empirical economics. Vol. 8,1983, page 203-214.
Further Evidence of the Determinants of Industrial Research
and Development Using Single and Simultaneous Equation Models
By/».£>. Loe^ Newark')^)
Abstract: This paper provides empirical evidence in favor of the Schumpeterian hypothesis using
single equation models. A simultaneous equation model is then developed which examines the
interaction of R & D, growth and profitability.
1. Introduction
The last two decades have witnessed a renewal of interest by economic researchers
in the determinants of Research and Development (R & D) and technological change,
as well as the effect of R & D on various economic variables. Of particular interest
have been tests of a Schumpeterian hypothesis that larger firms engage in R & D
proportionately more than smaller firms.^) Researchers have also been interested in
the relationship between profits or liquidity and R & D. Kamien/Schwartz [1982,
1975] have recently provided a very thorough and up-to-date review of the literature.
The empirical studies have examined R & D from two different viewpoints, namely,
R & D measured as outputs and R & D measured as inputs.* ) However, varying results
*) The author gratefully acknowledges the research support of the Rutgers University Research
Council. He is indebted to P. Asch, J. Cullity, M. Dutta, C.T. Koeller, J. Seneca and M. Willoughby
for helpful comments on various portions of this paper. A particular note of thanks is due Vincent
Lin, the managing editor and an anonymous referee for their valuable insights and comments.
^) Peter Loeb, Associate Professor of Economics at Rutgers, The State University of New
Jersey, Dept. of Economics, 360 High Street, Newark, NJ 07102, U.S.A.
^) The Schumpeterian hypothesis actually falls under the rubric of two hypotheses: i) a relationship between innovation and monopoly power and ii) a relationship between R & D and firm
size, i.e., larger firms have a more than proportionate effect on R & D than smaller ones. It is the
latter hypothesis which is examined in this paper [see Kamien/Schwartz, 1982 for a further discussion along with Schumpeter].
*) R & D output measures most commonly used include the number of patents [Scherer,
1965b], the number of "significant" innovations {Mansfield, 1963], and the number of new products introduced into the market [Anguilley;Bailey; Comanor, 1965; Vemon/Gusen]. R & D input measures most commonly used include R & D employment [Hamberg, 1964; Scherer, 1965a]
and R & D expenditures [Grabowski; Mansfield, 1964; Schmookler; Villard].
0377-7332/83/3-40203-214$2.50 © 1983Physica-Verlag, Vienna.
204
P.D. Loeb
have been obtained from these studies, and a general concensus has yet to be obtained
regarding the relationship between R & D and firm size and, more generally, the determinants of R & D.')
Most of the previous studies have investigated the above mentioned relationships
using linear regression analysis and the conventional accompanying statistics, i.e.,
R^, F-tests, and r-tests. More recently, Loeb/Lin [1977] have investigated the possible
determinants of R & D in the pharmaceutical industry via a set of specification error
tests developed by Ramsey [1969,1970, 1974]. These single equation studies have
attempted to investigate, aside from the Schumpeterian hypothesis, the potential
relationship between R & D and profits, as well as the relationship between R & D
and growth. In particular, ^aZ/ey [1972], Elliot [1971], Griliches [1973], Kennedy/
Thirlwall [1975], Mansfield [1968], Nadiri [1970], NSF [1972], and Smith/Oeamer
[1968] investigated the relationship of growth and productivity with R & D. Similarly,
the relationship between profits and R & D has been investigated by Comanor [1964],
Elliott[197l],Grabowski[1968lHamberg
[1966], Jo'hannisson/Lindstrom [1971],
and Smyth/Samuels/Tzoannos [1972].
The majority of the research efforts reviewed by Kamien and Schwartz, as well as
the study of Loeb and Lin, were conducted in a single equation setting indicating that
size, profitability, and growth were causal factors in R & D or vice versa.
This study examines the relationship between R & D and firm size as well as other
determinants of R & D using a relatively large and new data set. We examine the relationship between R & D and firm size and the determinants of R & D under various
functional formats suggested in past single equation studies. The study then suggests
a simultaneous equation model for R & D, growth and profitability.
2. The Data
Cross sectional data were obtained for 303 firms for the year 1971 on the following variables: R & D expenditures, assets, equity, employment, sales, and income. The
data are a subset of observations found in Fortune, and Standard and Poor's [1972].
Additional cross sectional observations were obtained for all data except R & D for
the years 1969,1970, and 1972. The firms cover almost all industrial categories, as
classified by Business Week [1975]. As such the sample is representative of most types
) In a recent paper, Fisher/Temin [1973J criticized many of these studies. In particular,
they criticized the use of R & D inputs as inappropriate for testing Schumpeter's proposition. They
argued that a proper test of Schumpeter's proposition should utilize measures of R & D output.
In defense of the studies which utilize input measures of R & D, it may be argued that these
measures were used due to the Umited avaUablility of R & D output data and that the limitations
associated with R & D input measures are implicitly recognized in these studies. Furthermore,
It may be argued that there is a close association between R & D input and R & D output, and
hence the results using either measure will not likely differ substantially from each other [see for
example the findings oiAnguilley and Scherer, 1965b].
Determinants of Industrial Research
205
of firms. Furthermore, the data source and sample size are similar to those found in
Scherer [1965a, 1965b] andHamberg [1964], except that it relates to a more recent
time period.* )
3. Single Equation Models of R & D
Single equation models for R & D were estimated using ordinary least-squares as the
estimation technique. The specifications were evaluated so as to select the best variant
of each model based on the criteria of: R^, r-tests, F-ratios, consistency of the signs
of the estimated coefficients with a priori expectations, and economic theory.')
3.1 R & D and Finn Size
We first re-examine various models of R & D which were suggested in significant
past studies. The models which we examine are:
(i)
log (R & D) = log flo + "l log Size + u
(ii)
R & D = flo + fli Size + fl^ Size ^ -t- u
(iii) R & D = Co + fli Size + Cj Size^ + Cg Size^ + u
(iv)
R & D = log ao + ai (log Size) + aj (log Size)^ + fls (log Size)^ + u
where:
R & D = a measure of research and development, namely,
(a) R & D expenditure in dollars,
(b) R & D intensity, i.e., R & D expenditure /size
Size = a measure of firm size, namely, sales
and
« = a random error term.
) The sample employs firm data from the following industries, among others: Aerospace,
Appliances, Automotive, Building Materials, Chemicals, Drugs, Electrical and Electronics, General
Machinery, Instruments, Leisure Time, Metals and Mining, Miscellaneous Manufacturing, Natural
Resources-Fuel, Office Equipment & Computers, Paper, Personal Care Products, Special Machinery,
Steel, Tire & Rubber, and Telecommunications.
) One must be cognizant that maximizing R^ may be a poor criterion for model selection
(see, for example, Dhyrmes]. Ramsey/Gilbert [1972] and Ramsey/Zarembka [1971] have shown
that the R criterion may select a misspecified model as the true model.
P.D. Loeb
206
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Determinants of Industrial Research
207
Equation (i) is of the form suggested by Hamberg [ 1964] and equation (ii) by
Grabowski [1968]. Equation (iii) is of the form suggested by Scherer [1965a, 1965b],
and equation (iv) by Scherer [1965a] zn^ Mansfield [1963].
Table 1 provides the regression results associated with the models specified above,
where R & D is in terms of R & D expenditures.
On a priori grounds, we expect the coefficient of size to be positive and the coefficients of (size)^ and (log size) to be positive or negative depending on whether larger
firms make more than proportionate expenditures on R & D than smaller firms.
The empirical results support the Schumpeterian hypothesis tested. All four models
prove to have significant size coefficients.*) The results concerning R & D expenditures
vis-a-vis firm size are dependent upon the model specification. One may choose the
optimal model from among models (2), (3), and (4) via the criterion of maximum R^.
Of these three specifications, model (3) proves superior. Based on this decision rule for
model selection, one would find support for the hypothesis that larger firms spend
proportionately more on R & D than smaller firms. One cannot choose between specifications (1) and (3) via the criterion of maximum i?^ since both models do not share
an identical regressand. Analysis of the ^statistics associated with the coefficients and
the F-ratios do not aid in the selection process either. However, LoeblLin [1977]
evaluating the identical models for the pharmaceutical industry found equations (1)
and (4) to be in violation of the full ideal conditions underlying the classical model
which suggests that they were misspecified, at least for that industry.') This provides
additional support for model (3).
3.2 Other Determinants of R & D
Since the capital intensity of firms varies across industries and since R & D expenditures can be expected to be determined in part by the capital intensity of the firm, a
variable to reflect such differences in capital intensities is analyzed. More specifically,
industries such as the telecommunication industry generally employ state of the art
technology and are capital intensive vis-a-vis, e.g., the leisure time industry. The very
nature of the products produced by the various industries requires different R & D
priorities in their budgets. Our model addresses this factor via the use of capital/labor
ratio. A firm's capitalAabor ratio (K/L) is measured as the ratio of stockholders'
equity to total employment.
*) Statements regarding significance are evaluated at the 1% level.
) The full ideal conditions underlying the classical model are:
(i)
ti~n (0, a'^D
(ii) /I is independent of X
(iii) X'X is of full rank.
rhe specification error tests applied detect the following types of misspecifications: Omission of
variables, misspecification of the functional form, simultaneous equation problems, heteroscedasticity and non-normality of the residuals.
P.D. Loeb
208
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Determinants of Industrial Research
209
Differences in R & D expenditures among firms may also arise due to differences
in the financial position of each firm, which in turn is related to the firm's profits.
It is often hypothesized that profits, or lagged profits are an explanatory factor of
R & D expenditures in that they are a source of liquidity from which to finance
R & D efforts.'") Alternatively, it has been argued that declining profits induce R & D
in an attempt to stem the decline [see Kamien/Schwartz, 1982, p. 96]. Kamien/
Schwartz [1982, p. 98] conclude that, "Liquidity or profitability may be 'threshold
factors,' necessary in some degree for R & D activity..." As such, we examine the
relationship between the firm's past profitability, measured as the ratio of income to
equity, and R & D expenditures.
Table 2 provides the regression results of specifications (i) through (iv) with a
profitability and a capital/labor variable included.
The regression results on R & D expenditures in Table 2 are consistent, once again,
with the Schumpeterian hypothesis. The profitability variable proved to be significant
and consistent with a priori expectations in models (2') and (3'). The capital/labor
ratio was found always to be insignificant.
Employing the critera of maximum R^, consistency of the signs of the coefficients
with a priori expectations, and significance of the coefficients, we may select model
(3') to be the most appropriate model among the alternatives evaluated.
3.3 Concluding Comment Regarding the Single Equation Models on R & D
The single equation models evaluated, utilizing a new and larger data set, provide
results which are in general agreement with the Schumpeterian hypothesis." )
4. A Simultaneous Equation Model of R & D, Growth, and Profitability
The only major R & D study conducted previously making use of a simultaneous
model was that of Mueller [1967]. Mueller, using cross-section data, developed a four
equation simultaneous model for capital investment, firm R & D outlays, advertising,
and cash dividend payments.
The R & D equation in the Mueller model is specified as:
R & D = /[Gross Capital Investment, Advertising, Cash Dividend Payments,
Industry R & D/Industry Sales, Ten-year Change in Sales, Profits
before Taxes^^, (Depreciation plus Depletion) ,, Sales].
) Grabowski [1968] has provided the strongest empirical evidence of the positive influence
of lagged after-tax profits (summed to depreciation and depletion) on R & D expenditure intensity {see also Branch].
) The cubic term in models 3 and 3' allows for inflection points and nonmonotonicity in the
estimated relation [see Scherer, 1965b for a further discussion]. The models suggested were also
evaluated using R & D intensity, i.e., R & D/Size, as a dependent variable. These results proved
inferior to those reported in Tables 1 and 2, indicating that multicollinearity is not adversely affecting results since f-statistics do not tend to zero.
210
P.D. Loeb
An interesting finding from this study was that sales did not have a positive effect on
R & D or investment. This was attributed to the inclusion of profits and depreciation
which are measures of expectations and command over resources. It was also found
that R & D and investment may prove to be substitutes for one another in that resources may be shifted from investment to R & D during periods when returns to investment may be low. A growth variable was incorporated into the R & D equation in
that firms experiencing a more rapid growth of sales may experience greater advantages
from inventions leading to cost reductions than firms with lower growth of sales.
Furthermore, rapidly growing firms may better be able to await the distant and uncertain returns from R & D than slower growing firms.
The empirical literature has suggested that R & D is functionally related to, among
other things, size and profitability [see, for example,Elliott;Hamberg, l966,Kamien/
Schwartz, 1975;Mueller; Schumpeter]. On the other hand, such studies have suggested
that profitability, in turn, is affected by R & D and growth of firms, while growth is
related to R & D and profitability [see, for example, BaZ/ey; Comanor, 1964;Mansfield,
1968; NSF;Smith/Creamer]. As such, a potential simultaneous relationship among
R & D, profitability and growth seems likely, and it is in this area which the present
study is directed.'^)
The following model is suggested to examine the simultaneous interaction among
the aforementioned variables:
(v)
R & D = /(Profitability, Size, Capital/Labor ratio)
(vi)
Profitability =g(R&D,
Growth)
(vii) Growth = /i (R & D, Profitability, Capital/Labor ratio)
(viii) Growthvi = Salesvi — Sales ;
4.1 The R & D Equation
It is suggested that profitability (measured as Income/Equity) affects R & D. More
specifically, profitabihty may account for the availabihty of funds or as a measure of
expectations [see Kamien/Schwartz, 1975, 24-25]. The size variable is included in this
equation to account for large firms being more innovative than small firms. Finally a
capital/labor ratio is included to adjust for inter-firm capital intensity differences.
^^) Kamien/Schwartz [1975] have suggested a potential simultaneous relationship between
profitability and R & D.
Determinants of Industrial Research
211
4.2 The Profitability Equation
It may be argued that R & D affects the profitability of firms in that it may lead to
increases in sales by the introduction of new or better products and/or decreases in
costs of production by providing a more efficient production technology.'^)
It may also be hypothesized that growth of firms affect profitability. More specifically, if sales increase in such a manner as to offset any potential increase in cost due
to diminishing returns, the firm will experience greater profitability, all else equal.
4.3 The Growth Equation
One can argue R & D expenditures may lead to the introduction of new and/or
better products which leads in turn to increases in sales. Hence the growth of sales
may be functionally related to R & D expenditures. Past profitability provides funds
for marketing activities in some later time period which may also result in a growth
of sales. Hence, lagged profitability is included in the equation to account for this
factor. Finally, a capital/labor ratio is included in the equation to account for interfirm differences due to varying capital intensities across firms.
5. Empirical Results of the Simultaneous Equation Model
Table 3 provides definitions of symbols used in the empirical estimates.
Variable
Research and Development
ProfitabUity
Size,
(Capital/Labor)^
Growth,
Symbol
R&D
-"t
Size,
(K/L),
^t
Measured As
R & D expenditures
Income,/Equity,
Sales,
(Equity/Employment),
(Sales, - Sales,, j)/Sales,_j
Tab. 3: Definitions of Variables
The hypothesized relationships were estimated using two stage least squares (2SLS).
The estimated equations are indicated below with f-statistics shown within parentheses.
R&D71 = - 9 2 . 3 1 9 +1196.69 7:71 + 0.046 Sales7i
(-2.040)
(3.057)
(29.436)
- 292.413
(-1.334)
(5)
'^) Data inavailability precluded the examination of the impact of lagged R&D activity on
profitability. Branch [1974] found some evidence suggesting that lagged R&D affects profitability in the cunent period.
212
P.D, Loeb
7771
G71
=0.009
(0.513)
-
0.677X 1 0 " ' R & D 7 1 -I- 1,376^71
(-0,386)
(4,355)
= 0,003
(0.150)
-I- 0,127 X 10-" R&D71 - 0,069 (K/L)7i
(1,164)
(-0.966)
4- 0.202 7r7o
(2,318)
0,297 Trgj,
(2.126)
(6)
(7)
All equations proved to be just or over identified,'*)
6. Interpretation of Results
6.1 The R&D Equation
All coefficients other than that associated with the (K/L)7i variable are found to be
significant at the 0,05 level. The sales variable has a positive effect on R & D, This is of
particular interest considering the negative effect of sales on R & D in the Mueller
study. This difference in results may be due to differences in model specifications.
Profitability, as expected, has a significant and positive effect on R & D, Finally,
the capital/labor ratio is found to have an insignificant effect on R & D. This latter
result is similar to that found by LoebI Lin [1977] for the pharmaceutical industry
using time-series data,
6.2 The Profitability and Growth Equations
As expected, the growth variable has a positive and significant effect on profitability.
However, the R & D variable has an insignificant effect on profitability.")
All factors in the growth equation have coefficients conforming with a priori expectations, R & D is found to have a positive effect (though not significant at the 0.05
14
) Various alternative simultaneous model specifications were evaluated. The introduction
into the R & D equation of a regressor of the form Size?! results in insignificant coefficients
associated with Sales and Sales^, (However, the signs of the coefficients generally conformed with
a priori expectations, i,e,, supported the Schumpeterian hypothesis,)
) The negative sign associated with the R & D variable seems to violate our a priori expectations. However, the negative relationship may be explained if current expenditures on R & D
are considered as an additional cost element with a return (higher profitability) due in some future
period.
If the profit equation is respecified as 7771 =g' {K& D71, Size7i), two stage least square estimation results in:
TTii = 0,108 + 0,720 X 10'^ R& D71 - 0,331 X lO""* Size7i ,
(4,702) (3,108)
(-3,046)
Hence, the profit equation is sensitive to the manner in which size is incorporated in the equation,
i,e,, sales vs, growth of sales (G^i).
Determinants of Industrial Research
213
level) on growth while the lagged profitability variables have positive and significant
effects on growth (at the 0,05 significance level). The capital/labor ratio proved insignificant.
7. Summary and Conclusion
This study provides empirical support for the Schumpeterian hypothesis using a
recent cross-section data set. This result is found upon evaluation of four well-known
single equation models. Additionally, a viable simultaneous equation model portraying
the interaction of R & D, profitability, and growth is presented. Additional support
for the relation between R & D and size is provided in that a simultaneous equation
model is a more realistic presentation of the situation being evaluated.
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Received April 22,1981
(revised version September 1,1983)