Silviase/jgov_v1.4_full_ann huggingface dataset:
the expectation of the market size in the coming year according to the theoretical consideration above, but we simply assume that the expectation of each firm corresponds to the current market size. We also include the time-specific constant term, $ \delta_{0t}^{X} $ , and the industry-specific constant, $ \delta_{1i}^{X} $ , in each equation.

The following parametric conditions are predicted according to the theoretical results. First, we expect that $ \beta_{1}^{I} $ , the effect of the knowledge level of the parent firm on overseas innovative R&D, is positive under the presence of the complementarity between home and overseas innovative R&D and a weak idea-exhaustion effect, as inequality (8) indicates. However, $ \beta_{1}^{I} $ is zero or negative in the absence of the complementarity (inequality [9]). By contrast, $ \beta_{1}^{A} $ , the effect on adaptive R&D, should be always positive, as shown in the last inequality of (7). These results come from that knowledge of parent firms raises gains from overseas innovative R&D only under the presence of complementarity, while it unambiguously raises gains from adaptive R&D. Second, $ \beta_{2}^{I} $ and $ \beta_{2}^{A} $ , the coefficients on knowledge of subsidiaries, are expected to be negative due to the idea-exhaustion effect. Third, $ \beta_{3}^{I} $ , the effect of the public knowledge of the host country on overseas innovative R&D, is positive, since the primary target of overseas innovative R&D is exploitation of foreign advanced knowledge. However, the effect on adaptive R&D, $ \beta_{3}^{A} $ , is zero, since its key input is knowledge of parent firms, rather than foreign public knowledge. Finally, $ \beta_{4}^{I} $ and $ \beta_{4}^{A} $ should be positive, reflecting positive effects of the market size of the host country on the size of overseas R&D.

Since many overseas subsidiaries in our sample reported zero for R&D expenditures, we start with the tobit model to estimate equation (10). A problem of this method is that the regressors are mostly endogenous and possibly correlated with the error term. To alleviate this, we apply Amemiya Generalized Least Squares (AGLS) developed in Amemiya (1974), using the one-year lagged regressors as instruments.

### 3.2 Impacts of Overseas R&D on Home and Overseas Productivity

Next, we estimate equations (1) and (2) to examine roles of overseas R&D in home and overseas productivity growth.

Because knowledge of parent firms and subsidiaries, $ A_{it}^{p} $ and $ A_{it}^{s} $ , determine
their R&D expenditures, we reduce equations (1) and (2) to functions of $ R\&D_{it}^{p} $ and $ R\&D_{it}^{sI} $ , and $ R\&D_{it}^{sA} $ . Accordingly, the estimation equations are given by

$$ \begin{aligned}\ln A_{ij,t+1}^{p}&-\ln A_{ijt}^{p}=\gamma_{1}^{p}\frac{R\&D_{it}^{p}}{Y_{ijt}^{p}}+\gamma_{2}^{p}\frac{\sum_{j}R\&D_{ijt}^{sI}}{Y_{ijt}^{p}}+\gamma_{3}^{p}\frac{\sum_{j}R\&D_{ijt}^{sA}}{Y_{ijt}^{p}}\\&+\gamma_{4}^{p}\bigg(\frac{R\&D_{it}^{p}}{Y_{ijt}^{p}}\times\frac{\sum_{j}R\&D_{ijt}^{sI}}{Y_{ijt}^{p}}\bigg)+\eta_{0t}^{p}+\eta_{1i}^{p}+\nu_{i,t+1}^{p},\\\ln A_{ij,t+1}^{s}&-\ln A_{ijt}^{s}=\gamma_{1}^{s}\frac{R\&D_{it}^{p}}{Y_{ijt}^{s}}+\gamma_{2}^{s}\frac{R\&D_{ijt}^{sI}}{Y_{ijt}^{s}}+\gamma_{3}^{s}\frac{R\&D_{ijt}^{sA}}{Y_{ijt}^{s}}\\&+\gamma_{4}^{s}\bigg(\frac{R\&D_{it}^{p}}{Y_{ijt}^{s}}\times\frac{R\&D_{ijt}^{sI}}{Y_{ijt}^{s}}\bigg)+\gamma_{5}^{s}\bigg(\frac{R\&D_{it}^{p}}{Y_{ijt}^{s}}\times\frac{R\&D_{ijt}^{sA}}{Y_{ijt}^{s}}\bigg)\\&+\eta_{0t}^{s}+\eta_{1i}^{s}+\nu_{i,t+1}^{s},\end{aligned} $$

where $ \eta_{0t}^{k} $ , $ \eta_{1i}^{k} $ , and $ \nu_{i,t+1}^{k} $ for k = p, s are time- and firm-specific constant terms and the error term, respectively. $ R\&D_{it}^{p} $ is represented by R&D expenditures in parent firm i. $ \sum_{j}R\&D_{ijt}^{sI} $ and $ \sum_{j}R\&D_{ijt}^{sA} $ indicate the total expenditures on innovative and adaptive R&D in all of firm i's overseas subsidiaries, respectively, while $ Y_{it}^{p} $ and $ Y_{ijt}^{s} $ are the value added of parent firm i and its subsidiary in country j, respectively. Notice that we use ratios of R&D expenditures to value added to correct for variations in firm sizes. The R&D ratio to value added is also used in Griliches (1980) and many other works on impacts of R&D on production or productivity, which is derived from assuming a Cobb-Douglas production function and a constant ratio of R&D stocks to value added.

In equation (11), we expect that $ \gamma_{1}^{p} $ , the direct effect of R&D activities of the parent firm on its own productivity growth, is positive. Also, $ \gamma_{2}^{p} $ is positive if overseas innovative R&D has direct effects on home. In addition, $ \gamma_{3}^{p} $ is expected to be zero, since overseas adaptive R&D should have no impact on home productivity. Finally, the coefficient on the interaction term between home and overseas innovative R&D, $ \gamma_{4}^{p} $ , is positive, only under the presence of complementarity between home and overseas innovative R&D, as equation (3) indicates. When the complementarity is absent, or equation (4) holds, $ \gamma_{4}^{p} $ is expected to be zero.

In equation (12), we expect that $ \gamma_{1}^{s} $ , $ \gamma_{2}^{s} $ , and $ \gamma_{3}^{s} $ , which represent direct effects of home and overseas R&D on productivity growth in overseas subsidiaries, are positive. The coefficient on the interaction term between home and overseas
innovative R&D, $ \gamma_{4}^{s} $ , is positive, only when home and overseas innovative R&D are complementary to one another. By contrast, $ \gamma_{5}^{s} $ , the coefficient on the interaction term between home R&D and overseas adaptive R&D, should be positive without ambiguity, since knowledge of parent firms always raises the marginal gains from overseas adaptive R&D.

By comparing the results from estimating equations (11) and (12) with the results from estimation of determinants of overseas R&D, we can check whether the three sets of results are consistent with one another. In particular, one of our primary interests is whether or not home and overseas innovative R&D are complementary. By examining the signs of $ \beta_{1}^{I} $ in equation (10), $ \gamma_{4}^{p} $ in (11), and $ \gamma_{4}^{s} $ in (12), we can easily find consistency between the three sets of regression results.

We start with the ordinary least squares (OLS) estimate of equations (11) and (12), while we then employ the fixed-effects (within) estimation to eliminate the firm-specific constant terms.

However, the regressors may not be strictly exogenous; They may be predetermined in the sense that the regressors for time t such as $ R\&D_{it}^{p} $ are not correlated with $ \nu_{i,t+1} $ but with $ \nu_{it} $ . Therefore, eliminating firm-specific constants by within transformation or first differencing yields correlation between the error term and the regressors in the transformed regression, even though the original regression equation (11) or (12) does not have this endogeneity problem.

To eliminate the possible endogeneity, we apply the differenced generalized method of moments (GMM) estimation developed in Arellano and Bond (1991) and the system GMM developed in Blundell and Bond (1998). In the case of the differenced GMM, we take first differences of both sides of each of equations (11) and (12) to eliminate the firm-specific constant terms and then apply GMM estimations to the first-differenced equation, using the lagged regressors as instruments. In the system GMM, we also estimate the original equation (11) or (12) by GMM, using the lagged first-differenced regressors as instruments, together with the estimation of the first-differenced equation as in the differenced GMM. The major advantage of the system GMM over the differenced GMM is that in the latter, instruments are weak if regressors have near unit root properties, whereas this problem can be alleviated in the former.
We apply two-step estimations of the differenced and system GMM to obtain larger efficiency. In addition, we use robust standard errors developed in Windmeijer (2000), which are consistent under the presence of any pattern of heteroskedasticity and autocorrelation $ ^{8} $ and correct for finite sample biases found in the two-step estimations.

## 4 Data

### 4.1 Description of the Data Sets

For the estimation in this paper, we combine two firm-level data sets for the period 1996-2001, one for Japanese firms, $ Kigyo\ Katsudo\ Kihon\ Chosa $ (Basic Surveys of Enterprise Activities) and the other for Japanese MNEs, $ Kaigai\ Jigyo\ Katsudo\ Kihon\ Chosa $ (Basic Surveys of Multinational Enterprises). Both data sets are collected annually by the Ministry of Economy, Trade and Industry. The year 1996 is the earliest year in which data for overseas R&D are available and distinction between overseas innovative and adaptive R&D is possible in a consistent manner. Since roles of R&D activities may vary substantially across industries, we focus on the four 2-digit manufacturing industries of which the average ratios of R&D expenditures to value added in parent firms are the largest among 17 industries in total: chemicals, electronic and other electrical equipment, transportation equipment, and precision machinery. These four industries contribute to 83 percent in the aggregate value added and 85 percent in the aggregate overseas R&D expenditures. Details of the data sets and variables used are presented in the Appendix.

Since the surveys include questions on roles of overseas R&D activities, we can classify R&D activities of each subsidiary as innovative or adaptive according to its responses to the surveys. $ ^{9} $ Specifically, we define R&D expenditures reported by each overseas subsidiary as expenditures on innovative R&D, if the reported functions of its R&D activities include basic research, applied research,
or development for the world market. Otherwise, R&D expenditures are considered as adaptive R&D expenditures. Notice that expenditures on innovative R&D according to our definition are likely to be overestimated, since some part of the expenditures that are in fact spent on adaptive R&D are classified as those on innovative R&D due to lack of information.

Parent firms in Japan may engage in R&D for adaptation for the foreign markets. However, since we do not have any kind of information on the possible adaptive R&D in parent firms, we simply assume that R&D expenditures reported by each parent firm represent expenditures on innovative R&D.

### 4.2 Measuring Productivity Levels

In our estimation, the knowledge levels of each parent firm and overseas subsidiary, $ A_{it}^{p} $ and $ A_{ijt}^{s} $ , are represented by the TFP level of the parent firm and subsidiary, respectively. The firm-level TFP level is given by

$$ \ln A_{i t}^{k}=\ln Y_{i t}^{k}-\beta_{K}\ln K_{i t}^{k}-\beta_{L}\ln L_{i t}^{k}\qquad k=p,s, $$

where $ Y^{k} $ , $ K^{k} $ , and $ L^{k} $ are the real values of value added and the capital stock and labor force in each firm. We assume $ \beta_{K} = 0.289 $ and $ \beta_{L} = 0.682 $ , which are obtained from all available firms in Japan using the method in Olley and Pakes (1996) that can eliminate biases due to endogeneity of inputs and attrition of the sample from exits of firms. $ ^{10} $ According to Monte Carlo studies in Van Biesebroeck (2004), this method provides in most cases better estimates of TFP levels than many others using, for example, index numbers, GMM, and stochastic frontiers. These estimates suggest that the production function is very close to constant returns to scale, although we statistically reject constant returns to scale according to their standard errors.

The aggregate TFP level of country j at time t is given by

$$ \ln A_{j t}^{h o s t}=\ln Y_{j t}^{h o s t}-\tilde{\alpha}\ln K_{j t}^{h o s t}-\left(1-\tilde{\alpha}\right)\ln L_{j t}^{h o s t}, $$

where $ Y_{jt}^{host} $ , $ K_{jt}^{host} $ , and $ L_{jt}^{host} $ are real GDP, the real capital stock, and labor force in country j, taken from the Penn World Tables Version 6.1 that update
Summers and Heston (1991). Aiyar and Dalgaard (2004) find that for cross-country TFP, the simple method using equation (14) with $ \tilde{\alpha}=1/3 $ is “a very good approximation to a more general formulation under which countries have different aggregate production functions which do not require a constant elasticity of substitution between factors.” Following cross-country estimates in Islam (2003), we assume $ \tilde{\alpha}=0.3742 $ , which might be a better estimate of $ \tilde{\alpha} $ than 1/3.

### 4.3 Summary Statistics

Our unbalanced panel data for overseas subsidiaries to examine determinants of overseas R&D has 2,017 observations, of which 621 reported positive R&D expenditures, whereas 330 and 332 reported positive innovative and adaptive R&D expenditures, respectively. $ ^{[11]} $ 364 out of the 621 observations with positive R&D expenditures were located in OECD countries, among which 209 and 186 performed innovative and adaptive R&D, respectively. Summary statistics of the variables used in estimation are shown in Table 1. On average, overseas subsidiaries spent 1.16 percent of value added on R&D in total, 0.70 percent and 0.46 percent on innovative and adaptive R&D, respectively. It should be noted, however, their standard deviations are large, indicating substantial variations among subsidiaries.

When we estimate impacts of overseas R&D on home and overseas productivity growth, we use a balanced panel of Japanese parent firms and their overseas subsidiaries, respectively. By using balanced panels, rather than unbalanced, we can use the same number of instruments for each observation in the same year in the differenced and system GMM estimations. These samples for Japanese firms and overseas subsidiaries include 133 and 82 firms, respectively, for each year. These numbers are substantially small, compared with the number of firms included in the original data sets, since very few firms report R&D expenditures every year during the period 1996-2001.

Among 665 $ (=133\times5) $ observations for Japanese firms in the period 1996-2000, $ ^{12} $ all observations reported positive own R&D expenditures, whereas 245 reported positive overseas R&D expenditures. Summary statistics of the vari-
ables used are shown in Table 2. The average R&D expenditure in parent firms is 10.7 percent of value added, while the average overseas R&D expenditure is 0.48 percent of value added of parent firms. This evidence suggests that the level of overseas R&D is substantially smaller than the level of home R&D, although overseas R&D shows an increasing trend over time as reported in Table 3.

In the balanced panel for overseas subsidiaries, 199 observations among 410 $ (=\text{82} \times 5) $ reported positive R&D expenditures. Summary statistics are presented in Table 4. The average ratio of overseas R&D expenditures to value added of overseas subsidiaries is 1.9 percent, which is larger than the average ratio in the unbalanced panel for the determinant regression. This probably reflects a tendency that firms that report R&D expenditures every year are more R&D-intensive than others that report only occasionally.

## 5 Estimation Results

### 5.1 Determinants of Overseas R&D Activities

The results on determinants of overseas R&D activities using the unbalanced panel data are reported in Table 5, which are mostly consistent with the theoretical predictions presented by inequalities (6)-(9).

We first focus on results on innovative R&D using tobit and AGLS reported in columns (1) and (2), respectively. The results in the first row show that the TFP level of each parent firm in Japan, $ A^{p} $ , has no significant effect on expenditures on innovative R&D in its overseas subsidiary. It is thus suggested that knowledge of parent firms has no impact on gains from overseas innovative R&D, or innovative R&D in Japan and abroad are not complementary to one another.

The second row indicates that the size of overseas innovative R&D is negatively correlated with its own current TFP level, $ A^{s} $ , indicating that performing R&D from a high knowledge level is more costly than from a low level due to idea-exhaustion effects.

The third row shows a positive effect of the public knowledge level of the host country, $ A^{host} $ , suggesting that Japanese firms try to exploit foreign advanced knowledge through innovative R&D. This effect is substantially large, implying that an increase in $ A^{host} $ by 44 percent, its standard deviation shown in Table
1, $ ^{13} $ raises the ratio of innovative R&D expenditures to value added by 1.9 percentage points.

Finally, the market size of the host country represented by its total GDP, $ Y^{host} $ , has a positive effect. $ ^{14} $ This market-size effect is also substantial in magnitude, since an increase in $ Y^{host} $ by 146 percent, its standard deviation (Table 1), is associated with a 1.6-percentage-point increase in the innovative R&D ratio.

Next, we examine results on adaptive R&D reported in columns (3) and (4) of Table 5. There are two major differences between the results on innovative and adaptive R&D. First, the TFP level of parent firms has a positive and significant effect on the size of its overseas adaptive R&D, despite its insignificant effect on innovative R&D. This is consistent with the theoretical prediction shown by the last inequality in (7), confirming that knowledge of parent firms is the primary input to overseas adaptive R&D.

Second, the tobit estimation indicates that the effect of the TFP level of the host country is significant but substantially smaller in size than the effect on innovative R&D; moreover, the effect is statistically insignificant in the AGLS estimation. It is thus suggested that overseas adaptive R&D does not employ public knowledge of the host country, or employs it less intensively than overseas innovative R&D. This confirms that the primary role of this type of overseas R&D is adaptation, rather than exploitation of foreign knowledge.

The results on the coefficients on $ \ln A^{s} $ and $ \ln Y^{host} $ are not very different from the previous results for innovative R&D. Namely, we find weak evidence of the idea-exhaustion effect, although the coefficient on $ \ln A^{s} $ is negative but insignificant in the AGLS estimation. In addition, the market-size effect is positive as before, although its magnitude is slightly smaller than in the case of innovative R&D.

Since the amount of innovative R&D expenditures in overseas subsidiaries is likely to be overestimated as suggested in the data section, we integrate overseas innovative and adaptive R&D expenditures and estimate determinants of overseas R&D in total as a robustness check. The results are reported in
columns (5) and (6) of Table 5, which are mostly between the results from using innovative and adaptive R&D separately.

In summary, the major determinant of overseas innovative R&D by Japanese MNEs are the public knowledge level of the host country, whereas those of adaptive R&D are the knowledge level of parent firms. The market size of the host country determines the sizes of both innovative and adaptive R&D.

### 5.2 Impacts of Overseas R&D on Home TFP Growth

To examine the direct effect of each type of overseas R&D on TFP growth in parent firms in Japan, we first exclude the interaction term from equation (11) for simplicity. Columns (1), (2), (3), and (4) of Table 6 report results from the OLS, fixed-effects, and differenced and system GMM estimations, respectively.

In each GMM estimation, the Hansen J statistic, the minimized value of the two-step GMM criterion function, is reported to test overidentifying restrictions, or the orthogonality between instruments and the error term. In addition, the difference between the Hansen J statistics from the two types of GMM is reported to test whether additional instruments used in the system GMM are orthogonal to the error term. According to the Hansen statistics and their difference, the instruments used in both GMM estimations are valid. Moreover, the p value of the difference Hansen statistic is sufficiently large, suggesting the validity of the additional instruments in the system GMM. Therefore, the system GMM is the most preferred specification among the four, and we will focus on the results from that method.

The effect of the size of R&D activities of parent firms, $ R\&D^{p}/Y^{p} $ , on their own TFP growth is positive and significant, indicating that an increase in R&D expenditures by one percentage point is associated with a 1.29-percent increase in the TFP level. This is larger than the existing estimates for Japanese manufacturing firms, such as those of Odagiri and Iwata (1986) and Goto and Suzuki (1989), which are mostly less than 0.5. However, because these estimates are obtained from OLS and our OLS result in column (1) is close to them, the larger effect in the system GMM estimation may have resulted from eliminating the firm-specific constant term and correcting for endogeneity.

Also, overseas innovative R&D, $ \sum R\&D^{sI}/Y^{p} $ , has a positive and significant
effect on home TFP growth, and the effect is similar in magnitude to the effect of home R&D. By contrast, overseas adaptive R&D, $ \sum R\&D^{sA}/Y^{p} $ , exhibits no significant impact on home TFP growth.

Next, to test the presence of complementarity between home and overseas innovative R&D, we include their interaction term as an additional regressor, $ ^{15} $ reporting the results in columns (5)-(8) of Table 6. According to the Hansen and difference Hansen statistics, the most preferred specification is again the system GMM. Although the result on the effect of home R&D is similar to the previous result, neither overseas innovative R&D nor its interaction term with home R&D has a significant effect. $ ^{16} $ These results suggest that while overseas innovative R&D has a direct effect on home TFP growth, it is not complementary to home R&D in the sense that overseas innovative R&D does not improve the marginal impact of home R&D.

### 5.3 Impacts of Overseas R&D on Overseas TFP Growth

In examining effects on TFP growth in overseas subsidiaries, we start with a simpler version of equation (12) in which the interaction terms are excluded. The OLS, fixed-effects, and differenced and system GMM estimations are performed, and the results are shown in columns (1)-(4) of Table 7. Since the system GMM is the most preferred specification according to the Hansen and difference Hansen statistics, we will focus on the results from that method.

The first row indicates that the effect of home R&D, $ R\&D^{p}/Y^{s} $ , on TFP growth in overseas subsidiaries is positive and significant. Qualitatively, the result indicates that the average size of home R&D, 943 percent of value added of the subsidiary, improves overseas TFP by 6 percent per year.

In the second row, we find that overseas innovative R&D, $ R\&D^{sI}/Y^{s} $ , has no significant effect on overseas TFP growth. According to this result, combined with the previous finding that overseas innovative R&D has a positive effect on home TFP growth, we may conclude that outcomes of overseas innovative R&D are mostly utilized in parent firms in the home country. This implies $ \delta^{s}=0 $ in