Evidence from OECD and Non-OECD Countries

Keywords: JEL Classification Numbers: O30, O31, O33, O47 innovation, R&D, patents, output, panel data, generalized methods of moments (GMM)

In this paper we examine the predictions of the non-scale endogenous growth theories that an increase in the share of researchers in labour leads to an increase in innovation and innovation raises per capita output. Using panel data from 41 OECD and non-OECD countries, we show that an increase in the share of researchers in labour increases innovation only in the large market OECD countries. In addition, innovation raises per labour GDP in the high income OECD countries only, while raising it in all non-OECD countries, except for the low income countries. These results provide strong support for the non-scale endogenous growth theories.

3 predictions of the non-scale endogenous growth theories for the U.S. economy, such as [START_REF] Griliches | Productivity, R&D and Basic Research at the Firm Level in the 1970s[END_REF], [START_REF] Jaffe | Demand and Supply Influences in R&D Intensity and Productivity Growth[END_REF], [START_REF] Aghion | Endogenous Growth Theory[END_REF] and [START_REF] Savvides | International Technology Diffusion and TFP Growth[END_REF].

Recent sector level cross-country analyses also support these models, [START_REF] Griffith | Mapping the Two Faces of R&D: Productivity Growth in a Panel of OECD Industries[END_REF] and [START_REF] Meliciani | The Relationship between R&D, Investment and Patents: A Panel Data Analysis[END_REF]. However, the macro level analyses of the non-scale endogenous growth models are limited to a few studies that cover only a small number of OECD countries. For example, Zachariadis (2004), [START_REF] Frantzen | R&D, Human Capital and International Technology Spillovers: A Cross Country Analysis[END_REF] and [START_REF] Gong | Endogenous Growth: Estimating the Romer Model for the US and Germany[END_REF] examine the relationship between total factor productivity (TFP) and R&D intensity using data from OECD countries and find a positive relationship between these variables.

The present study differs from the existing empirical analyses in that it employs macro level patent and R&D data for 26 OECD and 15 non-OECD countries to examine the non-scale endogenous growth theories. In particular, we look at the following predictions of these models: an increase in the share of researchers in labour force increases innovation, and innovation raises per capita output. In addition to the main variables of the non-scale endogenous growth models, we also include in our analysis international knowledge spillovers, overall human capital capacity of countries and the U.S. trade share of GDP. As indicated by [START_REF] Coe | North-South R&D Spillovers[END_REF], [START_REF] Lichtenberg | International R&D Spillovers: A Comment[END_REF] and [START_REF] Savvides | International Technology Diffusion and TFP Growth[END_REF], international knowledge spillovers are an important determinant of the TFP and output growth.

These studies show that the more open the countries are to trade, the more likely it is R&D in the total economy should be used to test the R&D models rather than the absolute value of R&D investment, or the absolute number of scientists and engineers. 4 that they will benefit from foreign R&D. We also incorporate the U.S. trade share of GDP into our analysis to capture the effect of knowledge spillovers from the U.S. on innovation, and to control for the effect of economic alliance with the U.S. on patent applications made in the U.S.

The findings of our analysis suggest that an increase in the fraction of researchers in labour increases innovation only in the large market OECD countries that include the G7. In addition, innovation raises per labour GDP in the high income OECD countries only, while raising it in all non-OECD countries except for the low income countries.

Moreover, the impact of international knowledge spillovers on innovation seems to be significant only in the large market OECD countries, while the effect of openness to trade on per labour GDP is positive in the majority of the OECD and non-OECD countries.

This study extends the earlier research program in several dimensions. Firstly, it employs aggregate patent data as well as R&D data to examine the non-scale endogenous growth theories. Although patent data have been widely used in the micro level studies, to the best of our knowledge, only [START_REF] Porter | Measuring the 'Ideas' Production Function: Evidence from International Patent Output[END_REF] employ aggregate patent and R&D data to examine the endogenous growth theories. 3 Our 3 [START_REF] Porter | Measuring the 'Ideas' Production Function: Evidence from International Patent Output[END_REF] employ data on patents and the number of scientists and engineers for 16 OECD countries to estimate the knowledge and output production functions using OLS and fixed effects regression techniques. Their findings show that both knowledge stock and the number of scientists and engineers increase the ideas production function, and that there is a positive relationship [START_REF] Porter | Measuring the 'Ideas' Production Function: Evidence from International Patent Output[END_REF] in that it is based on the non-scale endogenous growth models and it uses patent flows instead of patent stock in the estimation of the production function, as the former is shown to be a better proxy for innovation, [START_REF] Kortum | Equilibrium R&D and the Patent-R&D Ratio: U.S. Evidence[END_REF]. Secondly, different from the previous literature that mainly employs data from OECD countries, this analysis covers 26 OECD and 15 non-OECD countries. This allows us to compare the results across developed and developing countries. Finally, we employ both the fixed effects and generalized methods of moments (GMM) dynamic panel data analyses to increase the robustness of our findings.

The remainder of the paper is organised as follows: the next section introduces the model, section three describes the data, section four presents the empirical analysis and results and section five concludes.

II. MODEL

The first generation endogenous growth theories (R/GH/AH) consist of three sectors: R&D, intermediate goods and final goods sectors. The R&D sector produces new designs using knowledge stock and human capital. It then sells these designs to the intermediate goods sector that produces new capital goods for the final output sector.

The final output sector produces single consumption goods by using physical and between patent stock and aggregate output. They also find that the foreign knowledge stock has a negative effect on ideas production function.

β α β α - - = 1 ) ( ) ( ) ( ) ( ) ( t L t H t X t A t Y Y Y , (1)
where, Y, A, X, H Y and L Y are final output, technological innovation, physical capital that embodies both existing and new capital, human capital and labour employed in the final output sector, respectively. Technological innovation is created according to the following functional form:

) ( ) ( ) ( t H t A t A A λ = & , ( 2
)
where A is the knowledge stock and H A is human capital employed in the R&D sector.

The assumption that innovation is linear in knowledge stock is crucial for the longterm growth rate of output. Models in the form of (2), where innovation has unit elasticity with respect to both knowledge stock and human capital in the R&D sectors, yield a steady state growth rate that depends on the level of population. However, the scale effect of these models has been rejected by Jones (1995b) 3) is based on [START_REF] Dinopoulos | Endogenous Growth in a Cross-Section of Countries[END_REF]. The only difference between the innovation function in [START_REF] Dinopoulos | Endogenous Growth in a Cross-Section of Countries[END_REF] and [START_REF] Aghion | Endogenous Growth Theory[END_REF] Jones (1995a). Therefore, the final effect of an increase in population on innovation depends on which of these opposing effects are dominant. 5

1 ) ( ) ( ) ( ) ( = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = φ γ ψ φ t L t H t A t A A & , (3)
After describing the data in the next section, in section four, we estimate equation ( 1) and ( 3) to examine the predictions of the non-scale endogenous growth models for OECD and non-OECD countries.

III. DESCRIPTION OF THE DATA

The data cover patent applications, full time equivalent (FTE) researchers devoted to R&D sectors and other macroeconomic data. Patent data are obtained from the NBER patent citations database developed by [START_REF] Hall | The NBER Patent Citation Data File: Lessons, Insights and Methodological Tools[END_REF]. They include all utility patent applications in manufacturing sectors made in the U.S. Patent and Trademark Office by the inventors who reside in different countries. Utility patents are classified according to five main categories: chemicals, computers and 5 The DT model shown in equation ( 3) has been criticised on the grounds that it is not consistent with the micro foundations of R/GH/AH models, which implies that new ideas are discovered by individuals and therefore they depend inherently on the number of people. However, several authors including Young (1998) and [START_REF] Aghion | Endogenous Growth Theory[END_REF], developed micro foundations for equations similar to (3). We use patent data from the U.S. Patent Office to measure innovation, because they provide standardised data for all countries, as all inventors are subject to the same rules and regulations. Furthermore, the U.S. has the largest and the most active market in the world, leading to a high competition among the inventors of different countries to patent in the U.S. Thus, the U.S. patents should provide a good proxy for the rate of technological innovation of countries. However, there are also some potential drawbacks of using patent data from the U.S. to measure innovation. In particular, the geographical distance of the countries to the U.S. and the degree of their economic alliance with the U.S. might have an effect on the number of patent applications made to the U.S. Patent Office. These shortcomings have been taken into account in our econometric modelling.

In addition, following Jaffe and Palmer (1997) [START_REF] Kortum | Equilibrium R&D and the Patent-R&D Ratio: U.S. Evidence[END_REF]. The main drawbacks of using patent data to measure innovation include the variation in the intrinsic value of patents and the inability of patents to capture the whole range of innovations given that not all inventions are patented nor do all patents become successful innovations. However, as [START_REF] Comanor | Patent Statistics as a Measure of Technical Change[END_REF] and Griliches (1990Griliches ( , 1994) ) document in detail, in spite of these shortcomings, patent data still provide significant information on innovation.

Diagnostic tests of the data for unit root, heteroskedasticity and first order autocorrelation show that the series do not have unit root and heteroskedasticity in the majority of the countries, though they exhibit first order autocorrelation. 9 Throughout the analysis, the first order autocorrelation problem has been taken into account by using the first difference series. To determine the cross-country patterns of the main variables of the endogenous growth theories before the estimation of the model, we rank the OECD and non-OECD countries by their aggregate and per capita levels of GDP, patents and full time equivalent researchers. The rankings for per capita levels of these variables are reported in Tables 1 and2. As these tables show, both in the OECD and non-OECD countries, on average, countries with higher (lower) per capita output also tend to have higher (lower) per capita patents and the share of researchers in 9 See appendix II, Tables 1A through 4A for the results of the diagnostic tests. The panel data unit root test used in this paper is proposed by [START_REF] Levin | Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties[END_REF]. 12 population, indicating a positive correlation between these variables, as suggested by non-scale endogenous growth theories. To determine the correlations between the aggregate levels of output, patents and researchers, we also reported the rankings for these series in Tables 3 and4. Similar to the figures reported in the preceding tables, the number of patents and the full time equivalent researchers appear to be positively correlated with the GDP levels of countries.

Motivated by the results reported in Tables 1 through 4, we conducted the empirical analysis separately for the high and low income, and large and small market OECD and non-OECD countries. 10 In particular, as the figures in Tables 1 to 4 reveal, countries at the high and low ends of the rankings of aggregate and per capita GDP tend to have, on average, the corresponding levels of aggregate and per capita levels of patents and researchers, suggesting that the countries are not homogenous in terms of the variables of the model. 11 High and low income samples have been constructed by dropping the five median (one median) countries in the rankings of the per capita GDP of OECD (non-OECD) countries reported in the first columns of Tables 1 and2, and then referring to the countries above (below) the median as high (low) income sample. 12 The large and small market samples have been constructed in a similar manner using the rankings for the aggregate GDP reported in Tables 3 and4.

10 Market size is measured by the level of aggregate GDP.

11 Our presumption that the regression analysis for separate samples yields more robust results than the regression analysis for whole sample is also confirmed by the chow test.

12 We dropped only one median country from the rankings of the non-OECD country groups when constructing the samples as the non-OECD sample includes fewer countries.

IV. EMPIRICAL ANALYSIS

The estimations of the innovation and production functions have been carried out using the fixed effects and difference GMM analyses. The fixed effects analysis controls for the country specific factors, thus it yields consistent estimators provided that the regressors are exogenous, i.e. they are not correlated with the error term.

However, given that the growth regressions are likely to have omitted variable problem, the assumption that the regressors are not correlated with the error term might not hold in the estimation of the production function. To take into account the endogeneity problem to some extent we also employ difference generalized methods of moments (GMM) dynamic panel data estimation proposed by Arellano and Bond (1991), which yields consistent estimators in the presence of regressors that are not exogenous. The difference GMM simply estimates the first difference series by instrumenting them with their appropriate lagged levels. However, as has been pointed out by Blundell, Bond, and Windmeijer (2000), when the series are persistent and the length of the time series data is short, the instrument matrix loses its explanatory power, causing the difference GMM to yield downward biased estimators and large standard errors.

The system GMM analysis proposed by [START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF] substantially improves upon the difference GMM when the sample size is small and the series are persistent. However, because the system GMM uses a very large instrument matrix, the number of the cross sectional units needs to be sufficiently high for the results to 14 be consistent and efficient, [START_REF] Alvarez | The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators[END_REF]. 13 Because we have only 41 countries in our data, it was not possible to obtain reliable results with the system GMM estimation. Therefore, we used fixed effects and difference GMM estimations.

As mentioned above, in the presence of endogeneity, the fixed effects estimators could be upward biased while the difference GMM yields consistent estimators. However, the estimators of the difference GMM could be downward biased when the series are persistent and the sample size is small. Thus, using these two techniques allows us to check the reliability of our findings and to judge on the pertinence of these two methods. Although our results are not sensitive to the outliers, we still removed them using a standard procedure embodied in STATA. 14 All regressions include the year dummies to control for time specific factors.

Estimation of the Innovation Function

The regression model for the innovation function is constructed by taking the natural log of equation ( 3) in section II, and including the control variables and the time fixed effects in the model:

13 [START_REF] Alvarez | The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators[END_REF] show that the number of instruments should be lower than the number of cross sectional units for the results of the system GMM estimations to be robust. Otherwise, the system GMM estimators are biased towards those of the OLS.

14 This procedure, referred to as "hadimvo" in STATA, is developed by Hadi (1992[START_REF] Hadi | A Modification of a Method for the Detection of Outliers in Multivariate Samples[END_REF]. The results are not sensitive to the outliers.

+ + + = ) ( ) / ( ) ( ) ( Z Log L H Log A Log A Log A & , (4)
where A & , A and H A /L are technological innovation, knowledge stock and the ratio of human capital engaged in R&D to total labour force, respectively. Z is a matrix of control variables; μ is time fixed effects and ε is regression residuals. We measure A & by patent flows as suggested by [START_REF] Kortum | Equilibrium R&D and the Patent-R&D Ratio: U.S. Evidence[END_REF], and H A /L by the fraction of the full time equivalent researchers devoted to R&D in labour force. The effect of knowledge stock, A, on patent flows has been taken into account by including the lagged patent flows in the analysis. Here it is assumed that the patent flows not only contribute to innovation but also create a knowledge pool for future inventions.

The control variables include the gross ratio of the secondary school enrolment to the population of the secondary school age group, the U.S. trade share of GDP, and an interacted term of manufacturing imports and full time equivalent researchers. The secondary school enrolment rate is a proxy for the overall human capital capacity of a country; the U.S. trade share of GDP measures the technology spillovers from the U.S. and controls for the effect of countries' economic alliance with the U.S on their patent applications to the U.S. Patent Office; and the interacted term of manufacturing imports and full time equivalent researchers engaged in R&D capture the technology spillovers across countries. A positive sign on the coefficient of the interacted term indicates that the higher the imports of the manufacturing goods of a country are, the higher the effect will be of an increase in the number of researchers on innovation. The results of the fixed effects analysis are reported in Table 6. As observed from the table, the first lag of patent flows is positive in the majority of the samples, while the share of researchers in labour significant only in the full and large market OECD samples. 15 The effect of a 1% increase in the fraction of researchers in labour on patent flows is 0.23% in the full and 0.15% in the large market OECD sample. The remaining variables of the model are not significant in the majority of the samples except that knowledge spillovers and the U.S. trade share of GDP are significant in the large market OECD sample only. In particular, a 1% increase in knowledge spillovers and the U.S. trade share of GDP is associated with a 0.08% and 0.09% increase in patent flows, respectively. To check the robustness of the fixed effects results, we also report the findings of the difference GMM in Table 7. As the table shows, the main difference between the fixed effects and difference GMM results is that in the latter the coefficient of the share of researchers in labour is not significant in the full sample, while it is significant in the large market and high income OECD countries. However, because the p value of the sargan test for the high income sample is very low, the regression model of this sample does not yield robust results. Thus only the large market OECD sample remains to have positive returns to their researchers in terms of innovation. In this sample, a 1% increase in the fraction of researchers in labour leads to a 0.20% increase in patent flows, providing support for non-scale endogenous growth models. 15 See Table 5 for the list of the countries in each sample. that only these countries are able to utilize the intertemporal and cross-country knowledge spillovers to increase innovation. In addition, the U.S. trade share of GDP is not significant in any of the samples, while the secondary school enrolment is significant only in the high income OECD sample. 16 The fact that the U.S. trade share of GDP is not significant in any of the samples implies that there are not significant knowledge spillovers from the U.S. to other OECD countries. It also suggests that a closer economic alliance with the U.S. does not have a significant effect on patent applications made in the U.S. Furthermore, the secondary school enrolment does not seem to be a satisfactory proxy for the overall human capital capacity of countries, given that it is not significant in the majority of the samples.

In summary, we can conclude that the large market OECD countries that include the G7 verify the prediction of the non-scale endogenous growth models that an increase in the fraction of researchers in labour promotes innovation. They also effectively utilize the intertemporal and cross-country knowledge spillovers to increase their innovation. It is not surprising that only these countries are able to have significant returns to their researchers and absorb knowledge spillovers better, given that they allocate larger resources to R&D and innovative activities than other OECD countries. 16 Although the coefficient of the lagged patent flows is also positive in the full OECD sample, the regression model for this sample does not have an explanatory power, as indicated by the low p value of the sargan test.

Estimation of the Production Function

The regression model of the production function is derived from equation (1) in section II. In particular, after scaling output and investment in equation ( 1) by labour, and human capital by population, we include the openness to trade variable in the model and take the natural log of the equation. 17 The resulting regression equation is as follows:

ε μ γ β α + + + + + = ) ( ) ( ) ( z Log h Log x Log A Log y , ( 5
)
where y, A, x, h , z and μ are per labour output, technological innovation measured by patent flows, per labour physical investment, the secondary school enrolment rate, openness to trade and time fixed effects, respectively. The results of the fixed effects and GMM estimations for OECD and non-OECD samples are reported in Tables 8 through 12. 18 As observed from Table 8 that reports the fixed effects results for OECD samples, per labour investment has a positive coefficient in all samples, with a value ranging from 0.22 in the high income and 0.52 in the large market OECD countries. However, the 17 The production function has been scaled by the labour series, instead of population, to eliminate the multicollinearity problem arising from a high correlation between investment and labour.

18 See The findings of difference GMM reported in Table 9 are very similar to those of the fixed effects. The only two exceptions are that in the GMM analysis the patent flows remain significant only in the high income OECD sample and the secondary school enrolment becomes insignificant in all samples. 19 The coefficient of per labour investment is still positive in all OECD samples with a value ranging from 0.13 in the small market to 0.30 in the large market OECD countries. Returns to patent flows in terms of per labour GDP is marginally significant in the high income OECD countries only and the magnitude of these returns are lower (0.02) than those in the fixed effects 19 The results of the full sample are disregarded, as the regression model for this sample does not pass the sargan test. In addition, the degree of openness to trade seems to be still positively related to per capita income in the majority of the countries.

For a further robustness check, we also estimated per labour GDP in terms of the share of researchers in labour instead of patent flows. As seen from Table 10, only the high income OECD countries enjoy higher per labour GDP as a result of higher fraction of researchers in labour, providing strong support for the results obtained in the preceding section. Overall, combining the information obtained from the estimation of the production function with different techniques and different variables, we can conclude that only the high income OECD countries seem to verify the prediction of the endogenous growth theories that an increase in innovation promotes per capita GDP.

The findings also suggest that the majority of the OECD samples enjoy higher per labour GDP as a result of higher degree of trade liberalization, and per labour investment is an important determinant of per labour GDP in all samples.

The estimation results of the production function for the non-OECD countries are reported in Tables 11and 12. The fixed effects results (Table 11) seem to confirm our expectation that the variables of the model are positively associated with per labour GDP in the majority of the samples, with an exception that the secondary school enrolment is not significant in most of the samples and negative in the small market sample. As expected, returns to per labour GDP are positive in all samples and range between 0.22% in the small market and 0.58% in the large market non-OECD samples. The coefficient of patent flows is significant in the full, large market and high The difference GMM analysis appears to improve upon the fixed effects results. As observed in Table 12, per labour investment still has a positive impact on per labour GDP in all samples. Similar to the fixed effects results, the highest impact of per labour investment on per labour GDP is in the large market (0.35), while its lowest impact is in the small market non-OECD countries (0.11). As expected, the magnitudes of these impacts are lower in the GMM than in the fixed effects analysis.

Interestingly, all samples of the non-OECD countries, except for the low income countries, have positive returns to their patent flows. Specifically, a 1% increase in patent flows leads to a 0.08% increase in the high income and around 0.02% increase in the large and small market non-OECD samples. 20 Moreover, a higher degree of openness to trade is positively associated with per labour GDP only in the high and low income non-OECD countries, while the effect of an increase in secondary school enrolment rate is positive only in the large market and high income non-OECD countries. 20 The results for the full sample are disregarded here as the regression model for this sample does not have an explanatory power as indicated by the low p value of the sargan test. In summary, putting together the findings obtained from the fixed effects and difference GMM estimations of the production function for the OECD and non-OECD samples, we can conclude that, both in the OECD and non-OECD countries, the high income countries seem to benefit most from investing in innovation. In particular, according to the fixed effects and GMM results, returns to the patent flows of the high income OECD countries are between 0.02% and 0.07%, while the returns to those of the high income non-OECD countries are between 0.08% and 0.13%. Moreover, unlike the OECD samples in which only the high income countries have positive returns to their patent flows in terms of per labour GDP, in the non-OECD countries the large and small market samples also have positive returns, though their magnitudes are very modest (between 0.02% and 0.03%).

The fact that the high income countries have the highest returns to their innovation with respect to per labour GDP implies that, on average, the economic value of patents might be higher in high income countries compared to others. It also suggests that the way in which high income countries utilize new information and innovation in the production process might be different from other countries. Considering that the innovation activities are resource intensive and upgrading production process for new technology is an expensive process, it is not surprising that the high income countries have the largest returns to their innovation in terms of per labour GDP. The remaining variables of the production function also seem to confirm the theoretical expectations.

In particular, the contribution of per labour investment to per labour GDP is very significant in all samples, and the higher degree of openness to trade seems to be 23 associated with a higher per labour GDP in the majority of the samples. However, the coefficient of the secondary school enrolment appears to be insignificant in most of the samples, reflecting the fact that these series might not be a good proxy for the human capital capacity of countries.

V. CONCLUSION

The objective of this paper was to analyze the main implications of the non-scale endogenous growth theories using panel data from both developed and developing countries. In particular, we examined the following two implications of these models:

an increase in the fraction of researchers in total labour force leads to an increase in innovation, and an increase in innovation raises per capita output. Our findings show that an increase in the share of researchers in labour has a positive effect on innovation only in the large market OECD countries that include the G7. The fact that this result is robust to different regression techniques indicates that the market size, holding other things constant, is an important determinant of the effectiveness of R&D sectors in promoting innovation. However, we should also note that the large market OECD countries include the most industrialized countries that have high per capita incomes and established institutions, which are fundamental in promoting R&D sectors and achieving high level of technological innovation. Furthermore, historically, the large market OECD countries, the G7 in particular, have highly competitive R&D sectors and have been the world leaders in technological innovation. The findings also suggest that the developing countries benefit more from innovation than developed countries in promoting per labour GDP. In particular, according to the results of the analyses, innovation raises per labour GDP in the high income OECD countries only, while raising it in all non-OECD countries, except for the low income countries. In addition, the high income non-OECD countries have higher returns to their innovation in terms of per labour GDP than the high income OECD countries. As expected, a higher degree of openness to trade is associated with higher per labour GDP in the majority of the OECD and non-OECD countries. However, the effect of secondary school enrolment rate on innovation and per labour GDP seems to be insignificant in most of the samples.

Overall, the results of our empirical analysis lend strong support to non-scale endogenous growth models. However, a main limitation of this study is that the patent applications used in the analysis include only the applications made in the U.S. Patent

Office. Though the U.S. patent data have many advantages over the patent data that can be obtained from each country's patent offices, such as the standardization and the reliability of data, they might underestimate the propensity to patent, especially in the non-OECD countries. This study, therefore, can be extended to include case studies for developing countries that utilise sector level patent and R&D data, given that the aggregate data on patents are not reliable in these countries and the majority of these countries do not have aggregate R&D data. We should also not that the patents are only a limited proxy for technological innovation, as not all inventions are patented and not all patented inventions become innovation. However, in spite of these (OECD-MSTI 2003), R&D data were not available for non-OECD countries. GDP is in 1995 millions $U.S., per capita patents are per million people. 21 Korea, Mexico, Poland, Turkey and Hungary have data on researcher only after 1990, which might have contributed to their higher rankings in the number of researchers. The numbers of observations on researchers for these countries are: Korea 3, Poland 4, Hungary 8, Mexico 5 and Turkey 8. All the remaining countries have data on the number of researchers for 17 years, except for Greece, which has 9-year data. Note: Countries with aggregate GDP above (below) the median GDP are referred to as large (small) market OECD, and countries with per capita income above (below) the median per capita income are referred to as high (low) income OECD countries (median countries are dropped). Hungary, Korea, Mexico, Turkey and Poland are not included in the regression analysis of patent flows as these countries have less than 9 data points. The patent regression includes 21 OECD countries, while the GDP regression includes all 41 countries listed above. Israel is not included in the small market non-OECD sample as it is an outlier, i.e. it has the highest per capita income and patents.

F

F

  labour and technological innovation (new ideas). Both the R&D and final output sectors are perfectly competitive, while the intermediate goods sector is monopolistically competitive. The aggregate production is described by the standard Cobb-Douglas function:

  where A & , A, H, and L are technological innovation, knowledge stock, human capital in the R&D sectors and labour force, respectively; ψ measures instantaneous returns to scale in knowledge creation and γ is equal to λ/k ψ >0, where k is a constant. This specification of the innovation function leads to a balanced growth rate of per capita output that depends on the saving rate of physical and human capital as well as the growth rate of population. Equation (3) takes into account the opposite effects of an increase in population on the rate of innovation. On the one hand, an increase in the growth rate of population increases the rate of innovation, by increasing the human capital in the R&D sector, expanding the market for intermediate capital goods, raising the present value of the flow of profits and making investment in capital goods designs more attractive. On the other hand, more rapid population growth reduces the capital output ratio, and increases the interest rate through the standard neo-classical 4 Equation (

  the other variables of the model, the first lag of patent flows and knowledge spillovers are significant in the large market OECD sample only, implying

  Table5for the list of the countries in each sample. flows is significant only in the full, high income and low-income OECD countries. Specifically, a 1% increase in patent flows increases per labour GDP by 0.05% in the full, 0.07% in the high income and 0.04% in the low income OECD countries. As expected, the degree of openness to trade is positively associated with per labour GDP in all samples, providing support for the view that trade liberalization has a positive impact on per capita income. Though the t value of the secondary school enrolment rate is high in all samples, it has a significant impact on per labour GDP only in the full, high and low income OECD countries. More specifically, a 1% increase in the secondary school enrolment rate leads to a 0.19% increase in per labour GDP in the high income OECD, while it leads to a 0.10% increase in the full and low income OECD countries.

	Page 19 of 40	Submitted Manuscript
	coefficient of patent
	F o r
	P e e
		r
		R e v
		i e
		w
		19

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Page 25 of 40 Editorial

  results are able to provide consistent information on the relationships between R&D, innovation and per labour GDP. The main contribution of this study to the existing literature is that it provides a comparative analysis of the non-scale endogenous growth theories across developed and developing countries, as well as across samples with different income levels and market sizes.

	Submitted Manuscript
	F o r limitations, our F o r
	P e e P e e
	r r
	R e v R e v
	i e i e
	w w
	25 26

Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 1 .

 1 Rankings of OECD Countries by Per Capita GDP,Patents and Researchers, 1981-97

	Rank Country	Per Capita GDP	Country	Per Capita Patents	Country	Per Capita Researchers
	1	Switzerland	42840	Switzerland	175.90	Japan

Table 2 .

 2 Rankings of Non-OECD Countries by Per CapitaGDP and Patents, 1981-97 WDI 2003), patents (NBER Patent Citation Database). Non-OECD countries do not have R&D data. Per capita GDP is in 1995 $U.S. Per capita patents and researchers are per million people.

	Rank	Country	Per Capita GDP	Country	Per Capita Patents
	1	Hong Kong	18242	Israel	68.60
	2	Singapore	17557	Singapore	11.70
	3	Israel	13746	Hong Kong	10.00
	4	Argentina	6958	South Africa	2.89
	5	Brazil	4158	Bulgaria	1.55
	6	South Africa	4153	Venezuela	1.12
	7	Venezuela	3535	Argentina	0.70
	8	Malaysia	3240	Malaysia	0.43
	9	Colombia	2093	Brazil	0.31
	10	Romania	1693	Colombia	0.14
	11	Bulgaria	1584	Romania	0.10
	12	Philippines	1082	Philippines	0.07
	13	Indonesia	776	China	0.04
	14	China	374	India	0.03
	15	India	311	Indonesia	0.02
	Sources: GDP (

Table 3 .

 3 Rankings of OECD Countries byAggregate GDP, Patents and Researchers, 1981-97

	Rank Country	GDP	Country	Patent	Country	Researchers
	1	Japan	4546000	Japan	19286	Japan	545358
	2	Germany	2178000	Germany	7098	Germany	187722
	3	France	1395000	France	2752	United Kingdom	133591
	4	United Kingdom	990500	United Kingdom	2561	France	121763
	5	Italy	982500	Canada	1866	Korea	100850
	6	Canada	509300	Switzerland	1177	Italy	69541
	7	Spain	507400	Italy	1132	Canada	65678
	8	Netherlands	359100	Netherlands	858	Poland	51484
	9	Korea	328700	Korea	823	Australia	42654
	10	Australia	311500	Sweden	809	Spain	34024
	11	Switzerland	287300	Australia	433	Netherlands	27986
	12	Mexico	264400	Belgium	358	Sweden	25871
	13	Belgium	245100	Austria	339	Mexico	18382
	14	Sweden	220100	Finland	318	Switzerland	18121
	15	Austria	204500	Denmark	217	Belgium	18051
	16	Denmark	162200	Spain	134	Turkey	14583
	17	Turkey	136900	Norway	121	Finland	14128
	18	Norway	123800	Hungary	79	Hungary	12495
	19	Finland	121500	New Zealand	55	Norway	12284
	20	Greece	109400	Ireland	51	Denmark	11397
	21	Poland	105200	Mexico	41	Austria	10439
	22	Portugal	91590	Poland	12	Greece	8063
	23	New Zealand	53270	Greece	10	Portugal	7209
	24	Ireland	51630	Portugal	5	New Zealand	6030
	25	Hungary	47490	Iceland	4	Ireland	4177
	26	Iceland	6432	Turkey	3	Iceland	751

Table 4 .

 4 Rankings of Non-OECD Countries byAggregate and Per Capita GDP, 1981-97 21

	Rank	Country	GDP	Country	Patent
	1	Brazil	604700	Israel	339
	2	China	428600	South Africa	99
	3	India	263600	Hong Kong	59
	4	Argentina	223900	Brazil	46
	5	South Africa	142000	China	40
	6	Indonesia	138700	Singapore	40
	7	Hong Kong	105600	India	30
	8	Colombia	72670	Argentina	23
	9	Venezuela	67280	Venezuela	22
	10	Israel	66040	Bulgaria	14
	11	Philippines	64710	Malaysia	8
	12	Malaysia	59120	Colombia	5
	13	Singapore	55160	Philippines	4
	14	Romania	38560	Indonesia	3
	15	Bulgaria	13900	Romania	2
	Sources: GDP (WDI 2003), Patents (NBER Patent Citation Database), Researchers

Table 5 .

 5 List of the Countries in Each Sample

	Full Sample		High Income	Low Income	Large Market	Small Market
	OECD	Poland	OECD	OECD	OECD	OECD
	G7	Portugal	Austria	Greece	Australia	Denmark
	Canada	Spain	Belgium	Hungary	Canada	Finland
	France	Sweden	Denmark	Ireland	France	Greece
	Germany	Switzerland Finland	Korea	Germany	Hungary
	Italy	Turkey	France	Mexico	Italy	Iceland
	Japan	Non-OECD Germany	New Zealand	Japan	Ireland
	UK Non-G7 Australia	Argentina o Brazil r Bulgaria	Iceland Japan Norway	Poland Portugal Spain	Netherlands Spain UK	New Zealand Norway Poland
	Austria Belgium Denmark Finland Greece	China Colombia P Sweden Switzerland Hong Kong e India e Indonesia Non-OECD	Turkey Non-OECD	Non-OECD	Portugal Turkey Non-OECD
	Hungary	Israel	r Hong Kong	Colombia	Brazil	Israel
	Iceland Ireland Korea Mexico Netherlands South Africa South Africa Malaysia Singapore Philippines Israel R Romania Argentina Singapore Brazil e Romania Bulgaria Philippines Indonesia China v New Zealand Venezuela Venezuela India i e Norway	China India Argentina South Africa Indonesia Hong Kong	Philippines Malaysia Singapore Romania Bulgaria Venezuela
				w
				28

Table 6 .

 6 Fixed Effects Regression Analysis of Per Labour Patent Flows,OECD Samples, 1981[START_REF] ______ | Environmental Regulation and Innovation: A Panel Data Study[END_REF] All variables are in natural logs, and all regressions include time fixed effects. L1 stands for first lag. Knowledge sipllovers are measured as an interacted term of researchers and manufacturing imports.

		Full	Large	Small	High	Low
		OECD	Market	Market	Income	Income
	L1. Patent flows	0.259	0.709	0.154	0.279	0.035
		(4.40)***	(11.30)***	(1.50)	(3.29)***	(0.24)
	Researchers/labour	0.250	0.153	-0.662	0.241	-0.466
		(1.99)**	(2.07)**	(1.53)	(0.95)	(0.78)
	U.S. trade/GDP	0.103	0.093	0.129	0.008	-0.003
		(1.06)	(1.95)*	(0.62)	(0.06)	(0.01)
	Knowledge spillovers	0.073	0.077	-0.064	0.238	-0.353
		(0.68)	(1.67)*	(0.26)	(1.51)	(1.19)
	Secondary school enrolment	-0.120	-0.110	0.468	0.043	0.131
		(0.61)	(1.51)	(0.74)	(0.13)	(0.20)
	Constant	3.148	1.026	2.535	0.583	5.780
		(2.51)**	(1.46)	(0.84)	(0.26)	(1.63)
	Observations Number of ccode1 o r R-squared	319 22 0.53	142 9 0.94	121 9 0.51	167 11 0.53	74 6 0.68
	e e Absolute value of t statistics in parentheses * significant at 10%; ** significant at 5%; *** significant at 1% P Note:
		r
		R e v
			i e
			w
			29

Table 7 .

 7 OneStep Difference GMM Regression Analysis of Per Labour Patent Flows, All variables are in natural logs and all regressions include time fixed effects. Openness to trade is measured as the ratio of total trade to GDP.

	OECD Samples, 1981-1997
	Full	Large	Small	High	Low
	OECD	Market	Market	Income	Income

Table 9 .

 9 OneStep Difference GMM Regression Analysis of Per Labour GDP, OECDSamples, 1981Samples, -1997

	Full OECD	Large	Small	High	Low
	Sample	Market	Market	Income	Income

Table 10 .

 10 OneStep Difference GMM Regression Analysis of Per Labour GDP, OECDSamples, 1981Samples, -1997 All variables are in natural logs and all regressions include time fixed effects. D stands for first difference and LD stands for lagged dependent. Openness to trade is measured as the ratio of total trade to GDP. a/ H 0 : regressors are not correlated with the residuals. b/ H 0 : errors in first difference regression exhibit no second order serial correlation.

	Full OECD	Large	Small	High	Low
	Sample	Market	Market	Income	Income

Table 11

 11 All variables are in natural logs and all regressions include time fixed effects. Openness to trade is measured as the ratio of total trade to GDP.

	. Fixed Effects Regression Analysis of Per Labour GDP, Non-OECD
		Samples, 1981-1997
		Full Non-	Large	Small	High	Low Income
		OECD	Market	Market	Income
	Per labour investment	0.459	0.584	0.226	0.458	0.498
		(17.33)*** (19.24)***	(4.02)***	(11.03)***	(8.10)***
	Patent flows	0.019	0.032	0.022	0.135	-0.000
		(2.20)**	(3.03)***	(1.19)	(7.38)***	(0.03)
	Openness to trade	0.109	0.043	-0.127	0.105	0.110
		(5.37)***	(1.55)	(2.55)**	(3.18)***	(2.80)***
	Secondary school enrolment	0.023	0.272	-0.318	0.082	0.079
		(0.42)	(4.72)***	(1.94)*	(0.96)	(0.77)
	Constant	4.867	3.190	8.739	4.822	3.909
		(14.74)*** (11.28)***	(9.43)***	(7.82)***	(7.24)***
	Observations	217	103	65	109	95
	Number of ifs	15	7	5	7	7
	R-squared	0.85	0.96	0.89	0.86	0.90
	Absolute value of t statistics in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%
	Note:

Table 12 .

 12 OneStep Difference GMM Regression Analysis of Per Labour GDP,Non- OECD Samples, 1981[START_REF] ______ | Environmental Regulation and Innovation: A Panel Data Study[END_REF] All variables are in natural logs and all regressions include time fixed effects. D stands for first difference and LD stands for lagged dependent. Openness to trade is measured as the ratio of total trade to GDP. a/ H 0 : regressors are not correlated with the residuals. b/ H 0 : errors in first difference regression exhibit no second order serial correlation.

		Full Non-	Large	Small	High	Low
		OECD	Market	Market	Income	Income
	LD. Per labour GDP	0.669	0.442	0.679	0.566	0.696
		(20.45)***	(8.53)*** (12.96)*** (9.44)***	(19.55)***
	D. Per labour investment	0.167	0.345	0.116	0.207	0.209
		(8.31)***	(9.22)*** (5.03)***	(5.48)***	(8.04)***
	D. Patent flows	0.012	0.018	0.017	0.078	0.001
		(2.30)**	(2.31)**	(2.22)**	(5.05)***	(0.19)
	D. Openness to trade	0.028	-0.000	-0.013	0.057	0.027
		(2.21)**	(0.00)	(0.65)	(2.01)**	(1.84)*
	D. Secondary school enrolment 0.064	0.183	-0.094	0.134	-0.025
		(1.83)*	(4.50)*** (1.31)	(2.52)**	(0.66)
	Constant	0.032	0.013	0.028	0.027	0.033
		(2.25)**	(2.65)*** (2.18)**	(1.33)	(1.72)*
	Sargan test, p value a	0.00	0.99	1.00	0.99	0.96
	AR(2) test, p value b	0.73	0.95	0.69	0.99	0.67
	Observations	186	89	54	94	81
	Number of ifs	15	7	5	7	7
	Absolute value of z statistics in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%
	Note:

Page 38 of 40 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 1A .

 1A Heteroskedasticity and First Order Autocorrelation Test for the Fitted Values of Patents Figures in parenthesis are p values. 1/ The values of d-statistics below or above 2 indicate the presence of first order autocorrelation.

				Breusch-Pagan / Cook-Weisberg test for
		Durbin-Watson		heteroskedasticity 2 Ho: Constant variance, variables:
		d-statistics 1		fitted values of patent rate
	Australia	1.30 Italy	2.52	Australia 2.69 (0.10) Italy	0.09 (0.76)
	Austria	2.44 Japan	1.46	Austria	1.54 (0.21) Japan	5.46 (0.01)
	Belgium	2.03 Netherlands	1.22	Belgium 4.26 (0.03) Netherlands	3.13 (0.07)
	Canada	1.31 New Zealand	2.93	Canada	0.04 (0.83) New Zealand	0.00 (0.98)
	Denmark	2.09 Norway	1.99	Denmark 4.10 (0.04) Norway	1.06 (0.30)
	Finland	1.76 Portugal	1.86	Finland	0.05 (0.83) Portugal	0.83 (0.36)
	France	1.60 Spain	3.23	France	0.44 (0.50) Spain	0.83 (0.36)
	Germany	1.22 Sweden	1.46	Germany 0.15 (0.69) Sweden	7.81 (0.00)
	Greece	2.36 Switzerland	1.20	Greece	0.11 (0.73) Switzerland	0.03 (0.85)
	Iceland	1.57 UK	1.39	Iceland	0.47 (0.49) UK	3.03 (0.08)
	Ireland	1.95		Ireland	0.01 (0.92)
	Notes:

Table 2A .

 2A Heteroskedasticity and First Order Auto Correlation Test for the Fitted Values of Per Labour GDP Durbin-Watson d-statistic 1 Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of patent rate The values of d-statistics below or above 2 indicate the presence of first order autocorrelation.

	Argentina Australia Austria Belgium Brazil Bulgaria Canada China Colombia Denmark Finland France Germany Greece Hong Kong Hungary Iceland India Indonesia Ireland Israel Figures in parenthesis are p values. 1.42 Italy 1.75 Japan 0.81 Korea 1.06 Malaysia 1.72 Mexico 1.26 Netherlands 1.21 New Zealand 1.43 Norway 1.66 Philippines 1.80 Poland 1.37 Portugal 2.23 Romania 1.20 Singapore 2.47 South Africa 1.63 Spain 2.53 Sweden 1.42 Switzerland 1.84 Turkey 2.92 UK 2.10 Venezuela 1.74 o r 1.99 2.47 1.51 2.35 2.22 0.84 1.97 1.01 2.32 2.88 1.02 2.63 2.82 3.13 1.40 1.79 1.92 2.50 2.14 2.05 P e e Argentina Australia Austria Belgium Brazil Bulgaria Canada China Colombia Denmark Finland France Germany Greece Hong Kong 0.06 (0.80) 2.01 (0.15) 2.09 (0.14) 1.51 (0.21) 3.49 (0.06) 0.45 (0.50) 0.80 (0.36) 7.16 (0.00) 0.48 (0.48) 0.30 (0.58) 0.02 (0.88) 1.40 (0.23) 0.31 (0.57) 0.82 (0.36) 0.00 (0.94) Hungary 1.28 (0.25) Iceland 0.11 (0.74) India 0.11 (0.73) Indonesia 0.66 (0.41) Ireland 1.70 (0.19) Israel 0.78 (0.37) r R e v i e 1/ F w Italy Japan Korea Malaysia Mexico Netherlands New Zealand 1.36 (0.24) 0.05 (0.81) 0.79 (0.37) 0.22 (0.64) 0.17 (0.68) 0.07 (0.78) 0.00 (0.96) Norway 3.47 (0.06) Philippines 0.92 (0.33) Poland 0.61 (0.43) Portugal 2.15 (0.14) Romania 0.23 (0.63) Singapore 0.34 (0.55) South Africa 0.51 (0.47) Spain 1.12 (0.28) Sweden 0.41 (0.52) Switzerland 4.44 (0.03) Turkey 0.14 (0.71) UK 0.20 (0.65) Venezuela 0.09 (0.76)
	40

Table 6A :

 6A Summary Statistics Variables in GDP and TFP Regressions All variables are in natural logs. PL stands for per labour.

	Full Non OECD Sample		High Income non-OECD		Low income non-OECD
		(N=217)		Sample (N=109)			Sample (N=95)
	stats	sd	min max mean sd		min	max	mean sd	max mean min
	PL GDP	1.18 5.94 10.87 9.04 0.58	9.08	10.87 9.94 0.88 9.56 7.99 5.94
	PL inv	1.20 4.62 9.93 7.54 0.76	7.18	9.93	8.41 0.78 8.07 6.49 4.62
	Patents	1.46 0.00 6.48 2.94 1.15	1.39	6.48	3.79 1.26 4.42 2.10 0.00
	Sec.school 0.34 3.08 4.62 4.06 0.39	3.08	4.57	4.07 0.29 4.62 4.05 3.45
	Openness 0.97 2.58 6.02 3.95 1.14	2.58	6.02	4.17 0.55 4.79 3.54 2.63
		Full OECD sample	High income OECD Sample	Low income OECD Sample
		(N=418)		(N=187)			(N=146)
	Stats	sd	max mean min sd		max	mean min	sd	max	mean min
	PL GDP	0.64 11.32 10.52 8.53 0.16	11.32 10.98 10.61 0.62 10.86 9.85 8.53
	PL inv	0.66 10.09 8.94 6.74 0.27	10.09 9.41	8.85 0.64 9.24	8.30 6.74
	Patents	2.34 10.23 5.41 0.00 2.23	10.23 6.26	0.00 1.60 8.11	3.39 0.00
	Sec.school 0.22 5.06 4.55 3.72 0.11	5.06	4.64	4.45 0.27 4.80	4.42 3.72
	Openness 0.43 4.99 4.05 2.80 0.44	4.98	4.12	2.80 0.40 4.99	3.98 3.12
	Note:

Table 7A .

 7A Correlation Coefficients of the Variables in the GDP and TFP All variables are in natural logs. PL stands for per labour.

			Regressions
	OECD	PL GDP	PL Inv	Patents Sec.School Openness
	PL GDP	1
	PL Inv	0.9744*	1
	Patents	0.5322*	0.5260*	1
	Secondary school	0.2311*	0.2212* 0.2041*	1
	Openness	0.4280*	0.5267* 0.0689	0.3412*	1
	Non OECD	PL GDP	PL Inv	Patents Sec.School Openness
	PL GDP	1
	PL Inv	0.9658*	1
	Patents	0.5976*	0.5959*	1
	Secondary school	0.6596*	0.6225* 0.4059*	1
	Openness	0.2595*	0.1969* -0.1384* 0.3882*	1
	Note:

The category "others" include: agriculture-husbandry-food, amusement devices, apparel and textiles, earth working and wells, furniture and house fixtures, heating, pipes and joints, receptacles and miscellaneous.

The U.S. trade share of GDP for each country is calculated by adding up the absolute value of the United States' total exports and imports to and from each partner country and dividing this total by each country's GDP.

-Economic Development, Technological Change, and Growth, O31 -Innovation and Invention: Processes and Incentives < O3 -Technological Change|Research and Development < O -Economic Development, Technological Change, and Growth, O33 -Technological Change: Choices and Consequences|Diffusion Processes < O3 -Technological Change|Research and Development < O -Economic Development, Technological Change, and Growth, O47 -Measurement of Economic Growth|Aggregate Productivity < O4 -Economic Growth and Aggregate Productivity < O -Economic Development, Technological Change, and Growth

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript