Federal funding andd the level of private expenditure on basic research.

I. Introduction

Economists have long been interested in questions concerning the role of government in stimulating private-sector innovation. In the late 1950s, Blank and Stigler [2] asked, in particular, whether government-funded industrial research and development (R & D) activity was likely to stimulate or substitute for private-sector expenditure on R & D. A number of studies have since addressed this issue and most conclude in favor of the existence of a positive relationship between federal R & D expenditures and the level of private R & D investment.(1) Leyden and Link [8] have provided a theoretical rationale for this observed complementarity. They suggest that federally-funded industrial R & D activity may generate knowledge spillovers and other infratechnology that may raise the productivity of inputs into private R & D.

R & D is a heterogeneous activity, and a question which has received relatively little attention in the literature is the extent to which the apparent complementarity between federal and private industrial R & D spending holds for the different components of firms' R & D budgets. Cross-section evidence on this issue, produced by Link [13], suggests that:

(a) expenditures on development projects are the only component of private R & D that receive a stimulus from federal R & D allocations; and

b) that federal R & D in fact has a significantly negative effect on private expenditures on basic research.(2)

This latter finding is of more than passing interest, as there is evidence to suggest that the returns to private investment in basic research may be significantly higher than those to other components of private R & D.(3) The effectiveness of federal R & D expenditures as a mechanism for stimulating private R & D investment would be somewhat diminished if, as is indicated, they have the effect of diverting private expenditures away from basic research towards components of R & D which have relatively low expected returns.

The purpose of this paper is to offer a further examination of the relationship between federal R & D expenditures and private investment in basic research, from the perspective afforded by aggregate time series data. While such an approach necessarily sacrifices some of the information which may be gleaned from studies of inter-firm or inter-industry variations in research activity, it has the merit of permitting a more detailed consideration of the dynamics that may be present in the relationship between basic research and its determinants. Within this framework, we find evidence of a significantly positive relationship between federal R & D expenditure and private basic research, echoing the complementary relationship usually found in studies of total private R & D spending. The positive effect is most pronounced for federal spending on basic research, but federal expenditures on applied research and development also appear to provide a significant short-run stimulus to private basic research.

The layout of the rest of the paper is as follows. Section H discusses the underlying analytical framework, whilst section III presents the econometric results. Section IV provides some brief concluding remarks.

II. The Analytical Framework

Our investigation of the relationship between federal R & D expenditure and the level of private investment in basic research is couched within the following simple supply and demand framework, which describes the determination of the level of funds allocated to basic research at the individual firm level:

(Supply) [P.sub.S] = f(PBR, SALES) f1 > 0, f2 < 0 (1)

[Mathematical Expression Omitted]

Equation (1) describes the determination of the "supply price" (marginal cost) of funds for private expenditure on basic research (PBR). As a claim on the firm's resources, basic research is assumed to compete with alternative uses such as capital investment, advertising, promotional activities, etc. Assuming that expenditures on all such items - including spending on basic research - are characterized by diminishing returns, it follows that as additional funds are allocated to basic research at the expense of these competing claims, the opportunity cost of investing in such research will rise. Hence the positive sign attached to the partial derivative of PBR in this equation. This effect is reinforced if, as might plausibly be the case, the risk premium attached by the firm to the marginal unit invested in basic research rises with the level of spending in this area.

The availability of funds for private basic research is assumed to be a positive function of the firm's sales - issues of risk and moral hazard generally inhibit the ability of firms to raise external finance for R & D activity and necessitate the use of internally-generated funds. A rise in the level of SALES reduces the shadow price of funds for basic research, generating the negative sign for this variable in equation (1).

The negative sign on the derivative of PBR in equation (2) - for the "demand price" of funds for basic research - follows from the assumption, noted above, that there are diminishing returns to funds invested in PBR. Two factors may give substance to this assumption. Let x denote the probability of making a significant discovery and assume this to be a positive function of the level of the firm's basic research "effort," e.(4) The variable e is a positive function of the level of spending on basic research, PBR, i.e.,

[Mathematical Expression Omitted]

Diminishing returns to PBR may arise if either [ .sup2 x]/[ e.sup.2] < 0 , or if as PBR is increased firms face increasing costs of attracting scarce R & D inputs (scientists, engineers, etc.), so that additional units of spending on basic research yield diminishing increments to basic research "effort."

An increase in SALES has an ambiguous effect on the marginal returns to investment in basic research. A higher level of sales means that the benefits of the product of successful basic research (and any subsequent expenditure required to develop the innovation) can be spread over a greater number of units of output, so that the potential returns to investment in PBR are higher. On the other hand, it is possible that the returns to investment in PBR may fall relative to those on alternative investments (e.g., investment in plant and machinery) as sales rise.

The effects of federal R & D expenditures (FF) on the incentives for private investment in basic research are assumed to work through their impact on the demand price of funds for PBR. Here too, however, the effects are ambiguous. We again have the possibility that higher federal R & D expenditures may lead to an incr-ease in the price of scarce R & D resources, but acting in the opposite direction is the possibility that federal R & D spending may generate knowledge spillovers which raise the marginal returns to investment in basic research.(5) Additionally, however, the evidence of Link [ 131 suggests the possibility that federal expenditures may lower the expected returns from basic research relative to those from private expenditure on applied research and development.

The final argument in equation (2) is the level of private expenditure on applied research and development (PARD), and again there are similar conflicting effects at work: the possibility of higher costs of R & D inputs against, on the other hand, the possibility that expenditure on applied research and development may generate knowledge spillovers or provide other infratechnology which raises the marginal returns from investment in basic research.(6) Combining equations (1) and (2) and aggregating across firms leads to the following reduced form specification for the aggregate level of private expenditure on basic research:

PBR = h(SALES, FF, PARD). (4)

The discussion above suggests that there are ambiguities in the signs of each of die explanatory variables in this equation, the resolution of which must be left to empirical analysis.

Before moving on to this empirical analysis, we make three amendments to our basic equation. First, we allow for the possibility that there may be different spillover effects associated with different components of federal R & D expenditure. Accordingly, these are disaggregated into funds for basic research, and spending on applied research and development. Second, we follow Lichtenberg [9] and allow for the possibility that the effect of sales to the federal government on the incentives for private R & D may differ from that of non-government sales.(7) And third, we allow for the presence of dynamics in the relationship between private basic research and its determinants. Knowledge spillovers from private investment in applied research and development and federal R & D expenditure may take time to feed through to private basic research. More generally, we can think of equation (4) as determining the long-run level of PBR, but we might expect adjustment lags to lead to some short-run dynamics around this long-run solution. In the absence of detailed theoretical knowledge of the form that these dynamics might be expected to take, it seems best to leave their determination to the data. An error correction specification is therefore adopted to permit flexible modelling of the equation's dynamics.

III. Econometric Analysis

In common with most previous studies in this area, we adopt a linear specification for the empirical representation of equation (3).(8) As a preliminary to the detailed econometric modelling, Table I presents the results of tests for unit roots in the variables of interest. These indicate that each of the series is best characterized as integrated to order one (I(1)), and that PBR is therefore most appropriately modelled in difference form. The error correction specification enables us to do this, but to retain the long-run information contained in the levels of the variables.

Starting from an equation featuring up to two lags of the variables of interest, deleting insignificant terms and reparameterizing leads to the parsimonious specification shown in Table II.

Three points of interest stand out from the results. Chief amongst these is the finding of a significantly positive effect of federal R & D expenditure on the incentives for private investment in basic research. The equation predicts in fact that, ceteris paribus, an increase in real terms in the level of federal expenditure on basic research will be matched one for one by an increase in private expenditure in this area,(9) suggesting that the effects of knowledge spillovers from federal spending on basic research significantly outweigh any negative effects that such spending might have through raising the cost of R & D inputs.(10) Federal expenditure on applied research and development is also found to have a significantly positive effect on PBR in the short-run. Although these results are clearly at variance with Link's finding of a negative impact of federal R & D allocations on private basic research, the two sets of results are not necessarily inconsistent. Link's cross-section results indicate the response of an individual firm's basic research expenditure to an increased allocation from a given federal R & D budget. The time series results presented here, on the other hand, indicate the overall response of private sector spending on basic research to a change in the federal R & D budget. It is not inconceivable that the two may move in opposite directions.

  Table I. Unit Root Tests

Variable                  ADF        DF

PBR [dagger]             -1.47      -0.98
[delta] PBR              -2.76      -3.95(*)
FBR                      -1.82      -1.80
[delta]AFBR [dagger]     -2.99(*)   -5.28(*)
PARD                     -1.20      -0.85
[delta]PARD              -3.64(*)   -4.28(*)
FARD [dagger]            -2.49      -2.04
[delta]FARD              -2.10      -2.68(*)
GS                       -2.47      -1.36
[delta]GS                -4.37(*)   -3.68(*)
NGS                      -3.19      -2.19
[delta]NGS               -4.15(*)   -4.51(*)

  Sample: 1956-1988
  Notes: The ADF statistics are based on the t-statistic of [y.sub.3] in the fol
lowing OLS
regression:

  [Mathematical Expression Omitted]

where x denotes the series of interest and [delta] is the first difference opera
tor. The statistic
does not in fact follow a t-distribution,
but appropriate critical values may be found in Fuller [3]. The DF statistic is
calculated in a
similar manner
but with [delta][x.sup.t-1] omitted from the above regression. The ADF statistic
 is more
appropriate if the residuals from the regression
used to calculate the DF statistic are autocorrelated. Such instances are denote
d by a [dagger].
Note that the time trend was
excluded from the regressions used to calculate the test statistics for each of
the first
differenced variables, as its coefficient
was found to be insignificant. The DF test regression for [delta]FARD also omits
 an insignificant
constant term.
  (*)Denotes test significant at 5 percent level.
  The variables are:

  PBR = private expenditure on basic research in industry;
  FBR = federal spending on basic research in industry;
  PARD = private expenditure on applied research and development;
  FARD = federal funds for applied research and development in industry;
  GS = federal government purchases of goods and services;
  NGS = non-government purchases of goods and services.

  All variables measured in millions of 1982 dollars. Detailed sources are given
 in the Data
Appendix.

  Table II. The Determinants of Private Expenditure on Basic Research

  [delta PBR.sub.t] = 1133 - 1.1053[(PBR - FBR).sub.t-1] + 0.5960[delta][FBR.sub
.t] -
   0.0171[delta][PARD.sub.t-1]
                       (6.49) (7.21)                         (3.39)
       (1.73)
                       + 0.0783[PARD.sub.t-1] + 0.0236[[delta].sub.2][FARD.sub.t
] -
   0.0016[GS.sub.t-1]
                          (7.06)                 (5.20)
   (2.65)
                       + 0.0006[delta][NGS.sub.t-1] - 0.0008[NGS.sub.t-1]
                          (3.62)                       (6.25)

  Sample: 1955-1988, t-statistics in parentheses.
  [R.sup.2] = 0.743; AR(3) = 0.26; ARCH(3) = 0.56; Normality: [X.sup.2] 2) = 0.2
69; RESET = 0.55.
  Notes. The diagnostic statistics are as follows: AR(3) denotes an LM test for
serial correlation
up to third order in
the equation disturbances. It has an F distribution with (3, 22) degrees of free
dom. ARCH(3) is a
test for autoregressive
conditional heteroscedasticity - again up to third order - in the equation distu
rbances. It has an
F(3, 19) distribution. The
Normality test is the Bera-Jarque test based on the third and fourth moments of
the distribution of
the residuals, and it has
an asymptotic [X.sup.2](2) distribution. RESET tests for equation misspecificati
on by testing the
significance of the squares and
cubes of the equation fitted values when they are added to the list of regressor
s. This statistic
has an F(2, 20) distribution.

A second point of interest concerns the finding of a significantly positive effect on private basic research of previous expenditures on applied research and development (though lagged changes in PARD appear to have a small negative effect). This too suggests that the knowledge spillovers and other infratechnology creating effects of such expenditures outweigh any detrimental effects they might have on basic research via their effect on R & D input prices.

Finally, in contrast to most previous studies in this area, the equation predicts that, in the long-run, private investment in basic research responds negatively to an increase in sales, whether these are to the government or non-government sector. This departure from the findings of previous studies seems to be due to the presence in our model of private expenditure on applied research and development, which is positively correlated with the level of sales. When the terms in PARD are deleted from the equation in Table II, the coefficients on the lagged levels of GS and NGS become positive; significantly so in the case of the latter. Whatever the explanation, the result is evidence in favor of the proposition advanced in the previous section, that the relative returns to investment in basic research may be countercyclical.

Diagnostic Checking

The results reported in Table 11 indicate that the estimated equation performs satisfactorily against a range of diagnostic tests. As a further check on the equation's admissibility, Figure 1 plots the sequence of one-step Chow tests derived from recursive estimates of the equation's parameters. These indicate that the equation has a little difficulty tracking the sharp increase in expenditure on basic research in 1981 (see also, Figure 2 which plots the actual and fitted values of [delta]PBR), but the test statistic is not significant at the 5 percent level. Overall, the evidence on the hypothesis of stability of the equation's parameters is quite favorable.

Cointegration

The results of Table II suggest the possibility of a cointegrating relationship between PBR, FBR, PARD, GS and NGS. While tests for cointegration have only limited validity in the current context given the relatively small sample size available, the results reported below, obtained by estimating a levels equation for PBR (with the coefficient of FBR fixed at unity), are of some interest.

[PBR.sub.t] = 934 + 1.00[FBR.sub.t] + 0.0684[PARD.sub.t] - 0.0006[GS.sub.t] - 0.0007[NGS.sub.t]

[R.sup.2] = 0.934 DW = 1.41 DF = -4.25 Sample: 1953-1988

The parameters of this relationship are remarkably similar to the implied long-run solution to the error correction equation, with only the coefficient on GS showing any substantial difference. The Dickey-Fuller (DF) statistic exceeds the 5 percent critical value suggested by Blangiewicz and Charemza [1] for accepting the hypothesis of cointegration, with the value of the Durbin-Watson (DW) statistic providing further support [17]. Taken in conjunction with the results from Table II, these results suggest that we have uncovered a satisfactory long-run explanation for the level of private investment in basic research.

IV. Conclusions

This paper has used aggregate time series information to investigate the question of whether federal expenditures on R & D serve to stimulate private sector investment in basic research. The empirical results suggest that they do; confirming the complementary relationship which is generally found in studies of total private spending on industrial R & D. Federal expenditure on basic research in industry provides the strongest stimulus to the level of private expenditure, but federal spending on applied research and development is also found to have a significant short-run effect. These findings are in contrast to, but not necessarily inconsistent with, those of Link [13] who, in a cross-section study of inter-firm variations in R & D spending, found a negative relationship between federal R & D allocations and firms' expenditure on basic research.

This study has also produced evidence to suggest that private investment in basic research may be a countercyclical activity, in that it is found to be negatively related to the level of sales. This finding, which contrasts with that of previous studies in this area, is worthy of further investigation, perhaps using a wider set of macroeconomic control variables than has been employed here.

Data Appendix

Sources for R & D data are: 1953-1966, Historical Statistics of the United States; 1967-1988, Statistical Abstract of the United States, various issues.

PBR/PARD-Real Value of Private Expenditure on Basic Research/Applied Research and Development

Industry funded expenditure on Basic Research/Applied Research and Development in Industry ($ million), deflated by the GNP deflator, 1982 = 100 (source, Economic Report of the President 1990).

FBR/FARD-Real Value of Federal Expenditure on Basic Research/Applied Research and Development

Federally funded expenditure on Basic Research/Applied Research and Development in Industry ($ million), deflated by the GNP deflator.

GS-Real Value of Sales to the Federal Government

Federal government purchases of goods and services ($ million), deflated by the GNP deflator. Source: Economic Report of the President, 1990.

NGS-Real Value of Non-Government Sales GNP minus federal government purchases of goods and services ($ million), deflated by the GNP deflator. Source: Economic Report of the President, 1990.

References

[1.] Blangiewicz, Maria and Wojciech Charemza, "Cointegration in Small Samples; Empirical Percentiles, Drifting Moments and Customized Testing." Oxford Bulletin of Economics and Statistics, August 1990, 303-16. [2.] Blank, D. M. and George J. Stigler. The Demand and Supply of Scientific Personnel. New York: National Bureau of Economic Research, 1957. [3.] Carmichael, Jeffrey, "The Effects of Mission-Oriented Public R&D Spending on Private Industry." Journal of Finance, June 1981, 617-27. [4.] Fuller, Wayne A. Introduction to Statistical Time Series. New York: John Wiley, 1976. [5.] Griliches, Zvi, "Productivity, R&D and Basic Research at the Firm Level in the 1970s." American Economic Review, March 1986, 141-54. [6.] Levy, David M., "Estimating the Impact of Government R&D." Economics Letters, February 1990, 169-73. [7.] _____and Nestor E. Terleckyj, "Effects of Government R&D on Private R&D Investment and Productivity: A Macroeconomic Analysis." Bell Journal of Economics, Autumn 1983, 551-61. [8.] Leyden, Dennis Patrick and Albert N. Link, "Why are Governmental R&D and Private R&D Complements?" Applied Economics, October 1991, 1673-81. [9.] Lichtenberg, Frank R., "The Effects of Government Funding on Private Industrial Research and Development: A Re-assessment." Journal of Industrial Economics, September 1987, 97-104. [10.] _____, "The Private R&D Investment Response to Federal Design and Technical Competitions." American Economic Review, June 1988, 550-59. [11.] _____, and Donald Siegel, "The Impact of R&D Investment on Productivity - New Evidence Using Linked R&D-LRD Data." Economic Inquiry, April 1991, 203-29. [12.] Link, Albert N., "Basic Research and Productivity Increase in Manufacturing: Additional Evidence." American Economic Review, December 1981, 1111-12. [13.] _____, "An Analysis of the Composition of R&D Spending." Southern Economic Journal, October 1982, 342-9. [14.] _____, and G. Tassey. Strategies for Technology-based Competition: Meeting the New Global Challenge, Lexington, Mass.: Lexington Books, 1987. [15.] Mansfield, Edwin, "Basic Research and Productivity Increase in Manufacturing." American Economic Review, December 1980, 863-73. [16.] National Science Foundation. National Patterns of R&D Resources 1989. Washington D.C.: Government Printing Office, 1989. [17.] Sargan, J. D. and Alok Bhargava, "Testing Residuals From Least Squares Regression for Being Generated by the Gaussian Random Walk." Econometrica, January 1983, 153-74.

(*) Helpful comments on a previous draft of this paper were provided by George Stadier, Ian Molho and, in particular, an anonymous referee. I am grateful to them. The usual disclaimer applies. (1.) See, inter alia, Leyden and Link [81, Levy [6], Lichtenberg [9], Levy and Terieckyj [7] and Link [13]. Some studies have found evidence of a negative relationship. See, for example, Lichtenberg [10] and Carmichael [3]. (2.) Basic research projects are defined by the National Science Foundation [16] as, "original investigation for the advancement of scientific knowledge . . .which do not have specific commercial objectives, although they may be in fields of present or potential interest to the reporting company." (3.) See Lichtenberg and Siegel [11] for recent evidence; earlier studies include Griliches [5], Link [12] and Mansfield [15]. (4.) We abstract here from other potential influences on x, such as the possibility that the firm may be able to benefit through knowledge sharing or imitation, from the research activities of other firms. (5.) That is, federal R & D spending may raise the value of x/ e. (6.) It is more usual to see these effects as working in the opposite direction, but there is no reason to suppose that they may not also operate in the direction indicated. See Link and Tassey [14] for a general description of the role of infratechnology in facilitating the R&D process. (7.) In a more recent study, Lichtenberg [10] argues that in analyzing the effects of federal contract awards on private R & D activity, it may be necessary to distinguish between the effects of competitive and non-competitive procurement. Data limitations mean that an examination of this issue is beyond the scope of this paper. (8.) Experiments with a log-linear specification produced broadly similar results. A copy of these may be obtained on written request from the author. (9.) Given that FBR is included within the definition of GS, the ceteris paribus assumption requires that some other component of federal expenditure on goods and services is reduced to compensate for any increase in FBR. (10.) A test of the implicit restriction that the long-run coefficient of FBR is equal to unity does not reject the null hypothesis (F(1, 24) = 0.56).