Fundamental Stocks of Knowledge and

Productivity Growth

James D. Adams
Universityof Florida

This paper develops new indicators of accumulated academic sci-

ence and tests their explanatory power on productivity data from
manufacturing industries. Knowledge is found to be a major con-
tributor to productivity growth. Furthermore, a lag in effect of
roughly 20 years is found between the appearance of research in the
academic community and its effect on productivity in the form of
knowledge absorbed by an industry. Academic technology and aca-
demic science filtered through interindustry spillovers exhibit lags of
roughly 10 and 30 years each. Thus implied search and gestation
times far exceed developmental periods in studies of R & D. A clear
implication is that basic research declines relative to development in
the face of an exogenous rise in the real rate of interest.

I. Introduction
Nearly all researchers must wonder from time to time if academic
thought matters to the material progress of the world at large. But
whether the question is sparked by a disappointment with results or,

This paper has benefited from comments by Edwin Dean, Robert Evenson, Zvi
Griliches, Lawrence Kenny, Prakash Loungani, G. S. Maddala, Paul Romer, John
Ruser, Leo Sveikauskas, and Lester Telser and from the detailed remarks of two
referees. I am indebted to seminar participants at the Bureau of Labor Statistics,
National Science Foundation, University of Chicago, University of Florida, and sum-
mer Econometric Society meetings, University of Minnesota. Capable research assis-
tance was received from Brenda Brinton, Wen-He Liu, Amy Schmidt, and Roland
Sturm. This paper was begun under the auspices of the ASA/NSF/BLS Senior Re-
search Fellows Program. It was completed at the Center for the Study of the Economy
and the State, University of Chicago.

Journal of Political Economy, 1990, vol. 98, no. 4]

? 1990 by The University of Chicago. All rights reserved. 0022-3808/90/9804-0001$01.50

673
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 674 JOURNAL OF POLITICAL ECONOMY

more likely, is silenced by a belief in the power of thought over nature

and society, few answers to it have been forthcoming. This paper
begins to answer the question by studying the relationship between
measures of academicscience and multifactor productivity growth.
The question is certainly relevant enough. It is often thought that
application of scientific method is responsible for the burst in eco-
nomic growth since the eighteenth century. And in fact, the ground
swell of science appears to lead the acceleration in growth only slightly
(Kuznets 1959, lecture 2). Empirical study of the role of science in
growth bears directly on this belief.
In addition, the measured inputs at hand omit the very techniques
that organize production. This paper expands the list of inputs to
include indicators of fundamental knowledge, partially addressing
this sin of omission.
Science indicators are also interesting because they address more
than the residual element in growth. It is customary to divide growth
in output into explained and unexplained parts. The first is wholly
attributed to measured inputs. The second or residual part is identi-
fied with technology. But in models in which fundamental knowledge
is acquired at cost by maximizing firms and converted into technol-
ogy, this distinction is misleading. The demand for inputs is usually
increased by knowledge since rising incomes are observed. Thus the
material effects of knowledge extend beyond residual growth. The
argument is more forceful still when applied to recent studies that
account more thoroughly for factor growth since the residual is
smaller in these studies (notably, see Jorgenson, Gollop, and Frau-
meni 1987). Indeed, optimizing models could be devised that include
knowledge-induced growth in factors and give rise to equations of
induced growth differing from growth accounting formulas in the
larger role assigned to knowledge. Given time, I believe that this
approach will provide a truer estimate of the value of knowledge.
I turn next to a review of the literature. Economists have dealt with
the problem of growth accounting since at least the 1950s. Principally
this research has resulted in improved measures of factor quality.
Such measures incorporate, for instance, rising schooling in the case
of labor and increased sophistication of equipment in the case of
capital.1 This line of research has also resulted in measurement of
intermediate goods inputs and their contribution at the sectoral level.
A second important direction of research has extended the produc-
tion function to include deflated R & D expenditures in an attempt to
' Examples of early studies are Abramovitz (1956), Kendrick (1956), and Denison
(1962). The last begins the process of refining labor quality, extended to physical capital
in Gollop and Jorgenson (1980) and Gullickson and Harper (1986). Jorgenson (1986)
discusses some econometric methods for analyzing productivity data.

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 STOCKS OF KNOWLEDGE 675
capture externalities associated with technical change.2 External ef-
fects have been identified, although these are typically small com-
pared with the growth to be explained. While much has been learned
about growth from both styles of research, it has been difficult to
account for the sources of technical change behind growth despite
vast improvements in measurement.
Since I emphasize the role of technology in growth, I shall focus on
the R & D literature. Research and development has not been a large
contributor to productivity growth (Griliches 1980). At the same time,
few studies have linked the phenomenal growth in produced factors
with technology (see Jorgenson et al. [1987] for documentation). I
argue that R & D would explain too little even if it accounted for
productivity but left growth of inputs unexplained. Yet R & D must
certainly fail in the latter role also since the sources of its profitability
would remain unspecified. Something more basic has been left out.
The most plausible hypothesis is that technical change, growth in
R & D, and input growth can all be traced to the expansion of knowl-
edge. However, a knowledge metric that is broadly applicable to the
economy has so far remained outside the current generation of mea-
surements.3
The foregoing provides background for the first premise of this
paper: that theoreticalchange underlies most recent technical change
and growth. The assumption is not innocuous. For points of view
emphasizing instead learning by doing and imitation, see Rosenberg
(1976) and Schmitz (1989). The assumption is tested by introducing
capitalized measures of academic research into growth equations.
The measures build on the diversity and nonmalleability of the sci-
ences. Thus the second premise is capital heterogeneity (Hicks 1965;
Schultz 1971, chap. 2).4 This emphasis is paramount in recent work in
which knowledge diversity limits spillovers (Jaffe 1986).
The method follows key insights in Evenson and Kislev (1975).
Following their lead I utilize article count data in each science as

2 See Terleckyj (1980), Scherer (1982, 1984), and Griliches (1984). Sveikauskas
(1981) augments R & D measures with the scientific labor force but does not pursue the
approach taken here. Lucas (1967) views productivity growth as the result of adoption
of unmeasured technology but does not pursue knowledge as the driving force behind
adoption. Another paper relevant to the point of view of this paper is Nadiri and
Schankerman (1981).
3 To my knowledge, all the studies except the one by Evenson and Kislev (1975) have

dealt with industrial research activity and have not attempted to measure basic science
activity or its linkage with industry growth. But the Evenson and Kislev study is re-
stricted to agriculture.
4Schultz says elegantly of the shift to heterogeneous capital models that "in principle
this step implies, for purposes of economic analysis, that a technique is no more or less
than a unit of capital, that a set of techniques representing a technology is a capital
structure, and that a technical change is an alteration of capital structure" (p. 20).

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 676 JOURNAL OF POLITICAL ECONOMY

measures of knowledge, analogous to the use of patents as measures

of applied innovation.5 But the present work differs in crucial ways
from the earlier. Coverage of science and industry is broadened be-
yond agriculture. More important, data on accumulation of science
are supplemented with data on employment of scientists by field and
industry. The industrial composition of scientists identifies the map-
ping of sciences to industries. Knowledge divides along the lines of
academic science, and scientific employment links specialties to indus-
tries of use. Later this approach infuses content into concepts of own
and borrowed knowledge by industry.
Concerning the remainder of this paper, Section II sets up the an-
alytical framework. It sketches the transition to empirical counter-
parts for the theoretical stocks of knowledge and explains the estima-
tion strategy. Section III describes the data underlying the empirical
counterparts and provides a graphical analysis. Productivity estimates
are presented in Section IV. The productivity data are taken from the
Bureau of Labor Statistics; they are aggregated at the level of two-
digit manufacturing industries for the period 1949-83.6 I find that
knowledge strongly contributes to growth but that lags in effect are
exceptionally long by conventional standards: on the order of 20
years from the appearance of research in the science community to its
peak effect on production. The lag is greater for interindustry spill-
overs at approximately 30 years. However, computer science and en-
gineering reach production in something like 10 years after publica-
tion, as befits their applied nature. Section V concludes the paper and
explores directions for continued research.

II. Growth Accounting from the Perspective of

Knowledge Formation
Following Evenson and Kislev (1975) and Romer (1986), I reformu-
late the production function to include stocks of knowledge among
the inputs. Variations on standard growth accounting formulas then
follow readily. The discussion applies throughout to data aggregated
at the industry level.
A convenient Cobb-Douglas form is postulated for the empirical
work. The production function of the representative firm is
qt = e tztnzKNK mItn, (1)
where -yis the disembodied rate of technical change, and the Aqd (i = z9
K, I) are output elasticities of conventional inputs Zt, of the own stock
of knowledge KNtm, and of the borrowed stock It-n. Here m and n

5Patents and copyrights appear as indicators of innovation in Schmookler (1966),

Peltzman (1973), and Adams (1980).
6
U.S. Department of Labor (1983) provides an overview of the data.

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 STOCKS OF KNOWLEDGE 677
TABLE 1
DEFINITIONS OF SYMBOLS

Symbol Meaning

qt Output of the firm

Zt, KNtm, Itn Inputs of the firm: conventional inputs, total own knowledge, and
spillover knowledge
Total scientists in an industry
Ntm Own stock of knowledge per scientist
gt Productivity growth
'y Rate of disembodied economic growth
-q, ,U 1 Output elasticitiesof conventionalinputs, own knowledge,and
spillover knowledge
k Minimum lag between the creation of knowledge in the science
community and its absorption by industry
m Minimum lag between absorption and application of own knowl-
edge in industry
n Lag between absorption of own knowledge elsewhere and its ap-
plication to an industry
(e) t Share of field j in an industry's total scientific work force
cos 611 Correlation between scientific work forces in industries i and j;
cosine of the angle between their scientific work forces
NOTE.-Parameters are nonnegative throughout the table.

are lags between absorption and application; n plausibly exceeds m

since, in the case of 'tn, knowledge must be borrowed as well as
absorbed and applied. Table 1 is a comprehensive glossary of sym-
bols.
Equation (1) is increasing but strictly concave in its Zt and KNtm
arguments, requiring that O < -z < 1, 0 < rIK< 1, and O < -z + IK <
hold.7 Combined with setup costs, these assumptions yield optimally
sized firms. Social increasing returns to scale and a rising social mar-
ginal product of knowledge are possible once changes in the spillover
It-n are factored into (1), as in Romer (1986).8

A. The SubstantiveContent of Empirical

Knowledge Stocks
The industry stock of knowledge KNt-m is acquired through the allo-
cation of scientific personnel to learning about advances in science, so
qt is a nested production process and a function representing KNt-m
must be selected. The following discussion of the own stock of knowl-
edge in an industry is pivotal to the rest of the paper.

7 In terms of (1), a X percent increase in z and I would raise q by XAIK+hz percent. For
there to be decreasing returns, it is necessary that TJK + qz < 1
8 Inclusive of a X percent increase in I and in all other factors,
output increases by
+ 'z + 1I
?11K percent. The function exhibits increasing returns if the exponent including TI,
exceeds one.

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 678 JOURNAL OF POLITICAL ECONOMY

In a world of abundant data, the own stock would satisfy at least five
properties. First, it would be fundamental. It would depend on infor-
mation stocks or learning "pools" consisting of findings from basic
research. Second, the own stock would recognize heterogeneityof infor-
mation. To an important degree, I have satisfied these properties in
the measures reported below. Third, the industry stock of knowledge
would exhibit repetitiveuse of science. Firms draw repeatedly from the
information pools, implying that the entire stock affects growth, not
just the newly created flow. Even ancient innovations remain useful in
learning new things provided that they are important. They are use-
ful in 1990, if not in the same way they were useful in 1790 or 1890.
Here too the hypothetical property has been met with the actual
measures. Fourth, the knowledge stock would be interactive.It would
build on a distributed lag of scientific labor employed by industry
interacted with stocks of information. The technical work force tests
and applies scientific results at some cost. Diminishing returns at a
point in time suggest that research labor is spread over time and is
durable, yielding a stream of future services. The advantage of estab-
lished R & D firms over new entrants stems from this fact. Although
the stock of knowledge is an interaction between information stocks
and the industrial scientific work force, it has proved impossible to
satisfy interactivity given the available data on scientists. Following
changes in the census, these data begin in 1950. The employment
series are too short, especially in view of the comparably brief produc-
tivity data. As a result I simply use scientific employment to weight the
significance of sciences to industries. The fifth desirable feature is time
specificityof parameters of the industry stock. Variability in obsoles-
cence with the flow of new scientific results is the chief consideration
here. I nevertheless use constant rates of obsolescence in the
definitions because of evident complications in tracking obsolescence
over time.
Given these difficulties, the definitions below build on heterogene-
ous stocks of basic science discounted at constant rates of obsoles-
cence, weighted by the distribution of industrial scientists. But in
more favorable circumstances the specification would be different,
more like an interactive capital stock involving the human capital of
scientists and the information capital of academic science. This in-
teractive capital stock is subject to changing and perhaps accelerating
obsolescence.

B. Choice of Formulasfor the Empirical

Knowledge Stocks
Consider next the form of the industry knowledge stock. Difficulties
surrounding this choice are aptly illustrated by the following non-
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 STOCKS OF KNOWLEDGE 679
linear specification:
T F

KNt-m = >1(1 - 8)Z _l

Ojt m_ N~~kp (2)
z=rm j=1

Arguments of the function are the weights E>; scientific labor in field
j at time t - m, itrmj; and the stock of information in field at times
t - k - i, Nt-k-,, which receives repeated use for reasons given
above. Here m is the minimum lag between absorption and applica-
tion of knowledge. The weights 0, are industry-specific and capture
the importance of learning from a particular pool of knowledge. The
exponents 'ql and -qN are also industry-specific. These govern the
relative importance of the scientific labor force and the knowledge
pool in learning, the decline in the learning marginal product of each
of the two, and the extent of diminishing returns to learning.
Equation (2) has interesting properties but also many problems. On
the positive side, it accommodates diverse forms of knowledge rather
well because of additivity in the different forms. This dominates a
purely multiplicative form, forcing all knowledge acquired to be zero
when any element is zero. Nevertheless, (2) is problematic for an
exploratory analysis because of its nonlinear form. I therefore pro-
pose a linear form building on differences in knowledge use:
T F

KNt-m = >I it-mrNt-k-iij (3)

i=mj=1

As in (2), m is the minimum lag in application. As in (2), the stocks of

information are repeatedly accessed, as is shown by the sum over i.
Equation (3) is the total own stock of knowledge in an industry
underlying the empirical work. Essentially (3) is an index number
with stocks of scientific information as elements and numbers of in-
dustrial scientists as weights. Note that scientists in field j measure
influence in the index number interpretation
I take as exogenous the relative weight assigned by (3) to the jth
field of science. By the relative weight I mean the share of scientists
employed in field j by the industry. Thus the relative weight is (Atj =
It-,j'ilt- m where It_ and It_, are field j and total scientific employ-
ment in the industry. Divide (3) by itrn, obtaining
T F

Nt-m = E I ,
tjNt-k-iyj (4)
i=m j=1

Equation (4) is the own stock of industry knowledge per scientist.

Granted exogeneity of the wtj weights, (4) is exogenous, while the total
stock (3) is endogenous, since the science work force itrn is partly
endogenous and by definition KNt- m equals it-Ntr-m. The distinction
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 68o JOURNAL OF POLITICAL ECONOMY

matters to causal interpretations of the empirical work. Regressions

based on (4) report science effects only, while those based on (3)
report effects partly of the science work force. However, (3) should
not be devalued since the science work force has an exogenous com-
ponent of its own and is the only available measure on the overall
science intensity of industries.
Additional aspects of the definitions deserve comment. Two lags
appear. Firms need m periods to apply "useful" science to production,
but before application can begin, at least k periods are required by the
search for useful science, where, presumably, k > m. A minimum of
m + k periods pass before production is affected.9 Minimum lags are
treated as given here, despite their dependence in theory on the
intensity of R & D contests and information transfers. Also, (3) and
(4) have industries sampling from information stocks in different
proportions. Each implies that acquiredknowledge is a rented service
rather than capital owned by firms. I have explained how the short
series on scientists force this outcome.
Spillover knowledge stocks between industries are obtained
straightforwardly from (3) using Jaffe's (1986) method. His approach
assumes that R & D activities are weighted in proportion to their
technological closeness. Weights are cosines between technology vec-
tors of aggregates. Aggregates are industries, and technology vectors
are employments in science fields. The definition is then
N

,it-n = c OijtKNjt-m-n (5)

je~i,j='1
where cos Eijt is
F

> lzktljkt
k= 1
cos 0t, = F F 1(6)

[k= 1 )(k=1 )]

the cosine of the angle between the science employment vectors for
industries i and J. The term cos Oqt measures similarity of technology
in i andj. As science work forces become more similar, (6) approaches
one from below; as they diverge, (6) approaches zero from above.
The spillover between industries is a weighted sum of total own
knowledge stocks in all other industries. This is appropriate if the
scale of learning elsewhere governs the amount that the industry
learns. Both external scale and similarity of technical work forces then
govern the size of the spillover.

9 In practice I search for the combined lag k + m on scientific papers in the empirical
work below.

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 STOCKS OF KNOWLEDGE 68i
C. Functional Form of Knowledge in Productivity
GrowthRegressions
Growth accounting equations inclusive of academic science can now
be written in familiar form. Taking logs of (1), first differencing, and
using the notation D In Xt = In Xt I - In Xt- AXt/Xtyield
D In qt - y + -zD In zt + nKD In KNt-m+ 9ID In It_ no (7)
where KNtm and It-n follow (3) and (5), respectively. Total factor
productivity growth, defined in the Divisia sense of a percentage first
difference, follows immediately by subtracting the second term on the
right from both sides of the output growth identity (7):

gt yy + -qKD In KNtm + rj1DIn It-n. (8)

Expression (8) is not yet in desired form for the pooled time-series/
cross-section data of this paper. The log differentials of knowledge
are misspecified in this context (Griliches 1979, 1986). Output elas-
ticities of capital stocks are forced to be equal across industries, caus-
ing rates of return to be different. Yet rates of return should be equal
in capital market equilibrium. Coefficients of (8) can be made propor-
tional to rates of return. For the first term,

In Kt-m
KN = (_________
ln
QPKDKNt-m
DlIn Q
'qKD KNt~m- (9)
a ln KNtm Qt
where DKNt_m is the difference of (3), and PK is the rate of return.
The term DKNtm is approximately
F

DKNt_m-i, t+1-mjNt+1-m-k1 (I10)

if changes in the science work force are treated as small.'0 Then the
far right of (9) is the correct specification of the own knowledge term.

10 In terms of (3),
F F

D InKNt m-In KNt+ I m- InKNt m-,(In it +ImNt,) - Inl(Zlmi Ntii)

E(I 1Nt+ 1-k-mj + Alt-mjNt-1j)

F

it-mjlNtj

where Nt 1j _2S=m Ntk- ,I If Alt-r1llt-

-
0, as is reasonable for the data on scien-
tists, then the second term on the right of D in KNt-m is approximately zero and (10)
holds.

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 682 JOURNAL OF POLITICAL ECONOMY

The same exercise applied to the second term of (8) yields

q1D In It,-( aIn Qt I- PIDIt (11)
aIn~~t-nI) Qt
and
N

DIit- - X cos EZijtDKN~t-n. (12)

joz,j= 1
Substitution of (9)-(12) in (8) yields the regressions that are esti-
mated. Ratios of DKNt -m and DIt-n to output Qt are called own and
spillover intensities because they are input-output ratios. Since knowl-
edge is not in constant dollar units, coefficients of (9) and (11) are
proportional rather than equal to rates of return. In the regressions, I
search over k lags of 0-40 years for DKNt m and DIt-n, over m lags of
0-5 years for DKNt-m, over n lags of 0-10 years for DIt-n, and over
obsolescence rates of 1-25 percent for DKNt-m and DIt-n

III. New Data on the Accumulation of Academic

Science and Its Application to Industry
This section describes and graphs data sources for the own and spill-
over stocks, emphasizing steps leading to the differenced total own
stock (10). The spillover (12) follows directly. I begin with construc-
tion of the article count stocks Njt entering (10) and (12). Table 2 lists
major journals that provide time series of scientific papers. The re-
sulting series are worldwide annual counts of publications in nine
sciences: agriculture, biology, chemistry, computer science, engineer-
ing, geology, mathematics and statistics, medicine, and physics. The
breadth of coverage loses track of detailed differences within the
sciences. For example, engineering covers specialties emphasizing dis-
tinct applications. But one cannot separately weight articles by en-
gineering specialty in (10): employment data by industry and specialty
serving as the 1j,weights do not exist. The eight other fields are like-
wise predicated on data availability. Processing of the count data is
described in an appendix available on request.
I accumulate stocks of scientific papers Njt from the annual flows at
various obsolescence rates. To give an idea of the count data before
weighting according to definitions (10) and (12), figure 1 charts mean
stocks and flows of scientific papers over the period 1911-80. Flows
are unweighted averages of annual counts across the nine fields listed
above. Stocks are unweighted averages of article stocks accumulated
at best-fitting obsolescence rates of 13 percent."
' In terms of the notation of Sec. II, the unweighted mean flows are ii =
(2%=1 n!_)IF; the unweighted mean stocks are Nt = ()I, N,1)IF, where stocks are
defined using 8 = 0. 13.

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 STOCKS OF KNOWLEDGE 683
TABLE 2
BIBLIOGRAPHIC SOURCES OF THE ARTICLE COUNT DATA

Field of Science Time Period Source Index

Agriculture 1930-83 Series is the sum of article counts derived from
10 British abstracting journals:
Review of Applied Entomology
Plant Breeding Abstracts
Herbiage Abstracts
HelminthologicalAbstracts
Animal Breeding Abstracts
Nutrition Abstracts
Review of Applied Mycology
ForestryAbstracts
Horticultural Abstracts
Soils and Fertilizers
Biology 1918-26 Series is the sum of article counts taken from
two American journals:
Abstractsof Bacteriology
Botanical Abstracts
1927-83 Biological Abstracts
Chemistry* 1907-83 ChemicalAbstracts
Computer 1957-65 Science Abstracts(secs. 27-30)
science 1966-68 ControlAbstracts
1969-83* Computerand ControlAbstracts
Engineering, 1928-83 Engineering Index
combined*
Geology 1933-83 GeoRef
Mathematics 1868-1942 Jahrbuch uber die Fortschritteder Mathematik
and statistics (Berlin)
1943-83 MathematicalReviews
Medicine 1879-98 Index Medicus, 1st ser.
(1899) (interpolated)
1900-1902 BibliographiaMedica (Paris)
1903-20 Index Medicus, 2d ser.
1921-26 Index Medicus, 3d ser.
1927-40 QuarterlyCumulativeIndex Medicus
1941-50 CurrentList of Medical Literature
1951-83* Index Medicus, 4th ser.
Physics* 1896-1983 Physics Abstracts

NOTE.-Annual counts are estimates obtained by random sampling, except when marked by an asterisk.
*Indicates exact counts supplied by the index or abstracting journal over the time period.

Both world wars reduce flows of scientific activity. The decrease is

more acute during World War I, agreeing closely with the greater
weight of European science during this period. Scientific papers do
not recover their prewar peak for a decade in either war.
Figure 1 clearly shows that the decline in flows interrupts the in-
crease in stocks. Since stocks enter production with a lag of 20-30
years according to regression findings to be presented later, the slow-
down in science due to World War II may have a bearing on the
productivity malaise of the late 1960s to late 1970s.
Next consider collection of the employment weights 1,. The system
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 684 JOURNAL OF POLITICAL ECONOMY

000 0000
Ld ~~~~~~~~~~~~~~00000
C 000000000 0000000000

0000 +4+0~~0000
o?? +
4! + 4
V) o00ooo00o0 t000 +*+

z0 0 +
+ ++4+++

cn 4 + + ST+++OC+

0
++4~~~~~~~~~~ + 0 0 0 0 ?0STOCM'
(..) FLOW

1908 1923 1938 1952 1967 1982

YEAR
FIG. 1.-Stocks and flows of scientific papers, in hundred thousands, 1911-80.
Yearly averages across nine fields of science. Obsolescence rate is 13 percent.

of weights is the industrial distribution of scientists by field and indus-

try. After extensive processing, data were obtained for most two-digit
manufacturing industries and other major sectors outside manufac-
turing during the period 1950-85.12 Collection procedures are de-
scribed in another appendix available on request.
Figure 2 graphs unweighted averages of scientific employment by
manufacturing industry. Employment growth in the immediate post-
war era is extremely rapid, but a noticeable downturn begins in 1970
and continues through the late 1970s. Figure 1 offers an interpreta-
tion. The slowdown in science during World War II may have left
industry with temporarily less to learn a quarter century later.
Acquisition of elements of the differenced own and spillover stocks
of knowledge has been described, so I turn to the resulting variables.
Table 3 is a guided tour of the knowledge first differences in their
realized form. A point to remember is that own knowledge is limited
to 18 manufacturing industries by the productivity data, while the
spillover includes nine other sectors, such as governments and univer-

12 Scientific employment data for 1950-70 are available from the U.S. Department of

Labor (1973). Data for 1971-85 were derived from U.S. Scientistsand Engineers (various
issues), from the National Science Foundation (1981), and from unpublished NSF
sources. I thank Michael Crowley and Keith Wilkinson of the NSF for advice and access
to the data on scientists.

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 C
-

Lg
11J + + + + + + + + ~++
+ 4+ + + + + 4
L + + +
+
O a + +

zu +
lJ .+

z 4.

z0

V)

Z SCIENTISTS AND ENGINEERS

/.++++++
SCIENTISTS

1949 1955 1961 1967 1972 1978 1984

YEAR
FIG.2.-Scientists and engineers in thousands, 1953-83. Yearly averages across 18
manufacturing industries. Source: 1950-70, U.S. Department of Labor (1973); 1971-
83, unpublished NSF data.

TABLE 3
DEFINITIONS OF KNOWLEDGE FIRST DIFFERENCES

Concept Formula Preferred Lags Industry Coverage

Total own See eq. (10) 1 year on scientist 18 two-digit industries

knowledge in text weights; 20 years in manufacturing*
on scientific papers
Own knowledge Eq. (10) with 1 year on scientist 18 two-digit industries
per scientist scientists share weights; 20 in manufacturing*
replaced years on scientific
by shares papers
Spillover See eq. (12) 1 year on scientist 18 two-digit industries
knowledge in text weights; 30 years in manufacturing,*
on scientific papers nine sectors outside
manufacturingt

NOTE.-Knowledge first differences are (10) and (12) of the text. These are numerators of the knowledge
intensities.Preferred lags are lags observed as best fitting in the regressions;note the short lags on scientific
employmentweightsand the long lags on scientificpapers.Weightsare the numberof scientistsin an industryin
eachof the followingnine fields:agriculture,biology,chemistry,computerscience,engineering,geology,mathemat-
ics and statistics,medicine,and physics.Scientificpapersare similarlyclassified,as in table2.
The 18 manufacturingindustriesare food and kindredproducts;textiles;apparel;lumber;furniture;paper;
printing;chemicals;pertroleum;rubber and plastics;stone, clay, and glass; primarymetals;fabricatedmetals;
machinery,except electrical;electricalequipment;transportationequipment;instruments;and miscellaneous.
The sharesare proportionsof scientistsin any one field relativeto total scientificemploymentin an industry.
The nine sectorsoutside manufacturingare mining,construction,transportation,communications,publicutil-
ities, financeand services,federalgovernment,stateand localgovernment,and collegesand universities.Note that
coverageof own knowledgeis limitedby the regressionsampleand is less than coverageof the spillover.

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 686 JOURNAL OF POLITICAL ECONOMY

tn

Or)

0n 0

Lii 0 0 0 0 ~~~~~~~
0 000 00

ULr)i 0

J (0
o 0

Lft n

LI) 0

1952 1958 1964 1970 1976 1982

YEAR
FIG. 3.-Own stock of knowledge, 1953-80. Yearly averages across 18 manufactur-
ing industries. Source: See text and eq. (3).

sities. These sectors are large employers of scientists, and their activi-
ties rightly spill over into manufacturing. Another point is the prefer-
ence shown by the data for nearly current science employment
weights, but for long lags on the count stocks. The lag on scientists
agrees with evidence on developmental lags (U.S. Department of
Labor 1989), but little is known about gestation lags associated with
research, perhaps picked up by the longer lags on the count data.
The differenced own stock (10) in an average industry is shown in
figure 3. Unlike figure 1, which records the unweighted, average,
contemporaneousstock of scientific papers, figure 3 graphs article stocks
lagged 20 years, weighted by the contemporaneousnumber of scientists in
an industry and averaged across industries. After rising steeply dur-
ing the formative period, the own stock declines from the late 1960s
to the late 1970s. The decline is due to a fall in scientists and to a
decline in knowledge per scientist. Again, it is possible that the two
sources of decline are connected. Growth of own knowledge resumes
in the late 1970s. Figure 4 confirms this U-shaped pattern of growth
and decline by calculating the average percentage change across in-
dustries.
Figure 5 graphs the knowledge intensities entering the reported
regressions. Again these are ratios to real output of differenced own
and spillover knowledge as directed by (9) and (1 1). Lags on the own

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 LLJ

0?
O N
z o

y o
z
0

L 0

FIG. 4.-Percentage growth in the own stock of knowledge, 1953-80. Yearly aver-
ages across 18 manufacturing industries.

0-

(,1A

(Y ,??????000000 SPILLOVER INTENSITY

wO ++++++ OWN KNOWLEDGE INTENSITY

51 + + + +4 + + + + *

+ +4
z 4 ++

1950 1956 1962 1968 1973 1979 1985

YEAR
FIG. 5.-Own knowledge and spillover knowledge intensities, 1953-80. Yearly aver-
ages across 18 manufacturing industries. Definitions are given by eqq. (10) and (12),
respectively, divided by real output in each industry.

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 688 JOURNAL OF POLITICAL ECONOMY

u-)
oQ

a\
0~

z
z
3:-o
zo
0

0
n 1950 1956 1962 1%68 1973 1979 1985
YEAR
FIG. 6.-Own knowledge intensity per scientist and engineer, 1953-83. Yearly aver-
ages across 18 manufacturing industries.

and spillover stocks forming the numerators of the intensities are,

respectively, 20 and 30 years, since these were best fitting. The decline
in knowledge absorbed during the middle period is by now familiar.
Again the intensities turn up at the close, reflecting upturns in
scientific employment and in knowledge produced. To show that an
upturn in the article stocks matters, figure 6 charts own knowledge
intensity per scientist. This is (10) divided by total scientific employ-
ment Itin an industry. The intensity per scientist remains markedly U-
shaped. This concludes the graphical presentation.
The calculated knowledge measures have a number of strengths
but also weaknesses, as one should expect given the novelty of the
investigation. The scientific employment data are riddled with re-
spondent errors in the original surveys. The data are collected at 3-
year intervals, and collection ceased entirely during 1971-76. It is
fortunate that industrial scientific employment exhibits high serial
correlation even over a decade (Blank and Stigler 1957).
The knowledge definitions are most flawed in that they lack any
measure of impact other than scientific employment. The difficulty is
telling in comparisons between science fields. Is a medical article of
equal value to a chemical article? The employment weights answer no
because there are many more chemists than doctors in industry. How-
ever, the answer is inadequate because articles in different sciences

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 STOCKS OF KNOWLEDGE 689
are equally weighted when employments are the same. One answer is
to use citations, but these are limited at present.'3
Despite the reservations, these measures are the first to link aca-
demic science with economywide growth. In their favor, data on
worldwide scientific papers are superior to R & D expenditures in
some ways apart from their focus on basic research. They are largely
independent of particular industries, which contribute little to the
thrust of worldwide science. Also the article count data cover a longer
period, inviting flexibility in tests of lags in effect.
I close with comments on the productivity data. These are perme-
ated by errors in the underlying producer prices from the Bureau of
Labor Statistics, biasing the effects of research downward (Griliches
1979). Product quality in high-technology industries rises faster than
elsewhere, but improvements are swept up by prices. Producer prices
also incorrectly weight value added and are based on book rather
than transactions prices. All these problems are unavoidable. In addi-
tion, productivity declines with factor utilization, exhibiting a procy-
clicality not addressed by growth theory (Griliches and Lichtenberg
1984; Berndt and Fuss 1986; Morrison 1986). The very partial solu-
tion adopted here takes 5-year moving averages of productivity.

IV. Empirical Findings

Table 4 reports descriptive statistics for the data. Knowledge inten-
sities are evaluated at the 13 percent rate of obsolescence observed to
be best fitting in the regressions. Mean productivity growth is 0.8
percent over the full period.'4 Breaking time up into two periods
reveals the slowdown: productivity growth declines from 1.1 percent
before 1966 to 0.5 percent afterward. Productivity growth rates differ
widely by industry, as is shown by the standard deviation and ex-
tremes.
Now turn to the own knowledge intensities. Combined (lag = 20) is
(10) divided by real output, under the assumption of a 20-year lag on
scientific papers and a 1-year lag on scientists. Science only (lag = 20)
omits engineering counts and engineers. The mean intensity of com-
bined is five times that of science only, reflecting the dominance of
engineering employment. Own knowledge intensities vary greatly
across industries, but the science only intensity varies more since the
value of marginal product varies less for engineers than for scientists.
Combined per scientist is combined divided by total scientists and
13 Patent citation data fail to cite upstream basic science, while the Science Citation

Index dates only from 1972.

'4 The full period is 1953-80, given the 5-year moving averages of productivity
growth and the first differencing of the observations.

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 69o JOURNAL OF POLITICAL ECONOMY

TABLE 4
DESCRIPTIVE STATISTICS, 1953-80

Standard
Variable and Time Period Mean Deviation Minimum Maximum
Total factor productivity
growth:*
1953-80: .008 .012 - .034 .052
1953-66 .011 .012 - .032 .052
1966-73 .008 .010 - .019 .043
1973-80 .003 .013 - .033 .039
Own knowledge intensity,
1953_80:.
Combined (lag = 20) 352.4 347.6 22.6 1,648.8
Science only (lag = 20) 69.2 114.7 2.6 720.1
Combined per
scientist (lag = 20) 14.5 11.1 3.1 54.4
Spillover knowledge
intensity, 1953-80:*
Science only (lag = 30) 2,462.4 1,749.1 219.5 8,149.6
NOTE.-Sample consists of data on the 18 two-digit manufacturing industries listed in table 3. The number of
observations is 504.
* Variable is 5-year moving average of the Tornquist index of productivity growth. This is the log first difference
of real output minus the share-weighted average of log first differences of real input. Source: Bureau of Labor
Statistics, unpublished data.
t Own knowledge intensity is the stock defined according to (10) but divided by real output lagged one period.
Combined includes both science and engineering, while combined per scientist divides by the total number of
scientists and engineers. Source: See tables 2 and 3 and the accompanying text.
t Spillover intensity is the stock defined by (12), divided by real output lagged one period. Source: See tables 2 and
3 and the text.

engineers. Replacement of employment weights by employment

shares results in a much smaller mean per scientist intensity. The per
scientist intensity also differs less between industries. Much of the
variation in combined is in employment, indicating a differing value
of knowledge among industries. The lack of variation is a severe
disadvantage of the per scientist definition.
Table 4 concludes with the spillover intensity. A 30-year lag on
scientific papers is assumed. The spillover omits engineering because
of shortcomings in the cosine weights. Categories of science employ-
ment are highly aggregated in the data, and the cosine weights are
therefore less sensitive to differences in employment. This is espe-
cially true given the predominance of the highly aggregated en-
gineering category. I therefore drop engineering from the spillover,
improving measurement by increasing sensitivity of the cosine
weights to differences in scientific employment among the industries.
A comparison of own and spillover intensities shows that the latter
intensity is 35 times larger. Sectors employing large numbers of scien-
tists are omitted from the own intensity statistics because productivity
data are missing, yet they are retained intentionally in the spillover
(see table 3). These sectors employ over half of all scientific personnel.
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 STOCKS OF KNOWLEDGE 691
TABLE 5
SIMPLE CORRELATION COEFFICIENTS, PRODUCTIVITY GROWTH,
AND KNOWLEDGE INTENSITIES, 1953-80

Total Factor
Own Combined Spillover Own Science Productivity
Variable Intensity Intensity Intensity Growth
Own combined
intensity 1.00 -.13 .46 .26
Spillover
intensity 1.00 -.12 .09
Own science
intensity 1.00 .16
Total factor
productivity
growth 1.00
NOTE.-See table 3 and the text for definitions of variables. Lags are the preferred lags of table 3: own knowledge
embodies a lag of 20 years on scientific papers and a lag of 1 year on scientific employment weights; spillover
knowledge embodies a lag of 30 years on scientific papers and a lag of 1 year on scientific employment.

Table 5 displays correlations among knowledge intensities and pro-

ductivity growth. Own combined and science only intensities are posi-
tively correlated since they are partly the same variable. The spillover
is negatively correlated with own intensity. This sign is not surpris-
ing, if one assumes a division of industries between innovators and
free riders. All intensities are positively associated with productivity
growth.
Table 6-9 report growth accounting regressions. Estimates are (8)
in knowledge intensity form along the lines of (9)-(12).15 In interpret-
ing the results, note that the effect of own knowledge intensity is an
intraindustryspillover since research inputs earn the private marginal
product, and this contribution has already been deducted from out-
put in arriving at productivity. The spillover intensity is the interindus-
try spillover in view of this.
Table 6 summarizes distributed lag regressions in which the stocks
of scientific papers are broken into 5-year differences extending half
a century back in time. Own knowledge appears to have a positive
effect on balance, the spillover a negative effect. One reason for this
pattern is that spillover benefits are received much later, whereas the
distributed lag pattern places heavy weight on costly current learning
about spillovers. In any case, the large number of coefficients and the
accompanying collinearity make any interpretation hazardous.

15 Note that the knowledge intensities are free of spurious correlation with produc-
tivity growth, as long as errors in variables are not serially correlated. The reason is that
the 5-year moving average of productivity includes errors only from periods t + 2 and
t - 2, whereas the regressors include errors only from periods t and t - 1.

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 692 JOURNAL OF POLITICAL ECONOMY

TABLE 6
PRODUCTIVITY GROWTH ACCOUNTING EQUATIONS, 1953-80:
DISTRIBUTED LAG REGRESSIONS

EQUATION

VARIABLE OR STATISTIC (1) (2)

Constant .0051 -.0222

(4.4) (-2.4)
Sum of O'son own knowledge intensity increments* .020 .015
Sum of O's on spillover intensity increments -.028 -.027
Own industry scientists ... 3. 1E-5
(1.0)
University scientists ... - 26.2E-5
(-2.7)
Other scientists ... 5.6E-5
(2.8)
Adjusted R2 .259 .269
F 9.8 9.1

NOTE.-For definitions of own and spillover knowledge intensities, see Sec. II and table 3. t-statistics are in
parentheses.
* These are 5-year differences of own knowledge intensities lagged up to 45 years.
t These are 5-year differences of spillover knowledge intensities lagged up to 45 years.

Hereafter only stock effects of knowledge are reported. Table 7

applies identical lags to own and spillover intensities as well as their
component sciences. Scientific employment weights remain contem-
poraneous throughout the paper. Variations in lags apply only to the
accumulated scientific papers that constitute part of the knowledge
intensities. The fact that lags matter below proves that the count data
are an important contributor to imputed effects.
Equations 1-3 in table 7 omit industry dummies and include in-
terindustry productivity effects. The contribution of own knowledge
increases as lags rise to 20 years. The spillover effect rises even more
rapidly, yet it is positive only in equation 3. This suggests a longer lag
between creation and application for spillovers than own knowledge,
an issue explored below.
Equations 4-6 in table 7, which include industry dummies, present
an interesting contrast with equations 1-3. Clearly lags are more im-
portant than before: at first coefficients are smaller than those in 1-3,
but a reversal occurs at a lag of 20 years. Note that effects of knowl-
edge on interindustry productivity differences are omitted from 4-6.
Thus the findings imply that between-industry effects of knowledge
depend less on lags in effect of science, but more on long-run differ-
ences in industrial scientists. The results underscore the role of the
science work force in measuring the cross-sectional impact of science.
Note that the spillover lowers productivity at a lag of 0 or 10 years.

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 STOCKS OF KNOWLEDGE 693
TABLE 7
PRODUCTIVITY GROWTH ACCOUNTING EQUATIONS, 1953-80:
COMBINED AND SPILLOVER INTENSITY SPECIFICATIONS

EQUATION
VARIABLE OR
STATISTIC (1) (2) (3) (4) (5) (6)

Constant .0065 .0062 .0027 .0062 .0060 .0040

(5.7) (5.0) (2.2) (3.0) (2.9) (1.9)
Combined own
knowledge
intensity:
Lag = 0 .34E-5 .20E-5
(4.0) (.7)
Lag = 10 .64E-5 1.30E-5
(4.5) (2.3)
Lag = 20 1.01 E-5 2.04E-5
(6.4) (5.1)
Spillover
knowledge
intensity:
Lag = 0 -.75E-7 -2.88E-7
(-.9) (-2.2)
Lag = 10 - 1.59E-7 -9.79E-7
(-1.0) (-3.8)
Lag = 20 5.36E-7 10.02E-7
(2.1) (1.6)
Industry
dummies No No No Yes Yes Yes
Adjusted R2 .030 .042 .074 .237 .256 .283
F 8.8 12.0 21.2 9.2 10.1 11.4

NOTE -The omitted category among the industry dummies is food and kindred products The number of
observations is 504. t-statistics are in parentheses.

This probably reflects the costs of knowledge acquisition. Acquisition

could lower productivity in the short run, along the lines of the ad-
justment cost hypothesis. The negative coefficients of table 7 may be
capturing this phenomenon.
The constant term estimates disembodied growth according to (8).
As lags in effect of science rise to 20 years, the constant declines until
in equation 3 it is just a third (.0027/.0080) of sample mean productiv-
ity growth. The difference in intercepts is significant at the 1 percent
level. In this sense the knowledge intensities explain most of disem-
bodied growth. Finally, adjusted R2's seem low in 1-3. But productiv-
ity growth is the first difference of a very noisy time series. Given the
amount of noise in the data, the R2's are not low.
Table 8 reports specification experiments. Equations 1 and 2 are
variations on equation 3 in table 7 with respect to the spillover lag.
Clearly a 30-year lag fits best, suggesting an even longer lag on spill-
overs than on own knowledge. Equations 3 and 4 of table 8 repeat the

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 694 JOURNAL OF POLITICAL ECONOMY

TABLE 8
PRODUCTIVITY GROWTH ACCOUNTING EQUATIONS, 1953-80: EXPERIMENTS WITH LAGS
AND THE SPECIFICATION OF KNOWLEDGE

EQUATION
VARIABLE OR
STATISTIC (1) (2) (3) (4) (5) (6)

Constant .0052 .0021 .0055 .0039 .0070 .0014

(4.3) (1.9) (2.7) (2.0) (3.3) (.7)
Total own
knowledge
intensity:
Combined .9E-5 1.OE-5 2.1 E-5 2.OE-5
(lag = 20) (5.9) (6.6) (5.3) (5.0)
Science only:
Lag = 10 - 6.3E-5
(-4.9)
Lag = 20 12.3E-5
(7.3)
Spillover
knowledge
intensity:
Lag = 10 - .8E-7 -6.5E-7
(-.6) (-2.6)
Lag = 20 23.3E-7
(3.8)
Lag = 30 15.6E-7 16.1 E-7
(3.2) (3.4)
Industry
dummies No No Yes Yes Yes Yes
Adjusted R2 .067 .084 .289 .294 .281 .330
F 19.0 24.0 11.8 12.0 10.2 14.1
NOTE -Obsolescence rate is 13 percent throughout the table. See Sec. II and table 3 for the knowledge intensity
concepts. t-statistics are in parentheses.

procedure on equation 6 of table 7, with the same results. Note that

the estimate of disembodied growth falls further, to one-fourth of the
sample mean (.0021/.0080) in equation 2.
Science only replaces combined in equations 5 and 6. Now the
effect of own knowledge is negative at a lag of 10, whereas the effect is
positive when engineering is included (compare eq. 5 of table 8 with
eq. 5 of table 7). Relative magnitudes are reversed when the lag is
increased to 20 years. Science only enters more positively than com-
bined (compare eq. 6 of table 8 with eq. 6 of table 7). Consistent with
the more applied character of engineering studies, the findings sug-
gest that engineering lags are 0-10 years, compared with science lags
of about 20 years. If these lags were to be upheld in future studies,
they would imply strongly that exogenous increases in real rates of
interest would lead firms to substitute away from basic research in
favor of remaining investments, including short-term developmental
research.
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 STOCKS OF KNOWLEDGE 695
TABLE 9
TESTS OF THE LAG STRUCTURE OF KNOWLEDGE

F-STATISTIC
NULL ALTERNATIVE
HYPOTHESIS: HO HYPOTHESIS: H1 HOvs. H1 H1 vs. HO
Computer science Computer science 14.29 35.13
lag = 20 on own lag = 0
knowledge, lag =
30 on spillover
knowledge
Engineering lag = 10, Engineering lag = 0, 1.76 9.55
computer science computer science
lag = 0 lag = 0
Engineering lag = 20, Engineering lag = 10, 3.09 7.98
computer science computer science
lag= 0 lag= 0
Engineering lag = 20, Engineering lag = 0, .85 13.79
computer science computer science
lag= 0 lag= 0

NOTE.-Numerator and denominator degrees of freedom are 2 and 499 for the first test, and 1 and 500
thereafter. Note that F0 o5(2, oo) = 3.00 and F0 05(1, 0) = 3.84. Unless otherwise specified in the table, lags
on all fields are 20 years for own knowledge and 30 years for the spillover.

The hypothesis that technology has a shorter lag in effect than

science is formally tested in table 9 using the notion of the mean
encompassing test (Mizon and Richard 1986). The table reports F-
statistics for the incremental contribution of variables suggested
under the alternative hypothesis. For example, the special hypothesis
that the lag in effect on computer science is 0 rather than 20 years is
tested by seeing whether knowledge intensities involving a lag of 0
significantly increase the explained sum of squares over regressions
based only on variables with a lag of 20. The converse, that the com-
puter science lag is 20 rather than 0, is tested by seeing whether
variables based on a lag of 20 increase the explained sum of squares
over variables based on a lag of 0. If only one F-statistic is significant,
then one of the hypotheses is rejected. However, in the case just
mentioned, both alternatives receive support in the first row, and the
test is inconclusive. This suggests that the lag on computer science lies
between 0 and 20 years.
The remainder of the table tests lags on engineering conditioned
on a computer science lag of 0. The second row tests whether the lag
on engineering is 0 or 10 years; a lag of 0 is decisively rejected. Row 3
tests whether the lag is 0 or 20 years; again a lag of 0 is rejected. Row 4
tests whether the lag is 10 or 20 years. Now both hypotheses receive
support, implying a lag between 10 and 20 years. These findings
suggest that the lag in effect of academic research is on the order of
10 years in technology.
Table 10 splits the sample into two parts using 1966 as the break
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 TABLE 10
PRODUCTIVITY GROWTH ACCOUNTING EQUATIONS, 1953-80:
REGRESSIONS WITHIN SUBPERIODS

EQUATION

VARIABLE OR STATISTIC (1) (2) (3) (4)

A. Years 1953-66*
Constant .0041 .0036 .0036 .0038
(2.8) (2.5) (1.4) (1.5)
Total own knowledge
intensity:
Combined (lag = 20) .8E-5 .8E-5 2.2E-5 2.1E-5
(4.5) (4.2) (3.4) (3.2)
Spillover knowledge
intensity:
Science only (lag = 30) 15.1E-7 16.1E-7 25.5E-7 27.3E-7
(3.7) (3.7) (4.0) (3.9)
Energy shock variables:
Industry -.62 -.44
(-3.1) (-2.3)
Whole economy .77E-3 .63E-3
(2.4) (2.0)
Industry dummies No No Yes Yes
Adjusted R2 .102 .132 .378 .387
F 15.3 10.6 9.0 8.5
B. Years 1966-80t
Constant .0004 .0016 .0037 .0037
(.3) (1.0) (1.7) (1.6)
Total own knowledge
intensity:
Combined (lag = 20) 1.OE-5 l.IE-5 -.7E-5 -.8E-5
(4.1) (4.2) (-1.0) (-1.0)
Spillover knowledge
intensity:
Science only (lag = 30) 6.7E-7 4.7E-7 29.8E-7 29.6E-7
(1.6) (1.1) (4.6) (4.4)
Energy shock variables:
Industry -.40 -.07
(2.9) (-.6)
Whole economy .52E-3 .1OE-3
(2.4) (.6)
Industry dummies No No Yes Yes
Adjusted R2 .056 .080 .480 .477
F 8.9 6.8 14.1 12.7
NOTE-Industry energy shock is growth in the real energy price times the industry ratio of physical capital to
output; whole-economy shock is growth in the energy price times the capacity utilization rate in manufacturing.
* Mean of dependent variable is .011; sample size is 252.
t Mean of dependent variable is .005; sample size is 270.

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 STOCKS OF KNOWLEDGE 697
point. The table adds energy shock variables in an effort to explain
the productivity slowdown of the 1970s. Results are presented in two
panels. Consider equation 1, which omits industry dummies, thereby
retaining between-industry effects. Here the coefficient of own knowl-
edge is constant across panels, but the spillover weakens somewhat
after 1966. Now turn to equation 3. Since industry dummies are
included, effects are restricted to variation within industries. In this
case, own knowledge ceases to matter in the second period, while the
spillover strengthens. Productivity declines in the second period, so
there must be some attenuation in effect; but there is no obvious
explanation for the pattern of these results. One interpretation is that
own knowledge distinguishes between high- and low-growth indus-
tries in both periods but that spillovers are more important in ex-
plaining short-run growth after 1966. Elsewhere (Adams 1988) I doc-
ument a shift of science resources away from manufacturing during
this time. It is sensible to think that the effect of spillovers to manufac-
turing would increase in light of the changing role of science else-
where.
In an effort to see whether real energy prices cause part of the
slowdown, as has been suggested by several writers (Jorgenson et al.
1987; Griliches 1988), I have included industry and whole-economy
energy shock variables. The industry shock is the interaction of real
energy price growth and physical capital intensity in the industry.
The idea is that obsolescence of capital rises with the energy price and
with capital intensity.'6 Negative signs are both expected and ob-
served in equations 2 and 4. The whole-economy shock is the interac-
tion of growth in the real energy price and the capacity utilization rate
in manufacturing. A positive interaction between capacity and price
growth suggests that energy amplifies the cycle. This too is observed
in table 10, but neither shock alters the performance of the knowl-
edge intensities.
Other empirical work was carried out. Briefly, the nature of this
work was as follows. I estimated productivity regressions taking
growth in real factor prices into account. Since factor prices influence
and are influenced by industry growth, these were instrumental vari-
ables regressions.'7 For the first time, since I was seeking for ex-
ogeneity, own knowledge per scientist (see table 3) was entered in

16
Put differently, there is an extra term - 6KIQ in the equation, and 8 depends on
growth in the real energy price.
17
Instruments included in the productivity growth equation were knowledge inten-
sities, predicted values for real factor price growth, and sometimes industry dummies.
Included in the real factor price growth equations were real factor price growth else-
where for the input in question, the predicted value of productivity growth, and real
growth of gross national product.

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 698 JOURNAL OF POLITICAL ECONOMY

place of total own knowledge. I found that energy price significantly

slowed productivity growth, while materials and services were associ-
ated with increased productivity. Materials and services prices include
quality improvements to intermediate goods and may have promoted
growth in this way. Own knowledge per scientist was significant only
when industry dummies were included. The reason is that knowledge
per scientist did not capture cross-sectional differences in the use of
science.
An additional attempt was made to improve measurement of the
knowledge intensities. Education and article citation weights were as-
signed to the scientific employments and article counts entering into
the intensities.18 Since engineers and computer specialists received
less schooling than scientists, the education weights increased the
share of scientists in the data. The citation weights, which differed
more markedly than the education weights, again increased the
weight of scientists. 19 Despite the changes the reweighted knowledge
intensities performed only marginally better than the original mea-
sures reported above.
Table 11 assembles estimated contributions to productivity growth
from selected regressions. Estimates are products of means and re-
gression coefficients. The knowledge contributions are sizable deter-
minants of productivity growth. For instance, the total contribution
in the growth accounting equation (source I) is .0063 in the period
1953-66 and .0055 in the period 1966-80. It is interesting to note
that a larger share of growth is explained by own knowledge in the
first period. Another finding is that energy shocks are responsible for
a drop in productivity of .00 14, or about one-fourth of the slowdown
of .006 between subperiods. To see this, compare source II with
source V.
The decline in the contribution of knowledge between subperiods
can be decomposed in several ways. The full-period regressions hold

18
The education weights are standardized relative to chemists and are available only
for 1976-82. Fractions of scientists in each field with various degree levels are taken
from U.S. Scientistsand Engineers (various years). Years of schooling are assumed to be
16 for those with a baccalaureate and 18 for those with a master's. Years of schooling
for doctorates are the median years enrolled in doctoral programs plus the fraction
with a master's times 18 years plus the fraction with a baccalaureate times 16 years, all
from the National Research Council (1987). Mean years of schooling for each field are
the product of the fractions at each degree level times mean years of school at each
level. Relative years of schooling obtained by this procedure are 0.97 (agriculture), 1.02
(biology), 1.00 (chemistry), 0.93 (computer science), 0.93 (engineering), 0.99 (geology),
1.00 (mathematics and statistics), 1.14 (medicine), and 1.08 (physics). Unfortunately,
these estimates are not available prior to 1976.
19 Citation weights per article are drawn from the National Science Foundation
(1985, tables 1-7, 1-28). Relative weights (biology = 1.00) range from 0.54 for en-
gineering to 1.82 for medicine.

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 STOCKS OF KNOWLEDGE 699
TABLE 11
ESTIMATED CONTRIBUTIONS TO PRODUCTIVITY GROWTH, 1953-80

Own Spillover Energy

Period and Source Knowledge Knowledge Shocks
1953-66:
I .0041 .0022 ...
II .0033 .0038 .0005
III .0086 .0064 .0001
1966-80:
IV .0030 .0025 ...
V .0045 .0011 -.0009
VI - .0024 .0078 - .0013
NOTE.-Estimated contributions are regression coefficients times means of variables. Sources I-VI are as follows:

Source Equation Industry Dummies Full Period

I 2 of table 8 No Yes
II Panel A, 2 of table 9 No No
III Panel A, 4 of table 9 Yes No
IV 2 of table 8 No Yes
V Panel B, 2 of table 9 No No
VI Panel B, 4 of table 9 Yes No

regression coefficients constant. When one compares source I with

source IV on that basis, a decline in the knowledge contribution of
just .0008 appears. This is wholly due to declines in the knowledge
intensities. Evaluated at means, declines in knowledge intensities can
explain only 15 percent (.0008/.006) of the slowdown. If declines in
effect are included as in sources II and V, then the total decline in
effect of knowledge rises to .00 15, just 30 percent of the slowdown.
Therefore, other sources are the primary causes of the productivity
slowdown.
The declining effect of own knowledge over time noted in table 11
nevertheless poses a problem. In part it may be attributable to a defect
in the available data, which fail to distinguish between research scien-
tists and total scientists. Researchers in manufacturing probably fell
relative to total scientists during the 1970s since the industrial scien-
tific work force itself dropped, suggesting a declining payoff to do-
mestic manufacturing R & D. The decline could be due to several
causes: rising import competition, the temporary impact of a decline
in basic science activity during World War II mentioned in Section
III, or a true permanent fall in the value of science. I believe that the
first two are the more likely candidates, with the second plausibly the
winner, since import competition is more likely to spur R & D as a
means of survival than to discourage it. The last explanation is highly
implausible since R & D rose outside manufacturing in the United
States and rose in non-U.S. manufacturing in Europe and Japan.

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 700 JOURNAL OF POLITICAL ECONOMY

Unfortunately, there is little extant evidence that can resolve the

issue.

V. Conclusion
I believe that enough evidence has been amassed in support of the
argument that fundamental knowledge matters to warrant further
exploration of its role in the growth process. In fact a wide and deep
research agenda is suggested by the findings. The following questions
are raised: Can influence of knowledge be measured apart from sci-
entific employment? Are observed shifts in demand toward higher-
quality factors the result of the growth of knowledge? Can the in-
fluence of knowledge first be traced to its effects on R & D and from
there to products and processes? How large is the role played by the
international diffusion of basic science in the recent surge of trade
and in the twisting of the U.S. wage structure in favor of the highly
educated? Much remains to be done on these daunting and fascinat-
ing problems associated with the enhancement, through the slow ac-
cumulation of theory, of the ability to produce.

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