I. Introduction

Economic growth has many facets. It depends on the utilization of resources, the rate of population growth, the savings rate, the mode of organization of economic activity, technological know how, and more. Whereas the neoclassical theory treated technological progress as an exogenous process and focused instead on capital accumulation as the main endogenous source of output expansion, recent research has provided novel ways of dealing with technical progress. The latter studies view commercially oriented innovation efforts that respond to economic incentives as a major engine of technological progress and productivity growth (see Romer (1990) and Grossman and Helpman (1991)). In this view innovation feeds on knowledge that results from, cumulative R&D experience on the one hand, and it contributes to this stock of knowledge on the other. Consequently an economy’s productivity level depends on its cumulative R&D effort and on its effective stock of knowledge, with the two being inter-related. There exists, in fact, convincing empirical evidence that cumulative domestic R&D is an important determinant of productivity (see Griliches (1988) and Coe and Moghadam (1993)).

In a world with international trade in goods and services, foreign direct investment, and an international exchange of information and dissemination of knowledge, a country’s productivity depends on its own R&D as well as on the R&D efforts of its trade partners. Own R&D produces traded and nontraded goods and services that bring about more effective use of existing resources and thereby raises a country’s productivity level. In addition, own R&D enhances a country’s benefits from foreign technical advances, and the better a country takes advantage of technological advances in the rest of the world the more productive it becomes. The benefits from foreign R&D can be both direct and indirect. Direct benefits consist of learning about new technologies and materials, production processes, or organizational methods. Indirect benefits emanate from imports of goods and services that have been developed by trade partners. In either case foreign R&D affects a country’s productivity.

We study in this paper the extent to which a country’s productivity level depends on domestic and foreign R&D capital stocks. Following much of the theoretical and empirical literature, we use cumulative R&D expenditure as a proxy for a stock of knowledge. For every country in our sample we construct a stock of domestic knowledge that is based on domestic R&D expenditure and a foreign stock of knowledge that is based on R&D spending of its trade partners. For the construction of foreign R&D capital stocks we use import weighted sums of trade partner’s cumulative R&D spending levels. We explain the rational for this procedure in the theoretical section. For every country we also calculate a measure of total factor productivity defined as the log of output minus a weighted average of the logs of labor and capital inputs, where the weights equal factor shares. Having done these calculations, we estimate the effects of domestic and foreign R&D capital stocks on total factor productivity. Our estimates underline the importance of the interaction between international trade and foreign R&D.

Our sample consists of 21 OECD countries plus Israel during the period 1970-90. We find, using pooled time series cross section data, that both domestic and foreign R&D capital stocks have important effects on total factor productivity. Foreign R&D capital stocks have stronger effects on domestic productivity the larger the share of domestic imports in GDP. It follows that more open economies extract larger productivity benefits from foreign R&D than less open economies. Moreover, measuring the importance of the R&D capital stock by the elasticity of TFP with respect to the R&D capital stock we find that the foreign R&D capital stock is at least as important as the domestic R&D capital stock in the smaller countries, while in the larger countries (the G7) the domestic R&D capital stock is more important.

The next section contains a discussion of the theory that underlies our empirical specification. A brief review of the main features of our data is presented in Section III, and the sources and construction of the data are described in the Appendix. The main empirical findings and their economic interpretations are reported in Section IV. Section V concludes.

II. Theory

Our empirical equations build on some recent theoretical models of innovation-driven growth. Since the basic models of this theory have been widely discussed, we provide in this section only rudimentary details and focus instead on results that are needed for our purpose. ^2/ In the simplest case, a closed economy manufactures final output Y from an assortment of intermediate inputs x(j), jε[0,n], where n is a measure of available intermediate inputs. The production function can be written in the form:

where D is a linear homogeneous function of the employed inputs, given n.

Two stories appear to be common in the formulation of D. In one case the inputs are horizontally differentiated. A simple formalization of this view takes D to be a symmetric constant elasticity of substitution function, with the elasticity of substitution being larger than one, and every input to be manufactured with a unit of labor per unit output. Then all inputs are equally priced and equally employed in production. The result is that

where σ is the elasticity of substitution and X = nx represents aggregate employment of intermediates.

Aggregate use of intermediates X is proportional to the labor force employed in manufacturing. The measure of available inputs expands as a result of R&D investment. Entrepreneurs who seek monopoly profits invest resources in the development of new intermediate inputs. In this event the measure of available inputs n is a function of the country’s cumulative R&D effort. ^3/ It follows that the log of total factor productivity (TFP), as measured by logY - logL (where L stands for the available labor force and no capital is used in production), depends on a measure of cumulative R&D and the share of labor employed in manufacturing, X/L. In this model labor is employed either in manufacturing or in R&D. Therefore as long as R&D is a small share of GDP that does not differ greatly across countries and time periods (as it is indeed in our sample), ^4/ the ratio X/L is very close to one and it remains approximately constant. In this event we expect differences in cumulative R&D to explain most of the variation in TFP.

An alternative model treats intermediate inputs as vertically differentiated; namely, they come in different qualities. Here the effectiveness of input j in manufacturing depends on the number of times it has been improved. Inputs that have been improved more times are more productive. Input j that has been improved m times is λ times more productive than the same input that has been improved only m - 1 times (λ > 1). Now let D be a Cobb-Douglas function with equal coefficients on all inputs. The measure of available inputs is taken to be constant, and we choose for simplicity n = 1. As in the previous case, we assume that a unit of labor produces a unit of x(j). This production technology applies to all inputs and all quality levels. In this event only the highest inputs survive market competition. They are equally priced and employed in equal quantities in production. Under these circumstances

where X represents again the volume of employed inputs. Here I depends on cumulative R&D as follows. Suppose that at time t = 0 the quality of all inputs equals one. R&D that is targeted at improving input j generates a probability of success that is proportional to the R&D effort. The target is always the highest quality of j. If under these circumstances all products are targeted with equal intensity at a point in time t (as they will be in equilibrium) and we denote with ι(t) that instantaneous fraction of inputs that are improved per unit time, then ι(t) is proportional to the instantaneous R&D effort per product. This means that in a time interval of length dt innovators improve a fraction ι(t)dt of inputs. Given the Cobb-Douglas structure of the production function, this specification implies that at time T the average quality of inputs equals λ(^I(T)), where $\mathit{I}\mathrm{\left(}\mathrm{T}\mathrm{\right)}\mathrm{=}{\mathrm{\int }}_{\mathrm{o}}^{\mathrm{T}}\mathit{\iota }\mathrm{\left(}\mathrm{t}\mathrm{\right)}\mathrm{dt}$. Since ι(t) is proportional to the R&D effort at time t, it follows that I(T) depends on the cumulative R&D effort.

It is now straightforward to argue, as we did in the case of horizontally differentiated inputs, that total factor productivity depends on cumulative R&D and the share of labor absorbed in manufacturing. Relying again on the fact that in the data there is little variation in the share of R&D in GDP, we expect differences in cumulative R&D to explain most of the variation in TFP.

Two aspects of these examples require further elaborations. First, we have disregarded capital accumulation. Second, we have disregarded international trade.

In order to see how capital accumulation changes the basic relationship between TFP and cumulative R&D we now consider a simplified version of an extension proposed by Grossman and Helpman (1991), Chapter 5. ^5/ Let now the production function of final output Y be of the form

where K is the stock of capital and D depends on intermediate inputs in one of the two forms that we discussed above, and β is a parameter between zero and one. As before, intermediaries are manufactured from labor with one unit of input per unit output. In this case we measure logTFP by logY - β1ogK - (1-β)logL. It follows that logTFP equals (1-β)log(D/L). As before, D is given by (2) in the case of horizontally differentiated intermediate inputs and by (3) in the case of vertically differentiated intermediate inputs. Therefore in either case variations in TFP should be predominantly explained by variations in cumulative R&D, following the same arguments that we brought to bear on this issue in the simpler models with production that does not require capital. In fact, the previous models are a special case with β = 0. We conclude that the possibility of capital accumulation does not affect the result that differences in cumulative R&D should explain differences in total factor productivity.

Next consider international trade. The previous arguments apply in the absence of international trade in intermediate inputs, regardless of whether final output is traded or not. If this was the relevant case, we would be able to explain variations in a country’s total factor productivity with variations in its domestic R&D capital stock. Most international trade takes place in producer goods, however. In this event countries use extensively inputs that are manufactured by trade partners and inputs that were developed by trade partners. How does this change our conclusions?

In order to see as clearly as possible the role of international trade, consider an extreme case in which all intermediate inputs jε[0,n] are traded internationally, all of them are equally priced, and final output is not traded. Under these circumstances the above derived equations remain valid, except that now we need to interpret n as the measure of inputs that are manufactured in the world economy rather than in any particular country, and we need to interpret λ^I as the average quality of inputs in the world economy rather than in any particular country. It follows that with internationally traded intermediate inputs, n depends on cumulative R&D in the world economy and so does I. Therefore in this case variations in a country’s TFP are mostly attributable to variations in the world’s R&D capital stock. In particular, it follows that in this case domestic R&D has the same productivity effect as foreign R&D.

For empirical implementations of these models neither one of the extreme specifications of tradeability of intermediate inputs seems appropriate; there exist many tradeable inputs, but nontradeable inputs of goods and services are also prevalent. It is therefore most practical to formulate an empirical equation that allows for both traded and nontraded inputs. For these reasons we estimate equations in which variations in TFP are explained by variations in both the domestic and foreign R&D capital stocks. Our simplest equation has the following specification:

where i is a country index, logF is the log of total factor productivity (equal to logY - βlogK - (1-β)logL), S^d represents the domestic R&D capital stock and S^f the foreign R&D capital stock. ^6/ In this specification we allow the coefficients α to vary across countries. In the implementation, however, we will seek cross-country restrictions on the elasticities α^d and α^f. ^7/ The specification of (5) can be thought of as a multicountry extension of models relating TFP to only the domestic R&D capital stock, which would be a special case with α^f = 0.

The specification of (5) does not capture adequately the role of international trade. True, the foreign stock of knowledge S^f consists of import weighted foreign R&D capital stocks. But these weights are fractions that add up to one and therefore do not properly reflect the level of imports. We expect that whenever two countries have the same composition of imports and face the same composition of R&D capital stocks among trade partners the country that imports more relative to its GDP should experience a larger TFP benefit from foreign R&D. This is in line with the theoretical arguments presented above and can be strengthened with additional arguments that relate productivity gains to trade volumes (see Grossman and Helpman (1991), Section 6.5). For these reasons a modified specification of (5) that accounts for the interaction between foreign R&D capital stocks and the level of international trade seems preferable. To this end we estimate

where m stands for the fraction of imports in GDP. In this equation the elasticity of TFP with respect to the domestic R&D capital stock equals α^d while the elasticity of TFP with respect to the foreign R&D capital stock equals α^fm. It follows that whenever α^f is the same for all countries the latter elasticity varies across countries in proportion to their import shares. ^8/

III. Data

We provide in the Appendix details about data sources and the construction of the variables for estimation purposes. Here we only-highlight some features of the data. As shown in Table 1, over the 1970-90 period total factor productivity increased over time in all countries except for New Zealand. ^9/ But the upward trend was neither uniform across countries nor uniform over time. Japan and Norway experienced the fastest rate of productivity growth (with 68.3 percent and 56.6 percent, respectively) while in New Zealand productivity declined by 5.1 percent. Other countries had intermediate values. In the United States, for example, TFP increased by about 9.7 percent, in Canada by 17.0 percent, in Belgium by 37.7 percent, in the Netherlands by 26.0 percent, and in Sweden and Switzerland by about 11 percent. Figure 1 provides plots of TFP for six of these countries; they clearly exhibit substantial fluctuations.

Table 1.

Summary Statistics

Source: Tables 6, 8, 10, and 11.

Table 1.

Summary Statistics

	TFP growth (1970-90) in percent	${\mathrm{S}}_{\mathrm{1990}}^{\mathrm{d}}$	${\mathrm{S}}_{\mathrm{1990}}^{\mathrm{f}}$	m in percent
		${\mathrm{S}}_{\mathrm{1971}}^{\mathrm{d}}$	${\mathrm{S}}_{\mathrm{1971}}^{\mathrm{f}}$	1971	1990
United States	9.7	2.0	3.4	5.5	11.2
Japan	68.3	4.2	1.7	9.6	9.3
West Germany	22.6	2.6	1.6	19.1	26.1
France	41.7	1.8	1.7	15.3	22.8
Italy	40.6	2.8	1.4	15.6	19.6
United Kingdom	31.1	1.2	1.8	21.4	27.7
Canada	17.0	2.7	1.9	20.0	25.5
Australia	12.7	4.9	2.0	14.8	18.6
Austria	24.1	3.6	2.3	30.8	38.9
Belgium	37.7	2.1	1.5	43.9	88.2
Denmark	20.1	2.3	1.9	30.9	31.1
Finland	45.4	4.5	2.2	26.8	25.4
Greece	25.2	18.7	1.7	17.0	32.0
Ireland	37.7	3.7	2.3	42.1	56.1
Israel	41.3	7.3	1.6	50.0	52.0
Netherlands	26.0	1.5	1.9	45.1	53.9
New Zealand	-5.1	2.1	2.3	25.5	22.6
Norway	56.6	4.0	2.0	45.3	37.7
Portugal	32.4	2.0	1.4	33.6	44.9
Spain	18.7	7.0	1.2	14.7	21.4
Sweden	11.0	3.5	1.9	22.8	31.6
Switzerland	10.9	1.3	1.9	39.1	38.3

Source: Tables 6, 8, 10, and 11.

View Table

Table 1.

Summary Statistics

	TFP growth (1970-90) in percent	${\mathrm{S}}_{\mathrm{1990}}^{\mathrm{d}}$	${\mathrm{S}}_{\mathrm{1990}}^{\mathrm{f}}$	m in percent
		${\mathrm{S}}_{\mathrm{1971}}^{\mathrm{d}}$	${\mathrm{S}}_{\mathrm{1971}}^{\mathrm{f}}$	1971	1990
United States	9.7	2.0	3.4	5.5	11.2
Japan	68.3	4.2	1.7	9.6	9.3
West Germany	22.6	2.6	1.6	19.1	26.1
France	41.7	1.8	1.7	15.3	22.8
Italy	40.6	2.8	1.4	15.6	19.6
United Kingdom	31.1	1.2	1.8	21.4	27.7
Canada	17.0	2.7	1.9	20.0	25.5
Australia	12.7	4.9	2.0	14.8	18.6
Austria	24.1	3.6	2.3	30.8	38.9
Belgium	37.7	2.1	1.5	43.9	88.2
Denmark	20.1	2.3	1.9	30.9	31.1
Finland	45.4	4.5	2.2	26.8	25.4
Greece	25.2	18.7	1.7	17.0	32.0
Ireland	37.7	3.7	2.3	42.1	56.1
Israel	41.3	7.3	1.6	50.0	52.0
Netherlands	26.0	1.5	1.9	45.1	53.9
New Zealand	-5.1	2.1	2.3	25.5	22.6
Norway	56.6	4.0	2.0	45.3	37.7
Portugal	32.4	2.0	1.4	33.6	44.9
Spain	18.7	7.0	1.2	14.7	21.4
Sweden	11.0	3.5	1.9	22.8	31.6
Switzerland	10.9	1.3	1.9	39.1	38.3

Source: Tables 6, 8, 10, and 11.

Total Factor Productivity

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Total Factor Productivity

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Total Factor Productivity

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Between 1971 and 1990 the domestic R&D capital stock increased significantly in most countries. In Greece in particular it increased by a factor of 19, but this is an exception. In Israel and Spain this stock was sevenfold larger by the end of the period than at the beginning, and it had more than quadrupled in Japan, Australia, Finland, and Norway. Two countries, the United Kingdom and Switzerland, experienced the slowest expansion of their domestic R&D capital stock (20 percent and 30 percent, respectively). An important point to observe, however, is that the annual changes in this R&D capital stock were not uniform across countries, as can be seen from Figure 2.

Domestic Research and Development Capital Stocks

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Domestic Research and Development Capital Stocks

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Domestic Research and Development Capital Stocks

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Overall changes in foreign R&D capital stocks were less dramatic than in the domestic R&D capital stocks. Here the United States experienced the fastest expansion: more than threefold. At the same time, Spain faced the smallest increase (only 20 percent). Other countries enjoyed a doubling of their foreign R&D capital stocks with some variance around this figure. Fluctuations in the foreign R&D capital stocks around their time trends appear to be larger than for the domestic R&D capital stocks, as can be seen by comparing Figure 3 with Figure 2.

Trade Weighted Foreign Research and Development Capital Stock

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Trade Weighted Foreign Research and Development Capital Stock

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Trade Weighted Foreign Research and Development Capital Stock

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Finally, Table 1 provides data on import shares. In all countries except for Japan, Finland, New Zealand, Norway, and Switzerland the import share increased between 1971 and 1990. It has more than doubled in the United States and Belgium and only slightly increased in Denmark and Israel. Import shares declined slightly from 1971 to 1990 in Japan, Finland, New Zealand, Norway, and Switzerland. Moreover, there exist substantial differences in import shares across countries. Belgium had by far the largest import share in 1990 (88.2 percent) while Japan had the smallest (9.3 percent). And as shown in Figure 4, import shares fluctuated over time.

Import Share in GDP

Citation: IMF Working Papers 1993, 084; 10.5089/9781451954401.001.A001

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Import Share in GDP

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Import Share in GDP

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IV. Empirical Findings

We are interested in estimating the long-run relationship between total factor productivity and the foreign and domestic R&D capital stocks. Because almost all of our data exhibit a clear trend, and given our focus on the long-run relationship between total factor productivity and the foreign and domestic R&D capital stocks, we seek to estimate equations that are cointegrated. ^10/ The basic idea of cointegration is that two or more variables may be regarded as defining a long-run equilibrium relationship if they move closely together in the long run, even if they may drift apart in the short run. Given that there is a long-run relationship between the variables, a regression containing all the variables—the cointegrating equation—will have a stationary error term, even if none of the variables taken alone is stationary. If the error term is not stationary, the estimated relationship may be spurious (Granger and Newbold (1974)).

Cointegrated equations have very attractive econometric properties. The most important is that as the number of observations increases, OLS estimates of the cointegrating equation converge on the true parameter values much faster than in the case where the variables are stationary. This property is referred to as “super consistency” (Stock (1987)). ^11/ Moreover, super consistency does not require the assumptions of the classical regression model. This is reassuring, because our estimates of R&D capital stocks are likely to be measured with some degree of error given the need to calculate benchmarks, assume obsolescence rates, and so on; and because we cannot exclude that there are omitted relevant variables, such as proxies for the stock of human capital.

Cointegration techniques have been widely applied to time-series data. The implications of our models of international R&D spillovers, however, can only be persuasively verified with panel data. Although the econometrics of pooled cointegration are only now being developed, we conjecture that the super consistency result will hold or be strengthened with pooled data, and that the efficiency of the OLS estimates will increase substantially as the number of countries increases. In our case, we have 1970-90 data for 22 countries, giving 440 pooled observations. We interpret our estimates as pooled cointegrating equations, even though this means that there may be ambiguity in the interpretation of some of the econometric results. Except for Khan and Reinhart (1993), we are not aware of any applications of cointegrating techniques to panel data.

There are two preliminary issues to discuss before turning to the estimation results. The first concerns the nonstationarity of the variables in the cointegrating equation. The Dickey Fuller and the augmented Dickey Fuller tests on the time series for each country generally do not reject the presence of a unit root. As is well known, however, the power of these tests is very low, particularly with only twenty annual observations. Levin and Lin (1992) have recently derived the limiting distributions for unit root tests on panel data, and have shown that the power of these tests increases dramatically as the cross-section dimension increases. Unit root tests on the pooled data confirm that the variables are nonstationary, with the possible exception of m, as shown in the upper panel of Table 2.

Table 2.

Pooled Unit-Root and Exogeneity Tests

^1/Annual data 1972-90 for 22 countries, 418 observations. The critical values for the unit root test are from Levin and Lin (1992), Table 5.

^2/Annual data 1973-90 for 22 countries, 396 observations. The te2st statistics are based on regressions with ΔX (X = logS^d, logS^f, logS^f·m, and m) as the dependent variable and either 3 or 4 lagged values of ΔlogF and ΔX as the independent variables (the fourth lag was included if it was significantly different from zero). The Granger causality test is an F-test on the joint significance of all the lagged values of ΔlogF. If the estimated coefficients on the lagged values of ΔlogF are insignificantly different from zero, X is strictly exogenous.

F = log of total factor productivity.S^d = log of domestic R&D capital stock, beginning of year.S^f = log of foreign R&D capital stock, beginning of year.m = ratio of imports of goods and services to GDP.

Table 2.

Pooled Unit-Root and Exogeneity Tests

	Test Statistics			Critical Values
	DF	ADF	F(lags)	5 percent	10 percent
Unit-root tests1/
F	-5.94	-4.35
Sd	-2.43	0.73
Sf	-1.62	-3.00		-7.07	-6.78
Sf·m	-2.03	-2.06
m	-7.68	-5.65
Exogeneity tests2/
ΔSd			2.48(3)	2.60	2.08
ΔSf			6.53(4)	2.37	1.94
Δ(Sf.m)			11.20(3)	2.60	2.08
Δm			0.76(3)	2.60	2.08

^1/Annual data 1972-90 for 22 countries, 418 observations. The critical values for the unit root test are from Levin and Lin (1992), Table 5.

^2/Annual data 1973-90 for 22 countries, 396 observations. The te2st statistics are based on regressions with ΔX (X = logS^d, logS^f, logS^f·m, and m) as the dependent variable and either 3 or 4 lagged values of ΔlogF and ΔX as the independent variables (the fourth lag was included if it was significantly different from zero). The Granger causality test is an F-test on the joint significance of all the lagged values of ΔlogF. If the estimated coefficients on the lagged values of ΔlogF are insignificantly different from zero, X is strictly exogenous.

F = log of total factor productivity.S^d = log of domestic R&D capital stock, beginning of year.S^f = log of foreign R&D capital stock, beginning of year.m = ratio of imports of goods and services to GDP.

View Table

Table 2.

Pooled Unit-Root and Exogeneity Tests

	Test Statistics			Critical Values
	DF	ADF	F(lags)	5 percent	10 percent
Unit-root tests1/
F	-5.94	-4.35
Sd	-2.43	0.73
Sf	-1.62	-3.00		-7.07	-6.78
Sf·m	-2.03	-2.06
m	-7.68	-5.65
Exogeneity tests2/
ΔSd			2.48(3)	2.60	2.08
ΔSf			6.53(4)	2.37	1.94
Δ(Sf.m)			11.20(3)	2.60	2.08
Δm			0.76(3)	2.60	2.08

^1/Annual data 1972-90 for 22 countries, 418 observations. The critical values for the unit root test are from Levin and Lin (1992), Table 5.

^2/Annual data 1973-90 for 22 countries, 396 observations. The te2st statistics are based on regressions with ΔX (X = logS^d, logS^f, logS^f·m, and m) as the dependent variable and either 3 or 4 lagged values of ΔlogF and ΔX as the independent variables (the fourth lag was included if it was significantly different from zero). The Granger causality test is an F-test on the joint significance of all the lagged values of ΔlogF. If the estimated coefficients on the lagged values of ΔlogF are insignificantly different from zero, X is strictly exogenous.

F = log of total factor productivity.S^d = log of domestic R&D capital stock, beginning of year.S^f = log of foreign R&D capital stock, beginning of year.m = ratio of imports of goods and services to GDP.

The second issue concerns the estimated standard errors. Because the variables are nonstationary, the standard errors—and hence the significance tests—will only be unbiased if the independent variables are strictly exogenous (Cuthbertson et al. (1992), p. 139). For the two R&D capital stocks, we would expect this to be so since the equation relates total factor productivity to both stocks at the beginning of the year. Granger causality tests on the pooled data, however, give mixed results (see the lower panel in Table 2). Although it is possible to reject the null hypothesis that total factor productivity does not “cause”—in the sense that it does not “predict”—the import share or the domestic R&D stock (in the later case at the 5 percent level), the null hypothesis cannot be rejected in the case of the foreign R&D stock. Given these mixed results, only limited confidence can be placed on the estimated standard errors. In any event, the super consistency of the OLS estimator and our large sample diminishes the importance of confidence intervals and tests of hypotheses.

We report in Table 3 seven pooled cointegrating regressions based on equations (5) and (6), all of which include unreported country-specific constants. ^12/ Equation (i) is the basic specification where the estimated coefficients on the domestic and foreign R&D capital stocks are constrained to be the same for all countries. In equation (ii), the impact of domestic R&D is allowed to differ between the largest seven economies compared with the other 15 economies—this is done by interacting the domestic R&D stock with a dummy variable that takes the value of 1 for the seven largest economies (G7)—while constraining the impact of foreign R&D to be the same for all countries. ^13/ This constraint is dropped in equations (iv) through (vii) where the foreign R&D capital stock is interacted with the ratio of imports to GDP, thereby allowing for country-specific, time-varying elasticities on foreign R&D that are related to trade shares (as discussed in the theory section). Equations (iii), (v), and (vii) include the ratio of imports to GDP as an additional independent variable, but we cannot reject the hypotheses that the import share has no independent effect on total factor productivity (except for its interaction with the foreign R&D capital stock). ^14/

Table 3.

Total Factor Productivity Estimation Results

(Pooled data 1971-90 for 22 countries, 440 observations, standard errors in parentheses)

The dependent variable is log (total factor productivity). All equations include unreported, country-specific constants.S^d = log of domestic R&D capital stock, beginning of year.S^f = log of foreign R&D capital stock, beginning of year.G7 = dummy variable equal to 1.0 for the seven major countries and equal to 0 for the other 15 countries.m = ratio of imports of goods and services to GDP, both in the previous year.

Table 3.

Total Factor Productivity Estimation Results

(Pooled data 1971-90 for 22 countries, 440 observations, standard errors in parentheses)

	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)
log Sd	0.097	0.089	0.090	0.078	0.079	0.087	0.088
	(0.009)	(0.008)	(0.009)	(0.008)	(0.008)	(0.008)	(0.008)
log Sd·G7		0.134	0.133	0.156	0.156	0.185	0.185
		(0.016)	(0.016)	(0.015)	(0.015)	(0.017)	(0.017)
log Sf	0.092	0.060	0.062			-0.091	-0.089
	(0.016)	(0.015)	(0.015)			(0.026)	(0.026)
log Sf·m				0.294	0.299	0.508	0.506
				(0.041)	(0.041)	(0.074)	(0.074)
m			-0.033		-0.039		-0.013
			(0.050)		(0.047)		(0.047)
Standard error	0.049	0.046	0.046	0.044	0.044	0.043	0.043
R2	0.558	0.621	0.622	0.651	0.651	0.660	0.661
R2 adjusted	0.534	0.600	0.599	0.630	0.630	0.640	0.639
Augmented Dickey-Fuller	-4.662	-9.674	-4.774	-5.234	-6.648	-5.792	-5.815

The dependent variable is log (total factor productivity). All equations include unreported, country-specific constants.S^d = log of domestic R&D capital stock, beginning of year.S^f = log of foreign R&D capital stock, beginning of year.G7 = dummy variable equal to 1.0 for the seven major countries and equal to 0 for the other 15 countries.m = ratio of imports of goods and services to GDP, both in the previous year.

View Table

Table 3.

Total Factor Productivity Estimation Results

(Pooled data 1971-90 for 22 countries, 440 observations, standard errors in parentheses)

	(i)	(ii)	(iii)	(iv)	(v)	(vi)	(vii)
log Sd	0.097	0.089	0.090	0.078	0.079	0.087	0.088
	(0.009)	(0.008)	(0.009)	(0.008)	(0.008)	(0.008)	(0.008)
log Sd·G7		0.134	0.133	0.156	0.156	0.185	0.185
		(0.016)	(0.016)	(0.015)	(0.015)	(0.017)	(0.017)
log Sf	0.092	0.060	0.062			-0.091	-0.089
	(0.016)	(0.015)	(0.015)			(0.026)	(0.026)
log Sf·m				0.294	0.299	0.508	0.506
				(0.041)	(0.041)	(0.074)	(0.074)
m			-0.033		-0.039		-0.013
			(0.050)		(0.047)		(0.047)
Standard error	0.049	0.046	0.046	0.044	0.044	0.043	0.043
R2	0.558	0.621	0.622	0.651	0.651	0.660	0.661
R2 adjusted	0.534	0.600	0.599	0.630	0.630	0.640	0.639
Augmented Dickey-Fuller	-4.662	-9.674	-4.774	-5.234	-6.648	-5.792	-5.815

The dependent variable is log (total factor productivity). All equations include unreported, country-specific constants.S^d = log of domestic R&D capital stock, beginning of year.S^f = log of foreign R&D capital stock, beginning of year.G7 = dummy variable equal to 1.0 for the seven major countries and equal to 0 for the other 15 countries.m = ratio of imports of goods and services to GDP, both in the previous year.

The estimated equations explain about 60 percent of the variance in the 440 observations. All of the coefficients are of the expected sign and highly significant except for the estimated coefficients on the import share (m). The magnitudes of the estimated elasticities are plausible, and remarkably stable across the different specifications, particularly in the specifications that include logS^f·G7. ^15/ For the non-G7 countries, the estimated elasticities of TFP with respect to the domestic R&D stock are similar to those typically found in single-country studies (as summarized in Griliches (1988)). For the G7 countries, however, the estimated elasticities of TFP with respect to the domestic R&D stock are considerably larger than those from studies that do not include international R&D spillovers. Our rich cross-country data and our estimation procedure that focuses on the identification of long-run relationships are probably better able to estimate the social return to R&D than are single-country studies.

Levin and Lin’s critical values for pooled augmented Dickey-Fuller unit root tests can be used to test the stationarity of the residuals of our pooled cointegrating regressions. At the 10 percent confidence level, the critical value for the augmented Dickey-Fuller test reported by Levin and Lin is -6.78. The ADF test statistics on the residuals of the estimated equations reported in Table 3 indicate that only equation (ii) is cointegrated, although the ADF test statistic for equation (v) is only marginally below the critical value. Given the similarity of the regression results reported in Table 3, we conclude that the estimated equations are cointegrated, or very nearly so.

Equation (iv) is econometrically the most interesting and theoretically the most consistent with our model. In this equation, the impact of the foreign R&D capital stock varies across all countries and over time. Table 4 reports the estimated elasticities of total factor productivity with respect to the foreign R&D capital stocks—which is simply the estimated coefficient from Table 3 multiplied by the import share—for 1971, 1980, and 1990. ^16/ With the notable exceptions of Norway, Spain, and Switzerland, the estimated impact of foreign R&D rises, usually by a substantial amount from 1971 to 1980. In most of the countries, and especially in Belgium, the estimated impact of foreign R&D rises further during the 1980s. Although the domestic R&D capital stock has a much larger impact on total factor productivity in the large countries compared with the small countries, the smaller countries are more open and hence benefit from foreign R&D more than the larger countries. Indeed, foreign R&D has a larger impact on total factor productivity than does domestic R&D in all of the smaller countries except Australia, Finland, New Zealand, and Spain. Foreign R&D has the strongest impact on Belgium, followed by Ireland, the Netherlands, and Israel.

Table 4.

Country-Specific, Time-Varying Estimates of the Impact of R&D Capital Stocks on Total Factor Productivity

Based on equation (iv) in Table 3.

Table 4.

Country-Specific, Time-Varying Estimates of the Impact of R&D Capital Stocks on Total Factor Productivity

	Elasticity of total factor productivity with respect to:
	World R&D	Foreign R&D			Domestic R&D
	1990	1971	1980	1990	1971-90
United States	0.267	0.016	0.030	0.033
Japan	0.261	0.028	0.037	0.027
West Germany	0.311	0.056	0.072	0.077
France	0.301	0.045	0.061	0.067	0.234
Italy	0.292	0.046	0.067	0.058
United Kingdom	0.315	0.063	0.081	0.081
Canada	0.309	0.059	0.078	0.075
Australia	0.132	0.043	0.049	0.055
Austria	0.192	0.091	0.106	0.114
Belgium	0.337	0.129	0.181	0.260
Denmark	0.169	0.091	0.094	0.092
Finland	0.152	0.079	0.088	0.075
Greece	0.172	0.050	0.063	0.094
Ireland	0.243	0.124	0.180	0.165	0.078
Israel	0.231	0.147	0.154	0.153
Netherlands	0.236	0.133	0.146	0.158
New Zealand	0.144	0.075	0.086	0.066
Norway	0.188	0.133	0.124	0.111
Portugal	0.210	0.099	0.117	0.132
Spain	0.141	0.043	0.043	0.063
Sweden	0.171	0.067	0.087	0.093
Switzerland	0.190	0.115	0.106	0.113

Based on equation (iv) in Table 3.

View Table

Table 4.

Country-Specific, Time-Varying Estimates of the Impact of R&D Capital Stocks on Total Factor Productivity

	Elasticity of total factor productivity with respect to:
	World R&D	Foreign R&D			Domestic R&D
	1990	1971	1980	1990	1971-90
United States	0.267	0.016	0.030	0.033
Japan	0.261	0.028	0.037	0.027
West Germany	0.311	0.056	0.072	0.077
France	0.301	0.045	0.061	0.067	0.234
Italy	0.292	0.046	0.067	0.058
United Kingdom	0.315	0.063	0.081	0.081
Canada	0.309	0.059	0.078	0.075
Australia	0.132	0.043	0.049	0.055
Austria	0.192	0.091	0.106	0.114
Belgium	0.337	0.129	0.181	0.260
Denmark	0.169	0.091	0.094	0.092
Finland	0.152	0.079	0.088	0.075
Greece	0.172	0.050	0.063	0.094
Ireland	0.243	0.124	0.180	0.165	0.078
Israel	0.231	0.147	0.154	0.153
Netherlands	0.236	0.133	0.146	0.158
New Zealand	0.144	0.075	0.086	0.066
Norway	0.188	0.133	0.124	0.111
Portugal	0.210	0.099	0.117	0.132
Spain	0.141	0.043	0.043	0.063
Sweden	0.171	0.067	0.087	0.093
Switzerland	0.190	0.115	0.106	0.113

Based on equation (iv) in Table 3.

Estimates of the international R&D spillovers are presented in Table 5. Each entry is the estimated elasticity of total factor productivity in the country indicated in the row with respect to the R&D capital stock in the country indicated in the column. ^17/ Elasticities are largest with respect to the R&D capital stocks of the major countries, because their R&D capital stocks are relatively large and because the major countries account for a relatively high share of other countries’ imports, which are used as the weights in the computation of the foreign R&D capital stocks. The estimated R&D spillover elasticities are large. They are largest from the United States and Japan. The estimates imply that a 1 percent increase in the R&D capital stock in these countries increases total factor productivity in their trade partners by an average of 0.04 and 0.01 percent, respectively. This, of course, is only the first-round supply-side effect, which will be magnified via foreign trade multipliers.

Table 5.

Elasticities of Total Factor Productivity with Respect to R&D Capital Stocks in the G7 Countries—1990

Estimated elasticity of total factor productivity in the row country with respect to the R&D capital stock in the column country. Based on equation (iv) in Table 3. Averages are calculated using PPP-based GDP weights.

Table 5.

Elasticities of Total Factor Productivity with Respect to R&D Capital Stocks in the G7 Countries—1990

	U.S.	Japan	Germany	France	Italy	U.K.	Canada
United States	…	0.0218	0.0039	0.0013	0.0005	0.0024	0.0024
Japan	0.0255	…	0.0008	0.0003	0.0001	0.0003	0.0001
West Germany	0.0464	0.0097	…	0.0081	0.0024	0.0060	0.0002
France	0.0368	0.0049	0.0156	…	0.0024	0.0049	0.0001
Italy	0.0254	0.0027	0.0166	0.0076	…	0.0032	0.0001
United Kingdom	0.0530	0.0069	0.0131	0.0047	0.0012	…	0.0003
Canada	0.0720	0.0019	0.0005	0.0002	0.0001	0.0005	…
Australia	0.0409	0.0092	0.0019	0.0005	0.0002	0.0018	0.0001
Austria	0.0301	0.0102	0.0610	0.0040	0.0033	0.0030	0.0001
Belgium	0.0930	0.0116	0.0812	0.0339	0.0039	0.0230	0.0004
Denmark	0.0450	0.0063	0.0250	0.0036	0.0012	0.0066	0.0001
Finland	0.0357	0.0103	0.0165	0.0026	0.0012	0.0053	0.0001
Greece	0.0290	0.0138	0.0287	0.0064	0.0057	0.0071	0.0001
Ireland	0.1031	0.0094	0.0095	0.0029	0.0008	0.0378	0.0001
Israel	0.1189	0.0045	0.0121	0.0030	0.0017	0.0083	0.0001
Netherlands	0.0832	0.0075	0.0430	0.0084	0.0016	0.0112	0.0002
New Zealand	0.0462	0.0130	0.0020	0.0005	0.0002	0.0036	0.0002
Norway	0.0643	0.0084	0.0185	0.0033	0.0012	0.0096	0.0006
Portugal	0.0542	0.0093	0.0294	0.0156	0.0049	0.0128	0.0003
Spain	0.0358	0.0047	0.0098	0.0060	0.0018	0.0036	0.0001
Sweden	0.0500	0.0092	0.0204	0.0036	0.0011	0.0069	0.0001
Switzerland	0.0453	0.0080	0.0400	0.0085	0.0032	0.0056	0.0001
Average elasticity of foreign total factor productivity	0.0422	0.0138	0.0091	0.0032	0.0010	0.0033	0.0011
Elasticity of domestic total factor productivity	0.2339	0.2339	0.2339	0.2339	0.2339	0.2339	0.2339
Average elasticity of total factor productivity in all 22 countries	0.1211	0.0446	0.0266	0.0180	0.0154	0.0179	0.0103

Estimated elasticity of total factor productivity in the row country with respect to the R&D capital stock in the column country. Based on equation (iv) in Table 3. Averages are calculated using PPP-based GDP weights.

View Table

Table 5.

Elasticities of Total Factor Productivity with Respect to R&D Capital Stocks in the G7 Countries—1990

	U.S.	Japan	Germany	France	Italy	U.K.	Canada
United States	…	0.0218	0.0039	0.0013	0.0005	0.0024	0.0024
Japan	0.0255	…	0.0008	0.0003	0.0001	0.0003	0.0001
West Germany	0.0464	0.0097	…	0.0081	0.0024	0.0060	0.0002
France	0.0368	0.0049	0.0156	…	0.0024	0.0049	0.0001
Italy	0.0254	0.0027	0.0166	0.0076	…	0.0032	0.0001
United Kingdom	0.0530	0.0069	0.0131	0.0047	0.0012	…	0.0003
Canada	0.0720	0.0019	0.0005	0.0002	0.0001	0.0005	…
Australia	0.0409	0.0092	0.0019	0.0005	0.0002	0.0018	0.0001
Austria	0.0301	0.0102	0.0610	0.0040	0.0033	0.0030	0.0001
Belgium	0.0930	0.0116	0.0812	0.0339	0.0039	0.0230	0.0004
Denmark	0.0450	0.0063	0.0250	0.0036	0.0012	0.0066	0.0001
Finland	0.0357	0.0103	0.0165	0.0026	0.0012	0.0053	0.0001
Greece	0.0290	0.0138	0.0287	0.0064	0.0057	0.0071	0.0001
Ireland	0.1031	0.0094	0.0095	0.0029	0.0008	0.0378	0.0001
Israel	0.1189	0.0045	0.0121	0.0030	0.0017	0.0083	0.0001
Netherlands	0.0832	0.0075	0.0430	0.0084	0.0016	0.0112	0.0002
New Zealand	0.0462	0.0130	0.0020	0.0005	0.0002	0.0036	0.0002
Norway	0.0643	0.0084	0.0185	0.0033	0.0012	0.0096	0.0006
Portugal	0.0542	0.0093	0.0294	0.0156	0.0049	0.0128	0.0003
Spain	0.0358	0.0047	0.0098	0.0060	0.0018	0.0036	0.0001
Sweden	0.0500	0.0092	0.0204	0.0036	0.0011	0.0069	0.0001
Switzerland	0.0453	0.0080	0.0400	0.0085	0.0032	0.0056	0.0001
Average elasticity of foreign total factor productivity	0.0422	0.0138	0.0091	0.0032	0.0010	0.0033	0.0011
Elasticity of domestic total factor productivity	0.2339	0.2339	0.2339	0.2339	0.2339	0.2339	0.2339
Average elasticity of total factor productivity in all 22 countries	0.1211	0.0446	0.0266	0.0180	0.0154	0.0179	0.0103

Estimated elasticity of total factor productivity in the row country with respect to the R&D capital stock in the column country. Based on equation (iv) in Table 3. Averages are calculated using PPP-based GDP weights.

The United States has the strongest effect on Israel and Ireland (elasticities of 0.1189 and 0.1031, respectively) while Japan has the strongest effect on the United States. Germany has the strongest effect on Belgium and Austria, France has the strongest effect on Belgium, Italy has the strongest effect on Greece, and the United Kingdom has the strongest effect on Ireland.

The last row provides average elasticities, taking account of a country’s effect on both its own productivity and on the productivity of its trade partners. It shows that a 1 percent increase in the R&D capital stock in the United States raises the average productivity of all 22 countries by about 0.12 percent, while a 1 percent increase in the Japanese R&D capital stock raises the average productivity of the 22 countries by only 0.045 percent. This difference reflects partly the fact that the United States has an R&D capital stock which is about four times as large as Japan’s R&D capital stock. Since the elasticity of the United States is less than three times as large as the elasticity of Japan, it follows that the worldwide rate of return on investment in Japanese R&D is larger than the worldwide rate of return on investment in American R&D.

In order to obtain estimates of rates of return on investment in R&D, we need to multiply the elasticities with the appropriate ratios of output to R&D capital stocks. In particular, the rate of return on country j’s R&D capital stock in terms of country i’s output is:

where α_ij stands for the elasticity of country i’s output with respect to j’s domestic R&D capital stock (the entries in Table 5), Y_i stands for country i’s output, and S^d stands for country j’s domestic R&D capital stock. This formula can be used to calculate all cross-country rates of return on R&D investment as well as the rates of return for groups of countries. Rather than report all these rates of return, we report the average rates of return for two groups of countries: the G7 and the remaining 15 smaller countries. These averages should be more accurate than the rates of return that we can calculate for individual countries because the coefficient α^d was estimated to be equal across countries within each group. ^18/

Our calculations (based on the data in Tables 5 and 12) show that in 1990 the average own rate of return from investment in R&D was 122.6 percent in the G7 countries and 85.1 percent in the remaining 15 countries. This means that a $100 increase in the R&D capital stock in a G7 country raises its GDP by $122.6 on average, and that a $100 increase in the R&D capital stock of one of the smaller 15 countries raises its GDP by $85.1 on average (based on PPP). In addition, in 1990 the average worldwide rate of return from investment in R&D in the G7 countries was [155.0] percent. These estimated rates of return are very high. For the G7 countries the difference between the worldwide and the own rate of return is about 30 percent, which implies a large international R&D spillover; about one quarter of the benefits of R&D investment in a G7 country occur to its trade partners.

Our estimated rates of return are sensitive to the calculated benchmarks for the R&D capital stocks, because they are sensitive to the levels of the R&D capital stocks. A proportional increase in the levels of R&D capital stocks will not affect the estimated coefficients in Table 3 (due to the presence of country dummies), but it will reduce our estimate of own rates of return on investment in R&D. For this reason we place more confidence in the estimated elasticities than in the estimated rates of return. Nevertheless, the estimated rates of return are indicative of the importance of R&D. Of course, our rates of return refer to the social or economy-wide rates of return from R&D, and thus include beneficial externalities that would not be reflected in the private rate of return from R&D investment by a specific enterprise.

V. Closing Comments

The emerging new theory of economic growth builds around innovation driven productivity developments. It draws its inspiration from historical studies that have shown the importance of inventive activities for long-run economic growth on the one hand and the role of economic incentives in propagating these activities on the other. This theory also underlines international economic relations, and in particular international trade, as transmission mechanisms that link a country’s productivity gains to economic developments in its trade partners (see Grossman and Helpman (1993) for a review).

Although cross-country studies of economic growth have been recently in abundance, they typically focus on explaining output growth, as determined by the accumulation of labor, capital, and some additional economic and political variables. ^19/ The novelty of the new theory lies, however, in explaining the growth of total factor productivity, which is the component of output growth that is not attributable to the accumulation of inputs. For this reason we have chosen to follow the theory and focus on the central link between productivity and R&D.

Our evidence suggests that there indeed exist close links between productivity and R&D capital stocks. Not only does a country’s total factor productivity depend on its own R&D capital stock, but as suggested by the theory, it also depends on the R&D capital stocks of its trade partners. While the beneficial effects on TFP from domestic R&D have been established in the earlier empirical literature, the evidence of the importance of foreign R&D is new. Foreign R&D has a stronger effect on domestic productivity the more open an economy is to international trade. Our estimates of TFP with respect to R&D capital stocks suggest that in the large countries the elasticity is larger with respect to the domestic R&D capital stock than with respect to the foreign R&D capital stock, while in most of the smaller countries the elasticity is larger with respect to the foreign R&D capital stock. And our estimates suggest that the rate of return on R&D capital stocks is very high, both in terms of domestic output and in terms of international spillovers.

These results are encouraging; they suggest that our search for international R&D spillovers was not misplaced. Further explorations with disegregated data and an explicit treatment of R&D capital stock dynamics will undoubtedly provide valuable new insights.