# The impact of R&D investment on productivity - new evidence using linked R&D - LRD data.

THE IMPACT OF R&D INVESTMENT ON PRODUCTIVITY--NEW EVIDENCE USING
LINKED R&D--LRD DATA

This paper uses confidential Census longitudinal microdata to examine the association between R&D and productivity for the period 1972-1985. These data allow for significant improvements in measurement and model specification, yielding more precise estimates of the returns to R&D. Our results confirm the findings of existing studies:

1) positive returns to R&D investment

2) higher returns to company-financed research

3) a productivity "premium" on basic research

These results are robust to adjustments for "influential outliers." Also, our evidence suggests that the return to company-financed R&D is an increasing function of firm size.

I. INTRODUCTION

Robert Solow's studies in the late 1950s dramatically changed perceptions of the sources of economic growth. Until this time, the commonly held view was that improvements in economic welfare were achieved primarily through the use of more inputs, in particular, capital input. However, Solow [1957] reported that only 10 percent of the twofold rise in U.S. per capita output during the years 1909-1949 was due to growth in the capital/labor ratio. The remainder was attributed to more efficient use of inputs, or technological change. Solow also established a framework for estimating technological change, a productivity "residual" or a measure of changes in output that could not be explained by changes in input use. The Solow residual, in modified form, has become virtually synonymous with the measurement of total factor productivity (TFP) growth. Jorgenson and Griliches [1967] demonstrated that under the assumptions of constant returns to scale and competitive factor pricing, changes in total factor productivity measure shifts in a production function.

Rather than treat technological change as exogenous or "manna from heaven," many economists have explored its determinants. R&D investment is generally regarded as having a strong impact on productivity growth. Empirical analysis of the R&D-productivity connection has often been based on estimation of reduced-form equations derived from the R&D Capital Stock Model (Griliches [1979]), which extends the Solow model to include the stock of technical knowledge, or "knowledge capital," as a factor of production (in addition to the standard factors of production-physical capital, labor, intermediate materials, and energy). If the rate of depreciation of knowledge capital is assumed to be negligible, TFP growth (DTFP) is a function of the "intensity" of R&D investment (RDINT), which is usually measured as the ratio of R&D expenditure to sales: (1) DTF [P.sub.t] = [Alpha] + [Beta] RDIN [T.sub.t] + [u.sub.t] where [u.sub.t] is a classical disturbance term. The coefficient on R&D intensity ([Beta]) is interpreted as both the marginal product of knowledge capital and the "rate of return" to R&D investment.(1) Estimates of [Beta] at the company or line-of-business level are interpreted as measures of the private rate of return to R&D, or those that accrue to the firm or its investors. Due to incomplete appropriability or other factors, this return may not equal the social return to this activity.

Most empirical studies, especially those based on aggregate and sectoral data, have found evidence of a strong positive correlation between TFP growth and R&D investment. However, results using firm-level data have been mixed. The finding that these two variables are uncorrelated is cause for concern because it implies that firms may not be able to earn significant returns on their investment in R&D, making them less likely to undertake this investment in the future, even if it is socially desirable for them to do so. We believe that it is important to reestimate this relationship because it is highly likely that existing firm-level studies have been based on measures of TFP that are crude, imprecise, and unrepresentative.

Our objective in this paper is to reexamine the association between R&D and productivity growth using the most comprehensive and accurate longitudinal microdata yet available for productivity analysis. Dale Jorgenson of Harvard University has said of the data set used in this study, "The Longitudinal Research Data (LRD) set will ultimately transform research on productivity, especially at the microeconomic level, and not only there."(2) These data allow for improvements in measurement and model specification, yielding more efficient estimates of the effects of R&D on productivity. We discuss and adjust for some of the limitations of existing micro-level empirical studies, which have provided estimates of the private rate of return to R&D. While these studies have been useful, productivity estimates at the firm or line-of-business level contained therein are based on crude and incomplete measures of output and inputs. The most serious measurement problem has been an inability to control for diversification when calculating firms' productivity. More specifically, productivity estimation in these studies has often been based on the assumption that firms operate in only one line of business (4-digit SIC industry). To the extent that the relative prices of firms' outputs and inputs vary across industries, this approach introduces an element of noise into estimation of TFP growth. Even if it is uncorrelated with R&D intensity, this measurement error will reduce the efficiency of estimates of [Beta]. We demonstrate that measures of TFP growth based on linked Census R&D-LRD Data are more precise because we can calculate firms' real output and input at the 4-digit SIC industry level and aggregate to the firm level. As expected from the standard errors-in-variables model, this reduction in measurement error from improved deflation yields more efficient estimates of the rate of return to R&D.

We present an empirical example below that illustrates the extent to which more precise TFP measurement leads to more efficient estimates of rates of return to R&D. This example is derived from a pilot study performed by the authors (Lichtenberg and Siegel [1989]), based on linked R&D-LRD data for a sample of 115 firms for the years 1972-1980. Having demonstrated the desirability and feasibility of using linked Census R&D-LRD data to examine the R&D-productivity connection, we undertake a comprehensive analysis of rates of return to R&D, using a full sample of over 2,000 firms. Given our ability to disaggregate R&D investment, we can discriminate between the returns to R&D by source of funds (company-funded vs. federally-funded R&D) and by character of use (basic research vs. applied research and development). Also, the panel structure of our data allows us to explore the time series properties of these rates of return throughout the sample period (1972-1985). The sensitivity of our results to outliers (influential observations) is also examined. Finally, we address a "Schumpeterian" question: Are the returns to R&D related to firm size? The last section is devoted to a summary of the conclusions that can be drawn from our empirical analysis.

II. DESCRIPTION OF LINKED CENSUS R&D-LRD DATA

Our examination of these issues is based on two confidential longitudinal data sets that were made available to us as participants in the ASA/NSF/Census Research Program. The Longitudinal Research Database (LRD), which brings together data from the Annual Survey and Census of Manufactures, was used to measure productivity at the firm level (based on plant-level data). The LRD file is the richest source of annual data on manufacturing establishments, containing detailed information on their output and inputs. The characteristics of this file are described in full detail in McGuckin and Pascoe [1988].(3)

To study the relationship between R&D and productivity, we linked the LRD file to the NSF/Census firm-level Annual Survey of Industrial R&D (RD-1 Survey). The RD-1 Survey contains comprehensive data on firms' R&D investment and its distribution by source of funds (company vs. federally-funded R&D), character of use (basic vs. applied, product field), and many other classifications. The importance of the RD-1 Survey is demonstrated by the fact that it serves as the basis for the official United States R&D statistics, as published by the National Science Foundation.(4)

A previous study, Lichtenberg and Siegel [1989], was based on linked R&D-LRD data for a sample of 115 large firms. In this paper, we analyze the R&D-productivity connection for a substantially larger and more representative sample of firms--the complete universe of firms in the linked R&D-LRD data set--over 2,000 companies. Definitions and descriptive statistics for key variables appear in Table I. R&D intensity values are derived completely from information contained in the NSF R&D Survey. That is, R&D expenditure, employment, and sales figures reported are consolidated, domestic, firm-level values. We have computed average annual values of each variable for three periods, 1973-1976, 1977-1980, and 1981-1985. Total factor productivity growth (AVDTFP) is calculated according to standard practice: it is log change in real output minus a weighted average of the changes in real inputs, where the weights are the average (across the current and previous year) cost shares of the respective inputs. The cost shares are constrained to equal one (constant returns to scale), and capital's cost share is calculated as a residual.(5)

While measures of R&D intensity are based on company-level values, our estimates of firm productivity are derived from a time series extract of plants in the LRD file. This file consists of 20,493 manufacturing establishments that were sampled continuously in the Annual Survey of Manufactures (ASM) for the years 1972-1981. The data have been updated through 1985, although the panel is not "balanced" over the post-1981 period, primarily because of plant closings.(6) Thus, the LRD time series file is certainly not a random sample of manufacturing establishments.(7) It contains plants that "survived" until 1981--establishments that are relatively large and old. However, given that firms in the NSF R&D survey are highly likely to have most, if not all, of their establishments sampled with certainty in the ASM, our linked R&D-LRD dataset captures a very high percentage of a given R&D-performing firm's output.(8) This is demonstrated in Table I, as the mean value of the "coverage ratio" COVRAT (the ratio of a firm's total LRD shipments to its sales) suggests that on average, we are capturing a substantial proportion (approximately 82 percent) of each corporation's domestic sales, and an even higher proportion of its manufacturing shipments.

Table I shows that productivity performance improved in the later periods. Average annual TFP growth declined 1.4 percentage points during period one and remained virtually constant in periods two and three. This result is consistent with the general improvement in aggregate economic performance during these years.(9) A second stylized fact is that there is only a small degree of variation across periods in all measures of R&D intensity. For example, the average R&D intensities during periods one, two, and three were 2.4 percent, 2.4 percent, and 2.8 percent, respectively.(10,11) In the next section, we discuss how these linked R&D-LRD data can be used to estimate the effects of R&D on productivity growth.

III. REVIEW AND CRITIQUE OF EXISTING STUDIES

Previous studies have demonstrated that productivity growth is positively correlated with the intensity of R&D investment (usually measured as R&D expenditure per dollar of sales). Our reservations concerning attempts to assess the impact of R&D on productivity are not grounded in doubts relating to the theory that is used to explain this relationship.(12) Our concern is directed towards the poor quality of productivity measurement in some previous empirical applications of the basic theoretical model.

This model (see Griliches [1979]), common to most existing empirical studies, is based on a Cobb-Douglas production function, including the stock of technical knowledge as a factor of production: (1)

[Mathematical Expression Omitted]

An index of TFP is conventionally defined as (2)

[Mathematical Expression Omitted]

Taking logs, differentiating with respect to time, assuming constant returns to scale, imposing the condition that the output elasticities of the conventional inputs equal their respective shares in total cost (factors are paid their marginal products), and reparameterization of the output elasticity of R&D (see Terleckyj [1974], yields (3) DTF [P.sub.t] = [Lambda] + [Rho] (R/Q) + [Mu] where [Rho] is the marginal product of research capital, or the "rate of return" to R&D investment, [Lambda] is the rate of disembodied "external" technical change, and symbol [Mu] is a classical disturbance term.(13) Assuming zero or negligible depreciation of R&D, (R/Q) is measured as the "intensity" of R&D investment, or the R&D to sales ratio.(14) Equation (3) therefore constitutes the "intensity" version of the R&D Capital Stock Model.(15)

An important consideration in analyzing the effects of R&D on productivity is the level of aggregation of the data. Early studies used economy-wide or industry time series, leading to parameter estimates that were interpreted as measures of the social return to R&D.(16) Several R&D-productivity studies have also been undertaken at the firm level (Minasian [1969], Mansfield [1980], Link [1981a], Griliches [1980a; 1986], and Griliches and Mairesse [1984] and the business segment level (Clark and Griliches [1984]). A micro-level analysis is desirable because of greater degrees of freedom and, more importantly, because it provides evidence on the private returns to R&D, which, due to incomplete appropriability or other factors, may not equal the social return to this activity.

Recent examinations of the relationship between R&D and productivity (mainly micro-level studies) have yielded somewhat contradictory results. Papers based on data collected from the 1950s and 1960s have found positive effects of R&D on productivity. However, in several studies using 1970s data, including Agnew and Wise [1978], Griliches [1980b], Link [1981a], and Scherer [1981], the R&D coefficient failed to achieve statistical significance. On the other hand, Mansfield [1980], Griliches and Lichtenberg [1984a], Griliches and Mairesse [1984], Griliches [1986], and Lichtenberg and Siegel [1989] have found that the association between R&D and productivity did not collapse during the 1970s. The remainder of this paper will highlight and address several potentially important methodological problems inherent to micro-level studies of the R&D-productivity connection, which are caused mainly by data limitations. These restrictions may explain the results of studies that find insignificant returns to R&D and, thus, implicitly identify R&D investment as a factor contributing to the productivity slowdown.

One problem with these papers is that they are based only on data collected from firms whose shares are publicly traded. Also, public access files, such as Standard and Poor's Compustat file, which are derived from firms' 10-K reports to the SEC, contain information only on a single R&D variable, company-funded R&D expenditure. This lack of detailed R&D data is bothersome because recent empirical work by Mansfield [1980], Griliches [1986], Griliches and Lichtenberg [1984a], and Link [1981b] has focused on differences in productivity returns to specific components of R&D investment (e.g. basic research).(17)

Another concern is that productivity estimates in existing micro-level studies are based on crude and incomplete measures of output and inputs. Public access files include no information on the number of hours worked, and energy and materials data are often missing. The most serious problem in the calculation of TFP has been an inability to control for firm diversification. When computing real values of output and inputs, industry deflators must be applied to nominal variables. These deflators may vary greatly across different lines of business in a given firm. However, public information concerning a given firm's activity in different industries is remarkably limited.(18) As a result, in most firm-level studies, productivity estimation has been based on the assumption that firms operate in only one 4-digit SIC industry with real variables calculated according to a single set of price deflators.

In Lichtenberg and Siegel [1989], we illustrated the problems associated with the single-industry classification process with this simple example: Assume that a firm operates in two 4-digit SIC industries.

Let VQ[1.sub.t] = The firm's output in

If VQ[1.sub.t] > VQ[2.sub.t] then industry 1 is considered to be the firm's major line of business at time t, and industry 1's price deflator is used to calculate real output. Thus, the conventional (using publicly available information) methodology yields (M1) [Q[prime].sub.t] = (VQ[1.sub.t] + VQ[2.sub.t])/PQ[1.sub.t]. We believe that the proper way to measure real output is to take account of diversification(19) by deflating the firm's nominal output in each industry and then aggregating real output to the firm level.(20) The preferred measure of real output is (M2) [Q.sub.t] = VQ[1.sub.t]/PQ[1.sub.t] + VQ[2.sub.t]/PQ[2.sub.t]. It is clear that [Q.sub.t] and [Q[prime].sub.t] will grow at different rates if there are changes in the relative price of the two industries' outputs. Similar issues are associated with the measurement of real input of diversified firms.

It can be shown (see Lichtenberg and Siegel [1989]) that if we invoke the usual errors-in-variables assumptions concerning TFP measurement, the preferred method provides more efficient estimates of [Rho]:(21) where the additional error term, [[Epsilon].sub.2t], is due to a failure to control for diversification beyond a single 4-digit SIC industry.

[Mathematical Expression Omitted]

In order to assess the importance of these alleged gains in the precision of TFP estimation generated by the "preferred" methodology, we calculated variants of our regression model using (M1) and (M2) in Lichtenberg and Siegel [1989]. For a sample of 115 of the largest R&D performing companies, the standard deviation of the conventional measure of TFP growth was 29 percent higher. More importantly, the additional variance associated with the conventional methodology is also uncorrelated with R&D.

Estimates of were .079 (1.70) and .086 (2.28) using the standard (M1) and improved (M2) methods to calculate TFP, respectively, with corresponding t-statistics in parenthesis.(22) As expected from the errors-in-variables model, the point estimates under both methods are quite similar. However, LRD-based TFP measures provided more efficient estimates of the rate of return to R&D, as evidenced by a 31 percent increase in [R.sup.2] that arises when we calculate TFP under (M2). The relationship between R&D and productivity is statistically significant only when we appropriately account for firm diversification. This approach suggests that the finding of an insignificant coefficient on R&D intensity in previous studies may have been due in part to poor measurement. Due to the improvement in goodness of fit when we adopt (M2) rather than (M1), the advantages of using the LRD file to calculate TFP are apparent.

[Mathematical Expression Omitted]

IV. RATES OF RETURN TO R&D USING LINKED CENSUS R&D-LRD DATA

Our pilot study demonstrated the feasibility and desirability of using Census microdata to measure rates of return to R&D investment. This section analyzes the impact of R&D on productivity using the complete set of over 2,000 firms in the linked Census R&D-LRD data set. This is a highly representative sample of companies performing industrial R&D, including many small, private firms. Table II demonstrates that the companies in our sample accounted for 84 percent of R&D performed (by industrial firms) in the United States in 1976. The sample coverage ratios are also quite high for sales, employment, and all measures of R&D.

In section III, we discussed how use of linked R&D-LRD data allows us to measure productivity more precisely at the firm level. This is due to our ability to observe more complete measures of firms' output and inputs across industries. However, LRD estimates of a firm's productivity are based only on its continuously operating (between 1972 and 1981) manufacturing plants. We hypothesize that companies with a high percentage of their output in LRD establishments have their productivity measured more accurately than firms with low percentages of LRD activity. We found that the inability to measure firms' total output and inputs introduced an element of heteroskedasticity into OLS estimation of equation (3).

Thus, weighted least squares estimates for variants of equation (3) are presented in Table III. The weight for these regressions is [(COVRAT).sup.1/2], where COVRAT = the ratio of the firm's LRD shipments to its consolidated domestic net sales. These results are based on regressions of average annual TFP growth on average R&D intensity values for three periods, 1973-1976, 1977-1980, and 1981-1985.(23) In order to control (imperfectly) for inter-industry differences in R&D intensity due to differential "technological opportunity" and appropriability conditions, we measure each firm's R&D intensity as a deviation from the average R&D intensity in its home industry (2-digit SIC).(24) The parameter estimates of Table III will be compared with those from existing macro/industry and firm/line-of-business empirical studies in Table IV.

As discussed in section III, it is generally believed that parameter estimates from industry-level studies measure social returns to R&D, while estimates derived from micro studies capture private returns to R&D. Therefore, we do not expect parameter estimates based on models estimated at different levels of aggregation to be equal.(25) In the studies that are not based on the "intensity" model, the parameter of interest is [Alpha], the output elasticity of R&D. For each [Alpha caret], we have imputed a value of [Rho caret] (the estimated marginal product), dividing [Alpha caret] by the mean of R/Q. We are especially interested in comparing our results to those of previous studies based on the "intensity" model, using firm or line-of-business data.

The results of Table III confirm the existence of a positive relationship between the intensity of R&D investment and average annual productivity growth. Under competitive assumptions, our results imply private rates of return to R&D investment of 13.2 percent and 9.7 percent using expenditure and employment measures, respectively. A disaggregation of R&D by source of funds reveals that while the intensity of company-funded R&D investment (expenditure or employment) is a significant determinant of productivity growth, the intensity of federally-funded R&D investment is not. In addition, using both expenditure and employment measures, the hypothesis of homogeneity of returns to company and federally-funded R&D is rejected at the 1 percent level of significance.(26) The potency of privately-financed R&D (but not federally-financed R&D) has also been documented in Terleckyj [1974], Griliches and Lichtenberg [1984a], and Griliches [1986]. Since the returns to company and federally-funded R&D are different, we will focus on estimates of the return to company-funded R&D. Our estimate of a 35.3 percent rate of return to company-funded R&D is quite similar to the mean (of all previous studies) estimate of 29.2 percent for the same parameter, displayed in the last column of Table IV. Moreover, our estimates are based on more recent data than those in previous studies, and both our results and previous results suggest that [Rho] may have been higher in recent years; this could explain why our [Rho caret] is above the mean of previous [Rho caret]s.

A disaggregation of R&D by character of use indicates that the intensity of investment in basic research has a powerful impact on productivity growth, although the estimated rate of return of 133.8 percent to investment in basic research is substantially lower than Mansfield's [1980] estimate of 178.0 percent and Link's [1981b] estimate of 231.0 percent. The hypothesis of equality of returns to basic research and other types of R&D was rejected at the 1 percent level of significance.(27) This evidence of a "premium" on basic research confirms the findings of Griliches [1986], Mansfield [1980], and Link [1981b].(28,29)

The point estimates displayed in Table III are based on pooled regressions, imposing a common slope for each period (1973-1976, 1977-1980, and 1981-1985). To investigate the hypothesis that the returns to R&D varied across these three periods, we re-estimated the regression model, allowing for different slopes in all three periods.(30) These results are presented in Table V. Although we could not reject the hypothesis of equality of rates of return to R&D across periods, the results certainly suggest that the impact of R&D investment on TFP increased substantially in the later periods. In fact, the point estimate on total R&D (expenditure) is almost twice as high in period two. The rate of return to company-funded R&D, using expenditure or employment measures, is also dramatically higher in period two.

Table V also shows that our findings are consistent with two major empirical studies based on 1970s data. In period one, we calculate a 25.4 percent return to company-funded R&D, which is quite similar to estimates of 24.3 percent by Griliches [1986] and 27.5 percent by Mansfield [1980]. Turning to the character of use results, we observe that the "premium" on basic research increased slightly in period two, while the rates of return to applied research and development were insignificantly different from zero across periods. Ours is the first study of the relationship between R&D and productivity that is based on data from the 1970s and 1980s (1972-1985). A strong finding is that the returns to R&D appear to be rising over time. Some of the differences between our parameter estimates and those of existing studies may be due to differences in sample periods. In the next section, we examine the sensitivity of the full sample regression results (Table III) to outlying, influential observations.

V. IDENTIFICATION OF INFLUENTIAL OUTLIERS

Following Belsley, Kuh, and Welsch [1980] and Neter, Wasserman, and Kutner [1985], our research design is to detect outliers in the dependent and independent variables and determine whether these outliers are influential in the least squares regression fit. Cook [1977] has proposed an influence statistic that measures the change in the estimated parameter vector that results if the ith observation is deleted. It is well known (see Maddala [1977]) that the confidence region for [Beta] is expressed as (7) [([Beta caret]-[Beta]) [prime] X [prime] X([Beta caret]-[Beta])]/kMSE

MSE = mean square error Cook's influence statistic is defined in a similar manner, except it is based on a measure of the difference in the estimated parameter vector including and excluding the ith observation. (8) [Mathematical Expression Omitted] where [[Beta caret].sub.i] is the estimate of [Beta] without the ith data point. An equivalent expression for [D.sub.i] involves the residuals ([e.sub.i]) and leverage values ([h.sub.ii]):(31) (9) [Mathematical Expression Omitted] Relating values of [D.sub.i] to the F-distribution with k and n-k degrees of freedom, those observations having percentile values of 50 percent or more are considered influential observations. For each variant of the regression model (equation (3)), we detected observations that were influential and outliers in X and/or y.

The discovery of influential outliers led us to examine the sensitivity of our regression results to the following remedial measures:

1) reduction of the impact that influential observations have on the fitted regression function

2) deletion of influential outliers Deleting outlying influential observations is a somewhat drastic approach, unless the researcher is certain that the extreme values are due to what Belsley, Kuh, and Welsch [1980] call "gross measurement error"--keypunch errors or incorrect reporting. If these values are correct, then their deletion eliminates vital information. In our final sample, we believe that we have already discarded a non-negligible percentage of values reflecting gross errors in measurement. An alternative to the least squares estimator that minimizes the effect of egregious errors or outliers is the method of least absolute deviations. One of a class of robust estimators, this "bounded-influence" estimator minimizes the sum of the absolute deviations of the observations from their means. These estimates are less sensitive to outliers because the sum of absolute, rather than squared, deviations is minimized.(32)

In Table VI, we compare our earlier estimates of rates of return to R&D investment to estimates of these same parameters after deleting influential outliers (DEL) and those derived from the method of least absolute deviations (LAD). The LAD estimates of the rates of return to total R&D, company-funded R&D, and basic research are 29.5 percent, 26.6 percent, and 31.5 percent lower, respectively, than our original estimates. Our point estimates of these same three parameters decline 3.8 percent, 17.3 percent, and 24.4 percent, respectively, when influential outliers are discarded. These results are somewhat surprising. We expected the deletion of influential outliers to have a stronger impact on the parameter estimates than attempts to reduce their influence. Instead, the opposite pattern emerged, as the LAD estimates of these three rates of return are always lower than corresponding DEL estimates. Still, our original estimates of the effect of R&D investment on TFP growth are not dramatically sensitive to adjustments aimed at reducing the impact of influential outliers.(33) In the next section, we explore the relationship between rates of return to R&D and firm size.

VI. FIRM SIZE AND RATES OF RETURN TO R&D

The ideas of Joseph Schumpeter [1950] figure prominently in the belief that large firms are especially likely both to undertake, and be successful in, research activities. Recent papers by Griliches [1980a], Scherer [1984], Bound et al. [1984], and Cohen, Levin, and Mowery [1987] have found little evidence to support the position that firm size is positively correlated with R&D intensity. Link [1981a] suggested an alternative approach to empirical investigation of the Schumpeterian hypothesis. He examined and found evidence of a systematic relationship between firm size and the impact of R&D on productivity--large firms earned higher returns to R&D than small firms.

Estimation of variants of equation (3) was contingent on the assumption of a common rate of return, [Rho], among firms. In this section, we test whether R&D investment by large firms is more successful than that undertaken by small firms by investigating the possibility that p varies across firms according to size.(34) A test for the structural stability of regression parameters has been developed by Brown, Durbin, and Evans [1975]. The null hypothesis of this test is that the regression coefficients are constant over an index of firm size. An analysis of the cumulative sum of squared residuals determines where, if at all, a structural "break" or shift occurs. An attractive property of the Brown-Durbin-Evans "cusum" test is that it does not require prior information concerning the true point of structural change, unlike the Chow test. The use of prior information concerning structural shifts is often quite plausible when analyzing time series data.(35) However, in our context, the implementation of this type of strategy would be arbitrary. Link [1981a], having estimated rates of return to R&D investment based on the reduced-form version of the R&D capital stock model (using firm-level data), employed the Brown-Durbin-Evans test to examine the structural stability of these returns with respect to firm size.

Our findings, based on the same research design applied to a larger and more representative sample of firms, do not substantiate the Schumpeterian hypothesis. Using sales and employment as proxies for firm size, we were unable to reject the null hypothesis of structural stability for the rate of return to R&D.(36) Although we were unable to determine from the data whether different size "regimes" exist with respect to the rate of return to R&D, we ranked companies by size and divided the sample into three groups. Table VII contains estimates of rates of return to R&D, productivity growth, and R&D investment for these three size categories. The small degree of variation in the rate of return to total R&D across groups provides non-parametric evidence in support of structural stability. Mean TFP growth and R&D intensity values are also quite similar.

The returns to company-funded R&D, however, do appear to be higher for large firms. In fact, we observe statistically significant differences (at the 1 percent level of significance) in rates of return to company-funded R&D between the two groups of large firms and the smallest companies.(37) The apparent instability of this regression parameter compels us to implement the cusum test on this coefficient. One reason for this finding may be that appropriability conditions are more favorable for large firms. This is a subject for future research. We also note that federally-funded R&D appears to have a stronger impact on the productivity growth of small firms, although the coefficients are insignificant for all three size groups. This result, which could have important implications for federal contracting policy, also bears further examination.

Still, the evidence presented in Table VII demonstrates that our earlier findings concerning rates of return are consistent for each size classification of firms:

a) positive and significant coefficient on R&D intensity

b) higher returns to company-funded R&D

c) a productivity "premium" on basic research

VII. CONCLUSIONS

A sizable body of empirical research based on aggregate and industry-level time series data has provided evidence of a strong positive correlation between R&D investment and productivity growth. However, the results of studies based on firm-level data have been much less robust. In this paper, we have demonstrated that previous firm-level studies have contained imprecise measures of productivity. The main source of imprecision has been an inability to adequately control for the diversified activities of corporations. Use of the NSF/Census R&D-LRD Panel allows us to develop more precise estimates of TFP and the impact of R&D on TFP, primarily because the LRD file contains detailed data on the output and input of firms at the 4-digit SIC industry level.

We find that R&D investment was a significant determinant of productivity growth during the years 1972-1985. The R&D-productivity connection was strong throughout the 1970s, when there was a pervasive slowdown in productivity growth. Our results suggest that the rate of return to R&D was higher in the latter stages of the decade and especially in the 1980s. This may explain why manufacturing firms are devoting a larger percentage of their own funds to R&D projects in the 1980s. It appears that profitable research opportunities were plentiful during the 1970s and in recent years. Concern about a recent decline in the impact of R&D on technological progress, due to a diminution of technological opportunities (Baily and Chakrabarti [1988]), does not appear to be well founded.

We find that investment in basic research has a strong effect on productivity growth, while investment in other types of R&D apparently has either a small impact on TFP growth or none at all. This result is consistent with the findings of Mansfield [1980], Link [1981b] and Griliches [1986]. Given the high degree of uncertainty associated with basic research, it is not surprising that its mean rewards are greater than other, less risky forms of R&D.

Another important result is that, consistent with previous studies,(38) we observe a strong positive correlation between the rate of growth of TFP and privately funded R&D, while federally-funded R&D does not appear to be a significant determinant of TFP growth. At first glance, this result implies that firms benefit only from R&D that is privately financed. Perhaps private companies, rather than the federal government, are best able to judge the potential returns to industrial R&D. It must be emphasized, however, that there are two alternative explanations for this finding, each associated with difficulties measuring the benefits resulting from government-funded R&D projects. One measurement problem is that in industries with relatively high levels of publicly-financed R&D, such as the defense or space sectors, output is poorly measured and price indices do not accurately reflect improvements in quality.(39) A related concern is that federal R&D may have an indirect positive impact on productivity which is difficult to capture in our econometric framework. For example, federal R&D may improve economic welfare as a result of

a) stimulation of additional privately-financed R&D or

b) "spillovers" or benefits that accrue to industries or firms from R&D that is performed outside a given firm or industry

While some investigators (e.g. Levy and Terleckyj [1983]) have found there to be a positive simple correlation between company and government-financed R&D, Lichtenberg [1987] has demonstrated that this correlation is statistically "spurious," and that the true correlation is zero and perhaps even negative. Although there have been several investigations of the impact of spillovers, there is no reliable estimate of their contribution to productivity growth. Better methods and data are needed to improve our understanding of this process. At the present time, it is difficult to know whether the standard econometric framework underestimates the impact of federal R&D on economic growth.

In conclusion, the productivity slow-down of the 1970s cannot be blamed on R&D spending, since neither aggregate R&D intensity, nor the estimated contribution of R&D to productivity growth declined during this period. On the other hand, R&D deserves part of the credit for the revival of productivity growth during the 1980s, since during this decade both the extent and apparent efficacy of R&D investment increased. [Tabular Data 1 to 7 Omitted]

(1)Suppose a firm spends $1 on R&D today. If the stock of knowledge capital does not depreciate, it will be $1 greater in every period in the future. If the marginal product of this capital is [Beta], revenues will be $[Beta] greater in every future period. Hence the rate of return to investment in R&D is equal to [Beta], the marginal product of knowledge capital. If the stock of knowledge depreciates at a rate [Rho] > 0, the rate of return is [Beta] - [Rho]. (2)Brookings Papers on Economic Activity 3, 1987, 674. (3)Outside researchers, working through the Center for Economic Studies at the Census Bureau, can apply for access to the LRD file. McGuckin and Pascoe [1988] provide detailed information on access procedures and also describe several LRD projects. The LRD has been analyzed in a number of studies, including Lichtenberg and Siegel [1987; 1990a; 1990b], Davis and Haltiwanger [1989], and Dunne, Roberts, and Samuelson [1988]. (4)See Lichtenberg [1990] for a discussion of the RD-1 data, including a comparison of them with other (e.g. Compustat) R&D data. (5)Four factors of production are measured and deflated separately--capital, labor, energy, and materials. Explicit information on the construction of these variables is contained in the data appendix to Lichtenberg and Siegel [1989], which is available upon request from the authors. (6)Some plants are not observed after 1984 because they were dropped from the 1984 ASM survey panel. (7)For a more comprehensive discussion of this issue, see Lichtenberg and Siegel [1987]. (8)That is, although the LRD time series file is not a random sample of manufacturing plants, it is quite representative of establishments owned by companies that perform R&D. (9)Note that the standard deviation of TFP growth falls sharply in period three. In Lichtenberg and Siegel [1990], we found that the relative productivity of closed plants declined considerably in the years before failure (especially in the year immediately preceding failure). These plants are included in our sample in periods one and two. Thus, a probable cause of this significant reduction in the variance of productivity growth is the elimination of closed establishments in the last period. The bias that results from this does not appear to be severe because TFP does not increase sharply in period three. (10)The unbalanced nature of reporting is due to the fact that firms are not required to report R&D expenditure by character of use (basic vs. applied research and development) and R&D scientists and engineers by source of funds. (11)The anomalous values for the mean value of company-funded scientists and engineers in period one is driven by a few outliers, probably caused by the difficulties firms have in allocating R&D employment by source of funds. (12)In contrast, Nelson [1988] criticizes the interpretation of the empirical results contained in these studies. He argues that R&D intensity is not exogenous; in fact, it is determined by "technological opportunity" and appropriability conditions in specific industries. To some extent, we will control for these factors by measuring each firm's R&D intensity as a deviation from the average R&D intensity in its home industry (2-digit SIC). (13)It is common in this literature to refer to [Rho] as an "excess" rate of return (in excess of normal remuneration to conventional factors of production) because R&D expenditures are often already included in measures of K and L (see Schankerman [1981] for a discussion of the impact of this "double-counting"). The National Science Foundation [1980] reports that 46 percent of the cost of R&D is devoted to labor, 17 percent to materials and supplies, and 37% to overhead. Aggregation of different types of R&D costs does not pose a problem in estimating returns to R&D because all expenditures (even those for "variable" inputs) constitute investment. (14)Griliches and Lichtenberg [1984a] find that the assumption of zero depreciation, as opposed to alternative assumptions concerning the depreciation of R&D capital, yields the best fit to industry data. (15)As discussed above, TFP growth is measured as (4)

[Mathematical Expression Omitted]

[X.sub.it] = Quantity of factor i at time t (in real

terms). (16)Of course, the industry rate of return may not equal the social rate of return when there are interindustry R&D spillovers. Empirical evidence concerning the existence of such spillovers is somewhat mixed (see Griliches and Lichtenberg [1984b]). (17)Mansfield [1980], Link [1981b], and Griliches [1986] find evidence of a productivity "premium" on basic research. Griliches [1986] and Griliches and Lichtenberg [1984a] conclude that privately-financed R&D (but not federally-financed R&D) has a strong effect on productivity growth. (18)Compustat, for example, provides only one or several 4-digit SICs for the companies it samples. Most importantly, the distributions of the variables needed to construct total or partial productivity are unavailable at the line-of-business level. (19)Gollop and Monahan [1984], using quinquennial Census of Manufactures data, present evidence that firms became increasingly diversified during the period 1963-1977. Hence, the importance of accounting for diversification in productivity measurement also increased. (20)Clark and Griliches [1984] use business unit data (in ratio form and heavily masked to prevent disclosure) provided by large, diversified companies in the proprietary PIMS file to analyze the relationship between R&D and TFP growth. Although business units are still highly aggregative, this methodology, to some extent, addresses some of the concerns we have discussed. However, the use of divisional-level R&D data raises new concerns about measurement error in estimates of R&D, because R&D is often regarded as a corporate-level activity and cannot be easily assigned to specific industries (by definition in the case of basic research). (21)[[Mu].sub.t] is a classical disturbance term, [[Epsilon].sub.1t] is due to an inability to completely measure the "true" level of diversification and errors in the industry deflators (see Griliches and Lichtenberg [1989]). We assume that the error terms have zero mean, are pairwise uncorrelated, and are uncorrelated with both the independent variable and [[Mu].sub.t]. (22)These calculations are based on weighted least squares regressions of average annual productivity growth on average annual R&D intensity for two periods: 1973-1976 and 1977-1980, where the weights adjust for heteroskedasticity due to incomplete firm "coverage" in the LRD file. That is, we believe that estimates of firm productivity based on only a small fraction of its manufacturing plants are somewhat less reliable, or "noisy." Still, on average, we captured 85 percent of a firm's sales. (23)This paper does not attempt to analyze R&D lag effects (Griliches [1980a]) and relates TFP only to R&D performed in the current period. Griliches and Lichtenberg [1984a], using a similar methodology, found only a slight improvement in explanatory power when estimating these equations using lagged values of R&D. Our specification focuses on the R&D-TFP connection in the (relatively) long term, as do most of the studies cited in this paper. Thus, our findings may not necessarily provide additional evidence on the short term dynamics of the relationship between R&D and TFP. (24)All of our regressions control for these industry effects. (25)Several authors have avoided imposing the condition that factors are paid their marginal products and, instead, estimated Cobb-Douglas production functions directly, assuming only constant returns to scale with respect to the conventional inputs. The "level" and "growth rate" equations estimated in Griliches [1980a; 1980b; and 1986] are based on constant returns to scale and competitive markets for these inputs. (26)The t-statistics for tests of the expenditure and employment measures are 48.53 and 25.03, respectively. (27)The t-statistic for the test of equality of returns to basic research and applied research is 61.07. The t-statistic for the same test involving basic research and development is 65.78. (28)To make our results more comparable to the findings of Griliches [1986], we also regressed TFP growth on company-funded R&D intensity and the ratio of basic research to total R&D expenditure. The estimated coefficients and t-statistics (in parentheses) are, respectively, .313 (11.86) and .096 (8.86). These estimates are quite similar to the findings contained in the aforementioned study, although the "premium" on basic research is somewhat lower. (29)The same pattern of results emerges when we restrict our sample to include only firms reporting (zero or positive) expenditure on basic research. When we estimate variants of the regression model for the same set of companies, the estimated coefficients and corresponding t-statistics (in parentheses) for columns a, b, d, and e are (a) .137 (4.66); (b) .422 (6.17) .016 (0.41); (d) .135 (3.07); (e) .160 (3.37) .044 (0.62). (30)Scherer [1982; 1983] argues that specifications such as ours may not capture "true" changes in private returns to R&D over time. He believes that it is important to follow R&D from industry of origin to industry of use, as many firms "purchase" R&D from other firms implicitly when buying certain products and services. According to this view, we can truly measure the impact of R&D on productivity only by identifying these "interindustry technology flows." However, using more comprehensive data on "interindustry technology flows" than in Scherer's original study, Griliches and Lichtenberg [1984b] failed to find evidence to corroborate this hypothesis. (31)Where [e.sub.i] = y - X[Beta] = y - X[(X [prime] X).sup.-1] X [prime] y = y - Hy

The "hat" matrix (H) is a projection matrix, which is symmetric and idempotent (H [prime] H = H). Each diagonal element of the hat matrix, [h.sub.ii], is called the leverage, measuring the distance between the X values of the ith observation and the X values of the remaining observations. The value of [h.sub.ii] determines how influential the ith observation is in determining [y.sub.i] (32)As demonstrated by Charnes et al. [1955], the method of least absolute deviations estimates can be derived from the solution to a linear programming problem. However, standard errors for the parameter estimates are unknown the statistical properties of the sampling distribution of this estimator are not well defined. (33)With influential outliers deleted, we still reject the hypothesis of homogeneity of returns to company and federally-funded R&D. The same is true for the hypothesis of equality of returns to basic research and other types of R&D. (34)A strict Schumpeterian interpretation of the heterogeneity of [Rho] across companies might be that [Rho] is a function of firms' monopoly power. Large size is neither a necessary nor a sufficient condition for firms' ability to gain or maintain monopoly power. (35)The cusum test has been applied on macroeconomic time series data in Heller and Khan [1979]. (36)That is, the test statistic, [s.sub.r], based on the normalized cumulative sum of squared residuals, always falls within the 5 percent confidence intervals above and below the mean value line. Given the extremely large size of the sample, a plot of the [s.sub.r]'s against observation number (after these values have been sorted appropriately) cannot be displayed graphically. (37)The t-statistics for these tests are 2.75 (largest vs. smallest) and 2.97 (middle vs. smallest). The difference in rates of return to company-funded R&D between the largest and middle groups of firms is statistically insignificant. (38)See Griliches and Lichtenberg [1984a] and Griliches [1986]. (39)See Griliches [1979] for a full exposition of this argument.

REFERENCES

Agnew, Carson E. and Donald E. Wise. "The Impact of R&D on Productivity: A Preliminary Report." Paper presented at the Southern Economic Association meetings, 1978.

Baily, Martin N. and Alok K. Chakrabarti. Innovation and the Productivity Crisis. Washington, D.C.: Brookings Institution, 1988.

Belsley, David A., Edwin Kuh, and Roy E. Welsch. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons, 1980.

Bound, John, Clint Cummins, Zvi Griliches, Bronwyn H. Hall, and Adam Jaffe. "Who Does R&D and Who Patents?" in R&D, Patents, and Productivity, edited by Zvi Griliches, Chicago: University of Chicago Press, 1984, 21-54.

Brown, R. L., J. Durbin, and J. M. Evans. "Techniques for Testing the Constancy of Regression Relationships Over Time." Journal of the Royal Statistical Society (series B), December 1975, 149-63.

Charnes, Abe, W. W. Cooper, and R. O. Ferguson. "Optimal Estimation of Executive Computing by Linear Programming." Management Science, March 1955, 138-151.

Clark, Kim B. and Zvi Griliches. "Productivity Growth and R&D at the Business Level: Results from the PIMS Data Base," in R&D, Patents, and Productivity, edited by Z. Griliches. Chicago: University of Chicago Press, 1984, 393-416.

Cohen, W. M., R. C. Levin, and D. C. Mowery. "Firm Size and R&D Intensity." Journal of Industrial Economics, June 1987, 543-65.

Cook, R. Dennis. "Detection of Influential Observations in Linear Regression." Technometrics, February 1977, 15-18.

Davis, Steve J. and John Haltiwanger. "Gross Job Creation, Gross Job Destruction, and Employment Reallocation." Paper presented at National Bureau of Economic Research Summer Institute, 1989.

Dunne, Timothy, Mark J. Roberts, and Larry Samuelson. "Entry and Exit in U.S. Manufacturing." Rand Journal of Economics, Winter 1988, 495-515.

Gollop, Frank M. and James L. Monahan. "From Homogeneity to Heterogeneity: A Proper Index of Diversification." Mimeo, Bureau of the Census Technical Notes, 1984.

Griliches, Zvi. "Issues in Assessing the Contribution of Research and Development to Productivity Growth." Bell Journal of Economics, Spring 1979, 92-116.

______. "Returns to Research and Development Expenditures in the Private Sector," in New Developments in Productivity Measurement, edited by J. W. Kendrick and B. Vaccara. National Bureau of Economic Research Studies in Income and Wealth No. 44, Chicago: University of Chicago Press, 1980a, 419-54.

______. "R&D and the Productivity Slowdown." American Economic Review, May 1980b, 343-348.

______. "Productivity, R&D and Basic Research at the Firm Level in the 1970's." American Economic Review, March 1986, 141-54. Griliches, Zvi and Frank R. Lichtenberg. "R&D and Productivity Growth at the Industry Level. Is There Still a Relationship?" in R&D, Patents, and Productivity, edited by Z. Griliches. Chicago: University of Chicago Press, 1984a, 465-96.

______. "Interindustry Technology Flows and Productivity Growth: A Reexamination." Review of Economics and Statistics, May 1984b, 324-29.

Griliches, Zvi and Jacques Mairesse. "Productivity and R&D at the Firm Level," in R&D, Patents, and Productivity, edited by Z. Griliches. Chicago: University of Chicago Press, 1984, 339-74.

Heller, Robert H. and Moshin S. Khan. "The Demand for Money and the Term Structure of Interest Rates." Journal of Political Economy, January 1979, 109-29.

Jorgenson, Dale W. and Zvi Griliches, "The Explanation of Productivity Change," Review of Economic Studies, July 1967, 249-83. Levy, David M. and Nestor Terleckyj. "Effects of Government R&D on Private R&D Investment and Productivity: A Macroeconomic Analysis." Bell Journal of Economics, Winter 1983, 551-61.

Lichtenberg, Frank R. "The Effect of Government Funding on Private Industrial Research and Development: a Re-assessment." Journal of Industrial Economics, September 1987, 1-8.

______. "Using Longitudinal Establishment Data to Estimate the Internal Adjustment Costs Model." Review of Economics and Statistics, August 1988, 421-30.

______. "Issues in Measuring Industrial R&D." Research Policy, 19, 1990, 157-163.

Lichtenberg, Frank R. and Zvi Griliches. "Errors of Measurement in Output Deflators." Journal of Business and Economic Statistics, January 1989, 1-9.

Lichtenberg, Frank R. and Donald Siegel. "Productivity and Changes in Ownership of Manufacturing Plants." Brookings Papers on Economic Activity 3, 1987, 643-83.

______. "Using Linked Census R&D-LRD Data to Analyze the Effect of R&D Investment on Total Factor Productivity Growth." Center for Economic Studies Discussion Paper, U.S. Census Bureau, 1989.

______. "The Effects of Leveraged Buyouts on Productivity and Related Aspects of Firm Behavior." Journal of Financial Economics, September 1990a, 165-94.

______. "The Effect of Takeovers on the Employment and Wages of Central-Office and Other Personnel." Journal of Law and Economics, October 1990b, 383-409.

Link, Albert N. Research and Development Activity in U.S. Manufacturing. New York: Proger, 1981a.

______. "Basic Research and Productivity Increase in Manufacturing: Additional Evidence." American Economic Review, December 1981b, 1111-12.

Maddala, G. S. Econometrics. New York: McGraw Hill, 1977.

Mansfield, Edwin. "Basic Research and Productivity Increase in Manufacturing." American Economic Review, December 1980, 863-73.

McGuckin, Robert and George Pascoe. "The Longitudinal Research Data Base-Research Possibilities." Survey of Current Business, November 1988, 30-37.

Minasian, Jora R. "Research and Development, Production Functions and Rates of Return." American Economic Review, March 1969, 80-85. National Science Foundation. Research and Development in Industry, serial 1957-1980. Washington, D.C.: Government Printing Office, 1980.

Nelson, Richard R. "Modeling the Connections in the Cross Section Between Technical Progress and R&D Intensity." Rand Journal of Economics, Winter 1988, 478-85.

Neter, J., W. Wasserman, and M. Kutner. Applied Linear Statistical Models. Homewood, Ill.: Irwin, 1985. Nordhaus, William D. "Policy Responses to the Productivity Slowdown," in The Decline in Productivity Growth, series no. 22. Federal Reserve Bank of Boston, 1980.

Schankerman, Mark. "The Effects of Double-Counting and Expensing on the Measured Returns to R&D." Review of Economics and Statistics, August 1981, 454-58.

Scherer, F. M. "Research and Development, Patenting, and the Microstructure of Productivity." Final Report, National Science Foundation, grant no. PRA-7826526, 1981.

______. "Interindustry Technology Flows and Productivity Growth." Review of Economics and Statistics, November 1982, 627-34.

______. "R&D and Declining Productivity Growth." American Economic Review, May 1983, 215-18.

______. Innovation and Growth: Schumpeterian Perspectives. Cambridge, Mass.: MIT Press, 1984. Schumpeter, Joseph A. Capitalism, Socialism, and Democracy, 3rd ed. New York: Harper and Row, 1950.

Solow, Robert M. "Technical Change and the Aggregate Production Function." Review of Economics and Statistics, August 1957, 214-31.

Terleckyj, Nestor. Effects of R&D on the Productivity Growth of Industries. Washington, D.C.: National Planning Association, 1974.

FRANK R. LICHTENBERG AND DONALD SIEGEL, Associate Professor, Columbia University Graduate School of Business and Research Associate, National Bureau of Economic Research; and ** Assistant Professor, Harriman School for Management and Policy, SUNY-Stony Brook and Faculty Research Fellow, National Bureau of Economic Research. We wish to thank Zvi Griliches, Robert McGuckin, Dennis Mueller, F. M. Scherer, Frank Wykoff, and two anonymous referees for helpful comments and suggestions. Earlier versions of this paper were presented at the National Bureau of Economic Research, the University of Maryland, and the U.S. Census Bureau. This study is based upon activities supported by the National Science Foundation under Interagency Agreement No. SRS-8801036 "Industrial R&D and Productivity: Using an Expanded NSF/Census Data Linkage File." The research was conducted at the Center for Economic Studies, U.S. Bureau of the Census. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Census Bureau.

This paper uses confidential Census longitudinal microdata to examine the association between R&D and productivity for the period 1972-1985. These data allow for significant improvements in measurement and model specification, yielding more precise estimates of the returns to R&D. Our results confirm the findings of existing studies:

1) positive returns to R&D investment

2) higher returns to company-financed research

3) a productivity "premium" on basic research

These results are robust to adjustments for "influential outliers." Also, our evidence suggests that the return to company-financed R&D is an increasing function of firm size.

I. INTRODUCTION

Robert Solow's studies in the late 1950s dramatically changed perceptions of the sources of economic growth. Until this time, the commonly held view was that improvements in economic welfare were achieved primarily through the use of more inputs, in particular, capital input. However, Solow [1957] reported that only 10 percent of the twofold rise in U.S. per capita output during the years 1909-1949 was due to growth in the capital/labor ratio. The remainder was attributed to more efficient use of inputs, or technological change. Solow also established a framework for estimating technological change, a productivity "residual" or a measure of changes in output that could not be explained by changes in input use. The Solow residual, in modified form, has become virtually synonymous with the measurement of total factor productivity (TFP) growth. Jorgenson and Griliches [1967] demonstrated that under the assumptions of constant returns to scale and competitive factor pricing, changes in total factor productivity measure shifts in a production function.

Rather than treat technological change as exogenous or "manna from heaven," many economists have explored its determinants. R&D investment is generally regarded as having a strong impact on productivity growth. Empirical analysis of the R&D-productivity connection has often been based on estimation of reduced-form equations derived from the R&D Capital Stock Model (Griliches [1979]), which extends the Solow model to include the stock of technical knowledge, or "knowledge capital," as a factor of production (in addition to the standard factors of production-physical capital, labor, intermediate materials, and energy). If the rate of depreciation of knowledge capital is assumed to be negligible, TFP growth (DTFP) is a function of the "intensity" of R&D investment (RDINT), which is usually measured as the ratio of R&D expenditure to sales: (1) DTF [P.sub.t] = [Alpha] + [Beta] RDIN [T.sub.t] + [u.sub.t] where [u.sub.t] is a classical disturbance term. The coefficient on R&D intensity ([Beta]) is interpreted as both the marginal product of knowledge capital and the "rate of return" to R&D investment.(1) Estimates of [Beta] at the company or line-of-business level are interpreted as measures of the private rate of return to R&D, or those that accrue to the firm or its investors. Due to incomplete appropriability or other factors, this return may not equal the social return to this activity.

Most empirical studies, especially those based on aggregate and sectoral data, have found evidence of a strong positive correlation between TFP growth and R&D investment. However, results using firm-level data have been mixed. The finding that these two variables are uncorrelated is cause for concern because it implies that firms may not be able to earn significant returns on their investment in R&D, making them less likely to undertake this investment in the future, even if it is socially desirable for them to do so. We believe that it is important to reestimate this relationship because it is highly likely that existing firm-level studies have been based on measures of TFP that are crude, imprecise, and unrepresentative.

Our objective in this paper is to reexamine the association between R&D and productivity growth using the most comprehensive and accurate longitudinal microdata yet available for productivity analysis. Dale Jorgenson of Harvard University has said of the data set used in this study, "The Longitudinal Research Data (LRD) set will ultimately transform research on productivity, especially at the microeconomic level, and not only there."(2) These data allow for improvements in measurement and model specification, yielding more efficient estimates of the effects of R&D on productivity. We discuss and adjust for some of the limitations of existing micro-level empirical studies, which have provided estimates of the private rate of return to R&D. While these studies have been useful, productivity estimates at the firm or line-of-business level contained therein are based on crude and incomplete measures of output and inputs. The most serious measurement problem has been an inability to control for diversification when calculating firms' productivity. More specifically, productivity estimation in these studies has often been based on the assumption that firms operate in only one line of business (4-digit SIC industry). To the extent that the relative prices of firms' outputs and inputs vary across industries, this approach introduces an element of noise into estimation of TFP growth. Even if it is uncorrelated with R&D intensity, this measurement error will reduce the efficiency of estimates of [Beta]. We demonstrate that measures of TFP growth based on linked Census R&D-LRD Data are more precise because we can calculate firms' real output and input at the 4-digit SIC industry level and aggregate to the firm level. As expected from the standard errors-in-variables model, this reduction in measurement error from improved deflation yields more efficient estimates of the rate of return to R&D.

We present an empirical example below that illustrates the extent to which more precise TFP measurement leads to more efficient estimates of rates of return to R&D. This example is derived from a pilot study performed by the authors (Lichtenberg and Siegel [1989]), based on linked R&D-LRD data for a sample of 115 firms for the years 1972-1980. Having demonstrated the desirability and feasibility of using linked Census R&D-LRD data to examine the R&D-productivity connection, we undertake a comprehensive analysis of rates of return to R&D, using a full sample of over 2,000 firms. Given our ability to disaggregate R&D investment, we can discriminate between the returns to R&D by source of funds (company-funded vs. federally-funded R&D) and by character of use (basic research vs. applied research and development). Also, the panel structure of our data allows us to explore the time series properties of these rates of return throughout the sample period (1972-1985). The sensitivity of our results to outliers (influential observations) is also examined. Finally, we address a "Schumpeterian" question: Are the returns to R&D related to firm size? The last section is devoted to a summary of the conclusions that can be drawn from our empirical analysis.

II. DESCRIPTION OF LINKED CENSUS R&D-LRD DATA

Our examination of these issues is based on two confidential longitudinal data sets that were made available to us as participants in the ASA/NSF/Census Research Program. The Longitudinal Research Database (LRD), which brings together data from the Annual Survey and Census of Manufactures, was used to measure productivity at the firm level (based on plant-level data). The LRD file is the richest source of annual data on manufacturing establishments, containing detailed information on their output and inputs. The characteristics of this file are described in full detail in McGuckin and Pascoe [1988].(3)

To study the relationship between R&D and productivity, we linked the LRD file to the NSF/Census firm-level Annual Survey of Industrial R&D (RD-1 Survey). The RD-1 Survey contains comprehensive data on firms' R&D investment and its distribution by source of funds (company vs. federally-funded R&D), character of use (basic vs. applied, product field), and many other classifications. The importance of the RD-1 Survey is demonstrated by the fact that it serves as the basis for the official United States R&D statistics, as published by the National Science Foundation.(4)

A previous study, Lichtenberg and Siegel [1989], was based on linked R&D-LRD data for a sample of 115 large firms. In this paper, we analyze the R&D-productivity connection for a substantially larger and more representative sample of firms--the complete universe of firms in the linked R&D-LRD data set--over 2,000 companies. Definitions and descriptive statistics for key variables appear in Table I. R&D intensity values are derived completely from information contained in the NSF R&D Survey. That is, R&D expenditure, employment, and sales figures reported are consolidated, domestic, firm-level values. We have computed average annual values of each variable for three periods, 1973-1976, 1977-1980, and 1981-1985. Total factor productivity growth (AVDTFP) is calculated according to standard practice: it is log change in real output minus a weighted average of the changes in real inputs, where the weights are the average (across the current and previous year) cost shares of the respective inputs. The cost shares are constrained to equal one (constant returns to scale), and capital's cost share is calculated as a residual.(5)

While measures of R&D intensity are based on company-level values, our estimates of firm productivity are derived from a time series extract of plants in the LRD file. This file consists of 20,493 manufacturing establishments that were sampled continuously in the Annual Survey of Manufactures (ASM) for the years 1972-1981. The data have been updated through 1985, although the panel is not "balanced" over the post-1981 period, primarily because of plant closings.(6) Thus, the LRD time series file is certainly not a random sample of manufacturing establishments.(7) It contains plants that "survived" until 1981--establishments that are relatively large and old. However, given that firms in the NSF R&D survey are highly likely to have most, if not all, of their establishments sampled with certainty in the ASM, our linked R&D-LRD dataset captures a very high percentage of a given R&D-performing firm's output.(8) This is demonstrated in Table I, as the mean value of the "coverage ratio" COVRAT (the ratio of a firm's total LRD shipments to its sales) suggests that on average, we are capturing a substantial proportion (approximately 82 percent) of each corporation's domestic sales, and an even higher proportion of its manufacturing shipments.

Table I shows that productivity performance improved in the later periods. Average annual TFP growth declined 1.4 percentage points during period one and remained virtually constant in periods two and three. This result is consistent with the general improvement in aggregate economic performance during these years.(9) A second stylized fact is that there is only a small degree of variation across periods in all measures of R&D intensity. For example, the average R&D intensities during periods one, two, and three were 2.4 percent, 2.4 percent, and 2.8 percent, respectively.(10,11) In the next section, we discuss how these linked R&D-LRD data can be used to estimate the effects of R&D on productivity growth.

III. REVIEW AND CRITIQUE OF EXISTING STUDIES

Previous studies have demonstrated that productivity growth is positively correlated with the intensity of R&D investment (usually measured as R&D expenditure per dollar of sales). Our reservations concerning attempts to assess the impact of R&D on productivity are not grounded in doubts relating to the theory that is used to explain this relationship.(12) Our concern is directed towards the poor quality of productivity measurement in some previous empirical applications of the basic theoretical model.

This model (see Griliches [1979]), common to most existing empirical studies, is based on a Cobb-Douglas production function, including the stock of technical knowledge as a factor of production: (1)

[Mathematical Expression Omitted]

with Q(t) = output [A.sub.o] = a constant [Lambda] = a disembodied Hicks-neutral technical change parameter [X.sub.1] (t) = K(t) = the stock of physical capital [X.sub.2] (t) = L(t) = labor input [X.sub.3] (t) = M(t) = material (including energy) R(t) = the (unobservable) stock of technical knowledge [[Beta].sub.i] = output elasticity of factor i [Alpha] = output elasticity of the stock of R&D

An index of TFP is conventionally defined as (2)

[Mathematical Expression Omitted]

Taking logs, differentiating with respect to time, assuming constant returns to scale, imposing the condition that the output elasticities of the conventional inputs equal their respective shares in total cost (factors are paid their marginal products), and reparameterization of the output elasticity of R&D (see Terleckyj [1974], yields (3) DTF [P.sub.t] = [Lambda] + [Rho] (R/Q) + [Mu] where [Rho] is the marginal product of research capital, or the "rate of return" to R&D investment, [Lambda] is the rate of disembodied "external" technical change, and symbol [Mu] is a classical disturbance term.(13) Assuming zero or negligible depreciation of R&D, (R/Q) is measured as the "intensity" of R&D investment, or the R&D to sales ratio.(14) Equation (3) therefore constitutes the "intensity" version of the R&D Capital Stock Model.(15)

An important consideration in analyzing the effects of R&D on productivity is the level of aggregation of the data. Early studies used economy-wide or industry time series, leading to parameter estimates that were interpreted as measures of the social return to R&D.(16) Several R&D-productivity studies have also been undertaken at the firm level (Minasian [1969], Mansfield [1980], Link [1981a], Griliches [1980a; 1986], and Griliches and Mairesse [1984] and the business segment level (Clark and Griliches [1984]). A micro-level analysis is desirable because of greater degrees of freedom and, more importantly, because it provides evidence on the private returns to R&D, which, due to incomplete appropriability or other factors, may not equal the social return to this activity.

Recent examinations of the relationship between R&D and productivity (mainly micro-level studies) have yielded somewhat contradictory results. Papers based on data collected from the 1950s and 1960s have found positive effects of R&D on productivity. However, in several studies using 1970s data, including Agnew and Wise [1978], Griliches [1980b], Link [1981a], and Scherer [1981], the R&D coefficient failed to achieve statistical significance. On the other hand, Mansfield [1980], Griliches and Lichtenberg [1984a], Griliches and Mairesse [1984], Griliches [1986], and Lichtenberg and Siegel [1989] have found that the association between R&D and productivity did not collapse during the 1970s. The remainder of this paper will highlight and address several potentially important methodological problems inherent to micro-level studies of the R&D-productivity connection, which are caused mainly by data limitations. These restrictions may explain the results of studies that find insignificant returns to R&D and, thus, implicitly identify R&D investment as a factor contributing to the productivity slowdown.

One problem with these papers is that they are based only on data collected from firms whose shares are publicly traded. Also, public access files, such as Standard and Poor's Compustat file, which are derived from firms' 10-K reports to the SEC, contain information only on a single R&D variable, company-funded R&D expenditure. This lack of detailed R&D data is bothersome because recent empirical work by Mansfield [1980], Griliches [1986], Griliches and Lichtenberg [1984a], and Link [1981b] has focused on differences in productivity returns to specific components of R&D investment (e.g. basic research).(17)

Another concern is that productivity estimates in existing micro-level studies are based on crude and incomplete measures of output and inputs. Public access files include no information on the number of hours worked, and energy and materials data are often missing. The most serious problem in the calculation of TFP has been an inability to control for firm diversification. When computing real values of output and inputs, industry deflators must be applied to nominal variables. These deflators may vary greatly across different lines of business in a given firm. However, public information concerning a given firm's activity in different industries is remarkably limited.(18) As a result, in most firm-level studies, productivity estimation has been based on the assumption that firms operate in only one 4-digit SIC industry with real variables calculated according to a single set of price deflators.

In Lichtenberg and Siegel [1989], we illustrated the problems associated with the single-industry classification process with this simple example: Assume that a firm operates in two 4-digit SIC industries.

Let VQ[1.sub.t] = The firm's output in

current dollars, in industry 1 at time t VQ[2.sub.t] = The firm's output in current dollars, in industry 2 at time t PQ[1.sub.t] = The price deflator for industry 1 at time t PQ[2.sub.t] = The price deflator for industry 2 at time t

If VQ[1.sub.t] > VQ[2.sub.t] then industry 1 is considered to be the firm's major line of business at time t, and industry 1's price deflator is used to calculate real output. Thus, the conventional (using publicly available information) methodology yields (M1) [Q[prime].sub.t] = (VQ[1.sub.t] + VQ[2.sub.t])/PQ[1.sub.t]. We believe that the proper way to measure real output is to take account of diversification(19) by deflating the firm's nominal output in each industry and then aggregating real output to the firm level.(20) The preferred measure of real output is (M2) [Q.sub.t] = VQ[1.sub.t]/PQ[1.sub.t] + VQ[2.sub.t]/PQ[2.sub.t]. It is clear that [Q.sub.t] and [Q[prime].sub.t] will grow at different rates if there are changes in the relative price of the two industries' outputs. Similar issues are associated with the measurement of real input of diversified firms.

It can be shown (see Lichtenberg and Siegel [1989]) that if we invoke the usual errors-in-variables assumptions concerning TFP measurement, the preferred method provides more efficient estimates of [Rho]:(21) where the additional error term, [[Epsilon].sub.2t], is due to a failure to control for diversification beyond a single 4-digit SIC industry.

[Mathematical Expression Omitted]

In order to assess the importance of these alleged gains in the precision of TFP estimation generated by the "preferred" methodology, we calculated variants of our regression model using (M1) and (M2) in Lichtenberg and Siegel [1989]. For a sample of 115 of the largest R&D performing companies, the standard deviation of the conventional measure of TFP growth was 29 percent higher. More importantly, the additional variance associated with the conventional methodology is also uncorrelated with R&D.

Estimates of were .079 (1.70) and .086 (2.28) using the standard (M1) and improved (M2) methods to calculate TFP, respectively, with corresponding t-statistics in parenthesis.(22) As expected from the errors-in-variables model, the point estimates under both methods are quite similar. However, LRD-based TFP measures provided more efficient estimates of the rate of return to R&D, as evidenced by a 31 percent increase in [R.sup.2] that arises when we calculate TFP under (M2). The relationship between R&D and productivity is statistically significant only when we appropriately account for firm diversification. This approach suggests that the finding of an insignificant coefficient on R&D intensity in previous studies may have been due in part to poor measurement. Due to the improvement in goodness of fit when we adopt (M2) rather than (M1), the advantages of using the LRD file to calculate TFP are apparent.

[Mathematical Expression Omitted]

IV. RATES OF RETURN TO R&D USING LINKED CENSUS R&D-LRD DATA

Our pilot study demonstrated the feasibility and desirability of using Census microdata to measure rates of return to R&D investment. This section analyzes the impact of R&D on productivity using the complete set of over 2,000 firms in the linked Census R&D-LRD data set. This is a highly representative sample of companies performing industrial R&D, including many small, private firms. Table II demonstrates that the companies in our sample accounted for 84 percent of R&D performed (by industrial firms) in the United States in 1976. The sample coverage ratios are also quite high for sales, employment, and all measures of R&D.

In section III, we discussed how use of linked R&D-LRD data allows us to measure productivity more precisely at the firm level. This is due to our ability to observe more complete measures of firms' output and inputs across industries. However, LRD estimates of a firm's productivity are based only on its continuously operating (between 1972 and 1981) manufacturing plants. We hypothesize that companies with a high percentage of their output in LRD establishments have their productivity measured more accurately than firms with low percentages of LRD activity. We found that the inability to measure firms' total output and inputs introduced an element of heteroskedasticity into OLS estimation of equation (3).

Thus, weighted least squares estimates for variants of equation (3) are presented in Table III. The weight for these regressions is [(COVRAT).sup.1/2], where COVRAT = the ratio of the firm's LRD shipments to its consolidated domestic net sales. These results are based on regressions of average annual TFP growth on average R&D intensity values for three periods, 1973-1976, 1977-1980, and 1981-1985.(23) In order to control (imperfectly) for inter-industry differences in R&D intensity due to differential "technological opportunity" and appropriability conditions, we measure each firm's R&D intensity as a deviation from the average R&D intensity in its home industry (2-digit SIC).(24) The parameter estimates of Table III will be compared with those from existing macro/industry and firm/line-of-business empirical studies in Table IV.

As discussed in section III, it is generally believed that parameter estimates from industry-level studies measure social returns to R&D, while estimates derived from micro studies capture private returns to R&D. Therefore, we do not expect parameter estimates based on models estimated at different levels of aggregation to be equal.(25) In the studies that are not based on the "intensity" model, the parameter of interest is [Alpha], the output elasticity of R&D. For each [Alpha caret], we have imputed a value of [Rho caret] (the estimated marginal product), dividing [Alpha caret] by the mean of R/Q. We are especially interested in comparing our results to those of previous studies based on the "intensity" model, using firm or line-of-business data.

The results of Table III confirm the existence of a positive relationship between the intensity of R&D investment and average annual productivity growth. Under competitive assumptions, our results imply private rates of return to R&D investment of 13.2 percent and 9.7 percent using expenditure and employment measures, respectively. A disaggregation of R&D by source of funds reveals that while the intensity of company-funded R&D investment (expenditure or employment) is a significant determinant of productivity growth, the intensity of federally-funded R&D investment is not. In addition, using both expenditure and employment measures, the hypothesis of homogeneity of returns to company and federally-funded R&D is rejected at the 1 percent level of significance.(26) The potency of privately-financed R&D (but not federally-financed R&D) has also been documented in Terleckyj [1974], Griliches and Lichtenberg [1984a], and Griliches [1986]. Since the returns to company and federally-funded R&D are different, we will focus on estimates of the return to company-funded R&D. Our estimate of a 35.3 percent rate of return to company-funded R&D is quite similar to the mean (of all previous studies) estimate of 29.2 percent for the same parameter, displayed in the last column of Table IV. Moreover, our estimates are based on more recent data than those in previous studies, and both our results and previous results suggest that [Rho] may have been higher in recent years; this could explain why our [Rho caret] is above the mean of previous [Rho caret]s.

A disaggregation of R&D by character of use indicates that the intensity of investment in basic research has a powerful impact on productivity growth, although the estimated rate of return of 133.8 percent to investment in basic research is substantially lower than Mansfield's [1980] estimate of 178.0 percent and Link's [1981b] estimate of 231.0 percent. The hypothesis of equality of returns to basic research and other types of R&D was rejected at the 1 percent level of significance.(27) This evidence of a "premium" on basic research confirms the findings of Griliches [1986], Mansfield [1980], and Link [1981b].(28,29)

The point estimates displayed in Table III are based on pooled regressions, imposing a common slope for each period (1973-1976, 1977-1980, and 1981-1985). To investigate the hypothesis that the returns to R&D varied across these three periods, we re-estimated the regression model, allowing for different slopes in all three periods.(30) These results are presented in Table V. Although we could not reject the hypothesis of equality of rates of return to R&D across periods, the results certainly suggest that the impact of R&D investment on TFP increased substantially in the later periods. In fact, the point estimate on total R&D (expenditure) is almost twice as high in period two. The rate of return to company-funded R&D, using expenditure or employment measures, is also dramatically higher in period two.

Table V also shows that our findings are consistent with two major empirical studies based on 1970s data. In period one, we calculate a 25.4 percent return to company-funded R&D, which is quite similar to estimates of 24.3 percent by Griliches [1986] and 27.5 percent by Mansfield [1980]. Turning to the character of use results, we observe that the "premium" on basic research increased slightly in period two, while the rates of return to applied research and development were insignificantly different from zero across periods. Ours is the first study of the relationship between R&D and productivity that is based on data from the 1970s and 1980s (1972-1985). A strong finding is that the returns to R&D appear to be rising over time. Some of the differences between our parameter estimates and those of existing studies may be due to differences in sample periods. In the next section, we examine the sensitivity of the full sample regression results (Table III) to outlying, influential observations.

V. IDENTIFICATION OF INFLUENTIAL OUTLIERS

Following Belsley, Kuh, and Welsch [1980] and Neter, Wasserman, and Kutner [1985], our research design is to detect outliers in the dependent and independent variables and determine whether these outliers are influential in the least squares regression fit. Cook [1977] has proposed an influence statistic that measures the change in the estimated parameter vector that results if the ith observation is deleted. It is well known (see Maddala [1977]) that the confidence region for [Beta] is expressed as (7) [([Beta caret]-[Beta]) [prime] X [prime] X([Beta caret]-[Beta])]/kMSE

= F(1-[Alpha]; k, n-k) where X is a nxk matrix of independent variables [Beta] is a kx1 column vector of regression parameters [Beta caret] is a kx1 column vector of estimated regression parameters

MSE = mean square error Cook's influence statistic is defined in a similar manner, except it is based on a measure of the difference in the estimated parameter vector including and excluding the ith observation. (8) [Mathematical Expression Omitted] where [[Beta caret].sub.i] is the estimate of [Beta] without the ith data point. An equivalent expression for [D.sub.i] involves the residuals ([e.sub.i]) and leverage values ([h.sub.ii]):(31) (9) [Mathematical Expression Omitted] Relating values of [D.sub.i] to the F-distribution with k and n-k degrees of freedom, those observations having percentile values of 50 percent or more are considered influential observations. For each variant of the regression model (equation (3)), we detected observations that were influential and outliers in X and/or y.

The discovery of influential outliers led us to examine the sensitivity of our regression results to the following remedial measures:

1) reduction of the impact that influential observations have on the fitted regression function

2) deletion of influential outliers Deleting outlying influential observations is a somewhat drastic approach, unless the researcher is certain that the extreme values are due to what Belsley, Kuh, and Welsch [1980] call "gross measurement error"--keypunch errors or incorrect reporting. If these values are correct, then their deletion eliminates vital information. In our final sample, we believe that we have already discarded a non-negligible percentage of values reflecting gross errors in measurement. An alternative to the least squares estimator that minimizes the effect of egregious errors or outliers is the method of least absolute deviations. One of a class of robust estimators, this "bounded-influence" estimator minimizes the sum of the absolute deviations of the observations from their means. These estimates are less sensitive to outliers because the sum of absolute, rather than squared, deviations is minimized.(32)

In Table VI, we compare our earlier estimates of rates of return to R&D investment to estimates of these same parameters after deleting influential outliers (DEL) and those derived from the method of least absolute deviations (LAD). The LAD estimates of the rates of return to total R&D, company-funded R&D, and basic research are 29.5 percent, 26.6 percent, and 31.5 percent lower, respectively, than our original estimates. Our point estimates of these same three parameters decline 3.8 percent, 17.3 percent, and 24.4 percent, respectively, when influential outliers are discarded. These results are somewhat surprising. We expected the deletion of influential outliers to have a stronger impact on the parameter estimates than attempts to reduce their influence. Instead, the opposite pattern emerged, as the LAD estimates of these three rates of return are always lower than corresponding DEL estimates. Still, our original estimates of the effect of R&D investment on TFP growth are not dramatically sensitive to adjustments aimed at reducing the impact of influential outliers.(33) In the next section, we explore the relationship between rates of return to R&D and firm size.

VI. FIRM SIZE AND RATES OF RETURN TO R&D

The ideas of Joseph Schumpeter [1950] figure prominently in the belief that large firms are especially likely both to undertake, and be successful in, research activities. Recent papers by Griliches [1980a], Scherer [1984], Bound et al. [1984], and Cohen, Levin, and Mowery [1987] have found little evidence to support the position that firm size is positively correlated with R&D intensity. Link [1981a] suggested an alternative approach to empirical investigation of the Schumpeterian hypothesis. He examined and found evidence of a systematic relationship between firm size and the impact of R&D on productivity--large firms earned higher returns to R&D than small firms.

Estimation of variants of equation (3) was contingent on the assumption of a common rate of return, [Rho], among firms. In this section, we test whether R&D investment by large firms is more successful than that undertaken by small firms by investigating the possibility that p varies across firms according to size.(34) A test for the structural stability of regression parameters has been developed by Brown, Durbin, and Evans [1975]. The null hypothesis of this test is that the regression coefficients are constant over an index of firm size. An analysis of the cumulative sum of squared residuals determines where, if at all, a structural "break" or shift occurs. An attractive property of the Brown-Durbin-Evans "cusum" test is that it does not require prior information concerning the true point of structural change, unlike the Chow test. The use of prior information concerning structural shifts is often quite plausible when analyzing time series data.(35) However, in our context, the implementation of this type of strategy would be arbitrary. Link [1981a], having estimated rates of return to R&D investment based on the reduced-form version of the R&D capital stock model (using firm-level data), employed the Brown-Durbin-Evans test to examine the structural stability of these returns with respect to firm size.

Our findings, based on the same research design applied to a larger and more representative sample of firms, do not substantiate the Schumpeterian hypothesis. Using sales and employment as proxies for firm size, we were unable to reject the null hypothesis of structural stability for the rate of return to R&D.(36) Although we were unable to determine from the data whether different size "regimes" exist with respect to the rate of return to R&D, we ranked companies by size and divided the sample into three groups. Table VII contains estimates of rates of return to R&D, productivity growth, and R&D investment for these three size categories. The small degree of variation in the rate of return to total R&D across groups provides non-parametric evidence in support of structural stability. Mean TFP growth and R&D intensity values are also quite similar.

The returns to company-funded R&D, however, do appear to be higher for large firms. In fact, we observe statistically significant differences (at the 1 percent level of significance) in rates of return to company-funded R&D between the two groups of large firms and the smallest companies.(37) The apparent instability of this regression parameter compels us to implement the cusum test on this coefficient. One reason for this finding may be that appropriability conditions are more favorable for large firms. This is a subject for future research. We also note that federally-funded R&D appears to have a stronger impact on the productivity growth of small firms, although the coefficients are insignificant for all three size groups. This result, which could have important implications for federal contracting policy, also bears further examination.

Still, the evidence presented in Table VII demonstrates that our earlier findings concerning rates of return are consistent for each size classification of firms:

a) positive and significant coefficient on R&D intensity

b) higher returns to company-funded R&D

c) a productivity "premium" on basic research

VII. CONCLUSIONS

A sizable body of empirical research based on aggregate and industry-level time series data has provided evidence of a strong positive correlation between R&D investment and productivity growth. However, the results of studies based on firm-level data have been much less robust. In this paper, we have demonstrated that previous firm-level studies have contained imprecise measures of productivity. The main source of imprecision has been an inability to adequately control for the diversified activities of corporations. Use of the NSF/Census R&D-LRD Panel allows us to develop more precise estimates of TFP and the impact of R&D on TFP, primarily because the LRD file contains detailed data on the output and input of firms at the 4-digit SIC industry level.

We find that R&D investment was a significant determinant of productivity growth during the years 1972-1985. The R&D-productivity connection was strong throughout the 1970s, when there was a pervasive slowdown in productivity growth. Our results suggest that the rate of return to R&D was higher in the latter stages of the decade and especially in the 1980s. This may explain why manufacturing firms are devoting a larger percentage of their own funds to R&D projects in the 1980s. It appears that profitable research opportunities were plentiful during the 1970s and in recent years. Concern about a recent decline in the impact of R&D on technological progress, due to a diminution of technological opportunities (Baily and Chakrabarti [1988]), does not appear to be well founded.

We find that investment in basic research has a strong effect on productivity growth, while investment in other types of R&D apparently has either a small impact on TFP growth or none at all. This result is consistent with the findings of Mansfield [1980], Link [1981b] and Griliches [1986]. Given the high degree of uncertainty associated with basic research, it is not surprising that its mean rewards are greater than other, less risky forms of R&D.

Another important result is that, consistent with previous studies,(38) we observe a strong positive correlation between the rate of growth of TFP and privately funded R&D, while federally-funded R&D does not appear to be a significant determinant of TFP growth. At first glance, this result implies that firms benefit only from R&D that is privately financed. Perhaps private companies, rather than the federal government, are best able to judge the potential returns to industrial R&D. It must be emphasized, however, that there are two alternative explanations for this finding, each associated with difficulties measuring the benefits resulting from government-funded R&D projects. One measurement problem is that in industries with relatively high levels of publicly-financed R&D, such as the defense or space sectors, output is poorly measured and price indices do not accurately reflect improvements in quality.(39) A related concern is that federal R&D may have an indirect positive impact on productivity which is difficult to capture in our econometric framework. For example, federal R&D may improve economic welfare as a result of

a) stimulation of additional privately-financed R&D or

b) "spillovers" or benefits that accrue to industries or firms from R&D that is performed outside a given firm or industry

While some investigators (e.g. Levy and Terleckyj [1983]) have found there to be a positive simple correlation between company and government-financed R&D, Lichtenberg [1987] has demonstrated that this correlation is statistically "spurious," and that the true correlation is zero and perhaps even negative. Although there have been several investigations of the impact of spillovers, there is no reliable estimate of their contribution to productivity growth. Better methods and data are needed to improve our understanding of this process. At the present time, it is difficult to know whether the standard econometric framework underestimates the impact of federal R&D on economic growth.

In conclusion, the productivity slow-down of the 1970s cannot be blamed on R&D spending, since neither aggregate R&D intensity, nor the estimated contribution of R&D to productivity growth declined during this period. On the other hand, R&D deserves part of the credit for the revival of productivity growth during the 1980s, since during this decade both the extent and apparent efficacy of R&D investment increased. [Tabular Data 1 to 7 Omitted]

(1)Suppose a firm spends $1 on R&D today. If the stock of knowledge capital does not depreciate, it will be $1 greater in every period in the future. If the marginal product of this capital is [Beta], revenues will be $[Beta] greater in every future period. Hence the rate of return to investment in R&D is equal to [Beta], the marginal product of knowledge capital. If the stock of knowledge depreciates at a rate [Rho] > 0, the rate of return is [Beta] - [Rho]. (2)Brookings Papers on Economic Activity 3, 1987, 674. (3)Outside researchers, working through the Center for Economic Studies at the Census Bureau, can apply for access to the LRD file. McGuckin and Pascoe [1988] provide detailed information on access procedures and also describe several LRD projects. The LRD has been analyzed in a number of studies, including Lichtenberg and Siegel [1987; 1990a; 1990b], Davis and Haltiwanger [1989], and Dunne, Roberts, and Samuelson [1988]. (4)See Lichtenberg [1990] for a discussion of the RD-1 data, including a comparison of them with other (e.g. Compustat) R&D data. (5)Four factors of production are measured and deflated separately--capital, labor, energy, and materials. Explicit information on the construction of these variables is contained in the data appendix to Lichtenberg and Siegel [1989], which is available upon request from the authors. (6)Some plants are not observed after 1984 because they were dropped from the 1984 ASM survey panel. (7)For a more comprehensive discussion of this issue, see Lichtenberg and Siegel [1987]. (8)That is, although the LRD time series file is not a random sample of manufacturing plants, it is quite representative of establishments owned by companies that perform R&D. (9)Note that the standard deviation of TFP growth falls sharply in period three. In Lichtenberg and Siegel [1990], we found that the relative productivity of closed plants declined considerably in the years before failure (especially in the year immediately preceding failure). These plants are included in our sample in periods one and two. Thus, a probable cause of this significant reduction in the variance of productivity growth is the elimination of closed establishments in the last period. The bias that results from this does not appear to be severe because TFP does not increase sharply in period three. (10)The unbalanced nature of reporting is due to the fact that firms are not required to report R&D expenditure by character of use (basic vs. applied research and development) and R&D scientists and engineers by source of funds. (11)The anomalous values for the mean value of company-funded scientists and engineers in period one is driven by a few outliers, probably caused by the difficulties firms have in allocating R&D employment by source of funds. (12)In contrast, Nelson [1988] criticizes the interpretation of the empirical results contained in these studies. He argues that R&D intensity is not exogenous; in fact, it is determined by "technological opportunity" and appropriability conditions in specific industries. To some extent, we will control for these factors by measuring each firm's R&D intensity as a deviation from the average R&D intensity in its home industry (2-digit SIC). (13)It is common in this literature to refer to [Rho] as an "excess" rate of return (in excess of normal remuneration to conventional factors of production) because R&D expenditures are often already included in measures of K and L (see Schankerman [1981] for a discussion of the impact of this "double-counting"). The National Science Foundation [1980] reports that 46 percent of the cost of R&D is devoted to labor, 17 percent to materials and supplies, and 37% to overhead. Aggregation of different types of R&D costs does not pose a problem in estimating returns to R&D because all expenditures (even those for "variable" inputs) constitute investment. (14)Griliches and Lichtenberg [1984a] find that the assumption of zero depreciation, as opposed to alternative assumptions concerning the depreciation of R&D capital, yields the best fit to industry data. (15)As discussed above, TFP growth is measured as (4)

[Mathematical Expression Omitted]

[Q.sub.t] = Index of output at time t, [S.sub.it] = Share of factor i in the total cost of output at time t, factors i=K, L, M (including energy)

[X.sub.it] = Quantity of factor i at time t (in real

terms). (16)Of course, the industry rate of return may not equal the social rate of return when there are interindustry R&D spillovers. Empirical evidence concerning the existence of such spillovers is somewhat mixed (see Griliches and Lichtenberg [1984b]). (17)Mansfield [1980], Link [1981b], and Griliches [1986] find evidence of a productivity "premium" on basic research. Griliches [1986] and Griliches and Lichtenberg [1984a] conclude that privately-financed R&D (but not federally-financed R&D) has a strong effect on productivity growth. (18)Compustat, for example, provides only one or several 4-digit SICs for the companies it samples. Most importantly, the distributions of the variables needed to construct total or partial productivity are unavailable at the line-of-business level. (19)Gollop and Monahan [1984], using quinquennial Census of Manufactures data, present evidence that firms became increasingly diversified during the period 1963-1977. Hence, the importance of accounting for diversification in productivity measurement also increased. (20)Clark and Griliches [1984] use business unit data (in ratio form and heavily masked to prevent disclosure) provided by large, diversified companies in the proprietary PIMS file to analyze the relationship between R&D and TFP growth. Although business units are still highly aggregative, this methodology, to some extent, addresses some of the concerns we have discussed. However, the use of divisional-level R&D data raises new concerns about measurement error in estimates of R&D, because R&D is often regarded as a corporate-level activity and cannot be easily assigned to specific industries (by definition in the case of basic research). (21)[[Mu].sub.t] is a classical disturbance term, [[Epsilon].sub.1t] is due to an inability to completely measure the "true" level of diversification and errors in the industry deflators (see Griliches and Lichtenberg [1989]). We assume that the error terms have zero mean, are pairwise uncorrelated, and are uncorrelated with both the independent variable and [[Mu].sub.t]. (22)These calculations are based on weighted least squares regressions of average annual productivity growth on average annual R&D intensity for two periods: 1973-1976 and 1977-1980, where the weights adjust for heteroskedasticity due to incomplete firm "coverage" in the LRD file. That is, we believe that estimates of firm productivity based on only a small fraction of its manufacturing plants are somewhat less reliable, or "noisy." Still, on average, we captured 85 percent of a firm's sales. (23)This paper does not attempt to analyze R&D lag effects (Griliches [1980a]) and relates TFP only to R&D performed in the current period. Griliches and Lichtenberg [1984a], using a similar methodology, found only a slight improvement in explanatory power when estimating these equations using lagged values of R&D. Our specification focuses on the R&D-TFP connection in the (relatively) long term, as do most of the studies cited in this paper. Thus, our findings may not necessarily provide additional evidence on the short term dynamics of the relationship between R&D and TFP. (24)All of our regressions control for these industry effects. (25)Several authors have avoided imposing the condition that factors are paid their marginal products and, instead, estimated Cobb-Douglas production functions directly, assuming only constant returns to scale with respect to the conventional inputs. The "level" and "growth rate" equations estimated in Griliches [1980a; 1980b; and 1986] are based on constant returns to scale and competitive markets for these inputs. (26)The t-statistics for tests of the expenditure and employment measures are 48.53 and 25.03, respectively. (27)The t-statistic for the test of equality of returns to basic research and applied research is 61.07. The t-statistic for the same test involving basic research and development is 65.78. (28)To make our results more comparable to the findings of Griliches [1986], we also regressed TFP growth on company-funded R&D intensity and the ratio of basic research to total R&D expenditure. The estimated coefficients and t-statistics (in parentheses) are, respectively, .313 (11.86) and .096 (8.86). These estimates are quite similar to the findings contained in the aforementioned study, although the "premium" on basic research is somewhat lower. (29)The same pattern of results emerges when we restrict our sample to include only firms reporting (zero or positive) expenditure on basic research. When we estimate variants of the regression model for the same set of companies, the estimated coefficients and corresponding t-statistics (in parentheses) for columns a, b, d, and e are (a) .137 (4.66); (b) .422 (6.17) .016 (0.41); (d) .135 (3.07); (e) .160 (3.37) .044 (0.62). (30)Scherer [1982; 1983] argues that specifications such as ours may not capture "true" changes in private returns to R&D over time. He believes that it is important to follow R&D from industry of origin to industry of use, as many firms "purchase" R&D from other firms implicitly when buying certain products and services. According to this view, we can truly measure the impact of R&D on productivity only by identifying these "interindustry technology flows." However, using more comprehensive data on "interindustry technology flows" than in Scherer's original study, Griliches and Lichtenberg [1984b] failed to find evidence to corroborate this hypothesis. (31)Where [e.sub.i] = y - X[Beta] = y - X[(X [prime] X).sup.-1] X [prime] y = y - Hy

The "hat" matrix (H) is a projection matrix, which is symmetric and idempotent (H [prime] H = H). Each diagonal element of the hat matrix, [h.sub.ii], is called the leverage, measuring the distance between the X values of the ith observation and the X values of the remaining observations. The value of [h.sub.ii] determines how influential the ith observation is in determining [y.sub.i] (32)As demonstrated by Charnes et al. [1955], the method of least absolute deviations estimates can be derived from the solution to a linear programming problem. However, standard errors for the parameter estimates are unknown the statistical properties of the sampling distribution of this estimator are not well defined. (33)With influential outliers deleted, we still reject the hypothesis of homogeneity of returns to company and federally-funded R&D. The same is true for the hypothesis of equality of returns to basic research and other types of R&D. (34)A strict Schumpeterian interpretation of the heterogeneity of [Rho] across companies might be that [Rho] is a function of firms' monopoly power. Large size is neither a necessary nor a sufficient condition for firms' ability to gain or maintain monopoly power. (35)The cusum test has been applied on macroeconomic time series data in Heller and Khan [1979]. (36)That is, the test statistic, [s.sub.r], based on the normalized cumulative sum of squared residuals, always falls within the 5 percent confidence intervals above and below the mean value line. Given the extremely large size of the sample, a plot of the [s.sub.r]'s against observation number (after these values have been sorted appropriately) cannot be displayed graphically. (37)The t-statistics for these tests are 2.75 (largest vs. smallest) and 2.97 (middle vs. smallest). The difference in rates of return to company-funded R&D between the largest and middle groups of firms is statistically insignificant. (38)See Griliches and Lichtenberg [1984a] and Griliches [1986]. (39)See Griliches [1979] for a full exposition of this argument.

REFERENCES

Agnew, Carson E. and Donald E. Wise. "The Impact of R&D on Productivity: A Preliminary Report." Paper presented at the Southern Economic Association meetings, 1978.

Baily, Martin N. and Alok K. Chakrabarti. Innovation and the Productivity Crisis. Washington, D.C.: Brookings Institution, 1988.

Belsley, David A., Edwin Kuh, and Roy E. Welsch. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons, 1980.

Bound, John, Clint Cummins, Zvi Griliches, Bronwyn H. Hall, and Adam Jaffe. "Who Does R&D and Who Patents?" in R&D, Patents, and Productivity, edited by Zvi Griliches, Chicago: University of Chicago Press, 1984, 21-54.

Brown, R. L., J. Durbin, and J. M. Evans. "Techniques for Testing the Constancy of Regression Relationships Over Time." Journal of the Royal Statistical Society (series B), December 1975, 149-63.

Charnes, Abe, W. W. Cooper, and R. O. Ferguson. "Optimal Estimation of Executive Computing by Linear Programming." Management Science, March 1955, 138-151.

Clark, Kim B. and Zvi Griliches. "Productivity Growth and R&D at the Business Level: Results from the PIMS Data Base," in R&D, Patents, and Productivity, edited by Z. Griliches. Chicago: University of Chicago Press, 1984, 393-416.

Cohen, W. M., R. C. Levin, and D. C. Mowery. "Firm Size and R&D Intensity." Journal of Industrial Economics, June 1987, 543-65.

Cook, R. Dennis. "Detection of Influential Observations in Linear Regression." Technometrics, February 1977, 15-18.

Davis, Steve J. and John Haltiwanger. "Gross Job Creation, Gross Job Destruction, and Employment Reallocation." Paper presented at National Bureau of Economic Research Summer Institute, 1989.

Dunne, Timothy, Mark J. Roberts, and Larry Samuelson. "Entry and Exit in U.S. Manufacturing." Rand Journal of Economics, Winter 1988, 495-515.

Gollop, Frank M. and James L. Monahan. "From Homogeneity to Heterogeneity: A Proper Index of Diversification." Mimeo, Bureau of the Census Technical Notes, 1984.

Griliches, Zvi. "Issues in Assessing the Contribution of Research and Development to Productivity Growth." Bell Journal of Economics, Spring 1979, 92-116.

______. "Returns to Research and Development Expenditures in the Private Sector," in New Developments in Productivity Measurement, edited by J. W. Kendrick and B. Vaccara. National Bureau of Economic Research Studies in Income and Wealth No. 44, Chicago: University of Chicago Press, 1980a, 419-54.

______. "R&D and the Productivity Slowdown." American Economic Review, May 1980b, 343-348.

______. "Productivity, R&D and Basic Research at the Firm Level in the 1970's." American Economic Review, March 1986, 141-54. Griliches, Zvi and Frank R. Lichtenberg. "R&D and Productivity Growth at the Industry Level. Is There Still a Relationship?" in R&D, Patents, and Productivity, edited by Z. Griliches. Chicago: University of Chicago Press, 1984a, 465-96.

______. "Interindustry Technology Flows and Productivity Growth: A Reexamination." Review of Economics and Statistics, May 1984b, 324-29.

Griliches, Zvi and Jacques Mairesse. "Productivity and R&D at the Firm Level," in R&D, Patents, and Productivity, edited by Z. Griliches. Chicago: University of Chicago Press, 1984, 339-74.

Heller, Robert H. and Moshin S. Khan. "The Demand for Money and the Term Structure of Interest Rates." Journal of Political Economy, January 1979, 109-29.

Jorgenson, Dale W. and Zvi Griliches, "The Explanation of Productivity Change," Review of Economic Studies, July 1967, 249-83. Levy, David M. and Nestor Terleckyj. "Effects of Government R&D on Private R&D Investment and Productivity: A Macroeconomic Analysis." Bell Journal of Economics, Winter 1983, 551-61.

Lichtenberg, Frank R. "The Effect of Government Funding on Private Industrial Research and Development: a Re-assessment." Journal of Industrial Economics, September 1987, 1-8.

______. "Using Longitudinal Establishment Data to Estimate the Internal Adjustment Costs Model." Review of Economics and Statistics, August 1988, 421-30.

______. "Issues in Measuring Industrial R&D." Research Policy, 19, 1990, 157-163.

Lichtenberg, Frank R. and Zvi Griliches. "Errors of Measurement in Output Deflators." Journal of Business and Economic Statistics, January 1989, 1-9.

Lichtenberg, Frank R. and Donald Siegel. "Productivity and Changes in Ownership of Manufacturing Plants." Brookings Papers on Economic Activity 3, 1987, 643-83.

______. "Using Linked Census R&D-LRD Data to Analyze the Effect of R&D Investment on Total Factor Productivity Growth." Center for Economic Studies Discussion Paper, U.S. Census Bureau, 1989.

______. "The Effects of Leveraged Buyouts on Productivity and Related Aspects of Firm Behavior." Journal of Financial Economics, September 1990a, 165-94.

______. "The Effect of Takeovers on the Employment and Wages of Central-Office and Other Personnel." Journal of Law and Economics, October 1990b, 383-409.

Link, Albert N. Research and Development Activity in U.S. Manufacturing. New York: Proger, 1981a.

______. "Basic Research and Productivity Increase in Manufacturing: Additional Evidence." American Economic Review, December 1981b, 1111-12.

Maddala, G. S. Econometrics. New York: McGraw Hill, 1977.

Mansfield, Edwin. "Basic Research and Productivity Increase in Manufacturing." American Economic Review, December 1980, 863-73.

McGuckin, Robert and George Pascoe. "The Longitudinal Research Data Base-Research Possibilities." Survey of Current Business, November 1988, 30-37.

Minasian, Jora R. "Research and Development, Production Functions and Rates of Return." American Economic Review, March 1969, 80-85. National Science Foundation. Research and Development in Industry, serial 1957-1980. Washington, D.C.: Government Printing Office, 1980.

Nelson, Richard R. "Modeling the Connections in the Cross Section Between Technical Progress and R&D Intensity." Rand Journal of Economics, Winter 1988, 478-85.

Neter, J., W. Wasserman, and M. Kutner. Applied Linear Statistical Models. Homewood, Ill.: Irwin, 1985. Nordhaus, William D. "Policy Responses to the Productivity Slowdown," in The Decline in Productivity Growth, series no. 22. Federal Reserve Bank of Boston, 1980.

Schankerman, Mark. "The Effects of Double-Counting and Expensing on the Measured Returns to R&D." Review of Economics and Statistics, August 1981, 454-58.

Scherer, F. M. "Research and Development, Patenting, and the Microstructure of Productivity." Final Report, National Science Foundation, grant no. PRA-7826526, 1981.

______. "Interindustry Technology Flows and Productivity Growth." Review of Economics and Statistics, November 1982, 627-34.

______. "R&D and Declining Productivity Growth." American Economic Review, May 1983, 215-18.

______. Innovation and Growth: Schumpeterian Perspectives. Cambridge, Mass.: MIT Press, 1984. Schumpeter, Joseph A. Capitalism, Socialism, and Democracy, 3rd ed. New York: Harper and Row, 1950.

Solow, Robert M. "Technical Change and the Aggregate Production Function." Review of Economics and Statistics, August 1957, 214-31.

Terleckyj, Nestor. Effects of R&D on the Productivity Growth of Industries. Washington, D.C.: National Planning Association, 1974.

FRANK R. LICHTENBERG AND DONALD SIEGEL, Associate Professor, Columbia University Graduate School of Business and Research Associate, National Bureau of Economic Research; and ** Assistant Professor, Harriman School for Management and Policy, SUNY-Stony Brook and Faculty Research Fellow, National Bureau of Economic Research. We wish to thank Zvi Griliches, Robert McGuckin, Dennis Mueller, F. M. Scherer, Frank Wykoff, and two anonymous referees for helpful comments and suggestions. Earlier versions of this paper were presented at the National Bureau of Economic Research, the University of Maryland, and the U.S. Census Bureau. This study is based upon activities supported by the National Science Foundation under Interagency Agreement No. SRS-8801036 "Industrial R&D and Productivity: Using an Expanded NSF/Census Data Linkage File." The research was conducted at the Center for Economic Studies, U.S. Bureau of the Census. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Census Bureau.

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Title Annotation: | Longitudinal Research Database; Research and Development |
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Author: | Lichtenberg, Frank R.; Siegel, Donald |

Publication: | Economic Inquiry |

Date: | Apr 1, 1991 |

Words: | 9538 |

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