Trade and International R&D Spillovers among OECD Countries.

Mark Funk [*]

This paper examines the relationship between trade patterns and international research-and-development (R&D) spillovers using Kao and Chiang's (1998) and Kao's (1999) recently developed panel cointegration techniques. Monte Carlo--type tests demonstrate that the choice of weights used in constructing foreign R&D stocks is informative of the spillover transmission when panel cointegration techniques are employed. However, the evidence does not support a relationship between import patterns and R&D spillovers. The relationship between export patterns and R&D spillovers is then considered. Consistent with recent theoretical models (Ben-David and Loewy 1998), the evidence suggests that exporters receive substantial R&D spillovers from their customers.

1. Introduction

Does a country's trading partners affect its long-run growth? While many authors such as Edwards (1998) have found that relatively open economies tend to grow faster than relatively closed economies, it is less clear whether a country's trading partners affect its long-run growth. One plausible way trade partners may influence long-run growth is through the transfer of knowledge. Recent empirical work reveals an apparent link between international research spillovers and import patterns. Coe and Helpman (1995) uncover empirical evidence of a relationship between domestic productivity and import-weighted foreign research stocks. Using slightly different approaches, Coe, Helpman, and Hoffmaister (1997); Engelbrecht (1997a, b); and Lichtenberg and van Pottelsberghe de la Potterie (1998) find similar results. By linking knowledge transmission to import patterns, these results suggest that trade partners do influence long-run growth.

However, these results have come under some criticism. Keller (1998) questions whether any of these results can be interpreted as indicating a link between knowledge flows and imports. He finds that significant international spillovers are still estimated from foreign research-and-development (R&D) stocks constructed using randomly assigned weights. He interprets this result to imply that the choice of weights is not indicative of the knowledge transmission mechanism.

While this is an ingenious test, Keller is careful to point out that his results may be due to the time-series properties of the data. As with the other studies, Keller focuses on the long-run relationship between the nonstationary total factor productivity and R&D data series but estimates the relationship using standard OLS techniques. Kao and Chiang (1998) demonstrate that the ordinary-least-squares (OLS) estimator in a cointegrated panel is asymptotically normal but with a nonzero mean. Kao, Chiang, and Chen (1999) apply panel cointegration methods to Coe and Helpman's estimation and conclude that the evidence of a relationship between imports and research spillovers is weak.

This paper reexamines the empirical relationship between trade and R&D spillovers using the panel cointegration techniques developed by Kao and Chiang (1998). As this paper shows, accurate estimates and inference tests of the cointegrating relationship indicate no long-run relationship between imports and international flows of knowledge, confirming Kao, Chiang, and Chen's (1999) results. Keller's experiment is reconsidered next. This paper finds that when panel cointegration techniques are employed, the choice of weights used in the construction of the foreign R&D stocks is informative. As a final contribution, this paper considers exports as an alternative transmission mechanism. Ben-David and Loewy (1998) describe how even the technological leaders may gain knowledge spillovers from their export relationships. The very strong evidence presented here supports their model. The new evidence suggests that previous studies may have overstated the role of imported inputs in international R&D spillovers while un derstating other transmission mechanisms.

The rest of the paper proceeds as follows. Section 2 outlines a simple model of innovation and productivity growth. Section 3 discusses the nonstationary nature of the data and the recent advances in panel unit root tests and panel cointegration. A reevaluation of the relationship between randomly generated import patterns and international spillovers appears in section 4. Section 5 assesses the role of exports in transmitting international research spillovers. Section 6 concludes with a brief summary and suggestions for further research.

2. Model

While the existence and transmission of international research spillovers plays a role in a variety of models of trade and growth, the empirical tests of international research spillovers are usually motivated by appeals to endogenous growth models, such as those in Grossman and Helpman (1991). One important feature that distinguishes the Grossman and Helpman models from other endogenous growth models is the emphasis on trade as the means of international knowledge diffusion. In the Grossman and Helpman--style models, research undertaken by profit-seeking firms results in new intermediate goods that are then used in the final-goods sector. Assuming that the intermediates are imperfect substitutes, with an elasticity of substitution in production greater than one, the final-goods producers exhibit "variety-loving" behavior and productivity in the final-goods sector will be a positive function of the number of inputs available. Since the past and present research efforts determine the number of inputs availabl e, the economy's cumulative R&D efforts--its R&D stock--determines the productivity in the final-goods sector. If trade in intermediate goods occurs, then both the domestic R&D stock and the R&D stocks of trade partners will determine domestic productivity.

Research may also contribute to a publicly available stock of knowledge. Researchers during the innovation process may draw on the public knowledge stock as a source of technical or scientific knowledge. By increasing the stock of public knowledge, current research reduces the cost of future innovations. Moreover, domestic research may spill over to foreign economies by increasing the public stock of knowledge available to foreign researchers. The knowledge created in research may be transmitted through trade since trade increases the number of contacts by which knowledge may be exchanged. If the knowledge is transmitted largely by trade, then again a country's trade partners will impact its long-run growth.

While Grossman and Helpman (1991; pp. 166-71) argue that both imports and exports encourage knowledge flows, the literature that has emerged has argued largely that imported intermediate goods play a central role in the transmission of knowledge. Coe and Helpman offer the first empirical test of this assumption. They pool productivity and R&D data for 22 OECD countries for the years 1971 to 1990. They then estimate the effect of foreign R&D stocks on productivity levels by OLS regression of the equation

ln [F.sub.i] = [[alpha].sub.i] + [[alpha].sup.d]1n [S.sup.d] + [[alpha].sup.f] ln [S.sup.f], (1)

where F is the business-sector total factor productivity, [[alpha].sub.i] is a fixed effect, [S.sup.d] is the domestic R&D stock, and [S.sup.f] is the foreign R&D stock. As is standard in the literature, the domestic R&D stock is defined as the depreciated sum of all previous domestic research. The foreign R&D stock is defined as the weighted sum of the domestic R&D stocks of all other sampled nations:

[[S.sup.f].sub.i] = [[[sigma].sup.k].sub.j=1] [m.sub.i,j][[S.sup.d].sub.j],

where the weight [m.sub.ij] in this case is the bilateral import share, that is, the volume of imports to country i from country j divided by the total imports to i from all nations in the sample. By adjusting the contribution of foreign R&D to the foreign knowledge stock, the weights reflect preconceptions of the knowledge sources and recipients, the proportion of knowledge that is spillable, and the channels of knowledge diffusion. [1] As such, the weights may reflect the geographic, technological, or economic distance between the research performer and the spillover recipient. Coe and Helpman's definition of the foreign R&D stock assumes that knowledge flows through imports.

The argument that imports are the primary method of international knowledge diffusion raises a few questions. Grossman and Helpman (1991, pp. 166-7) suggest two reasons why bilateral import shares may be correlated with international research spillovers: Bilateral import shares are a proxy for contacts between residents and firms residing in different nations, and the knowledge embodied in imported intermediate inputs increases the productivity of the end user. As for the first justification, Grossman and Helpman also use it as an explanation for why bilateral export shares may be correlated with international spillovers. As for the second justification, Griliches (1979) calls spillovers of this type "pecuniary," and they are distinct from the pure knowledge spillovers between researchers that have dynamic growth effects. Pure spillovers occur when the knowledge created by one researcher reduces the innovation cost of another researcher. Pecuniary spillovers occur when the price of a new intermediate input f ails to capture the input's full marginal product and have no implications on long-run growth.

3. Data and Methodology

I use Coe and Helpman's data on the R&D stocks and productivity of 22 OECD nations from 1971 to 1990 to estimate Equation 1 (for the details of the data construction, see Appendix A). The bilateral trade data used to construct the trade-share weights come from the IMF's Direction of Trade. One of Coe and Helpman's more important contributions is the emphasis that they place on the long-run, cointegrated relationships. As Lau (1999) has shown, unit roots and cointegration are a distinguishing feature of endogenous growth models. Since the data series appear nonstationary, Coe and Helpman interpret their regressions as pooled cointegration. Coe and Helpman, Engelbrecht (1997a, b), Keller (1998), and Lichtenberg and van Pottelsberghe (1998) derive their estimates from OLS regressions, which with nonstationary data results in superconsistent coefficient estimates but biased and asymptotically nonnormal standard errors. Coe and Helpman acknowledge that inference tests of their results are unreliable and that the details of panel cointegration had (at the time) yet to be worked out, but they choose to emphasize the theoretical consistency of their results. Since then, considerable progress has been made in the understanding of panel unit roots and panel cointegration, and reliable estimates of the long-run, cointegrated relationships can now be obtained.

Several panel unit root tests currently exist. The power of these tests is substantially greater than the tests for a single time series in that the failure to reject a unit root occurs much less frequently. Im, Pesaran, and Shin (1997) suggest using the average ADF t-statistic, which they call the t-bar test. They show that for small samples, such as the OECD since 1970, the power of the t-bar test exceeds Levin and Lin's (1992, 1993) tests. Results of the Im, Pesaran, and Shin (IPS) t-bar unit root test appear in Table 1. Based on this test, it appears that all the data series contain a unit root. Maddala and Wu (1996) point out that in the presence of cross correlations among the cross sections, the IPS test and other panel unit root tests suffer size distortion. Using bootstrap methods, Maddala and Wu (1996) and Wu (1997) demonstrate that correcting for cross correlations decreases the probability of rejecting the null of a unit root. This suggests that the inferences from the IPS tests in this setting a re accurate, and all the data series contain a unit root.

Since using standard OLS techniques on nonstationary panel data may lead to false inferences in that the OLS estimates may indicate a relationship where none exists, this paper uses the dynamic OLS (DOLS) and fully modified OLS (FMOLS) methods for panel cointegration developed by Kao and Chiang (1998). The standard OLS estimates are also provided in order to better assess the sensitivity of the parameter estimates to the different procedures. To briefly illustrate these techniques, suppose that we have the cointegrated regression for a panel of i 1, 2, ..., N countries from time t = 1, 2, ..., T,

[Y.sub.it] = [[alpha].sub.i] + [X.sub.it][beta] + [V.sub.it]

where [v.sub.it], are the stationary residuals and [X.sub.it] is the m-dimensional vector of regressors, each integrated of order one I(1),

[X.sub.it] = [X.sub.it-1] [[epsilon].sub.it]

We are interested in obtaining an estimate of the cointegrating vector [beta], which is the long-run relationship between X and Y, and in obtaining a statistic for inference tests.

The panel DOLS estimator corrects for endogeneity and serial correlation by including leads and lags of the differenced I(1) regressors in the regression

[Y.sub.it] = [[alpha].sub.i] + [X.sub.it][beta] + [[[sigma].sup.[q.sub.2]].sub.j=[q.sub.1]] [c.sub.ij][delta][X.sub.it+j] + [[micro].sub.it].

The FMOLS estimator can be shown as

[[beta].sub.FM] = [[[[[sigma].sup.N].sub.i=1] [[[sigma].sup.T].sub.i=1] ([X.sub.it] - [X.sub.i])([X.sub.it] - [X.sub.i])'].sup.-1] {[[[sigma].sup.N].sub.i=1] [[[sigma].sup.T].sub.t=1] ([X.sub.it] - [X.sub.i])[[Y.sup.+].sub.it] - T[[[delta].sup.+].sub.[epsilon]u]]},

where [[[delta].sup.+].sub.[epsilon]u] is the serial correlation correction term and [[Y.sup.+].sub.it] is the endogeneity correction. For panels of the size used in this paper (22 countries over 20 years), Kao and Chiang (1998) demonstrate that DOLS outperforms FMOLS in parameter estimation and inference testing.

It is necessary to test for cointegration before applying these procedures. Kao (1999) provides an augmented Dickey-Fuller (ADF) type of test of the null hypothesis of no cointegration. This test assumes a common [beta] (implying a common cointegrating relationship) across the panel members, as is assumed in the FMOLS and DOLS. The asymptotic distribution of the test converges to a standard normal distribution N(0, 1). The ADF-type test is based on an ADF regression on the residuals 4 from the estimating equation,

[e.sub.i,t] = [rho][e.sub.i,t-1] + [[[sigma].sup.k].sub.j=1] [[gamma].sub.j][e.sub.i,t-j] + [v.sub.it],

and is defined as

ADF = [t.sub.ADF] + [square root]6N[[sigma].sub.v]/2[[sigma].sub.0v]/ [square root][[[sigma].sup.2].sub.0v]/2[[[sigma].sup.2].sub.v] + 3[[[sigma].sup.2].sub.v]/10[[[sigma].sup.2].sub.0v]

where [t.sub.ADF] is the t-statistic of [rho] from the ADF regression and [[sigma].sub.v] and [[sigma].sub.0v] are defined in Kao (1999).

Kao, Chiang, and Chen (1999) apply the DOLS and FMOLS procedures to Equation 1; their results are replicated in Table 2 for comparative purposes. The DOLS estimated coefficients on the import-weighted foreign R&D stocks are small and statistically indistinguishable from zero. The EMOLS results tell a slightly different story, as the estimated spillover remains statistically significant. Since the DOLS procedure has better finite sample properties in terms of the bias in both the parameter estimates and the standard errors, the inclination is to accept the DOLS results over the FMOLS results.

Other studies indirectly support these results. Coe, Helpman, and Hoffmaister (1997) found a similar result in their analysis of R&D spillovers to developing nations. In that study, first differences were used to avoid problems with nonstationarity, and they found that the bilateral import-weighted foreign R&D was statistically insignificant unless interacted with the import share of GDP.

Additionally, while studies using disaggregated data also find evidence of international research spillovers, the evidence that the spillovers are linked to imports is less clear. Branstetter (1996) and Bernstein and Mohnen (1998) examine spillovers between the United States and Japan. Both studies find that Japan benefits much more from U.S. research than the United States does from Japanese research. Combined with the weak evidence of import-based R&D spillovers when appropriate panel cointegration techniques are used, these results would seem to imply that imports are not a vital means of knowledge transmission.

By implementing the recently developed panel cointegration techniques, this paper provides a clearer picture of the long-run relationship among productivity, trade, and foreign research. Two questions must be addressed before the role of trade can be fully determined. Keller's question comes first: Is the choice of weights used in the construction of foreign research stocks informative? The second question, addressed in section 5, is whether exports play a central role in the international transmission of knowledge.

4. Random Bilateral Shares

Keller (1998) performs what he calls a counterfactual estimation in which Coe and Helpman's OLS regressions are repeated with the foreign research variables weighted by randomly derived import patterns. He then compares the average estimated result from this experiment with the estimated results from a regression based on the true trade patterns. He finds that the average estimated coefficient on the randomly weighted foreign R&D is statistically significant and larger than the coefficient on the import-weighted foreign R&D. This suggests that the choice of weights is irrelevant to finding international spillovers, which means that Coe and Helpman's approach cannot be used to determine the relationship between import patterns and research spillovers. If Keller's criticism is accurate, then it is inappropriate to infer that the weights represent the transmission mechanism.

However, Keller's finding may be due to the use of OLS on nonstationary panel data. As Kao and Chiang (1998) demonstrate, the OLS estimator on panel cointegrated data is asymptotically normal but with a nonzero mean. Moreover, they find a substantial estimation bias in samples of moderate size, such as the OECD since 1970. As a consequence, Keller's conclusion may be based on a false inference drawn from biased estimates. This paper applies the FMOLS and DOLS panel cointegration techniques to Keller's analysis. The random import shares are constructed using the GAUSS uniform distribution random number generator. First, a 22-by-22 matrix is filled with random elements representing the volume of imports from the row country to the column country. The diagonal elements are then set to zero. Dividing each column by its sum yields the random bilateral share. As the matrix represents the randomly generated bilateral shares for a single year, this procedure is repeated for each of the 20 years in the sample period. The foreign R&D stocks are then calculated using the random bilateral shares as the weights, as in Equation 2. Finally, Equation 1 with the randomly weighted foreign R&D stocks is estimated using OLS, FMOLS, and DOLS.

Table 3 contains the average result from 1000 replications of this procedure. The coefficient on the foreign R&D stocks [S.sup.f] indicates spillovers. The variable [S.sup.d] is the domestic R&D stock, and G7 is a dummy variable for the G7 nations. The results of interest are the average coefficient and the average t-statistic on the foreign R&D variable. As can be seen, using OLS substantially increases the probability of finding a significant result: The average t-statistic is 2.53, and over 70% of all OLS t-statistics on foreign R&D were greater than 1.96. Given the short period of this panel, the fully modified OLS regressions offer only minor improvements over the OLS regressions. Nonetheless, the average t-statistic in the fully modified OLS falls to 1.92, with just 50% of the FMOLS estimates statistically significant. The DOLS results tell a very different story. The average DOLS t-statistic is just 0.76, and only 16% of the DOLS coefficient estimates were statistically significant.

As a second test, the regressions were limited to cases where the IPS panel unit root test indicated a unit root in the foreign R&D variable. [2] Doing so doubled the size of the average estimated coefficient on foreign R&D in all four procedures but did not substantially alter the average t-statistic. When panel cointegration methods are applied, it appears that the choice of weights is informative in that 84% of the randomly weighted foreign R&D stocks do not generate international spillovers.

5. Exports

What is the role of export relationships in the international transmission of knowledge? Grossman and Helpman (1991, pp. 166-70) argue that sellers may gain from the knowledge base of their buyers. Research spillovers from customers may occur, for example, if buyers offer advice on potential productivity enhancements. Moreover, by increasing the price of failing to improve or by increasing the rewards for succeeding, the stronger competitive pressures of the international marketplace may encourage firms to more aggressively pursue productivity enhancements. As Chuang (1998) argues, successfully exporting products requires the producer to be familiar with the foreign buyers' demands, including buyer requirements on product specifications and quality. The knowledge acquired by examining customer demands may be used to enhance own productivity. As for trade between the advanced countries of the OECD, BenDavid and Loewy (1998) show how even the technological leader may benefit from knowledge spillovers acquired through export relationships.

There is some evidence supporting this claim in the North-South context. Westphal et al. (1984), for example, state that Korean exporters benefited substantially from knowledge flows originating from their foreign customers. To test whether advanced countries benefit from their export relationships as suggested by Ben-David and Loewy (1998), I constructed new foreign R&D measures using the same domestic R&D data but with bilateral export shares as a weight in place of the bilateral imports shares. Using bilateral export shares as weights removes the emphasis from knowledge acquired through direct, hands-on experience with imported intermediate inputs and places more emphasis on the pure idea exchange and knowledge spillovers gained from formal and informal contacts. The IPS panel unit root test in Table 1 could not reject a unit root in the export-weighted foreign R&D. The cointegration tests presented in the second column of Table 4 strongly rejected the null of no cointegration. Again, the relationship bet ween domestic productivity and export-share-weighted foreign R&D is estimated using OLS, FMOLS, and DOLS. Table 5 reports the results.

The bilateral export relationships appear to be a better measure of the potential for knowledge transfer. The export-weighted foreign research measures are large and statistically significant in all four regressions. Based on these estimates, a 1% increase in the bilateral-export-weighted foreign R&D stocks results in about a .1% increase in domestic productivity. The estimated coefficients on the domestic R&D stocks fall, as might be expected if previous estimates were biased upward by the failure to capture properly the effects of foreign R&D. For the smaller countries, foreign research is much more powerful than domestic research: The estimated elasticity of domestic productivity with respect to foreign research is approximately twice as large as the elasticity with respect to domestic research. When import-weighted measures of foreign research are included in the regression, as shown in Table 6, the export measures are again large and statistically significant, while the import-weighted measures are agai n small (less than .01) and statistically insignificant. The strength and similarity of the results across procedures and specifications suggests that exporters benefit from the knowledge stocks of their trade partners.

The import-weighted and export-weighted foreign R&D stocks have differing implications for the benefits of international knowledge flows. Unless the knowledge embodied in imports is somehow extracted and increases the productivity of domestic researchers, the impact of an imported intermediate has a one-time, static effect. The knowledge acquired by advanced countries through their export relationships, however, may be exploited further through "learning by doing" as the exporter produces for the external market, as in Feeney (1999). Moreover, since the import-weighted foreign R&D stocks potentially capture both negative and positive pecuniary spillovers, the export-weighted foreign R&D stocks may better capture pure knowledge spillovers. Lastly, the competitive effects of the international marketplace may affect the ability to benefit from international spillovers. Exporters may be driven by market forces to quickly acquire and adapt foreign technologies. Importers may be driven out of research or out of bus iness by more technologically advanced foreign competitors, as in Grossman and Helpman (1991, chap. 9).

The estimated elasticities of productivity with respect to the R&D capital stock of the G7 are shown in Table 7. Using the DOLS estimated coefficient of 0.113 on the bilateral-export-weighted foreign R&D stock from Table 5, the elasticity of productivity in country i with respect to the R&D stock of country j, [[eta].sub.ij], is calculated as

[[eta].sub.ij] = [[alpha].sub.f] [x.sub.ij][[S.sup.d].sub.j]/[[sigma].sub.k[neq]i] [x.sub.ik][[S.sup.d].sub.k],

where [x.sub.ij] is the share of exports from i going to j, [[S.sup.d].sub.j] is the domestic R&D stock of country j, and [[alpha].sub.f] = 0.113 is the estimated coefficient on the export-weighted foreign R&D.

The estimated elasticities indicate that the United States is the dominant source of R&D spillovers. In fact, for the average small country, the elasticity of domestic productivity with respect to U.S. research (0.062) is larger than the elasticity of productivity with respect to own research (0.054). Germany is also a substantial source of spillovers, although German spillovers appear localized to Europe. A 1% increase in the German R&D stock results in a 0.02% increase in productivity, on average, in other nations. The estimates presented here also bolster the findings of Branstetter (1996) and Bernstein and Mohnen (1998), who find that Japan benefits much more from U.S. research than the United States does from Japanese research. By contrast, results from import-weighted foreign R&D indicated that the elasticity of U.S. productivity with respect to Japanese research was larger than the elasticity of Japanese productivity with respect to U.S. research.

6. Conclusion

What is the relationship between trade and growth? This paper reexamines the role of trade in the international transmission of the knowledge created in R&D. Coe and Helpman (1995) and others suggest that international research spillovers occur primarily through imports. The panel cointegration tests provided here yield a different conclusion. Consistent with earlier studies, this paper finds that when panel cointegration methods are used, there is no evidence that research spillovers among the OECD nations are transmitted through imports. Next, this paper addresses Keller's (1998) critique and finds that when panel cointegration tests are applied, the choice of weights used in the construction of the foreign R&D stocks is in fact informative. Finally, this paper finds strong evidence indicating that exporters receive substantial research spillovers from their customers.

Several extensions seem worth pursuing, especially considering the level of aggregation in the data used in this paper. This paper does not differentiate between the types of goods and services being traded. Recent work by Xu and Wang (1999) differentiates between capital and noncapital goods and finds that trade in capital goods is a significant channel of R&D spillovers. Combining their approach with the approach of this paper would likely yield valuable new insights. Analysis that disaggregated the data by industry may also prove interesting. Other channels of research transmission, such as direct investment, also remain largely unexplored.

(*.) Department of Economics, Saint Louis University, 3674 Lindell Boulevard, St. Louis, MO 63108, USA; E-mail [e-mail].

I would like to thank two anonymous referees, Deborah Swenson, Rob Feenstra, Peter Lindert, and Jack Strauss for constructive comments and suggestions. The usual disclaimer applies.

Received February 1999; accepted March 2000.

(1.) Constructing a foreign research stock as the simple sum of foreign R&D expenditures is equivalent to assuming that every dollar spent on research by foreign countries contributes the same increment to the foreign research stock. For example, unweighted foreign research stocks means that for Japan, Greek research is interchangeable at the margin with U.S. research. Moreover, since the United States performs over halt of all OECD research, the simple sum approach essentially turns the question of whether imports contain research spillovers into the question of whether U.S. research spills over to foreign countries.

(2.) Keller states that the average coefficient on randomly weighted foreign R&D should approximate the coefficient on unweighted foreign R&D. However, since the United States accounts for over 50% and just four countries (United States, Japan, Germany, and the United Kingdom) account for over 80% of all OECD research, small fluctuations in the bilateral shares of these countries can have large effects on the foreign R&D stocks of other countries. As a result, over half of all randomly constructed foreign R&D stocks were stationary, thus motivating the regressions using only nonstationary foreign R&D stocks. When the random weights are drawn once and then held constant throughout the sample period, the results are nearly identical to the results from regressions using unweighted foreign R&D stocks.

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                Im, Pesaran, and Shin t-Bar Unit Root Test
Productivity                                    -.132
 [S.sub.d] (domestic R&D stock)                 -.705
 [S.sub.f] (import-weighted foreign R&D stock)  -.945
 [S.sub.fx] (export-weighted foreign R&D stock) -.943
T = 20, N = 22, two lags in the ADF regression. [H.sub.0]: Data contain
a unit root. Common time effects removed from all data series by
subtracting cross-section means. Five percent significance = -1.65.
               R&D Spillovers and Bilateral Import Patterns
                 OLS             FMOLS           DOLS
[S.sub.d]    .090 (10.92) [*] .078 (4.30) [*] .092 (4.25) [*]
G7*[S.sub.d] .135 (8.60) [*]  .127 (3.37) [*] .116 (2.59) [*]
[S.sub.f]    .059 (4.06) [*]  .075 (2.45) [*] .044 (1.20)

Dependent variable = TFP (total factor productivity), number of observations = 352.

[S.sub.d] = domestic R&D stock; G7 = dummy for the G7; [S.sub.f] = bilateral = import-weighted foreign R&D stock; [S.sub.fx] = bilateral-export-weighted foreign R&D. All variables in log levels and indexed. All equations include unreported group fixed effects. The DOLS regressions include one lead and two lags of the differenced regressors. The estimation was performed in GAUSS and COINT 2.0 using the Kao and Chiang programs for FMOLS and DOLS that were helpfully provided by Kao. Absolute t-statistics in parentheses.

(*.)Significant at the 5% level.

                           Random Trade Partners
                                 Average         Average
                               OLS Result      FMOLS Result
[S.sub.d]                     .105 (15.75) [*] .101 (6.46) [*]
G7*[S.sub.d]                  .147 (9.51) [*]  .141 (3.73) [*]
[S.sub.f]                     .015 (2.53) [*]  .018 (1.92) [**]
Percentage of random-weighted     71%              50%
 foreign R&D stocks with t-
 statistic greater than 1.96
                                Average
                              DOLS Result
[S.sub.d]                     .109 (5.86) [*]
G7*[S.sub.d]                  .118 (2.63) [*]
[S.sub.f]                     .008 (0.76)
Percentage of random-weighted     16%
 foreign R&D stocks with t-
 statistic greater than 1.96

Dependent variable = TFP (total factor productivity), number of observations = 352. Bilateral trade relationships randomly generated in 1000 regressions. [S.sub.d] = domestic R&D stock; [S.sub.f] = foreign R&D stock; G7 dummy equaling one for the G7 nations. All variables in log levels and indexed. All equations include unreported group fixed effects. The DOLS regressions include one lead and two lags of the differenced regressors. The estimation was performed in GAUSS and COINT 2.0 using the Kao and Chiang programs for FMOLS and DOLS that were helpfully provided by Kao. Absolute t-statistics in parentheses.

(*.)Significant at the 5% level.

(**.)Significant at the 10% level.

                            Cointegration Tests
                                      Equation 1
                                      Using Both
         Equation 1    Equation 1   Import-Weighted
        Using Import- Using Export-   and Export-
          Weighted      Weighted       Weighted
         Foreign R&D   Foreign R&D    Foreign R&D
Kao-ADF    -2.54 [*]     -2.38 [*]      -2.39 [*]
Null hypothesis: [H.sub.0]: No cointegration. Cointegration tests
calculated from the residuals of the OLS estimation. Kao's ADF test
distributed N (0, 1).
(*.)Rejection of the null at the 5% level.
               R&D Spillovers and Bilateral Export Patterns
                 OLS            FMOLS           DOLS
[S.sub.d]    .071 (8.47) [*] .053 (3.03) [*] .054 (2.62) [*]
G7*[S.sub.d] .116 (7.45) [*] .103 (2.84) [*] .084 (1.94) [**]
[S.sub.fx]   .094 (6.96) [*] .100 (3.81) [*] .113 (3.62) [*]

Dependent variable = TFP (total factor productivity); number of observations = 352. [S.sub.d] = domestic R&D stock; G7 = dummy for the G7; [S.sub.f] = bilateral-import-weighted foreign R&D stock; [S.sub.fx] = bilateral-export-weighted foreign R&D. All variables in log-levels and indexed. All equations include unreported group fixed effects. The DOLS regressions include one lead and two lags of the differenced regressors. The estimation was performed in GAUSS and COINT 2.0 using the Kao and Chiang programs for FMOLS and DOLS that were helpfully provided by Kao. Absolute t-statistics in parentheses.

(*.)Significant at the 5% level.

(**.)Significant at the 10% level.

                     R&D Spillovers and Trade Patterns
                  OLS            FMOLS            DOLS
[S.sub.d]     .071 (8.18) [*] .052 (2.82) [*]  .046 (2.10) [*]
G7*[S.sub.d]  .116 (7.43) [*] .103 (2.82) [*]  .089 (2.06) [*]
[S.sub.fx]    .094 (5.55) [*] .096 (3.30) [*]  .122 (3.51) [*]
[S.sub.f]    -.001 (-.033)    .007 (.214)     -.003 (-.083)

Dependent variable = TFP (total factor productivity); number of observations 352. [S.sub.d] = domestic R&D stock; G7 = dummy for the G7; [S.sub.f] = bilateral-import-weighted foreign R&D stock; [S.sub.fx] = bilateral-export-weighted foreign R&D. All variables in log levels and indexed. The DOLS regressions include one lead and two lags of the differenced regressors. All equations include unreported group fixed effects. The estimation was performed in GAUSS and COINT 2.0 using the Kao and Chiang programs for FMOLS and DOLS that were helpfully provided by Kao. Absolute t-statistics in parentheses.

(*.)Significant at the 5% level.

              Elasticities of Total Factor Productivity with
               Respect to R&D Capital Stocks in the G7, 1990
               R&D Performer
Spillover         United                                United
Recipient         States     Japan Germany France Italy Kingdom Canada
United States      0.000     0.058  0.016  0.008  0.002  0.015  0.011
Japan              0.106     0.000  0.003  0.001  0.000  0.002  0.000
Germany            0.072     0.006  0.000  0.011  0.004  0.013  0.000
France             0.062     0.006  0.025  0.000  0.005  0.012  0.000
Italy              0.065     0.005  0.021  0.012  0.000  0.008  0.000
United Kingdom     0.083     0.005  0.014  0.007  0.001  0.000  0.001
Canada             0.109     0.003  0.000  0.000  0.000  0.001  0.000
Australia          0.062     0.042  0.003  0.002  0.001  0.003  0.000
Austria            0.034     0.004  0.055  0.005  0.005  0.006  0.000
Belgium            0.043     0.003  0.029  0.018  0.003  0.012  0.000
Denmark            0.050     0.009  0.026  0.005  0.002  0.016  0.000
Finland            0.058     0.005  0.019  0.006  0.001  0.018  0.000
Greece             0.052     0.003  0.030  0.009  0.008  0.009  0.000
Ireland            0.053     0.005  0.013  0.006  0.001  0.033  0.000
Israel             0.097     0.005  0.004  0.002  0.001  0.003  0.000
Netherlands        0.041     0.002  0.037  0.009  0.003  0.018  0.000
New Zealand        0.077     0.024  0.003  0.001  0.001  0.006  0.000
Norway             0.056     0.004  0.017  0.008  0.001  0.023  0.001
Portugal           0.053     0.003  0.022  0.014  0.002  0.015  0.000
Spain              0.061     0.003  0.016  0.016  0.003  0.012  0.000
Sweden             0.072     0.004  0.016  0.005  0.001  0.012  0.000
Switzerland        0.057     0.011  0.022  0.006  0.003  0.011  0.000
Average
 elasticity        0.062     0.010  0.018  0.007  0.002  0.011  0.001
Estimated elasticity of total factor productivity in the
row country with respect to the R&D stock in the column
country, based on the DOLS regressions in Table 5.

Appendix: Data Sources

The data on domestic R&D stocks and total factor productivity come from Coe and Helpman (1995) and can be obtained from Helpman's Web page: http://www.economics.harvard.edu/faculty/helpman/helpman.html. Coe and Helpman in turn derived their R&D data from the OECDs Main Science and Technology Indicators. The bilateral trade data used to construct import share and export share weights come from the IMF's Direction of Trade. I made several minor modifications to Coe and Helpman's import-weighted foreign R&D data. All the differences are due to my use of the most recent trade statistics; the slightly different trade data cause no qualitative differences in the empirical results.