is sought as a means of estimating the
economy’s potential output under conditions of sustainable “maximum
employment, production, and purchasing power,” and, hence, esti­
mating the rate at which this potential has grown in the past, is grow­
ing now, and could grow in the future. This means that our interest




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

17

centers on long-run or secular relationships more than on short-run,
cyclical movements.
With this objective in view, characteristics of the desired function,
describing production relationships in the economy can be reduced to
these:
(1) It should incorporate measures of as many of the identifiable
productive resources as is possible in light of availability of data,
especially—
(а) labor;
(б) tangible capital: plant, equipment, etc.;
(c) the state of technology and its changes; and
(d) other intangibles such as research, health, education, etc.
(2) It should incorporate a procedure for separating changes asso­
ciated with cyclical and other short-run fluctuations from changes
reflecting secular influences.
(3) Provision should be made to separate changes in output due to
shifts in the production function itself in response to changes in tech­
niques, etc., from changes in output reflecting increases in the supply
of the productive services of labor and capitgd.
(4) A procedure is needed for allowing for influences on aggregate
output and on the productivity of inputs arising solely out of shifts
in demand between goods and services with varying requirements
for productive resources—i.e., between those with higher or lower
requirements for capital, and higher or lower requirements for labor.
(5) If possible, specific provision should be made to measure the
influence of changes in quality of inputs and outputs on the production
function.
(6) Since the absolute magnitudes of the measures of inputs and
outputs for the economy as a whole will depend on the particular
price structure used to price inputs and outputs and on various con­
ventions of mensuration, these absolute levels will be of little signifi­
cance. Primary attention must center on changes between time
periods—year to year — and on relative proportions between measures
in each period. Therefore the form of the function should be chosen
so as to operate in terms of rates of change.
(7) If possible, the functional form chosen should be linear or involve
only linear transformation so as to take advantage of the high speed
computing possibilities of electronic data processing equipment.
This is of special importance in view of the high intercorrelations
between the inputs which made it necessary, as will be seen below, to
run successive approximations to locate the preferred fit of the formula
to the statistical record of past economic performance.
(8) Last, but not least, the formula should be framed to reduce the
high intercorrelations as far as feasible, especially between the inputs,
or in statistical terms, the independent variables in the function.
In light of these criteria, the search for an aggregate production
function, started with a theoretical form that was a variation of, and
elaboration upon, the now classic Cobb-Douglas function which is
linear in the logarithms. In its original form it was applied to manu­
facturing, first to U.S. data, covering various series of years and
regions, then to time series for other countries, and then to crosssection data for large numbers of manufacturing industries for each
of several years, here and abroad. In form, the function was:
P = b L k C1
-*
5 0 5 0 6 — 60--------




&

18

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

Wlierc P was an index of manufacturing production, L was labor input
(index of average number of wage earners in manufacturing), C was
the capital input (index of fixed capital in manufacturing) and b and k
were constants to be found bv the classical least squares regression
method.
In this form the function assumes that the sum of the exponents is
unity, and hence that there existed constant returns to scale. In
later studies this restriction was removed and more refined variations
on data used, with the function assuming the form
P=bL*C*

so that k-\-j could be equal to, less than, or greater than unity. The
studies of Professor Douglas and his associates, as well as others,
tended to arrive at estimates of k + j close to or equal to unity, though
with some tendency toward diminishing returns. (28)
This later form of the Cobb-Douglas function was chosen as a
starting point and modified in light of subsequent research results
and of the changes in availability of data. Five modifications were
made:
(1) Labor input, expressed in man-hours, was split into two com­
ponents, first, a secular component (Lp) based on longrun or secular
changes in the rates of participation of the population in the labor
force and secular trends in hours of work and second, a cyclical
component, the ratio of actual labor input to the potential labor

inpui (i£ > (2) Capital (measured as a gross stock in constant prices) was used
in the form of a ratio of the stock of capital to the potential labor input
(K/ Lp).

(3) The influence of changes in technology on productive efficiency
was captured in part by inserting a new variable, the average age of
the capital assets surviving in the capital stock in each year (£). The
lower the average age of the capital stock, the closer the productive pro­
cess was assumed to approximate the latest, most efficient techniques;
the older the average age, the less the stock incorporates the most effi­
cient known techniques. This is a measure of qualitative changes in
the capital stock (K).
(4) A time trend (t) was introduced to measure the influence of all
those intangibles which could not he measured directly. This is a
proxy variable, accounting in this case for technical and other changes,
or in technical terms for any kind of shift in the production function.
(5) An index (X) was introduced, so constructed as to measure the
influence of change in demand on the total productivity of the inputs.
This index (X ) reflects changes in the composition of demand between
products and services requiring varying amounts of labor and capital
per unit.
Inserting these changes in the classic Cobb-Douglas production
function, a formula was obtained in the following form, where 0 a
represents output:
0 . = A X P[ % ] [ £ J . t ^

The formula was tested against statistical data by least squares, by
procedures outlined along with the results in chapter III. The
formula had to be modified further during the fitting process.



C

hapter

III. T h e S t a t i s t i c a l A n a l y s i s

of

O utput

The statistical analysis of the historical record of the output of the
U.S. economy and of the major output-determining factors proceeded
in five stages:
(1) Assembling of historical data on an annual basis for output and
each of the related variables needed for the equation developed in
chapter II.
(2) Transforming of the basic variables, where necessary, into the
form required in order to fit the equation to the data.
(3) Fitting the equation to the data, using the classic least-squares
regression procedure, making modifications of the equation as tests
with the data progressed, and obtaining a final fit by successive
approximations.
(4) Interpreting the function obtained in economic terms to test
its reasonableness in light of economic analysis and other previous
related studies.
(5) Computing the potential output of the economy for 1909-60,
using the derived production function.
The variables and their measurement

As indicated previously, output of the economy is a result of a wide
variety of forces. The growth in the economy’s potential output is
therefore similarly effected by a range of factors far too large to be
incorporated directly in the computations at this time. Fortunately,
it is possible to measure output for the economy as a whole, and the
two major productive factors, labor and capital. As will be seen later,
these dominate the rate of growth and cyclical fluctuations to such
an extent that the variables that are not measured directly can be
represented indirectly by a proxy or stand-in. In the historical
analysis covering the years 1909-58, the influences on our potential
economic growth were subjected to statistical analysis making use of
the following measurements of output and inputs.
(1)
Output.— The measure of output is the GNP deflated (adjusted
for changes in prices) to prices prevailing for each of the component
goods and services in the year 1954. This series is constructed by the
National Income Division, Office of Business Economics, Department
of Commerce, and published regularly on an annual and quarterly
basis in the “Survey of Current Business” (29).
GNP measures the market value of the output of goods and services
produced by the Nation’s economy before deduction of depreciation
charges and other allowances for business and institutional con­
sumption of durable capital goods. The series in real terms, which
was utilized in this study, reprices this output in terms of prices




19

20

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

prevailing on the average during the year 1954. It, therefore, covers
changes in constant dollars of the total purchases of goods and services
by consumers and Government, net foreign investment, and gross
private domestic investment, including the change in business
inventory.
(2) Labor.—Labor input has been measured in terms of the total
number of man-hours or the product of employment multiplied by
the average hours worked per year per person engaged in production.
Two measures of labor input were used. The first of these was a
series on actual labor input in man-hours which represented the
product of the total number of persons actually employed multiplied
by actual average annual hours worked per person employed (30).
The second measure of labor input was the total man-hours of
labor available for productive activity in the economy, whether
actually employed or not.
It was arrived at by a study of trends in rates of participation in
the labor force of men and women in various age groups, and by a
study of trends in the average annual hours worked per person en­
gaged in production. It was assumed for the historical period (190958) that about 4 percent of the labor force was unemployed when the
economy was operating at its potential output. Other percentages
could have been assumed without changing the basic historical
analysis except as to the relative level of the series (31).
(3) The stock of capital.—To measure the supply of capital serv­
ices available for use in production an estimate of the gross capital
stock of the private economy prepared by Dr. George Terborgh was
utilized (32).
In this series the gross capital stock represents the value, in con­
stant dollars, of all capital assets surviving from past installations at
any particular point in time. It is, therefore, gross of depreciation.
It includes private plant and equipment in agriculture, mining, manu­
facturing, commercial, and similar types of activities, but specifically
excludes residential structures, inventories, and all Government assets.
(See chart II, p. 21.)
These stocks were computed by the application of survival curves
to data on prior installations in constant prices. (See chart III,
p. 22.) Since these curves gave estimated percentages of original
installations surviving after given intervals, it is possible to compute
the survival at any point from or prior installations and to trace the
movement of the survival over any given time (33).
(4) The age of capital.—To measure the degree to which the existing
capital stock incorporates available technology, it was decided to use
as one variable in the analysis a computation of the average age of
surviving capital assets included in the above estimate of capital
stock. This also was the work of Dr. Terborgh.




C hart II
Com puted Gross Stocks o f Business Plant and Equipment at Constant (1 9 5 9 ) Prices* (Ratio Scale)

POTENTIAL
ECONOMIC
GROWTH
I
N TH
E
UNITED
STATES

Source: Capital Goods Review, No. 39.




A mimeographed description
21

•The 1959 stock includes, of course, a partially estimated installation figure for that year.
of sources and methods for this and subsequent charts is available on request.

22

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES
C h a rt

III

Estimated Percentages of O riginal Installations
of Plant and Equipment Surviving After the
Periods Indicated *

Pr« »
«en

•These survival curves imply average service lives of
about 17 years for equipment and 50 years for plant.
Source: Capital Goods Review, No. 39.

The procedure used in computing the capital stock on the basis of
survival curves made possible this computation of the age of capital.
Since the survivals are dated by year of origin, it is possible from the
computation to derive not only the total stock, but its age composi­
tion as well. From this, the weighted average age can be com­
puted (34).
(5)
All other variables.—Because there were a number of important
influences which could not be measured directly, the analysis included
a time trend having a constant rate of increase per year. This time
trend is a proxy or stand-in for the many other variables mentioned
at the outset, such as changes in managerial skill, technological
progress, improvements in the health and education of the labor
force, and so forth. It was found that there was no basis for varying
this rate from period to period.
Three transformations

It was necessary to transform some of the basic information so as to
place three of the terms in the form in which they appear in the
equation of the production function. These three transformations




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

23

produced a cyclical term, a transformation of the capital stock variable
and a new variable used to measure the influence on productivity of
changes in the composition of demand.
(1) The cyclical term.—The central focus, as already indicated, is
upon the longrun or secular relationships. On the other hand, the
actual historical data contained within themselves movements
related to shortrun deviations from the secular movements, including,
of course, those relating to the business cycle. It was necessary,
therefore, to construct some term that could be used statistically to
pull out or neutralize the influence on the relationships of these
shortrun and cyclical movements in the historical data.
This was done by the use of the labor inputs. Both a measure of
the potential labor input (Lp) and a measure of the actual labor
input each year (La) were available. The ratio obtained by divid­
ing the actual labor input by the potential labor input, which is
divorced from cyclical and other shortrun movements, yields a
variable which fluctuates with the cycle and other short-term devia­
tions. It will be noted from the description of these two basic
series above that this ratio represents the actual man-hours worked
each year in the whole economy divided by the potential labor input
in man-hours which could have been worked if the economy had op­
erated smoothly in line with the longrun trends in population and
labor force participation. By proxy, this variable also took care
of any other cyclical or shortrun fluctuations, since these were
very highly correlated with the ratio of man-hours worked to the
potential man-hours. This cyclical variable is indicated at the end
of the previous chapter

and is shown as the top line on chart

IV.
(2) The capital transformation.— It was obvious from the beginning
that the stock of capital had grown very rapidly over the last 50 years
and hence its movements would be highly correlated with the growth
of the potential labor force and with the time variable. (See chart
IV.) It was decided to transform the capital stock variable by
dividing it by the measure of potential labor input giving the term
Thus, taken in combination with the term Lp in the equation,
we have a formulation in which the capital stock has an effect upon
output independent of increases in the potential labor input, only
if it rises faster or slower than the potential labor input, so that
the capital-labor ratio rises ir falls. This means that the poten­
tial labor input (Lp) measures the influence on output of the in­
crease in available labor and the associated capital at some constant
capital-labor ratio, and with the average age, or technological state of
the capital stock, held constant.

The capital-labor ratio m

meas-

ures the effects on output of a deepening of capital—of a substitution
of capital for labor in production.




24

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

Chart IV
GROSS NATIONAL PRODUCT IN CONSTANT DOtLARS
AND RELATED VARIABLES, 1 9 0 9 -1 9 5 8
Pret
ecn

Source• a 2.
T ble




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

25

(3)
Index adjusting for the composition of demand.—Each type of
goods or service produced in the economy requires at any given point
in time a certain amount of labor and capital for its production. The
amount of each will depend on the state of technology, the character
of the goods or services produced and the ratio of output to capacity.
Naturally in historical series of data, changes in the composition of
demand could bring about changes in the amount of goods and services
that could be produced with given amounts of labor and capital if the
change in the aggregate meant a shift toward products and services re­
quiring more labor or more capital or less of either or both. In the
measurement of productivity, this so-called mix effect has been widely
recognized (35).
The procedure employed was to construct an index which measured
the changes in the amounts of labor and capital required to produce a
dollar of output of each of the major classes of goods and services
measured in the GNP in constant dollars. The index was constructed
by applying a set of capital-output ratios and a set of labor-output
ratios to each of a number of categories of goods and services among
the components of GNP (36). This variable, denoted Xa, is shown
on chart IV.
It may be noted that the major influences on the movements of this
index over time have been the decline in the relative importance of
agriculture, shifts between goods and services, and shifts between
government and private shares in the total GNP. The index also
reflects in wartime the extreme shift of demand to fit the requirements
of the war effort. In general, as will be noted on Chart IV, the economy can produce more from a given amount of capital and labor with
the wartime composition of demand than when a more nearly peace­
time composition of output is demanded.




2
6

T a b le 1.— The variables used in the analysis, and their components, 1909-58 1

Year

Time
units

Total

Potential
—0.9QMpHp labor force

Years

(000)

94.06
96.59
98.48
101.64
102.47
100.70
99.97
107.06
110.70
114.88
107.94
107.23
96.87
103.75
111. 57
109.46
113.46
117.38
116.91
118.04
120.36
112.62
103.75
92.37
92.54
92.62
97.74
106.82
111.42
103.80

34,785
35,708
36,274
37,341
37,896
37,475
37,669
40,126
41,531
43,998
42,313
41,497
39,361
41,383
43,938
43,315
44,512
45,795
45,900
46,382
47,611
45,465
42,607
39,274
39,615
42,739
44,224
47,078
48,233
46,379

Mix factor for produc­
tivity of labor and
capital
Potential

■ | i - 100

Percent

2,704
2,705
2,715
2,722
2,704
2,688
2,659
2,668
2,665
2,611
2,551
2, 584
2,461
2,507
2,544
2,527
2,549
2,563
2,547
2,545
2, 528
2,477
2,435
2,352
2,336
2,167
2,210
2,269
2,310
2,238

Average
age of
gross
tangible
capital

1.32
1.81
2.33
4.09
3.06
—.04
-2.42
3.51
5.88
9.24
2.45
.88
-1.41
-5.10
.79
-2.94
—.62
1.56
-.19
-.4 4
.42
-7.77
-17.87
-33.23
-33.91
-34.09
-27.03
-15.90
-10.97
-19.10

K

K

Billions of Dollars per
1959 dollars man-hour

214.7
219.9
225.9
234.1
243.3
252.0
258.6
265. 5
273.9
280.6
287.9
297.3
303.8
309.4
319.2
331.1
342.4
354.2
366.1
377.7
390.9
403.1
409.2
408.8
405.3
402.0
400.4
401.9
406.5
409.6

2.313
2.381
2.346
2.397
2.447
2.491
2.526
2.567
2.620
2.670
2.733
2.796
2.814
2.837
2.874
2.938
2.999
3.064
3.126
3.186
3.261
3.321
3.347
3.321
3.270
3.237
3.225
3.246
3.288
3.314

Xp

k

Years

2

14.50
14.60
14.72
14.87
15.06
15.19
15.37
15. 55
15.69
15.78
15.97
16.10
16.21
16.34
16.40
16.43
16.50
16.48
16.48
16.50
16.49
16.47
16.78
17.30
17.91
18.53
19.19
19.31
19.48
19.81

1954=100

95.72
95.90
96.07
96.25
96.43
96.61
96.78
96.96
97.14
97.32
97.50
97.68
97.86
98.02
98.11
98.19
98.29
98.38
98.47
98.56
98.65
98.74
98.83
98.92
99.02
99.11
99.20
99.29
99.38
99.47

Actual

xa

1954=100

95.61
95.87
95.79
96.27
96.28
96.33
96.70
96.83
97.47
97.59
97.47
98.47
98.10
97.89
98.51
98.60
97.96
98.04
97.66
97.52
98.81
98.13
98.09
97.59
96.68
99.21
100.10
100.30
100.40
98.79

STATES

2,704
2,700
2,696
2,692
2,687
2,683
2,678
2,669
2,661
2,654
2,642
2,630
2,619
2,607
2,596
2,585
2,573
2,562
2,551
2,540
2,529
2,518
2,507
2,496
2,486
2,460
2,429
2,394
2,366
2,338

Ha

Ratio of
gross
tangible
capital to
potential
labor input

UNITED




35,764
36, 596
37,196
37,785
38,535
39,274
39,825
40,364
40,921
41,286
41,540
42,099
42,942
43,564
44,423
45,415
46,211
46,995
47,822
48,624
49,376
50,219
50,815
51,370
51,951
52,581
53,234
53,860
54,437
55,063

E.

= E aX H a

Gross
tangible
capital

TH
E

3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29

92.84
94.86
96.28
97.65
99.42
101.16
102.39
103.43
104. 54
105.17
105.35
106.30
107.96
109.05
110.71
112.69
114.17
115. 59
117.11
118.55
119.87
121.38
122.28
123.08
123.93
124.20
124.15
123.80
123.64
123.60

La

Total

Ratio of
actual to
potential
labor input

I
N

1931........................
1932 .......................
1933........................
1934........................
1935........................
1936.........................
1937........................
1938.........................

0
1

2

<
000)

Actual
average
annual
hours per
employee

Billions of
man-hours

HP

Actual em­
ployment,
including
Armed
Forces
overseas

GROWTH

1909.........................
1910.........................
1911........................
1912........................
1913........................
1914........................
1915........................
1916........................
1917........................
1918........................
1919.........................
1920........................
1921.........................
1922........................
1923........................
192 4
1925
192 6
192 7
1928.........................
1929........................

Billions of
man-hours

M p

Potential
average
annual
hours per
employee

ECONOMIC

Lp

Actual labor input

POTENTIAL

Potential labor input

193 9

195 8

123. 60
123. 55
124. 48
125. 63
127. 10
128. 44
329. 23
130. 05
130. 78
131. 80
132. 98
133. 68
134. 60
135. 44
136. 19
137. 07
137. 92
139. 00
140. 38
141. 48

55,686
56,306
57,124
58,053
59,155
60,202
61,010
61,834
62,630
63,479
64,409
65,134
65,942
66,705
67,416
68,145
68,854
69,692
70,6S0
71, 538

2,312
2,286
2,270
2,254
2,238
2,222
2,206
2,191
2,175
2,163
2,150
2,138
2,126
2,115
2,104
2,095
2,086
2,078
2,069
2,060

108. 53
113.58
124.42
138.31
156.31
160.04
150.03
131. 50
130.32
131.03
126.38
128.90
135.89
137.90
139.79
134. 51
139.01
141.04
139. 59
133.11

47,769
49,606
54,097
59,056
64,864

6 ,0 0
62

64,363
58,917
59.264
60,216
58,702
60,491
64,191
65.264
66,219
6-1,829
66,260
67,483
67,729
65,896

411.1
415.2
422.3
426.7
425.4
424.4
427.2
439.3
460.0
482.7
502.7
521.3
541.4
561.7
582.1
601.5
620.7
642.5
665. 3
683.6

a 326
3.360
3.392
3.396
3.347
3.304
3.306
3.378
3. 517
3.663
3.781
3.899
3.985
4.148
4.275
4.388
4.501
4.623
4.739
4.832

20.06
20.15
20.11
20.40
20.80
21.16
21.21
20.67
20.04
19.49
19.11
18.81
18.48
18.12
17.88
17.73
17.45
17.21
17.09
17.11

99.56
99.66
99.72
99.79
99.86
99.91
99.98
100.05
100.09
100.16
100.21
100.23
100.25
100.25
100.28
100.28
100.30
100.30
100.32
100.32

99.38
99.91
10-1.10
102.10
104.70
103.16
102.30
99.28
99.10
99.34
99.49
100.30
100.20
100.30
100.70
100.30
100.01
100.10
99.69
100.90

point to the left one place). In the logarithms, this meant that the characteristic was
topped
the m ^ i S ^ d w l a Z T t ^ S

I
N
TH
E
UNITED
STATES

27




-1 3.8 9
-9 .3 7
- .0 5
10.10
23.00
24.59
16.09
1.11
-.3 5
-.5 8
-5 .2 0
-3 .7 1
.97
1.81
2.64
-1 .9 1
.81
1.46
—. 58
-6 .2 9

GROWTH

1 For output (Oa), see table 2.
’ ,A««•**>” is 'irawn t0
that
of capital, though presented here In c-onventionai units, years, was used in the equation in units of decades (moving the decimal

2,272
2,277
2,300
2,342
2,410
2,424
2,331
2,232
2,199
2,176
2,153
2,131
2,117
2,113
2.096
2,075
2,098
2,090
2,061
2,057

ECONOMIC

195 7

30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49

POTENTIAL

194 0
194 1
194 2
194 3
194 4
194 5
194 6
194 7
194 8
194 9
195 0
195 1
195 2
1053..........................
195 4
195 5
195 6

28

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

Fitting the production function to the historical data

The variables to be used to derive a production function for the
American economy for the period 1909-58 now are complete. The six
variables are shown on chart IV. The equation was fitted by the
classic method of least-squares to obtain the regression of output
(Oa) on the other variables, the equation being initially in the form
given at the end of chapter II with modifications as will be seen be­
low. The data were first translated into logarithms and punched on
cards suitable for feeding as input to an IBM 650 electronic computer.
Seven separate runs of the data were made on the computer, each
run yielding a correlation matrix, regressions between different com­
binations of the variables and various statistical measures such as
averages, standard deviations, Z , and a computation of the residuals
?2
for selected equations together with the Durban-Watson statistic to
test- for autocorrelation.
This procedure could be used only because of the generosity and
cooperation of the Bureau of Labor Statistics and the Board of
Governors of the Federal Reserve System, who made time available
on their IBM 650 computers.
Two difficulties in finding the structural relationship involved in
the aggregate production function have already been noted: a high
degree of correlation of the dependent variable (Oa) and four of the
dependent variables (Lp, K /L p , k, and X) with the time trend (t); and
the aggregation problems arising from combining data for a large num­
ber of enterprises with varying characteristics into a simple model for
the economy as a whole. In addition, the usual complexities asso­
ciated with time series of economic data had to be dealt with in the
analysis. As is well known, in time series the data for each year are
not independent observations arising from random samples of the un­
known universe but instead values for each year depend on what hapEened in the preceding year or years. Furthermore, it was clear that
oth the variables and the equations were subject to error so that the
structural parameters could not be determined accurately simply by
a direct fit by the least-squares method.
The procedure evolved to overcome these familiar problems was as
follows:
(1) Seven successive runs of the data were made on the IBM 650,
with several forms of the equation being fitted on each run.
(2) After each run the coefficients for each variable in each form of
the equation were tabulated, along with R2 Durbin-Watson statistic,
,
<’s and r s between variables; and charts were prepared showing—
r
(a) actual and computed values for the more promising
equations;
(b) scatters of residuals from the equations with some or all of
the variables; and
(c) interrelationships between values of the coefficients in the
different equations—particularly the dependence of the coeffi­
cients of the other variables on the value of the coefficient for
time (t).
(3) The several values of the coefficients for each variable found
on each run were tested in the light of—
(a) their standard errors;
(b) results of other research reported in the literature)




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

29

(c) effects of variations in coefficients of other variables, par­
ticularly time (t) ;
(d) effects of variations in the values of the coefficients on the
time pattern of the residuals; and
(e) the possible economic meaning of the coefficients, and hence
their reasonableness from viewpoint of economic theory.
(4) The basic data was reexamined in light of the results to deter­
mine whether the tests pointed to possible errors or biases in the
data themselves or in the form in which they were specified.
(5) In the light of analysis of each run, specifications were developed
for the next run with two types of modifications each time:
(a) changes in the form of relationship specified for one or
more variables; and
(b) specifications or restrictions as to the values which the
coefficients of one or more of the variables would be allowed to
assume.
In all, during the 7 runs over 50 variations in the basic equation
were obtained. Furthermore, after the fourth run, the data were
fitted by graphic correlation techniques to test visually what had been
learned to that point concerning the shape, values, and implications
of the most probable values of the coefficients. The equation at this
point assumed its final form and the final runs merely refined the fit
to take care of minor discrepancies revealed by the graphic test.
The final form of the equation, therefore, had to meet three tests.
First, the meaningfulness of the regression coefficients, that is, do
the coefficients make sense from a priori knowledge of the system?
Second, what is the effect of additional variables, or of changes in
the form in which variables are used in the equation, on R2? Is the
proportion of the variation in the independent variable (Oa) explained
by the equation, as measured by R2, raised enough by each variable
to justify the loss of degrees of freedom involved by using it? Third,
what is the effect on the standard deviation and the coefficients of
the other variables of adding each variable to the system? What is
the effect upon the Durban-Watson statistic, that is, on the auto­
correlation?
The strictly statistical tests, by themselves, were informative but
not decisive. The lowest R2 obtained was .88 and the highest was
.9964, with most of the equations having an R2 between .94 and .97.
In no case was the Durbin-Watson statistic large enough to warrant
a belief that autocorrelation had been reduced to insignificant pro­
portions. The value of R2, however, was highly correlated with the
values of the coefficients of some of the variables—especially the
capital-labor ratio (K/Lp ), time (£), and potential labor input (Lp).
This made it possible, in combination with the charts showing the
interrelationships of (Lp) and (K/Lp) with (t)7 to narrow the range
within which would fall any acceptable values of the coefficients for
these three variables. Both economic theory and previous studies
provided bases for further narrowing the search for acceptable
parameters—particularly for these three.
First, it was possible to define narrowly the range within which the
coefficient for time (t) undoubtedly would be found. The runs
included cases in which the time trend was free to assume any value,
was restrained to predetermined values, and equations in which
time was dropped out altogether. From these, it was possible to



30

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

conclude that the (t) coefficient must be at least as large as .00753 or
1.75 percent per year and less than .00966 or 2.25 percent per year.
If the time trend was outside this range, the signs of other coefficients
came out reversed or the coefficients assumed nonsense values. With
a high time trend (about 3-4 percent a year), the labor and capital
coefficients either reversed or became insignificant. At the other
extreme, for example, the coefficients for labor and capital (especially
capital) became excessively high, indicating an annual rate of return
to capital of almost 2 to 1.
In this study, time (t) is a proxy for the influence on output of
shifts in the production function due to such factors as changes in
qualities of inputs and changes in technology. Other studies have
investigated this aspect in terms of trends in productivity of labor
and capital. The two that are most nearly comparable to our (t) in
concept and measurement are those of Kendrick (30) and Solow (19).
Kendrick found that for the private domestic economy, physical
output per unit of labor and capital combined (weighted) rose by 2.1
percent per year 1919-57 and by 1.3 percent per year 1889-1919.
Solow arrived at an upward shift of the production function at about
1.5 percent per year for the period 1909-49 with the rate about 0.9
to 1.2 percent per year before 1930 and about 1.9 to 2.25 percent
per year after that date. His analysis covered the private nonfarm
economy. Both of these studies used data almost identical with
that used in this study. In our analysis, the acceleration in the rate
of change is accounted for largely by changes in the age of capital
(k) So that the coefficient for (t) should lie with the range of Kendrick’s
and Solow’s rates for the period after 1919—or in between 1.9 and
2.25 percent which is indeed the case.
The coefficient of the capital-labor ratio (KjLp) was sensitive to
values assumed by time (t) because of the high intercorrelation
between the two variables (about .96). For time trends within the
acceptable range arrived at above, the coefficient of KjLp assumed
values between .12 and .57 with values between .3 and .4 for the
equations with the highest R2, the most reasonable coefficients for
other variables and the most rational pattern of residuals between
actual and computed outputs (Oa-Om). Solow (19) found a value
of .353 as a coefficient for his capital-labor ratio using an equation
form of the Cobb-Douglas type. It seemed reasonable, therefore, in
light of all considerations, to use a coefficient of .35 for the capitallabor ratio (K /Lp ), especially as this would be consistent with the
distribution of GNP between property and labor incomes.
With the time trend (t) assumed to lie close to 2 percent per year
and the coefficient for KjLp fixed at .35, experiments were possible
with the coefficient of potential labor input (Lp) varied over a range
from less than 1 (decreasing returns to scale) to above 1 (increasing
returns to scale). Results of other investigators have been somewhat
ambiguous but generally pointed to slightly decreasing returns to
scale (38). Tests revealed no significant sensitivity of the equation
to any reasonable variation in the coefficient of Lp away from 1.0,
so it was finally fixed at unity.
With the coefficients of Lp and K /Lp fixed and that of (t) restricted
to a narrow range, it was only necessary to arrive at the optimum
forms for the cyclical component S 3



the capital age variable (Jc),

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

31

and the mix variable (X ) ; after which the optimum fit could be found
by least-squares. The mix variable (X) by definition has a coefficient
of 1 since it is a measure of changes in productivity of labor and
capital combined, assuming all input efficiencies constant but the
composition of demand variable.
It was clear at an early stage that a linear form for the cyclical
variable m

was not adequate and a nonlinear form had to be

adopted. This was parabolic in logs—a result consistent with the
economic theory of production with fixed supplies of factors, fixed
technologv, fixed mix of demand, and variable rates of use of inputs.
The final equation therefore used both log

and j^log y -J as

variables.
The experiments clearly pointed to a nonlinear form also for the
age of capital (k) but with a negative curvature in the relevant range.
This agreed with expectations. An increase in age of tlie capital
stock (k) implies that, other things being equal, the technological
efficiency of the capital stock is reduced below what it would be if
capital, on the average, were younger and approximated more nearly
the best production techniques known at the time. The curvature
also was reasonable since the older the capital stock becomes, on the
average, the smaller would be the proportionate effect on efficiency
of a further aging of the capital stock. Consequently, the age of
capital entered the final equation as both log k and [log k]2
.
The final equation

With these points arrived at, the final fit was arrived at on the
seventh run.
The final equation chosen on the basis of the many tests was:
log 0 m —
~
-5.43104+log L p . 9104 log (La )
+
/Lp
—3.39[log (La p
/L )]2+ . 35 log (K/Lp — 5 M l l log &
)
+ 10.356(log k)2+ X + M 8 m
N.B.— O m is tlie predicted value of gross national product and is the equation's
estimate of Oa. The relation of O m to O a is shown in column 3 of table 2.
N.B.B.— The average age of capital k has been measured in decades when
fitting the equation because of the scaling problem introduced by a squared term
if coded input is used.

The equation provided a high degree of explanation of the variations
in output (Oa). The R2 was .9898 and the closeness of the fit can
be seen from the chart V, where the log of the predicted value is plotted
vertically against the log of the actual output on the horizontal axis.
It will be noted that the dots, representing the various years, are
clustered closely around the 45° line which represents a perfect
correspondence between predicted and actual output. All of the
variables were statistically significant as measured by their standard
errors (37).
How sensitive are predicted values to variations in the cauation?
A test was made by making predictions of potential output lor 1959
and 1975 using eight different versions of the equation and similar
values for the inputs. The results showed a maximum deviation from
the output computed by the final equation equal to about 12 percent,
with six of the eight equations staying within 2 percent. Seven of the
sixteen predictions fell within V/2 percent of the final equations results



32

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES
C h a p te r

V

GROSS NATIONAL PRODUCT IN CONSTANT DOLLARS
1 9 0 9 -1 9 5 8 , ACTUAL VS. PREDICTED
Log Predicted GNP

Source: Table 2.

and four were within less than 1 percent. The only predictions which
deviated by more than 2){ percent were computed from two equations
rejected because the time trends were 0 in one and 2.9 percent per
year in the other—values which were both irrational and in disagree­
ment with other previous results. Also, in both these equations, the
coefficients of Lp and KjLp were either statistically insignificant or
assumed values which could not be accepted as reasonable on economic
grounds. In particular, the coefficients of K/Lp in the two equations
were extreme—indicating an almost insignificant contribution of
capital deepening in one case and an excessively high contribution in
the other.




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

33

Interpreting the production junction in economic terms

What can be said about economic sense of this statistically derived
production function? It is perhaps useful at the outset to consider
the relative importance of the various factors in explaining changes
in output.
(1) The increase in the potential labor input and the associated capital (capitallabor ratio held constant), accounts for between one-quarter and one-third of the
change in potential output.
(2) The change in the ratio of the capital stock to the potential labor input
accounts for between one-eighth and one-sixth of the change in potential output.
(3) The variation in the age of the capital stock accounts for between 2 and 4
percent of the change in potential output.
(4) The many factors represented by the time trend, as a proxy, account for
between one-half and two-thirds of the total annual increase in potential output.
(5) The other changes in output were determined by changes in the mix or
composition of demand as between industries with different rates of productivity
and by variations in the ratio of actual man-hours to potential man-hours.

To students of the production function, certain economic implica­
tions of the present formulation will be readily apparent. The
coefficient for the potential labor input {Lp) is given at unity. Since
this term carries with it by implication an associated stock of capital
with a fixed ratio to the potential labor input and a fixed average age
of the capital stock, this coefficient of unity implies constant returns
to scale. The work of Douglas, Tintner and Solow (38) reached the
conclusion that there might be some evidence of a tendency toward
decreasing returns to scale, at least in manufacturing. This study
suggests that if any such tendency prevailed in the economy as a
whole over the last half century, then it must have been quite small
and was covered up during this period by the overriding effect of
technological improvement which would tend to offset any tendency
to diminishing returns (39). Experiments, which varied arbitrarily
the coefficient of Lp above and below 1, gave no indication whatso­
ever of improvement of fit to the data.
The cyclical term in the final equation^0.9104l o g ^ —3.39
seems reasonable in light of both theory and other empirical research.
Its parabolic shape (due to the squared term) implies that at low rates
of operation of the economy ^60 to 90 percent for

an increase in

inputs will yield a more than proportionate increase in output (Oa),
i.e., there will be a cyclical rise in productivity. As operations ap­
proach full employment ^100 on the

scale^, the cyclical change in

productivity dies out and increases in inputs yield equivalent increases
in output.
When demand pushes operations to exceptional high rates, as
happened during World War II, output increases do not keep pace
with rising inputs—all other variables held constant. This is con­
sistent with the fact that at these high rates of operation it is necessary
to bring into use less efficient resources; older, standby plant and equip­
ment are put back into use, and less efficient labor is employed.
Furthermore, with labor markets exceptionally tight (unemployment
fell below 1 percent at the peak of war production), there is a tendency




34

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

to hoard labor so that available labor is not used at its most efficient
rate.
The value of 0.35 for the coefficient of the capital-labor ratio (K/Lp)
appears consistent with some prior studies. For manufacturing
Douglas found values for his capital coefficient ranging from 0.10 to
0.31 for time series data and from 0.25 to 0.47 for cross-section studies
(40). Solow obtains a value of 0.353 for the coefficient of his capitallabor ratio, when a Cobb-Douglas type function was fitted to data for
the private, nonfarm economy (41). Tintner obtained a coefficient
for capital of 0.332 for the total private economy (42).
The comparison of these other results with our own are not con­
clusive in view of the differences in data coverage, definition and form
in which the capital variable is introduced into the production function.
The previous study closest to this one in its treatment of capital in
capital-labor ratio form (Solow’s) gives the same result, as already
indicated.
That version of Douglas* own functions which comes closest to this
study (time series for American manufacturing; series IV) adjusted
each variable for time trends and correlated deviations from these
trends. This is equivalent to introducing time as an explicit variable
as done above (43). In this version Douglas found his capital
coefficient (j) to be 0.30—a value also close to the 0.35 found for the
total economy. Douglas, himself, came to the conclusion that the
long-run norm for (j), his capital coefficient, for the period he studied
(1899-1922) was probably about 0.34 in manufacturing.
If the compensation of capital roughly corresponded to the con­
tribution which an increase in the K/Lp ratio made to output (Oa),
then with a coefficient of 0.35 for K /Lp , we would expect the property
share in GNP on the income side of the national account to be between
30 and 40 percent. Depending on the definition of the property share
adopted, its value is in this range, and a rough estimate for the
1909-58 period is about 35 percent.
With a KjLp coefficient of +0.35, we would expect the capital
output ratio (K/Oa) to be falling and at a roughly proportionate rate
over the long run. Indeed, this is the case.
The influence of the age of capital (k) is inverse and nonlinear as
one would expect on theoretical grounds. This variable is an indirect
measure of the degree to which the capital stock (K ) incorporates the
latest technology; when the average age rises, the capital stock is less
modern, and vice versa. It would be expected, a priori, that an
increase in the average age of the capital stock (k) would be accom­
panied by a reduction in the output (Oa) obtained from any given
combination of K and L so the coefficient of k would be negative as
it is.
Further, the influence would be expected to be nonlinear. When
the average age is low—stock generally very up to date—an increase
in the average age would imply a larger proportionate drop in technical
efficiency, than when the average age is quite high and the capital
stock already relatively out moded on the average. The negative
slope of k and its parabolic shape give this result for the relevant range
of the curve.
The time trend (0.00884) has a rate of rise of 2.07 percent per year
and over the period 1909-58, it accounts for between one-half and
two-thirds of the rise in output. This result agrees closely with those



POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

35

of Kentrick (44), Solow (45), the Bureau of Labor Statistics (46),
and the staffs’ study of 1957 (47).
Potential output: 1909-60

The production function derived above can be used to compute
what the potential output could have been each year if there had
prevailed a state of full use of resources. Two assumptions must be
made. First, a value must be assumed for the cyclical term in the
equation

This variable was constructed on the assumption

that Lp, the potential labor input, reflected a constant rate of em­
ployment of 96 percent of the labor force and that average annua]
hours worked followed their trend without short-run, cyclical varia­
tions. If we use this as our standard for full employment, La can
be set equal to Lp each year, the cyclical term becomes 1 and can be
dropped out. The second assumption is that the potential output
must reflect history as it had happened up to each year—bygones
must be bygones. Thus, the Lp, K, and k assume the values in their
actual historical series without adjustment for what might have been
if full use of productive resources had in fact been continually achieved.
Potential output computed on this basis is shown in table 2, p. 37,
and on chart VI. The movements are what one would expect—
rapid growth during periods of relatively continuous prosperity with
minor setbacks, as in the 1920’s arid 1950’s, with actual output (Oo)
vaiying around the potential (Op). On the other hand, the potential
grew more slowly during the depressed years of the 1930’s and output
(Oa) fell substantially below’ potential (Op).




(I c nt n pic s
n o sa t r e )

POTENTIAL

POTENTIAL GROSS NATIONAL PRODUCT COMPARED TO ACTUAL
1909-1959, AND PROJECTED FOR 1975

3
6

Chart VI

ECONOMIC
GROWTH
I
N TH
E
XJN
ITED
STATES

Source: A
ctual, D artm t of C m
ep
en
om erce;
P
otential, Staff, Join E
t conom C m
ic om ittee.




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

37

T able 2.— Actual, 'predicted, and potential gross national product in 1954 dollars
for the United Stales, 1909-60
[In billions of 1954 dollars}

Year

1909..............................................
1910..............................................
1911..............................................
1912..............................................
1914..............................................
1915..............................................
1916..............................................
1917..............................................
1918..............................................
1919..............................................
1920..............................................
1921..............................................
1922..............................................
1923..............................................
1924..............................................
1925..............................................
1926..............................................
1927..............................................
1.928..............................................
1929..............................................
1930..............................................
1931..............................................
1933..............................................
1934..............................................
1935..............................................
1936..............................................
1937..............................................
1938..............................................
1939..............................................
1940..............................................
1941..............................................
1942..............................................
1943..............................................
1944..............................................
1945..............................................
1946..............................................
1947..............................................
1948..............................................
1949..............................................
1950..............................................
1951..............................................
1952..............................................
1953..............................................
1954..............................................
1955..............................................
1956..............................................
1957..............................................
1958_________________________
1959. _________ _____________
I960..............................................
p=preliminary.




Actual gross
national
product in
1954 dollars
03

Predicted
gross
national
product in
1954 dollars
om

104.1
106.8
109. 5
116.1
117.0
112.1
114.4
120.0
120.5
132.9
132.6
125.6
114.9
133.2
149.2
149.0
161.8
170.8
170.5
171.8
181.8
164.5
153.0
130.1
126.6
138. 5
152.9
173.3
183.5
175.1
189.3
205.8
238.1
266.9
296.7
317.9
314.0
282.5
282.3
293.1
292.7
318.1
341.8
353.5
369.0
363.1
392.7
400.9
408.3
399.0
425.6p

102.2
105.6
108.3
112.7
114.1
113.7
113.8
122.2
128.1
134.3
129.4
132.5
120.0
131.1
144.6
146.1
153.6
163.3
166.8
172.6
183.6
175.1
158.1
129.4
130.1
131.8
148.9
174.5
189.7
175.2
192.6
209.1
239.4
271.1
305.5
315.9
314.3
280.3
280.6
290.7
299.9
303. 7
329.5
346.1
364.3
363.2
387.9
409.0
418.6
413.9

ow o a
+

0.982
.989
.989
.901
.975
1.014
.995
1.018
1.063
1.011
.976
1.055
1.044
.984
.969
.981
.949
.956
.978
1.005
1.010
1.064
1.033
.995
1.028
.952
.974
1.007
1.034
1.001
1.017
1.016
1.005
1.016
1.030
.994
1.001
.992
.994
.992
1.025
.955
.964
.979
.987
1.000
.988
1.020
1.025
1.037

Potential
gross
national
product in
1954 dollars
Op
101.0
103.9
106.4
108.9
111.3
114.5
116.5
118.7
121.8
125.0
126.7
130.4
134.4
137.9
143.0
149.5
154.9
161.6
168.5
175.2
178.5
190.1
192.5
192.2
193.0
195.2
199.5
204.1
209.7
216.3
222.7
229.0
236.1
246.0
256.9
268.8
277.1
279.5
284.3
290.8
303.1
314.1
326.6
340.2
354.6
369.2
386.0
404.5
423.3
437.5
456. Ip
472.6p

Oa+Op

1.031
1.028
1.029
1.066
1.051
.979
.982
1.011
.989
1.063
1.047
.963
.855
.905
1.043
.997
1.045
1.057
1.012
.981
1.018
.865
.795
.677
.656
.710
.766
.849
.875
.809
.850
.899
1.008
1.085
1.155
1.183
1.133
1. on
.993
1.008
.966
1.013
1.047
1.039
1.041
.983
1.017
.991
.965
.912
.931p

C h a p t e r I V. P o t e n t ia l G r o w t h : P r o sp e c ts

and

P roblem s

The preceding chapters have reviewed the relationship of potential
output to the goals of the Employment Act; the problem of analyzing
output in terms of an aggregate production function; and derived
statistically the coefficients for such a function. In the present chap­
ter, attention turns to the future. How fast could the American
economy's output grow over the next decade or two if the full pro­
duction potential for growth which is inherent in the structure of the
economy is achieved? What are the implications for policy of different
assumptions as to the underlying factors influencing our economic
growth? What range of possibilities can we reasonably contemplate
as a basis for discussion of the issues of public and private economic
policy?
At the outset it must be recognized that the further ahead we
attempt to project our potential for economic growth the more uncer­
tain are the resulting estimates and the less likely it is that we can
really effectively apply the results. On the other hand, too short
a period would not allow time for underlying forces to work out their
longer term consequences. After a review of the various considera­
tions it was decided that the year 1975 would be the terminal date
for these projections. It is to be understood that the projections for
the year 1975 are an average of expectations for several years centered
at 1975.
The preparation and analysis of potentials for future growth of the
U.S. economy proceeds below in three stages: (1) the alternative
assumptions corresponding to high, medium, and low projections will
be reviewed; (2) the projections themselves will be presented together
with analysis of the reasons for deviations, if any, of the future po­
tentials from past trends; and (3) the implications of future potential
growth rates will be explored, particularly in respect to policy issues
which may be associated with them.
Alternative assumptions: 1959-75

Three alternative projections of potential output and of its rate of
growth to 1975 were prepared; high (labeled A), medium (B), and low
(C). These projections reflect trends of population, participation in
the labor force, unemployment, hours of work, changes in the capital
stock, and the average level of prosperity. These projections, which,
of course, are subject to some error, are designed to indicate a realistic
range of potential growth rates that our economy might experience
over the next decade. Table 3, page 40, summarizes these projections.
The projections of population and labor force used in the three
alternative projections to 1975 are derived from those prepared by the
Bureau of the Census, U.S. Department of Commerce (48) and the
Bureau of Labor Statistics, Department of Labor (49). These were
modified slightly to maintain consistency with the other assumptions
of the three projections.
38




POTENTIAL ECONOMIC GKOWTH IN THE UNITED STATES

39

(1) The A or high projection.—Projection A assumes that our eco­
nomic affairs are managed in both the private and public area to main­
tain a high level of prosperity. While occasionally minor recessions
might occur, it is assumed that the Nation will not experience a deep
and prolonged depression, such as interrupted growth during the
decade of the 1930’s. The precise combination of public and private
economic policies this projection would require is left unspecified.
Unemployment is assumed to average about 3 percent by the mid1970’s, i.e., about 97 percent of the labor force will be employed in an
average prosperous year in the 1970’s compared to the 96 percent
assumed in computing the potential output for 1909-60 in chapter
III. Under such conditions, job opportunities could be expected to
be sufficiently abundant to attract a relatively large proportion of the
population into the labor force.
In line with the degree of tightness in labor markets, average annual
hours are assumed to decline at a rate of about 0.4 percent per year,
slightly slower than the rate of fall over the last half century.
The rate of capital accumulation (rate of growth of the gross capital
stock) is assumed to proceed at a rate of 3.2 percent per year, a rather
conservative estimate of the rate in view of past periods of prosperity
(50>
*
The composition of demand is assumed to follow the historical pat­
terns typical of previous periods of strong growth, with allowance
for the effects of continued strong national security demands. This
implies about the same share of services in GNP as in 1955-57, reflect­
ing a rise in the share for private housing and government and a fall
for consumer services other than housing. The shares of construction
and nondurable goods are assumed to fall moderately, while the share
of durables rises somewhat above the 1957 share.
(2) The B, or medium projection.—The medium projection (B)
assumes somewhat more modest success in maintaining continuous
maximum emplo3r
ment, but again assumes no deep, prolonged depres­
sion will occur.
Unemployment is assumed to average about 4 percent, the same
assumption used in preparing the historical potential output estimates
in chapter III, shown on chart VI. This means 96 percent of
the labor force employed on the average. Labor markets, therefore,
would be somewhat less tight than under “A” and participation rates
of the population in the labor force would represent a continuation
of recent trends.
Average annual hours of work are assumed to decline at a rate of
about 0.5 percent per year, slightly less than the average rate over
the last half century.
The rate of capital accumulation is assumed to be more modest but
still in line with the assumption that serious depression will be avoided.
This means that the gross stock is assumed to rise at 2.7 percent per
year.
The composition of demand is assumed to have little effect on
the growth rate directly through the mix variable, with the rise in
the mix term (Xp) being only 0.001 percent per year.
(3) The G or low projection.—The low (C) projection assumes a con­
tinuation of public and private policies in such mixture that there
will be fairly frequent interruptions to growth, inadequate mobility
of capital and labor, and more slack on the average than in each of the
other two projections.



40

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

Unemployment is expected to average somewhat higher than in
the past best years or about 5 percent. Employment will average,
therefore, about 95 percent. Such slack in labor markets is assumed
to be accompanied by a slower rate of growth in the labor force as
participation rates reflect the lower level of job opportunities.
In line with the degree of slackness in labor markets, average annual
hours of work are assumed to decline at an average rate of about 0.6
percent per year. This is about the average over the past half
century— an acceleration over the A and B assumptions consistent with
past experience that reduction in hours of work are more likely under
slack conditions than when labor markets are relatively tight.
The rate of capital accumulation is assumed to be lower as industries
are constantly faced with the threat of excess capacity at higher
investment rates and labor is freely available to substitute for capital
at peak demand periods. This means a rise in gross stocks at about
2.2 percent per year, a low rate compared to past periods of prosperity.
In all three projections the assumed change in the age of the capital
stock reflects the corresponding rates of growth of capital stock,
though the assumptions may tend to underestimate the rate of
decline in the age of the capital stock under the assumed conditions.
If this is the case, then a downward bias is imparted to the three
projections.
The alternative projections

The alternative projections, derived by inserting the above assump­
tions in the formula for output derived in chapter III, yield a series
of estimates of potential output of GNP in 1954 dollars for the year
1975. The time trend was not varied between the alternative pro­
jections and was the same as derived for the period 1909-58. The
rates of growth implied by these are summarized in table 3.
T able 3.— Selected in d ica to rs of econom ic growth p otentials , 1 9 5 9 - 7 5 1
(Percent increase per year2
]

Indicator

Total labor force___________________________
Total employment, including the Armed Forces.
Average annual hours of work_______________
Total man-hours___________________________
Stock of private plant and equipment in con­
stant prices______________________________
Average age of capital stock____ _____________
Composition of demand____________________
Gross national product in constant prices
From 1959, actual (preliminary estimate)
From 1959 potential ....... rT
,
m
___

Rate of
growth,
1909-58

1.4
1.4
-.6
.9
2.4
.3
.1
2.9

Projected potential growth rates, 1959-75
A

B

O

1.9
31.9
-.4
1.6

1.7
*1.7
-.5
1.2

1.5
*1.5
—.6
.9

3.2
-.2
.015

2.7
-.1
.001

2.2
0
-.005

5.2
4.6

4.7
4.0

4.2
3.5

1 Some rates of change in this table vary slightly from those given in the similar table 4-1, p. 101 of the
“Staff Report on Employment Growth and Price Levels” because of the incorporation of later data and
refinements of analysis not then available.
2 Computed by compoimd interest formula, using initial and terminal years.
8Assumes 97 percent of the labor force employed in 1975.
* Assumes 96 percent of the labor force employed in 1975.
5Assumes 95 percent of the labor force employed in 1975.

It should be repeated at this point that the projections for the year
1975 do not necessarily assume achievement of maximum economic
growth each and every year between now and 1975. It is quite




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

41

obvious that economic fluctuations or international complications or
changes in policies, public and private, other than assumed, could
increase or decrease the Nation's production potentials by 1975.
Long-run tendencies, incorporated in the production function used to
make these projections, indicate that economic growth at these rates
is a feasible achievement.
Even if these rates are achieved or even exceeded, it does not follow
that output in the year 1975 will fall precisely in line with one of these
projections. Any individual year, such as 1975, may exhibit short-run
characteristics driving it ahead of or causing it to fall below the longrun rate. In addition, our national economic accounts undoubtedly
will be much improved in scope and accuracy over these 16 years and
such revisions may appreciably affect the projected levels as well as
rates of growth. Finally, it must be reemphasized that these projec­
tions assume a stable level of prices—more technically—they assume
that the GNP deflator will remain unchanged at the level of 1954.
The projections, therefore, represent changes in real output valued at
1954 prices.
A glance at the projected rates of growth in table 3 reveals that the
lowest rate of growth (C) is expected to be about 3.5 percent, measured
from the potential output calculated for 1959 or about 4.2 percent
per year measured from the preliminary estimate of the actual output
for 1959. This, the lowest of the three projected rates, is signifi­
cantly higher than the 50-year average of about 3 percent per year.
The middle or B projection, indicates a projected rate of growth of
potential output of 4 percent per year, measured from the output
potential for 1959 or 4.7 percent per year, measured from the pre­
liminary estimate of actual output during 1959. The highest projec­
tion (A) indicates a possible rate of growth of 4.6 percent per year
measured from 1959 potential output levels and about 5.2 percent
measured from the preliminary estimate of actual output for 1959.
Both the A and B projections indicate rates of growth that sub­
stantially exceed the average rate over the last 50 years.
Why do these projections, even the lowest, show an acceleration of
the growth rate compared to the average rate of 3 percent achieved
over the past 50 years? The first and foremost reason for this differ­
ence is found in one basic assumption used for the projections: namely,
there will be no deep, prolonged depression during the next 15 years
such as interrupted growth during the preceding 50 years—specifically,
the period from 1929 to 1941. This assumption has deep and per­
vasive influences on the projections. Increased stability of the
economy makes a very substantial contribution to an increase in the
growth rate, affecting the rate of growth of the labor force, the rate
of decline in hours of work, the rate of accumulation of capital, the
speed with which new technology is incorporated in actual production
processes and the composition of demand. The pervasive influences
of this assumption together with other developments are reflected in
three main factors which account for most of the difference between
past and future growth rates:
1.
The annual average rate of growth in the total labor force over
the next 15 years is likely to range between 1.5 percent and 1.9 percent
per year as compared to an average over the previous 50 years of about
1.4 percent. The growth of the population of working age, therefore,




42

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

will make possible a somewhat higher rate of growth in the future than
over the past 50 years.
2. The gross stock of private plant and equipment in constant prices
is assumed to grow between 2.2 percent and 3.2 percent per year over
the next 15 years compared to an average of about 2.2 percent per year
over the preceding half century. It is notable that the average rate
of increase over the past 50 years has been held down by the fact that
between 1929 and 1939 there was very little growth in the stock of
capital due to the low levels of investment during this decade. In
fact, from 1930-31 until 1945 the growth in gross capital stock (K)
was barely sufficient to keep pace, on the average, with the rise in the
potential labor input (Lp) so that the capital-labor ratio remained
almost constant for over a decade. There was a capital widening to
keep up with growth in the labor supply, in other words, but no capital
deepening to contribute to a rise in the productivity of the system.
3. The average age of the capital stock is assumed to remain con­
stant or decline slightly over the next 15 years, whereas the average age
of the capital stock actually increased over the preceding 50 years,
reaching a peak during World War II and declining since that time.
(See chart IV, p. 24.) The average rate of increase over the entire
50-3^ear period was about one half of 1 percent a year, but over most
of the period (1909-45) the rate of increase was slightly over 1 percent
per year. Since an increase in the average age of the capital stock
tends to retard the rate of growth, and a decline in the average age
tends to stimulate the rate of growth, this factor will be a modest
stimulant to the economy over the next 15 years, whereas it has been
a restrictive influence over most of the preceding half century.
It should be noted that the different assumptions as to the rate of
employment (or unemployment) have little direct impact on the rates
of growth projected to 1975. In fact, the direct effect would show
up in the second or third decimal place, if at all. The differences in
this assumption have their effects indirectly through effects on the
other variables: Labor force, hours of work, capital stock, age of
capital, and composition of demand.
In general, the assumptions chosen for these three projections are
conservative. Competent students of the various component factors
have prepared analyses of historical tendencies and future prospects
under reasonably prosperous conditions which would lead to even
higher rates of growth. (39) Indeed, no allowance has been made in
these projections for an acceleration in the time trend which has
prevailed over the last 50 years. This time trend of approximately
2 percent per year expresses the average influence over the past half
century of a wide range of forces which we could not measure directly
but which have strong influences on the growth of the economy.
These include the level and progress in educational achievements for
the population, the extent and nature of research and development
efforts, and any changes in the speed with which improved production
arrangements—other than those requiring significant changes in the
capital stock per man-hour—are introduced throughout the produc­
tion processes.
It would not be at all surprising if the accelerated rate of research
and development of recent years, assuming this continues in the
future, should have some tendency to accelerate the rate of growth
through its impact on the state of technology. Nor would it be sur­



POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

43

prising if efforts in the educational field should succeed in raising the
efficiency of labor and management in the private and public areas
of economic activity faster than occurred over the past half century
during which efforts in these directions were interrupted for extended
periods of time by both wars and degression. Finally, it would not
be surprising either if a more pervasive knowledge among manage­
ments of the best production practices would raise productivity faster
than in the past. Even today, in the United States there are very
significant differences, far wider than seems unavoidable, between the
best practices and those of the least efficient firms in any given line
of production.
Studies of the Bureau of Labor Statistics in connection with its
direct collection program in the early years following World War II
developed a considerable body of information about individual plants
within certain industries. For example, when the plants in certain
industries were classified into four groups ranging from the lowest to
the highest in man-hour requirements in unit of output, wide varia­
tions showed up. In gray iron foundries, the highest group, the least
efficient, that is, required almost four times as many man-hours per
unit of output as the lowest 01* most efficient group. Furthermore,
the lowest group obviously contained some plants which did better
than the average and some plants in the highest group exceeded the
group average. The spread, therefore, was even wider than the
group figures revealed (51).
Implications of the projections

These projections have the following implications:
(1) Without changing our economic system in any fundamental
way, that is, without instituting elaborate controls or having the
Government impose a pattern of consumption, and without Govern­
ment-imposed, forced high rates of capital accumulation, our economy
can grow at a rate as high as 4.6 percent per year. On the other hand,
it could prove extremely difficult to achieve rates substantially greater
than this within our economic system.
(2) If we avoid stumbling into real depression, the rate of growth
may be only as low as 3.5 percent per year, higher than the 50-year
average of 3 percent per .year which was achieved despite a prolonged
interruption in the 1930’s. Thus, there is a considerable range of
possible growth rates, even within a range of assumptions which
exclude depression and a forced-draft economy.
(3) There is a moderate inherent tendency for the rate of growth
of the economy to rise in the coming decade if unemployment can
be held on the average to about 4 percent, or less, of the civilian
labor force. This is due to the increase in the rate of growth in the
labor force and to the fact that the rate of increase in the capital
stock and the decline in the average age of the capital stock would not
be restricted as in the past by long periods of low investment such as
occur in periods of prolonged depression. So long as recessions are
neither too frequent nor deep, the rate of accumulation of capital can
be quite favorable to growth.
(4) Our economic growth is within our own control. If the Govern­
ment pursues growth-facilitating policies, the economy will expand
near the upper limit of the range. If, on the other hand, the Govern­
ment, as a matter of policy, sacrifices economic growth to the pursuit




44

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

of other objectives, our economy will perform sluggishly, will add less
to our capacity, and our potential growth will tend to be near the
lower limit of the above range or even below.
(5)
In recent years, including currently, the output of the economy
has been well below its potential and probably would be in the 1970’s
under the assumptions of the C projection.
From the standpoint of public and private policy, this stud\r
and these projections imply that wide differences in the rate of
growth can develop in the future, depending on the degree to which
public and private policies contribute: (1) To increased mobility of
labor and capital to meet the changing demands of our dynamic
economy; (2) to a rapid rise in educational attainment to keep pace
with requirements of the changing technology associated with higher
rates of growth and the high mobility this technological change re­
quires; (3) to a high and growing rate of research and development
expenditures as a basis for a high rate of technological progress; and
(4) to maintenance of such proportions between the growth in invest­
ment and in consumption as will not only provide for a high rate of
growth of capital stocks and the achievement of a relatively low age
of the stock, but also will produce a growth in final demand for
private and public consumption sufficient to maintain operations of
the continually growing capacity at rates of operation which will
maintain private incentives for a high rate of investment and of
technological progress.




PART II
T

e c h n ic a l

M

a t e r ia l s

These technical materials supply explanations of terms, sources, and
expansions on details of technique to supplement the discussion in
part I. The sections of these materials below are numbered in se­
quence, numbers corresponding to those inserted at appropriate places
throughout part I.
(1) This prevision of America’s future was that of George Tucker,
writing in 1912. See Joseph Dorfman, “The Economic Mind in
American Civilization,” volume II, pages 540-541, the Viking Press,
New York, 1946.
(2) This forecast, made in 1872 by a Connecticut doctor, is an
interesting, and indeed curious, example of reason and imagination
applied to the problem of predicting future economic, social, political,
and technological changes. See L. P. Brockett, M.D., “Marvels That
Our Grandchildren Will See; or One Hundred Years Progress in the
Future,” published as part of L. Stebbins, “One Hundred Years
Progress of the United States,” Hartford, Conn., 1872.
(3) The Employment Act of 1946, section 2.
(4) Ibid.
(5) The legislative history of the Employment Act of 1946 was
reviewed by the staff of the Joint Economic Committee and a memo­
randum prepared in April 1955 entitled “The Significance of the
Words ‘Maximum Employment’ as Used in the Employment Act of
1946.” See hearings on relationship of prices to economic stability
and growth, Joint Economic Committee, 85th Congress, 2d session
(1958), page 1.
(6) During World War II and the transition in 1945-47, a number of
projections were made of postsvar prospects and of the postwar levels
of employment and output consistent with full employment. Among
these were:
Bassie, V. Lewis, “Consumers’ Expenditures in War and Transition,” Review
of Economic Statistics, August 1946.
Cornfield, Jerome, Evans, W. Duane, and Hoffenberg, Marvin, “Full Employ­
ment Patterns 1950," U.S. Department of Labor, Bureau of Labor Statistics,
serial No. R1868, reprint from Monthly Labor Review of February and March
1942.
Dewhurst, J. Frederic, and associates, “America's Needs and Resources,” The
Twentieth Century Fund, Inc., New York, 1947.
George, E. G., in Dun's Review:
I. Gross National Product Projections: “The Background and Relation to
Current Issues," March 1945, pp. 9-14.
II . Contrasting Estimates; Range and Reasons, May 1945, pp. 9ff.
I I I . Measuring the Labor Force in 1950, June 1945, pp. 9ff.
Goldenweiser, E. A. and Hagen, E. E., “Jobs After the War," Federal Reserve
Bulletin, May 1944.
Hagen, Everett E . and Nora B. Kirkpatrick, “The National Output at Full
Employment in 1950," American Economic Review, September 1944.
Hart, Alfred G., “Model Building and Fiscal Policy," American Economic
Review, September 1945.




45

46

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

Hauser, Phiiip M., “Wartime Population Changes and Postwar Prospects,”
Journal of Marketing, January 1944, pp. 238-247.
Johnson, Arno H., “Fifty-Seven Million Jobs,” address before the Sales Executive
Club of New York, Feb. 6, 1945.
Livingston, S. Morris, “Markets After the War,” U.S. Department of Commerce,
Washington, D .C ., March 1943. [Available as S. Doc. 40, 78th Cong., 1st sess.
“Postwar Manpower and Its Capacity to Produce,” Survey of Current Busi­
ness, U.S. Department of Commerce, April 1943.
“Postwar Income Potentials,” in Measuring and Projecting National Income,
National Industrial Conference Board, Studies in Business Economics,
No. 5, March 1945, pp. 23-27.
Mayer, Joseph, “Postwar National Income,” The Brookings Institution, pamphlet
No. 55, Washington, D .C ., 1944.
Montgomery, D ., “Reconversion to What?”, Antioch Review, September 1945,
v. 5, pp. 309-319.
National Planning Association, “National Budgets for Full Employment,” plan­
ning pamphlets Nos. 43 and 45, April 1945—study made during spring and
summer of 1944.
Roos, C. F., hearings on S. 380 (Full Employment Act 1945) before a subcommittee
of the Senate Banking and Currency Committee, 1945, pp. 906-912.
Schlotterbeck, Karl T ., “Postwar Reemployment,” The Brookings Institution,
pamphlet No. 54, Washington, 1943.
Slichter, Sumner H., “Jobs After the War,” Atlantic Monthly, October 1944.
Tucker, Rufus S., “Projections of National Income,” National Industrial Con­
ference Board, Business Record, December 1944 and January 1945.
U.S. Department of Agriculture, “What Peace Can Mean to American Farmers,”
miscellaneous publications: No. 562, May 1945; No. 570, July 1945; No. 582,
October 1945; and No. 589, December 1945.
U.S. Department of Commerce, Bureau of the Census, “Normal Growth of the
Labor Force in the United States: 1940 to 1950,” prepared by John D . Durand,
mimeographed series, P-44, No. 12, June 12, 1944.
Warburton, C., “Normal Production, Income, and Employment, 1945 to 1965,
Based on a Statistical Analysis of Past Data.” Southern Economic Journal,
January 1945, v. 11, pp. 219-245.
Weiler, E . T ., “Wartime Savings and Postwar Inflation,” Survey of Current
Business, July 1943.
Woytinsky, W. S., “Prospects of Permanent Full Employment,” International
Postwar Problems, American Labor Conference on International Affairs,
September 1944, vol. 1, pp. 485-515.
“Postwar Economic Perspectives,” Social Security Bulletin, March 1946,
vol. 9, pp. 11, 25; December 1945, vol. 8, pp. 18-29; January 1946, vol. 9,
pp. 8 -16 ; and February 1946, vol. 9, pp. 9—
16.

(7)
Projections of employment, production and purchasing power
needed to carry out the policy declared in section 2 of the Employment
Act were made in accordance with section 3(a) of the act in the
Economic Report of the President from 1947 to 1952. These are cited
below:
Date of report :
Pages
January 1947______________________________________________
9 -1 1
January 1948______________________________________________
45-47
January 1949 1____________________________________________
36, 38
January 1950 1_____________________________________________ 75, 78, 80
Januarv 1 9 5 1 1_____________________________________________
76-77
July 1 9 5 1 2................... .........................................................................
60-63
January 1952 1_____________________________________________
1 1 3 -1 1 4
1Contained in the Annual Economic Review, a Report to the President by the Council of Economic
Advisers. (This review is printed with the Economic Report of the President.)
2Contained in The Economic Situation at Midyear, a Report to the President by the Council of Economic
Advisers.

(8)
Projections of the levels of employment and production needed
to carry out the objectives of the Employment Act and, summaries
of the economic outlook based on the annual Economic Report of the
President, the Joint Economic Committee’s hearings, and other




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

47

sources, have been made by the staff of the Joint Economic Com­
mittee for use of the committee. For these, refer to Joint Economic
Committee’s Reports on the Economic Report of the President, as
follows:
Page

1948
1950
1951
1952
1954
1955
1956
1957
1958
1959

Staff report_________________________________________________
Staff materials______________________________________________
Staff materials______________________________________________
National defense and the economic outlook for 1953 (fiscal year)..
Staff materials______________________________________________
Staff materials______________________________________________
Staff materials______________________________________________
Staff materials______________________________________________
Staff materials______________________________________________
Staff materials______________________________________________

11 ff.
37 ff.
26 ff.
29 ff.
35 ff.
79 ff.
77 ff.
38 ff.
17 ff.
45 ff.

Also the following other publications:
“The Economic and Political Hazards of an Inflationary Defense Economy,”
(materials prepared by the staff of the Joint Economic Committee), committee
print, February 1951.
“Inflation Still a Danger,” (report of the Joint Economic Committee, together
with materials on national defense and the economic outlook prepared by the
committee staff) (S. Rept. 644), August 1951.
“Sustaining Economic Forces Ahead,” (materials prepared for the Joint Com­
mittee on the Economic Report by the committee staff), committee print,
December 1952.
“Potential Economic Growth of the United States During the Next Decade,”
(materials prepared for the Joint Economic Committee by the committee
staff), committee print, October 1954.

(9) This was discussed at length by various witnesses and con­
tributors to the study by the Joint Economic Committee in 1958,
entitled “The Relationship of Prices to Economic Stability and
Growth.” See especially the summary of the arguments by Beryl
Sprinkel in his paper “Maintaining Economic Growth, Stability,
and Stable Prices,” in the commentaries submitted by economists
from labor and industry, pages 63 ff.; also, in the compendium of
papers submitted by panelists appearing before the Joint Economic
Committee in connection with the same study, see those contributed
under part I, on “Employment Act Objectives and the Stabilization
of Prices” (pp. 1-74).
(10) This was outlined at length by Dr. Edwin G. Nourse in bis
paper “Employment Act Objectives and the Stabilization of Prices,”
in the study mentioned in note 9 (compendium of papers submitted by
panelists appearing before the Joint Economic Committee, pp. 13-22).
(11) For a discussion of the definition and nature of economic
growth and its study see:
Paper by Grover W. Ensley, entitled “The Employment Act of 1946: The
Dynamics of Public Economic Policy.” Compendium of papers submitted
by panelists appearing before the Joint Economic Committee, in connection
with its study of the relationship of prices to economic stability and growth,
pages, 1 -1 2 . (85th Cong., 2d sess.)
Goldsmith, Raymond W., “The Comparative Study of Economic Growth and
Structure,” National Bureau of Economic Research, 1959.
“Staff Report on Employment Growth, and Price Levels,” prepared by Joint
Economic Committee staff, especially chapter II , pages 33-34. (86th Cong..
1st sess., December 1959).

(12) Perhaps the most provocative and widely discussed recent
essay based on the distinction between an increase in material goods
and services and an increase in welfare was the book by John K.
Galbraith, “The Affluent Societv,” Houghton Mifflin Co., Boston,
1958.



48

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

(13) The monthly report on employment, labor force, and unem­
ployment is based on the monthly current population survey of a
sample of households. The basic concepts, definitions, and classifica­
tion scheme remained unchanged from the survey’s inception in 1940
until January 1957. There have been a number of changes in sample
design and procedures.
Civilian labor force data beginning with May 1956 are based on a
330-area sample. For January 1954-April 1956 they are based on a
230-area sample; for 1946-53 on a 68-area sample; for 1940-45 on a
smaller sample; and for 1929-39 on sources other than direct enumera­
tion.
Effective January 1957, persons on layoff with definite instructions
to return to work within 30 days of layoff and persons waiting to start
new wage and salary jobs within the following 30 days are classified as
unemployed. Such persons had previously been classified as employed
(with a job but not at work). The combined total of the groups
changing classification has averaged about 200,000 to 300,000 a month
in recent years. The small number of persons in school during the
survey week and waiting to start new jobs are classified as not in the
labor force instead of employed, as formerly. Persons waiting to open
new businesses or start new farms within 30 days continue to be classi­
fied as employed.
Beginning July 1955, monthly data are for the calendar week ending
nearest the 15th of the month; previously, for week containing the 8th.
Annual data are averages of monthly figures.
For the years 1940-52, estimating procedures made use of 1940
census data; for subsequent years, 1950 census data were used.
The effects of this change on the historical comparability of the data
are explained in the Annual Report on the Labor Force, 1954, series
P-50, No. 59, April 1955, page 12.
These changes have had measurable effects on the magnitudes shown
by the survey. For example, for 1957, unemployment was 4.0
percent of the civilian labor force on the old definition but 4.3 percent
according to the new definitions adopted January 1957.
(14) Stanley Lebergott has shown that, although the proportion of
the population exposed to possible unemployment has risen markedly
since the early years of the 19th century, the average percent of the
labor force unemploj^ed has shown no distinct trend at all. Changes
enabling the economy to operate with lower unemployment in propor­
tion to the numbers exposed to its threat have fully offset the increase
in the proportion of the population exposed to possible unemployment.
See hearings, “Study on Employment, Growth, and Price Levels,”
part 3, pages 577-585.
(15) The effects of job shifting, labor mobility, changes in the
age-sex composition of the labor force, and other factors on unem­
ployment rates was examined in two new studies made for the Joint
Economic Committee in connection with the current study of em­
ployment, growth, and price levels, by the Bureau of Labor Statistics,
U.S. Department of Labor. See Study Paper No. 6, “The Extent
and Nature of Frictional Unemployment,” and No. 23, “Unemploy­
ment in Surplus Labor Market Areas,” in press, January 1960.
(16) This was not a determination by the staff that 4 percent was
the percentage consistent with the objectives of the Employment Act.




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

49

Indeed, it would have no authority to make such a determination.
The staff has stated a number of times that this percentage was de­
rived from studies of the past history of employment and unemploy­
ment of the United States. See, for example, “Potential Economic
Growth of United States During the Next Decade,” opere citato, page
6.
(17) Domar, Evsey D., “Essays in the Theory of Economic
Growth,” New York, Oxford University Press, 1957, page 16.
(18) The pioneering work of Prof. Paul H. Douglas, his early
colleague, Charles W. Cobb, and his other associates in his work on
the production function was incorporated in a long series of journal
articles and in his book on wages. The first of these was: Cobb, C. W.,
and Douglas, Paul H., “A Theory of Production,” American Eco­
nomic Review, supplement, volume XVIII, March 1928, pages
139-165.
The results were incorporated in Professor Douglas’ book on wages
in 1934 and later work in a further series of articles. This work
was summed up and evaluated in his presidential address before the
American Economic Association at Chicago, 111., December 29, 1947,
entitled “Are There Laws of Production?” The most convenient
source for his work on this problem is the reprint of his book on wages:
“The Theory of Wages,” by Paul H. Douglas, incorporating a reprint
of the article “Are There Laws of Production?”, Augustus M . Kelley,
New York, N.Y., 1957.
(19) See:
G. Tintner, “A Note on the Derivation of Production Functions from Farm
Records,” Econometrica, volume 12 (1944), pages 26 ff.
------------ and O. H . Brownlee, “Production Functions Derived From Farm
Records,” Journal of Farm Economics, volume 26 (1944), pages 566 ff.
C. G. Hildreth, “A Study of Production Functions From Farm Record Data”
(unpublished thesis, Ames, Iowa, 1947).
W. H . Nichols, “Labor Productivity Functions in Meat Packing,” Chicago, 1948.
M. J. J. Verhulst, “The Pure Theory of Production Applied to the French Gas
Industry,” Econometrica, volume 6 (1948), pages 295 ff.
E . O. Heady, “Production Functions From a Random Sample of Farms,” Journal
of Farm Economics, volume 28 (1946), pages 989 ff.
W. W. Leontief, “Introduction to a Theory of the Internal Structure of Functional
Relationships,” Econometrica, volume 15 (1947), pages 361 ff.
Robert M. Solow, “Technical Change and the Aggregate Production Function”
in the Review of Economics and Statistics, August 1957, volume X X X I X ,
No. 3, pages 312-320.

(20) On linear programing, see:
Robert Dorfman, Paul A. Samuelson, and Robert M. Solow, “Linear Programing
and Economic Analysis,” New York: McGraw-Hill Co., Inc., 1958
T . C. Koopmans (ed.), “Activity Analysis of Production and Allocation,” John
Wiley & Sons, Inc., New York, 1951.
Robert Solow, “On the Structure of Linear Models,” Econometrica, volume 20
(1952), pages. 29 ff.

(21) On input-output, see, for example:
Oskar Morgenstern (ed.), “Economic Activity Analysis,” John Wiley & Sons,
Inc., New York, 1954.
Netherlands Economic Institute, “Input-output Relations,” Proceedings of a
Conference on Inter-industrial Relations Held at Driebergen, Holland, 1953,
II. E . Stenfort Kroese N. V., Leyden, 1953.
Conference on Research in Income and Wealth, “Input-Output Analysis; An
Appraisal,” Studies in Income and Wealth, volume 18, Princeton University
Press, Princeton, N.J., 1955.




50

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

W. D . Evans and M. Hoffenberg, “The Interindustry Relations Study for 1947,”
The Review of Economics and Statistics, volume 34 (1952), pages 97 ff.
Wassily W. Leontief, “The Structure of American Economy, 19 19 -19 39,” 2d
ed., Oxford University Press, New York, 1951.
—* * and others, “Studies in the Structure of the American Economy,” Oxford
——
University Press, New York, 1953.

(22) For critical analyses of production functions, see:
M. Bronfenbrener, “Production Functions,” Econometrica, volume 12 (1944),
pages 35 ff.
D . Durand, “Some Thoughts on Marginal Productivity, With Special Reference
to Professor Douglas’ analysis,” Journal of Political Economy, volume 45 (1937),
pages 740 ff.
J. Marschak and W. H . Andrews, “Random Simultaneous Equations and the
Theory of Production,” Econometrica, volume 12 (1944), pages 143 ff.
H . Menderhousen, “On the Significance of Professor Douglas’ Production Func­
tion,” Econometrica, volume 6 (1938), pages 143 ff.
M. W. Reder, “An Alternative Interpretation of the Cobb-Douglas Functions,”
Econometrica, volume 11 (1943), pages 259 ff.
E . Schneider, “Theorie der Production” (Vienna, 1934).
R . G. D . Allen, “ Mathematical Analysis for Economists,” London, 1938, pages
502 ff.
S. Carlson, “A Study in the Pure Theory of Production,” London, 1939.
P. H . Wicksteed, “The Coordination of the Laws of Distribution” (reprint),
London, 1932.
Burgess Cameron, “The Determination of Production,” Cambridge University,
1954.
Francis Seton, “Production Functions in Soviet Industry,” American Economic
Review; Papers and Proceedings, volume 49 (May 1959), No. 2, pages 1-1 4 ,.
W. P. Hogan, “The Limitations of Capital Coefficients: A Comment,” American
Economic Review, volume 49 (March 1959), No. 1, pages 138 ff.
Irma Adelman, “Some Observations on Full Employment Versus Full Capacity,”
American Economic Review, volume 46 (June 1956), No. 3, pages 412 ff.
D . Hamberg, “Production Functions, Innovations, and Economic Growth,”
Journal of Political Economy, volume L X V I I (June 1959), No. 3, page 228 ff#

(23) There is an extensive literature on the definition of measure­
ment of capacity. In recent years, attempts at constructing sta­
tistical indicators of capacity, or of changes in capacity, have brought
about renewed discussion of some of these points in a more practical
setting. These include the series of surveys of manufacturing ca­
pacity made by the Department of Economics of the McGraw-Hill
Publishing Co. in connection with their annual survey of business
plans for capital expenditures. See particularly their checkup on
manufacturing capacity in connection with the survey in the fall of
1958, dated October 6, 1958; the discussion by Sanford S. Parker
and his associates of Fortune magazine in their September 1958
issue in an article entitled “How Much Over-capacity in U.S. Manu­
facturing?” , and his talk before the American Statistical Association,
December 10, 1958; and the paper by William F. Butler, entitled
“ Capacity Utilization and the Rate of Profitability in Manufactur­
ing,^ American Economic Review, proceedings, May 1958, volume
XLVIII, No. 2, pages 239-248. Dr. George Teborgh has also
considered this capacity problem and some of his work is presented in
“Capital Goods Review,” published by Machinery and Allied
Products Institute. See particularly No. 39, September 1959, and
No. 22, May 1955.
(24) See Paul H. Douglas, “Are There Laws of Production?” , and
his other works as cited above in technical note No. 15. Also Gerhard
Tintner, “Econometrics,” John Wiley & Sons, Inc., New York, 1952,
particularly pages 51-53.




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

51

(25) See Tintner, opere citato, pages 53, 55-56, 91-132, 303-304,
and other studies cited in his notes.
(26) See Tintner, opere citato, pages 134-143; Eobert M. Solow,
“Technical Change and the Aggregate Production Function” in The
Eeview of Economics and Statistics, August 1957, volume X X X IX ,
No. 3, pages 312-320.
(27) For a convenient survey of the theory of production and pro­
duction functions, see Paul H. Douglas, opere citato, and Sune Carlson,
“A Studv on the Pure Theory of Production,” Kelly & Millman, Inc.,
i956.
(28) Douglas, opere citato the reprint of his address, “Are There
Laws of Production?”
(29) The series used was taken from “U.S. Income and Output,”
a supplement to the Survey of Current Business, table 1-2, pages
118-119, and table 1-16, pages 138-139.
(30) For employment and hours of work, the figures used were
preliminary data prepared by Dr. John Kendrick in his study for the
National Bureau of Economic Eesearch entitled “Productivity Trends
in the United States” (in preparation), a summary of which was pre­
sented by Dr. Solomon Fabricant in his statement before the Joint
Economic Committee at hearings in connection with the Study of
Employment, Growth, and Price Levels (pt. 2, “Historical and Com­
parative Bates of Production, Productivity, and Prices,” p. 281).
We are indebted to the National Bureau for permission to use these
preliminary data in our study prior to completion and publication
of Dr. Kendrick's volume.
(24)
Derivation of potential labor input (Zp
).—The potential labor
input variable (L p measures the total amount of man-hours poten­
)
tially available for economic activity during the calendar year. It is,
conceptually speaking, equal to the potential labor force multiplied
by the average of the potential annual hours of each employee. The
labor force was assumed to be 96 percent employed, that is, an arbi­
trary level of 4 percent unemployment w a postulated for the model.
^s
This figure was selected because there was the self-imposed constraint
that the model would be built within the existing institutional frame­
work, one characteristic of which is an amount of frictional unemploy­
ment. On the basis of past experience, 4 percent seemed to be repre­
sentative of unstrained full employment. It is underlined, however,
that this figure intends no policy recommendations or value judgments.
For purposes of the model, the figure is unimportant because the
mathematical technique used— that is, correlation analysis in loga­
rithms— turns this percent into a constant that is absorbed in the
constant of the equation without effecting the regression coefficients
or the forecast. With the assumption of a constant level of unem­
ployment, movement within the labor input series reduces to changes
in the labor force and changes in the average annual hours. The
final data used for both of these series is a smoothed aggregation of
individually derived subseries. The procedure was different for each
series.
Potential labor force (M p
).— The derivation of a potential labor force
faces both conceptual and technical problems. On the one hand
there is the difficulty of reconciling the pre-1940 definitions of gain­
fully employed with the subsequent labor force concept, which itself




52

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

has changed even as recently as 1957. Then granting the solution
of this problem there is the difficulty introduced by inaccurate meas­
urement particularly in the earlier period and by shifting patterns
of employment in several of the age-sex groups.
These problems seemed to call for an indirect derivation using
population figures and participation rates. Available MRLF data
were used in the later period, and decennial census figures with inter­
polations covered the earlier years.
The participation rate of each of the age-sex groups in table 4 of
Bureau of the Census series P-50, were fitted in a multiple regression
against an index of unemployment, armed forces, and time. The
results proved to be consistent with previous studies in this area and
provided a basis from which to project the growth of the labor force.
The most significant changes seemed to be the increasing participa­
tion of women and the decreasing participation of men under 20 and
over 64 years of age. The trend value of the participation rate de­
picting full employment was then applied to the population within
each age-sex group and the resulting aggregation provided a potential
labor force for the early years which was consistent in concept and
level with the more reliable recent years. The aggregated series was
tied in at 1950 to the trend labor force figures provided by the Bureau
of Labor Statistics. See table 1, p. I ll, “Hearings on the January
1959 Economic Report of the President.,,
Potential average annual hours (
.Hp ).—A satisfactory mathamatical
representation of the changing average annual hours proved to be
extremely difficult because of substantial structural and institutional
changes during the period. The general pattern was a gradual de­
cline until the thirties, a sharp decline until the late forties and then a
slowing down of the decline into the fifties. There are of course
several explanations for this behavior. In the early third of the
period both the general shortening of hours and the shift of labor
out of agriculture into the relatively shorter houred industrial occupa­
tions account for much of the decline. The major downturn in the
thirties, particularly after 1934, seems to come from a combination
of the effects of the depression, minimum age and wage law's, and of
the increased effectiveness of organized labor. The sharp impact of
these institutional changes seems to have run its course by the late
forties and the lower rate of decline of the earlier period returns, this
time partially accounted for by increasing proportion of women in
the work force, the added premium of leisure, and longer vacations,
among other reasons.
The functional representation of the otherwise logical pattern is
troublesome. A constant rate of decline over the entire period, that
is a linear function in logarithms, is scarcely representative of any
part of the period and makes economic nonsense when extrapolated.
A second-degree parabola is impossible because the series shows an
inflexion point during the thirties. Yet, a cubic parabola, though
fitting the period under observation satisfactorily, will provide a
minimum point and eventually an upturn on extrapolation because
of the nature of the equation. And, the logistic curve, sometimes
called the Pearl-Reed growth curve, proved too inflexible to fit
the data.
The hurdle was finally overcome by a hand-fitted series for the
potential hours. Essentially this boiled down to making linear inter­



POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

53

polations over short and economically meaningful periods for hours
in each of three sectors— agriculture, private nonfarm, and govern­
ment. This resulted in about a 0.4 percent rate of decline in the most
recent years which corresponds closely to the rate of decline in the
early years, and a more rapid rate in the 1930’s and 1940’s.
(32) The estimate of capital stock, prepared by Dr. Terborgh, is
that underlajdng Capital Goods Review, No. 39, September 1959,
published by Machinery & Allied Products Institute, Washington,
(33) Dr. Terborgh describes the procedure and his results in
Capital Goods Review, No. 39, September 1959. He comments on
possible shortcoming of his procedure as follows:
This calculation is subject to at least one serious defect. The same estimated
survival curves are used throughout. Even if these curves were correct for assets
installed in one period, they would not necessarily be so for the installations of
other periods. There is no reason to believe that mortality rates have held con­
stant in the past. Because of this instability, actual changes in stocks must have
differed appreciably from changes computed on the assumption of constancy.
It is difficult to appraise the magnitude of the errors arising from this assump­
tion. They may be substantial. We are reasonably sure, however, that they
are not sufficient to vitiate the computed results fundamentally. Though no
more than crude approximations, these results offer a significant indicator of
major changes in the stock of productive facilities. Needless to say, they should
be read for major changes only.
A further warning is in order. Since our calculations relate to the grand total
of business capital goods—agricultural, industrial, public utility, transportation,
commercial, and miscellaneous—extreme care should be exercised in drawing
inferences for particular classes or product lines. There have been wide differ­
ences from one line to another in past installation and survival rates, and the
overall picture may, therefore, be of limited significance for any one of them
taken singly.

(34) See Capital Goods Review, No. 40, Machinery & Allied
Products Institute, December 1959. The average age refers to a
weighted combination of the Terborgh series for plant and for equip­
ment.
(35) The problem of allowing for the influence of changes in the
composition of demand on productivity and costs was discussed in
“Productivity, Prices, and Incomes” (materials prepared for the
Joint Economic Committee by the committee staff), committee print,
June 1957. See particularly the analysis of effects on share of em­
ployee compensation in national income (a related issue), pages
49-50, 59-60. See also, hearings on employment, growth, and price
levels part. 2, testimony of Soloman Fabricant, page 281 and following
pages; Bulletin No. 1249, U.S. Department of Labor, “Trends in Out­
put Per Man-Hour in the Private Economy, 1909-58,” January 1960,
especially pages 12-14; and Study Paper No. 17, “Prices and Costs in
Manufacturing Industries,” by Charles L. Schultze and Joseph L.
Tryon.
(36) In the past, two basic techniques have been used, particularly
in the study of productivity, to make allowance in time series for the
influence of changes in the composition of demand. One of these used
by Kendrick, for example in the study cited in note 30 above, involves
combining the inputs with weights reflecting the relative importance
of each industry or, as in Kendrick’s case, by the average compen­
sation. The other technique derives measures, such as measures of
productivity, for each of a number of components of the gross national
product, then combines the outputs resulting from the component



54

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

sectors such as agriculture, private, nonfarm, manufacturing, govern­
ment, etc. In this study we constructed instead a so-called mix index
(.X) making use of a breakdown of GNP by type of product or service
recently initiated by the Department of Commerce and the inputoutput technique. First, estimates were prepared, utilizing mainly
the Department of Commerce data on GNP, by type of product for
each year 1909-58. These values were in constant 1954 prices. The
breakdown was that provided in “ United States Income and Output,”
A Supplement to the Survey of Current Business, November 1958,
table VII-6, page 224. The input- output-table developed by the
Federal Government at the Bureau of Labor Statistics for the year
1947 was utilized to distribute estimates of man-hours worked in each
of about 50 industries and capital stocks in each of these industries to
the final goods and service accounts in the GNP. The procedure
made use of the table given by Evans and Hoffenberg (note 21 above)
showing the direct and indirect deliveries of each of the 50 industries
to each of the number of final demand sectors. The contributions of
each industry to each of these broad final demand sectors was broken
down into the final categories required for our purposes by inspection
of the basic input-output table. Some rough tests showed that more
refined procedures would not make enough difference to be worthwhile
at this point.
With the man-hours and capital stocks distributed from industries
to final goods and service categories, these were then totaled for each
category of the gross national product. We then had the total number
of man-hours and the total stock of capital employed in producing the
particular quantity of goods or services produced in each category.
Dividing the man-hours by the gross national product in each category
gave a labor-output coefficient and division of the capital stock by
the output gave a capital-output coefficient for each category of GNP.
These two sets of labor and capital ratios were used as weights in
combination with the annual estimates of GNP by categories of goods
and services to derive an index with 1954 equal to 100. Since this
index used the changing composition of demand for each year at a
constant set of labor-output and capital-output ratios, the resulting
index expressed the change in the output which the system is capable
of generating each year because of changes in the mix of demand but
assuming that the efficiency with which inputs were used would remain
constant throughout all years.
Potential mix index {X p was computed by fitting a trend through
)
the actual index for the individual years. In both the index of actual
mix (X a) and the index of potential mix (Xp the labor and capital
)
components were combined with changing weights based essentially
on those used by Kendrick. See note 30 above.




POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

55

The GNP categories and the corresponding labor and capital co­
efficients are as follows:
Capital per
dollar of
output

GXP category

Services:
Government gross national product______________________________
Other_______________________________________________________
Net exports _ _______________________________________________
Housing_____________________________ _______ _______________ }
Other consumption_______ ______ ______________ _____________
Construction____________________________________________________
Nondurables:
Consumers__________________________________________________
Government
_ __- _____ _ ______ ___________________
Net exports
_
_________________________________
Change in business inventories _________________________________
Durables:
Consumers__________________________________________________
Government ______________________________________________
Net exDorts _______________________________________________
Change in business inventories ___________ ___________________
Producer __________________________________________________

Labor manhours per
dollar of
output

0
1.3
2.71
4.807 J
1
1.205

0.478
.404
0
.045
.4
.650

1.422
2,317
8.190
1.534

.530

1. 345
1.322
2. 502
1.335
1.02

.476

(37) The coefficients and their standard errors were:
Variable

Coefficient

Standard error

log||

+.9104

.0591

[ logS T

~ 3-39

,58

log k

-5.6411

.7069

[lo g *]*

+10.356

1.358

t

+.00884

.00025

The coefficients of Lp and KjLp were stipulated on the final run as a
result of the preceding tests. However, their coefficients were sta­
tistically significant on those runs where their coefficients came out
close to the final values stipulated on the seventh run.
(38) See Douglas, opere citato, and Solow, opere citato, for dis­
cussion of relation of production function to returns to scale.
(39) See, for example, William Fellner, “Trend and Cycles in
Economic Activity,” Henry Holt & Co., New York, 1956, chapters
8 and 9.
(40) See Professor Douglas’ presidential address, reprinted in the
Kelly reprint of his “Theory of Wages,” note (15) above.
(41) Solow, opere citato, page 319.
(42) Tintner, opere citato, pages 134-138.
(43) See for example, Tintner, opere citato, pages 301, 302.
(44) See hearings, part 2, pages 283-346.
(45) Solow, opere citato.
(46) Bureau of Labor Statistics, Bulletin No. 1249, “Trends in
Output Per Man-Hour in the Private Economy, 1909-58.”




56

POTENTIAL ECONOMIC GROWTH IN THE UNITED STATES

(47) See “Productivity, Prices, and Incomes,” Joint Economic
Committee, opere citato.
(48) U.S. Bureau of the Census, series P-25, No. 187, November
10, 1958, “Illustrative Projections of the Population of the United
States, by Age and Sex, 1960 to 1980.”
(49) U.S. Bureau of Labor Statistics, Bulletin No. 1242, “Popula­
tion and Labor Force Projections for the United States, 1960 to 1975.”
(50) George Terborgh has prepared projections of installations and
gross stocks which are somewhat higher than our assumptions. See
Capital Goods Review, No. 22, May 1955.
(51) See the speech of Ewan Clague, Commissioner of Labor
Statistics, before the Chicago Association of Commerce and Industry,
May 26, 1959, entitled “Productivity—What It Is and How It Is
Measured,” especially page 6 and chart 2.




o