Kurt A Hafner
email: kurt.hafner@sowi.uni-bamberg.de

The Pattern of International Patenting and Technology Diffusion*

Keywords: Productivity, R&D, Patents, Technology Diffusion, Nonstationary Panels JEL-Classifaction: C12, C23, O30, O40 Productivity, R&D, Patents, Technology Diffusion, Nonstationary Panels Normal, Justified, Indent

The paper focuses on the impact of R&D expenditure on labor productivity using international patent applications as a technology diffusion indicator. Considering the relationship between research and productivity, the pattern of international patenting reflects the channel between the source and the destination of transferred technology. Accounting for nonstationarity and cointegration, I find that patent-related foreign R&D spillovers are present for a panel of 18 OECD countries. Moreover, Non-G7 OECD countries benefit more from foreign rather than domestic R&D activities. Estimates also show that there is no significant spillover effect from bilateral trade, but confirm the impact of FDI on domestic labor productivity.

Introduction

There is an unobservable link between research in one country and productivity in other countries. As widely discussed by [START_REF] Keller | International technology diffusion[END_REF], trade, FDI and patents best reflects these unobservable connections. While many studies question empirically bilateral trade and FDI as possible technology diffusion channels, patents are not used to quantity foreign spillover effects in an appropriate way. Recently, there are empirical studies such as Xu and Chiang (2005) or Chen and Yeng (2005) using patent statistics as a proxy for technological progress as proposed by [START_REF] Griliches | Patent statistics as economic indicators: a survey[END_REF]. To quantify patent-related spillover effects properly, I take the view that patents should be related to R&D expenditure as a channel and not be used as a proxy for technology. In distinguishing between the source of technology and the transmission, one is able to measure and compare different technology diffusion channels. To my knowledge, there is no empirical work on foreign patents and its use as a channel to quantify foreign spillover effects. Hence, I propose to use the pattern of international patenting to analyze technology diffusion empirically and follow [START_REF] Eaton | International technology diffusion: theory and measurement[END_REF]: "we think that patenting abroad is a much more direct, albeit imperfect, indicator of where ideas are going". Accordingly, patents reflect in a direct way the channel between the source and the destination of transferred technology.

In general, productivity as well as R&D expenditure data is nonstationary, and both variables are cointegrated within a long-run relationship. To account for nonstationarity and cointegration, and to deal with endogeneity, I use estimation techniques proposed by [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF]. The advantage of not transforming variables in differences but of relying on level terms is to make use of the embedded information about common trends and long-run equilibrium properties. In analyzing the steady state equilibrium between productivity and R&D expenditure, estimates in levels by [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] estimation techniques measure the unobservable connection best and quantify foreign spillover effects properly. [START_REF] Coe | International R&D spillovers[END_REF] and through re-examining their econometric findings, [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF] confirm the impact of domestic R&D on TFP but reject any diffusion of foreign technology. Moreover, according to [START_REF] Keller | International technology diffusion[END_REF], there is no strong empirical evidence for learning-by-exporting spillovers beside case studies dealing with East and Southeast Asia's export success in the 1960s. Indeed, country studies, such as [START_REF] Ghatak | Exports, export composition and growth: cointegration and causality evidence for Malaysia[END_REF] for Malaysia, [START_REF] Biswal | Export-led growth hypothesis: cointegration and causality analysis for Taiwan[END_REF] for Taiwan and [START_REF] Liu | Relationships between economic growth, foreign direct investment and trade: evidence from China[END_REF] for China, find evidence for an export-led growth taking into account cointegration and testing for causality. While there might be a theoretical consensus about trade-related spillover effects and the importance of a country's openness to trade, empirically it seems to be difficult to quantify the extent and direction of technology diffusion from international trade.

The same criticism applies to a second strand of the literature that considers FDI as a channel for technology diffusion. Following [START_REF] Keller | International technology diffusion[END_REF], such subsidiaries might pick up new technologies from their host countries (outward FDI technology transfer) or provide technology to domestic firms (inward FDI technology transfer). Again, the macro evidence is not straightforward, as Xu and Wang (2000) mention, and the impact of technology transfer either from or to host countries still needs empirical validation. [START_REF] Chakraborty | Foreign direct investment and growth in India: a cointegration approach[END_REF], for example, find amongst other things that GDP in India is not Granger caused by inward FDI and that the causality is vice versa. However, much of the literature on FDI spillovers uses micro (firm or plant level) data instead and account for heterogeneity across sectors and firms within a country. Recently, empirical micro evidence for economically important FDI spillover effects have been found by [START_REF] Haskel | Does inward foreign direct investment boost the productivity of domestic firms?[END_REF] and [START_REF] Griffith | Productivity convergence and foreign ownership at the establishment level[END_REF] for the United Kingdom and by [START_REF] Keller | Multinational enterprises, international trade, and productivity growth: firm-level evidence from the United States[END_REF] for the United States. [START_REF] Branstetter | Is foreign direct investment a channel of knowledge spillover? Evidence from Japan's FDI in the United States[END_REF] finds evidence for FDI spillover both from and to investing Japanese firms in the United States. In spite of that, the implied economic magnitude still is unclear. Moreover, case studies, such as [START_REF] Larrain | Intel: A case study of foreign direct investment in Central America[END_REF], which analyze the impact of Intel's FDI in Costa Rica in the 1990s, may offer some fruitful insights on how to determine firm specific technology transfer. However, country specific analysis using micro data as well as particular case studies do not overcome the lack of general quantitative evidence and understanding.

Given these mixed results for trade-and FDI related spillover effects, I use the pattern of international patenting as a channel for technology diffusion. The idea is that patenting domestic research efforts abroad determines the transfer of technology. Local firms may take legal advantage of patented foreign knowledge by paying royalties. Adding foreign knowledge to a country's own R&D stock, even in the case of limited domestic R&D spending, is likely to increase the efficiency of domestic input factors. In this context, international spillover effects are patent-related.

The Pattern of International Patenting

A patent holder receives a temporary legal monopoly at the cost of public disclosure of the underlying technical information. To protect themselves from imitators, inventors have to patent their innovations at home and abroad. The inventor's choice is to relate the costs of filing a patent application and of technical disclosure to the likelihood of imitation and the monopoly rents in specific markets. Hence, strategic and/or market seeking decisions drive inventors to patent only the best and most valuable innovations. However, patent figures show that most of the patents are filed at home rather than abroad. This might be the result of either technological immobility or less foreign protection as mentioned by [START_REF] Eaton | International technology diffusion: theory and measurement[END_REF]. Given the tight distribution of productivity levels across countries in relation to the skewness of domestic research activity, [START_REF] Eaton | International technology diffusion: theory and measurement[END_REF] reject technology immobility and point to a lesser protection provided by foreign patents. However, according to [START_REF] Branstetter | Do stronger patents induce more innovation? Evidence from the 1988 Japanese patent law reforms[END_REF], there is no empirical evidence in the case of Japan that stronger patents induce more innovation and therefore more patents. The bulk of foreign patent appli- B.4 in Appendix B. 1 Concurrently, the same pattern holds regarding business related R&D (BERD) expenditure. Hence, in explaining the small variation in productivity levels, we might expect a higher impact due to foreign rather than domestic research activity for smaller and/or less advanced countries given the asymmetric R&D spending pattern across countries. International patent statistics by the World Intellectual Property Organization (WIPO) and OECD provide only count numbers. Specific information about the value of patents is not given. However, some patents are more valuable and their economic impact differs between countries. Hence, using patent count data may serve to determine the direction rather than the magnitude of international technology diffusion. In summary, the paper examines the effects of domestic and foreign business related R&D expenditure on labor productivity by the use of international patent applications as the technology diffusion channel. Patent-related spillover effects for G7 and Non-G7 OECD countries are of main interest. Additionally, I incorporate trade and FDI spillover effects to discuss the overall picture of technology diffusion and carry out some robustness tests.

Framework

This section discusses the theoretical framework and introduces the regression equation used to quantify foreign technology diffusion (i.e. patent (P)-, trade (M)-and FDI (F)-related spillover effects). Let us first consider the following aggregated production function: As outlined, empirical results seeking spillover effects by embedded technology in input factors are mixed. Consequently, the paper focuses on technical change A and its impact on input efficiency. An increase of R&D expenditure-used as a proxy for technical changeaugments the efficiency of input factors used in final output production. In using and/or modifying foreign technology, countries increase their technological knowledge and capabilities.

) , ( * L K F A Y = , (1)
As a result, domestic input productivity and output are likely to increase.

The Regression Model

Contrary to [START_REF] Coe | International R&D spillovers[END_REF] and other related studies, I try to explain the impact of technical change on productivity of single rather than total input factors. 2) is a proxy for technical change A.

Since the benefits of domestic research activity depend on domestic markets and traded volumes, the impact on LP due to domestic R&D spending differ between G7 and Non-G7 countries. Hence, modification of equation (2) leads to:

t i f t i t i f d t i d G d t i d i t i S b S G S LP , , , , 7 , , log log 7 log log + + + + = , (3)
with G7 as a dummy variable, which is equal to one for the seven major countries and zero otherwise.

Variable Definitions

By the use of the perpetual inventory method, I follow [START_REF] Coe | International R&D spillovers[END_REF] Patent count data mainly serve to determine the direction rather than the intensity of technology diffusion. Hence, as a reference, I do not specify foreign technology intensity explicitly:

1 , ,

= P t i t i b b . (5)
However, in gauging technology intensity to distinguish between the impact of foreign and domestic research and therefore between countries, one could use two different measures.

First, the use of patent-related foreign technology should be more efficient in countries with their own research activity and with higher domestic R&D spending. Hence, a country that spends more on R&D relative to its GDP should benefit more from foreign technology diffusion. In relating business related R&D expenditure (

t i D R , &
) to GDP ( t i Y , ), I define patentrelated foreign technology intensity as: Second, market seeking and/or strategic decisions by inventors from major research countries lead to a high non-resident to resident patent application ratio in small countries. Given almost similar productivity levels across OECD countries, the impact of foreign technology from abroad must be higher in countries with a high share of foreign patent applications to domestic patent applications. For this reason, the ratio of foreign to total patent applications may also serve as a proxy for patent-related foreign technology intensity:

t i t i P t i t i Y D R b b , , , , / & = . ( 6
= j t ji i j t ji P t i t i a a b b , , , , / , N j ,..., 1 = . ( 7
)

Trade-and FDI-Related Spillover Effects

To capture trade-related spillover effects, [START_REF] Coe | International R&D spillovers[END_REF]

+ = i j t ji F f t i F f t i f t i FDI S S S 1 , , 1 , , , , ) 1 ( , N j ,..., 1 = , ( 10
)
with t ji FDI , as foreign direct investment from country j to country i and as a time-and country-invariant depreciation rate. Again, the benchmark for the FDI inflow stock is calculated as described in Appendix A. Note that equation ( 10) is a proxy of foreign technology by FDI and interpretation is different compared to equation ( 4) and ( 8), where patents and bilateral trade are diffusion channels. Hence, I do not express FDI-related technology intensity explicitly:

1 , , = F t i t i b b . ( 11
)

Data

The paper measures the impact of international technology diffusion on LP. The OECD has published data on BERD since about 1965 mainly for the G7 countries as well as for Switzerland. In order to get a complete (balanced) data set for all OECD countries from the beginning of 1965, one has to estimate missing R&D expenditure figures. [START_REF] Coe | International R&D spillovers[END_REF] estimated such missing figures by relating real R&D expenditure to real output and investment.3 However, the lack of R&D data as well as patent numbers limits the analysis in this paper to 1981-2001 and to 18 OECD countries. 4 Converting R&D expenditure flows into R&D capital stocks I use the perpetual inventory method and follow the procedure suggested by [START_REF] Griliches | Issues in assessing the contribution of R&D to productivity growth[END_REF] in calculating the R&D benchmark capital stock for each country. 5 The time-and country-invariant depreciation rate is assumed to 10%. 6 The R&D expenditure data is from the OECD Main Science and Technology Database and is in million constant US$ (PPP)

The gation bias: the more the foreign patent applications (imports) in a single country are, the higher the foreign R&D capital stock is. In this context, a merger between countries would always increase the foreign R&D capital stock. An alternative approach would be a ratio of foreign patent application (or imports as proposed by [START_REF] Lichtenberg | International R&D spillovers: a comment[END_REF]) to foreign GDP. This formulation would reflect the intensity as well as the direction of technology transfer but circumvent the aggregation bias. Since it will also aggravate the business cycle problem with foreign GDP in the denominator, I rather ignore the aggregation bias and rest on R&D capital stock expressed by equation ( 4) and ( 8). Nonetheless, I compare the alternative weighting measures in section 6.3. as part of the robustness tests.

7

The OECD provides FDI flow-and stock data in their International Direct Investment Statistics. However, data on inward and outward positions are not complete for some countries or periods. I therefore prefer to use FDI flow data and to calculate stock variables.

Nonstationary Panels and Estimation Techniques

In general, productivity as well as R&D expenditure data exhibit a clear trend and unit root tests confirm nonstationarity, whereas the error term of the pooled regression may or may not be stationary. If the error term is stationary, variables are cointegrated, and there is a common trend binding all variables. If not, the estimated relationship is spurious and no long-run relationship between variables exists. Moreover, the cointegration literature does not assume strictly exogenous regressors. There might also be feedback from productivity to R&D and endogeneity as well as serial correlation drives and biases estimators. 9

To address nonstationarity and endogeneity and to avoid spurious correlation among variables, I use estimation techniques proposed by [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] and adopt their techniques as in [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF] and [START_REF] Funk | International R&D spillovers and convergence among OECD countries[END_REF]. 10 The advantage of not transforming variables in differences but of relying on level terms is to make use of the embedded information about common trends and long-run equilibrium properties. Hence, in analyzing the steady state equilibrium between domestic productivity and foreign R&D expenditure, estimates in levels quantify foreign technology diffusion properly.

Unit Root Tests

There Suppose that a variable is driven by its lagged value, an autoregressive coefficient and an error term. The autoregressive coefficient i of the lagged value determines the degree of dependence or nonstationarity. The LLC test assumes, as [START_REF] Breitung | Testing for unit roots in panel data: Are wages on different bargaining levels cointegrated?[END_REF], that

9 [START_REF] Baltagi | Econometric analysis of panel data[END_REF] provides an excellent overview for nonstationary issues as well as cointegration. 11 To allow for a limited degree of dependence across units, cross sectional averages are subtracted from the observed data without affecting the limit distribution of the panel unit root test, see [START_REF] Levin | Unit root test in panel data: asymptotic and finite sample properties[END_REF]. To test for the long-run cointegration relationship (i.e. stationarity of the error term), one can either use the corresponding error terms in the error correction (EC) model or the proposed cointegration tests presented by [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF], [START_REF] Mccoskey | A residual-based test of the null of cointegration in panel data[END_REF] and Pedroni (2004).

Turning to the EC model, the first step is to estimate long-run equilibrium values in levels by removing units as well as time effects (transformation for a two-way fixed effects model).

The resulting residuals (i.e. error correction terms) are used in the second step to estimate the EC model. The t-statistic of the lagged error correction term now indicates whether it is significantly different from zero or not. A cointegration relationship amongst variables exists if the t-statistic is significant.

Cointegration tests analyze either the null hypothesis of no cointegration, as the Dickey-Fuller and the augmented Dickey-Fuller type tests proposed by [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF]

Empirical Results

To keep the analysis comparable to estimations of [START_REF] Coe | International R&D spillovers[END_REF] and to [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF], I first estimate patent-related spillover effects for all OECD countries using [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF]'s estimation techniques. Next, I divide countries between G7 and Non-G7 and reduce estimates to the use of the DOLS estimator. I also incorporate trade-and FDI-related spillover effects to complete the analysis of technology diffusion. Finally, I conduct some robustness tests to validate the derived results.

Patent-Related Spillover Effects

Initially, nonstationary and cointegration tests have to confirm that the data is nonstationary and the variables are cointegrated. Once confirmed, I quantify patent-related spillover effects and discuss the impact of the different technology intensity measures on labor productivity.

12 For further information as well as for analytical derivation see [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF]. 2) with ( 4) and ( 6). However, given the overall picture of test statistics confirming cointegration, I conclude that there is a long-run relationship between the cointegrated variables. Finally, with nonstationary and cointegrated data, the focus turns to the empirical results.

F

[Table 2]

Patent-Related Spillover Effects by OLS with Bias Correction, FM-OLS and DOLS

Table 3 lists coefficients and their test statistics in parentheses estimated by OLS with bias correction, FM-OLS and DOLS for the three technology intensity measures.

Starting with the impact of domestic R&D capital stock on labor productivity, the estimated coefficients for equation ( 2) with ( 4) and ( 5) are fairly comparable to the results from Kao, Chiang and Chen (1999) re-estimating [START_REF] Coe | International R&D spillovers[END_REF] paper. 13 Moreover, the estimated coefficient by OLS with bias correction and FM-OLS are quite similar, whereas the coefficient from the DOLS estimator is about two percentage points higher. This is the result of the two different ways of removing the nuisance parameter (serial correlation) and accounting for endogeneity. The FM-OLS estimator corrects the dependent variable by the long-run covariance and applies usual OLS. Hence, coefficients will change only slightly. The DOLS estimator, however, introduces leads and lags with a bigger impact on coefficients compared to pooled OLS. Turning to equations ( 2) with (4) in combination with either (6) or 13 Both papers estimate the impact of domestic R&D amongst others variables on TFP. However, the impact of domestic R&D on either total or labor productivity should not vary largely. The coefficient is 0.097 for Coe and Helpman (1995) using pooled OLS. For Kao, Chiang and Chen (1999) the coefficient is 0.084 by the use of OLS with bias correction or FM-OLS and 0.107 by DOLS. 7), estimates suggest a higher elasticity for domestic R&D capital stock, which vary between 0.11-0.20 percent. As a first result, the estimated coefficients for domestic R&D capital stock differ largely depending on the estimation technique and on the assumptions on foreign R&D capital stocks. However, the t-statistics are significantly large and domestic R&D capital stock is significant at least at the 5% level in each case.

[Table 3]

To quantify the impact of foreign R&D capital stocks on domestic labor productivity, I multiply the coefficients with their intensities. Given ratios of domestic R&D expenditure to GDP less than three percent, the impact of foreign R&D capital stock reduces for equations ( 4) and ( 6) to almost 0.02 percent in the best and zero in the worst case. For the case of patent weighted foreign R&D capital stocks given by equations ( 4) and ( 7), a ratio less than one reduces the estimated coefficient even further. Such low coefficients for foreign technology diffusion in relation to the impact of domestic R&D are not very plausible. Otherwise, one could not explain the small variation in productivity levels across different countries. However, without any additional specification for technology intensity as by equation ( 5), the impact of foreign R&D capital stock on domestic factor productivity is about 0.22 percent for OLS with bias correction/FM-OLS and 0.17 percent for DOLS. All coefficients are significant at a 1% level.

Given the superiority of the DOLS estimator over OLS with bias correction and FM-OLS and considering equations ( 4) and ( 5) as an adequate approximation of technology spillover effects, I conclude that there are patent-related spillover effects. Hence, a one percent increase in domestic or foreign R&D capital stock leads to a 0.10 percent or 0.17 percent increase in domestic labor productivity, respectively. However, the impact of domestic R&D on factor productivity differs between G7 and Non-G7 OECD countries. Table 4 shows estimation results by DOLS for equations (3) with (4) in combination with ( 5)-( 7). I also list cointegration test statistics by Pedroni ( 2004) although a cointegrated relationship amongst productivity and R&D expenditure will not change due to a division of countries.

[Table 4]

As expected, test statistics from Pedroni (2004) confirm cointegration. Again, coefficients for foreign R&D capital stock expressed by (4) in combination with ( 6) or ( 7) are too low. Due to the discussed lack of plausibility in explaining productivity levels across OECD countries, the analysis reduces to equation ( 3) with ( 4) and ( 5) in the first column in Table 4. The impact of domestic research activity for G7 countries rises to 0.25 percent while for Non-G7 OECD countries it remains nearly unchanged. However, the differences between both sets of countries are not statistically significant in this case. Again, both coefficients are comparable to [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF] and to [START_REF] Coe | International R&D spillovers[END_REF]. The elasticity for foreign R&D capital stock reduces to 0.14 percent but is still significant at a 1% level. As expected, the impact on labor productivity for Non-G7 OECD countries is higher due to foreign rather than domestic R&D activities. This emphasizes the importance of technological spillover effects from abroad for these countries. Nevertheless, tests do not confirm that the coefficient for foreign R&D capital stock is significantly larger than the coefficient for domestic R&D capital stock. To discuss the overall picture of technology diffusion, I incorporate trade-and FDI-related spillover effects to the analysis. Bearing in mind that the impact on labor productivity differs between G7 and Non-G7 OECD countries and that patent-related spillover effects are best quantified without any specific technology intensity, a regression for technology diffusion can be written as: with patent-, trade-and FDI-related spillover effects as described by equation ( 4) with (5), equation ( 8) with ( 9) and equation ( 10) with ( 11), respectively.

t i F f t i F f M f t i M t i M f P f t i P f d t i d G d t i d i t i S S b S S G S LFP , , , , , , , , , , , , 7 ,
Table 5 shows the impact on labor productivity for G7 and Non-G7 OECD countries by DOLS according to three different scenarios: first, patent-and trade-related spillover effects, second, patent-and FDI-related spillover effects and third, patent-, trade-and FDI-related spillover effects. Table B.1 in Appendix (B) confirms unit roots for foreign R&D stocks related to bilateral trade and FDI. Moreover, test statistics of Pedroni ( 2004) as well as of [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] in Table B.2 in Appendix (B) show stationarity of the error term for each regression and therefore confirm cointegration. I also repeat the estimates of equation ( 3) with ( 4) and

(5) in the first column in Table 5.

Including bilateral trade pattern, estimates in the first scenario are quite close to those derived for equation ( 3) with ( 4) and ( 5): the coefficient for patent-related foreign R&D spillover effects (0.125) remains significant at a 1% level and still exceeds the coefficient for domestic R&D capital stock for Non-G7 OECD countries (0.104). Interestingly, the DOLS es- [START_REF] Kao | International R&D spillovers: an application of estimation and inference in panel cointegration[END_REF]. However, coefficients are slightly lower compared to the first column.

Considering the second scenario and adding FDI inflow stocks instead of trade weighted R&D stocks to the regression, the domestic R&D coefficients for Non-G7 countries reduces by more than 50%. Coefficients for G7 countries as well as for patent-related spillover effects are substantially lower than those in the first column. However, the differences between both sets of countries are now statistically significant (the coefficient for G7 countries is significant at a 1% level) and my key results remain robust: there are patent-related R&D spillover effects, and the impact on labor productivity for Non-G7 countries is higher due to foreign rather than domestic R&D activities. According to the estimates, there is a positive impact on domestic labor productivity of about 0.06 percent from FDI inflows. Both coefficients for technology diffusion are significant at a 1% level. Finally, testing whether the coefficient for patent-weighted foreign R&D capital stock is significantly larger than the coefficient for domestic R&D capital stock lead to ambiguous results: significance is rejected by the DOLS estimator but confirmed by the FM-OLS estimator.

By the third scenario, estimation of equation ( 12) leads to no major change in the results compared to the second scenario and coefficients as well as test results rarely change due to the incorporation of bilateral trade as a diffusion channel. Estimates again confirm the impact and importance of patent-and FDI-related spillover effects on labor productivity and negate any bilateral trade significance.

[Table 5]

Robustness Tests

This section returns to patents once again and analyses three modifications to the econometric modeling to test the robustness of the derived results for patent-related spillover effects. First, (1998) critique on using a specific weighing choice as in equation ( 4). Third, being aware of the aggregation-bias using patent-based weights as in equation ( 4), I introduce a different weighting method to reflect the direction of technology transfer.

To compare, I estimate equation ( 3) with ( 4)/( 5) by the use of the DOLS estimator. Equation (4) changes respectively, whereas equation ( 5) remains unchanged. According to the modification, nonstationarity testing results from LLC and IPS are in Table 6 as one goes down rows, whereas estimation results and cointegration test statistics from [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] are in the corresponding column of Table 7.

[Table 6]

Total Factor Productivity

The GGDC also provides TFP data for 13 countries 14 over a period of 21 years. Test statistics confirm nonstationarity of TFP in the first row of Table 6 and cointegration in the first column of Table 7. I also find a highly significant impact of domestic R&D on TFP (0.171).

However, I do not find any significant patent-related spillover effect on TFP contrary to the estimated results in Table 4 but comparable to the results of Kao, Chaing and Chen (1999) for the case of trade-related spillover effects. One could possibly argue by the smaller number of countries and/or calculation and measurements errors, but I suggest further work on TFP and its use to quantify foreign spillover effects. To summarize, there are patent-related spillover effects in the case of labor productivity, whereas in the case of TFP there are none. 14 The 13 OECD countries are respectively: Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Netherlands, Spain, Sweden, United Kingdom, and USA. If randomly assigned weights generate statistically significant results, as [START_REF] Keller | Are international R&D spillovers trade-related? Analyzing spillovers among randomly matched trade partners[END_REF] Monte Carlo Simulation on the results of [START_REF] Coe | International R&D spillovers[END_REF], the finding and size of spillovers are independent of the weighting method. If so, the choice of patent-based weights in equation ( 4) or any other empirically observed pattern cannot be used to quantify patentrelated spillover effects. However, before turning to the estimation results, one has to be sure that the variables are nonstationary: test statistics by LLC with one lag and IPS with both lags reject the null hypothesis of nonstationarity of randomly weighted foreign R&D stocks. Given nonstationarity of the remaining variables-as listed and discussed in Table 1-a stationary error term and therefore cointegration is not likely to exist. This is confirmed at least by the DF and t DF tests of [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] in the second column of Table 7. Hence, the findings of randomly created spillover effects are spurious owing to absent cointegration and Keller's (1998) critique is inappropriate. Table 7 does not report t-statistics of the estimated coefficients.

[Table 7]

Non Aggregation-Bias: Alternative Patent-Based Weighting Approach

Accounting for the aggregation-bias, I change the patent-based weighting approach by the use of foreign GDP instead of the sum of foreign patent applications in the denominator of equation (4). Turning to Table 6, the LLC as well as IPS testing procedure confirms nonstationarity for alternative weighted foreign R&D capital stocks at least for the 10% level. Three of four tests from [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] in Table 7 confirm cointegration and the estimated coefficients for domestic R&D capital stocks for G7 and Non-G7 OECD countries are significant at the 1% level. Table 7 shows also a significant impact on labor productivity of foreign R&D capital stocks. Quantifying patent-related spillover effects, the estimated coefficient (0.023) in 4. A possible explanation could be the absorbing effect of foreign GDP as part of the weighting approach and the distortion of foreign business cycle impacts. However, according to the estimates in Table 4 andTable 7, the result of patent-related spillover effects is robust to the patent weighting scheme.

Conclusion

I use international patent applications as a diffusion channel to measure the impact of technology spillover effects on factor productivity. In considering the relationship between research and productivity, the pattern of international patenting reflects the link between the source and the destination of transferred technology. Analyzing a panel data set with 18 OECD countries from 1981 to 2001 by estimation techniques appropriate to data exhibiting nonstationarity and cointegration, I find evidence of patent-related foreign spillover effects.

Moreover, a one percent increase in R&D spending abroad raises labor productivity between 0.08 and 0.14 percent. For Non-G7 OECD countries, the impact on labor productivity is higher due to foreign rather than domestic R&D activities. However, this conclusion should be taken with some care since test statistics are mixed confirming significance. Additionally, estimates show that there is no significant influence on labor productivity from bilateral trade, whereas FDI inflows are confirmed as a major source of technology transfer. Conducting robustness tests, the evidence of patent-related spillover effects on labor productivity is robust to different patent-based weighting scheme. Moreover, randomly assigned weights as a counterfactual to determine foreign R&D are shown to be inappropriate emphasizing the role of foreign patents as a main technology diffusion channel.

Deleted: . ), the expected value of stocks and flows is given by:

* ) 1 ( ) ( S g S E t t + = , * ) 1 ( ) ( F g F E t t + = . (A.2)
Finally, substitution of equation (A.2) in equation (A.1.1) leads to 0 S as the benchmark:

) ( ) ( ) ( 0 g F E S E S t t + = = , 0 = t . (A.3)
Subsequent stock data are given by: [START_REF] Griliches | Issues in assessing the contribution of R&D to productivity growth[END_REF] and applied in [START_REF] Coe | International R&D spillovers[END_REF].

1 1 ) 1 ( + = t t t F S S , T t ,..., 1 = . (A.
The country and time-invariant depreciation rate is assumed to 10%. Table A.1 lists figures in million constant US$ (PPP) for 18 OECD countries. The benchmark relates to the year 1981 for all countries and is calculated following equation (A.3) and the procedure suggested by [START_REF] Griliches | Issues in assessing the contribution of R&D to productivity growth[END_REF]. Depreciation rate is assumed to 10%. Average and annual average growth rates are calculated over the period, where R&D expenditure data was published.

FDI Capital Stock Data

Due to negative figures for some countries at the beginning of the sample, I calculate the average-and annual average growth rates as well as the expected flow by the use of FDI inflow data over the first 10 years. .3). Depreciation rate is assumed to 10%. Average-and annual average growth rates as well as the expected flow are calculated over the first 10 years, where FDI inflow data was published 3) with (4)/(5) and equation ( 3) with (4)/( 5) and ( 8)/(9) from 1981-2001; 14 countries for equation ( 3) with (4)/( 5) and ( 10)/(11) and equation ( 12) from 1981-2001) Equations:

(B) Additional Estimation Results and Tables

(3) with (4)/(5) (3) with (4)/( 5) and ( 8)/(9)

(3) with (4)/( 5) and ( 10 3) with (4)/(5) and equation ( 3) with (4)/( 5) and ( 8)/(9) from 1981-2001; 14 countries for equation ( 3) with (4)/( 5) and ( 10)/(11) and equation ( 12) from 1981-2001) Equations:

(3) with (4)/(5) (3) with (4)/( 5) and ( 8)/(9)

(3) with (4)/( 5) and ( 10 denotes that the coefficient is significantly different from zero at a 10% (5%) [1%] level. All equations include unreported, country-specific constants. The variable G7 acts as a dummy variable, which is equal to one for the seven major countries and zero for the non-G7 countries. Assumption: Lag (2) and Lead (2). a Two test statistics are given by Pedroni ( 2004) based on a pooled Phillips and Perron type test in which the null hypothesis is no cointegration. Regressors are assumed strictly exogenous. Residuals are derived from an OLS estimation. 3) with (4)/(5) and equation ( 3) with (4)/( 5) and ( 8)/(9) from 1981-2001; 14 countries for equation ( 3) with (4)/( 5) and ( 10)/(11) and equation ( 12) from 1981-2001 ) Equations:

(3) with (4)/(5) (3) with (4)/( 5) and ( 8)/(9)

(3) with (4)/( 5) and ( 10 denotes that the coefficient is significantly different from zero at a 10% (5%) [1%] level. All equations include unreported, country-specific constants. The variable G7 acts as a dummy variable, which is equal to one for the seven major countries and zero for the Non-G7 countries. Assumption: Lag (2) and Lead (2). denotes that the coefficient is significantly different from zero at a 10% (5%) [1%] level. All equations include unreported, country-specific constants. The variable G7 acts as a dummy variable, which is equal to one for the seven major countries and zero for the non-G7 countries. Assumption: Lag (2) and Lead (2). a [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] presents four Dickey-Fuller type test statistics with the null hypothesis of no cointegration.

Formatted

  and received by the five leading research nations: United States, Japan, Germany, Great Britain and France. The United States is the dominating source of submitted foreign patents followed by Germany and Japan as shown in Table

  Calculating productivity figures, one can distinguish the number of persons engaged and the number of hours actually worked. I use worked hours as labor input. Figures on labor productivity per hour worked in constant US$ (PPP) are from the Total Economy Database provided by the Groningen Growth and Development Center (GGDC). Figures on TFP are calculated from TFP growth rates provided from the Total Economy Growth Accounting Database by the GGDC.

  OECD also has been publishing patent figures since the early 1980s. As discussed, I use country specific patent data as the main technology diffusion channel. The OECD does not provide bilateral data. Patent statistics published by the WIPO however do. Since 1975, the WIPO offers annual figures on foreign patent application and grants broken down by and for each country (Industrial Property Statistics Publication B Part I). However, figures based on patent applications instead of grants are more reliable and complete. I prefer to use patent applications. Moreover, the WIPO lists patent data for more than 150 years (for at least some countries) and, in addition, for poorer and less developed countries. Incorporating trade-and FDI-related spillover effects to the analysis, figures consist of data published by the OECD in the Monthly Statistics of International Trade and the International Direct Investment Statistics, respectively. To relate domestic R&D capital stocks to , I use figures on import as well as on GDP in million current US$.GDP data (market price, value) is from the OECD Economic Outlook Database. To generate FDI inflow capital stocks, I apply once again the perpetual inventory method. 7 A R&D deflator as well as PPP data converts FDI figures into million constant US$ (PPP). 8 Due to the lack of adequate FDI inflow data over the period 1981-2001, Greece, Iceland, Ireland and Norway are chopped from the pooled sample in the case of FDI-related spillover effects. This reduces the number of observed units to 14 OECD countries.Like[START_REF] Coe | International R&D spillovers[END_REF], I calculate LP and TFP as indexed figures (1995=1). However, due to the index bias of the right hand side regressors in[START_REF] Coe | International R&D spillovers[END_REF] criticized by[START_REF] Lichtenberg | International R&D spillovers: a comment[END_REF], domestic and foreign R&D variables are expressed in levels. Moreover, technology diffusion weights as signified by foreign patent applications (and by bilateral import shares) sum up to one and might indeed have an aggre-

  are three common tests for unit roots on a balance data set: Levin, Lin and Chu (2002) (LLC) tests, Im, Pesaran and Shin (2003) (IPS) tests and the residual-based Lagrange multiplier test by Hadri (2000) (LMH).

  or the Phillips and Perron type tests of Pedroni (2004) does, or the null hypothesis of cointegration, as the residual-based Lagrange Multiplier test by McCoskey and Kao (1998) does. All tests have in common that residuals are derived by estimating the cointegration variables. However, onlyfor tests presented by[START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] andPedroni (2004) can residuals be derived from OLS estimation. For McCoskey and[START_REF] Mccoskey | A residual-based test of the null of cointegration in panel data[END_REF] an efficient estimation technique other than OLS is necessary.Estimation Techniques: Panel-, Fully Modified-and Dynamic-OLSThe presence of cointegration and unit roots considerably affect the asymptotic distributions in time series as well as in panel analysis. However, cointegration equations have attractive properties: as the number of observations increase in T and N, the OLS estimation of the cointegrated variables converges in the long-run equilibrium to the true value. Nevertheless, for moderate sample size, the estimation bias remains substantial due to endogeneity and serial ,[START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] discuss three different estimators: OLS with bias correction, full modified (FM-) and dynamic (D) OLS estimators. While the FM-OLS estimator corrects for endogeneity and serial correlation by modifying and adjusting the dependent variable, the DOLS estimator introduces leads and lags of the differentiated regressors to the estimation.[START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] derive the following limiting distribution: the OLS estimator is normally distributed with non-zero mean, whereas the FM-OLS and DOLS estimators are asymptotically normal with zero mean. They find that the OLS estimator has a non-negligible bias in finite samples and that the DOLS estimator performs better in estimating the panel equations than does the OLS estimator with bias correction or the FM-OLS estimator. As a result, they propose to use the DOLS estimator to accommodate cointegration and unit roots.12

  Spillover Effects for G7 and Non-G7 OECD Countries by DOLS

  . (2004) Panel cointegration: asymptotics and finite sample properties of pooled time series tests with an application to the PPP hypothesis. Econometric Theory 20(3), 597-625. Xu, B., Chiang, E.P. (2005) Trade, patents and international technology diffusion. Journal of International Trade and Economic Development 14(1), 115-135. Xu, B., Wang, J. (2000) Trade, FDI and international technology diffusion. Journal of Economic Integration 15(4), 585-601. WIPO. Industrial Property Statistics Publication B Part I. www.wipo.org.

  Productivity Estimation Results for G7 and Non-G7 OECD Countries by DOLS; Patent-, Trade-and FDI-Related Spillover Effects (Pooled data for 18 countries for equation (

  While DF and t DF are based on the assumption of strict exogeneity of the regressors, of the regressors with respect to the errors. Residuals are derived from an OLS estimation.

Table B

 B is aggregate output, K as capital and L as workforce are input factors and A represents technical change. There are two ways to achieve output growth: either to augment the use of input factors by higher capital investment and labor effort or to increase the efficiency of input factors and therefore A.[START_REF] Coe | International R&D spillovers[END_REF] regard output growth as driven by innovation in the production of intermediate goods based on the[START_REF] Grossman | Innovation and growth in the global economy[END_REF] model. In a simple form, final output Y is produced by an aggregate of intermediate inputs which itself is the result of the use of primary input factors and research activity. Intermediate inputs can be either horizontally differentiated, in which case output growth depends on the measure of available intermediate goods, or vertically differentiated, in which case productivity depends on the quality of inputs. In both cases, aggregate output increases with the usage of intermediate goods.

	where Y
	F o r
	P
	e
	e r
	R e v
	i e
	w
	.4 in Appendix (B) presents data on foreign patent application filled by non-residents from 18 OECD
	countries for 2001.
	7

Thus, the part of output growth which is not attributable to the accumulation of primary inputs is due to R&D investments in the intermediate goods production. Hence, international trade in intermediate goods creates access to foreign technology.

  2 In specifying TFP, susceptible to calculation and measurement errors and estimated coefficients might be less reliable due to inherent biases. Due to the more reliable data on labor input and to a lack of data for an adequate stock of business sector capital, I use labor productivity (LP).Nonetheless, I also list estimates on TFP in section 6.3. as part of the robustness tests. Taking into account the time and cross section dimension, the regression equation for LP is:

	figures are more t i f t i t i f d t i d i t i t i S b S A LP , , , , , , log log log log + + + = =	,
	i ,..., 1 =	N	and	t ,..., 1 =	T	, (2)
	where i is country and t is time index, d t i S , and f t i S , represents domestic and foreign R&D
	F i, is the error term. The term t capital stock and t i b , captures intensity of foreign technology o r diffusion. Note, that the right hand side of equation (
	P
	e
	e r
	R e v
				i e
					w
							8

: LP Deleted: TFP Deleted: LP

	F o r
	P
	e
	e r
	R e v
	i e and calculate the domestic R&D capital stock as described in Appendix A. Turning to foreign R&D capital w
	stocks and their intensity, definitions of f t i S , and t i b , differ according to the channel for tech-
	nology diffusion and are explained in the following subsections.

Deleted

9 Patent-Related Spillover Effects

	Foreign R&D capital stock is defined as the patent weighted average of domestic R&D capital
	stocks from abroad:
		S	i	, f t	S	i	, f t	,	P	=	1 a	ji	, t	j	i	(	a	ji	, t	S	, d t j	)	,	j ,..., 1 =	N	,	(4)
										j	i
	with	t a , as patent application of country j in country i. Note that the ratio of ji	a	ji	t , /	a	ji	t ,
																											j	i
	defines country j's technology diffusion channel to country i.

  10 A GAUSS code for the estimation techniques is freely available on the homepage of Chihwa Kao at Syracuse University, NY: http://web.syr.edu/~cdkao/.

	each i is the same for all units ( = i		), that the error term is a stationary process and that
	units are independent across sections. 11 For unit roots, the LLC test proposes a null hypothesis
	of unit roots or nonstationarity (	H	0	:	=	1	) against the alternative hypothesis that all individ-
	ual series in the panel data are stationary (	H	1	:	<	1	). Relaxing the restrictive assumption of a
	homogeneous	across units assumed by the LLC tests, the IPS test allows for heterogeneous
	autoregressive coefficients. The general IPS setting is based on averaging individual unit
	roots test statistics and assumes that the error term is serially correlated across cross-sectional
	units. The IPS test examines the null hypothesis that each series has a unit root (	H	0	:	i	=	1	)
	against the alternative hypothesis that at least one individual series in the panel is stationary
	(	:	1	F o r	H : 0	stationari	ty	) against the
	P alternative hypothesis of a unit root in panel data (	H : 1	arity nonstation	). All test procedures
	e have in common that a deterministic component, such as an individual and/or time trend, can
	be included. Moreover, their adjusted test statistics obey asymptotically the standard normal e r distribution.
	N	According to Baltagi (2001, p.239): "LLC and IPS tests require N R v e 0 / T , i.	such that
									i e
									w
									Deleted:
									15

1 < i H

). Finally, LMH limits the determination of a variable to a random walk of part of the error term and to a stationary error process. As a result, there is no autoregressive coefficient. The LMH test assumes that each time series is stationary ( e. N should be small enough relatively to T". As a result, in finite samples there are size distortions if N is small or N is large relative to T. Moreover, both tests suffer a dramatic loss of power if time trends are included. Given the fact that classical hypothesis testing ensures that the null hypothesis is rejected only if there is strong evidence against it, I try to overcome this lack of power by testing both nonstationarity as well as stationarity for the null hypothesis.

  To analyze whether the data follows a nonstationary path or not, I apply unit root tests by LLC and IPS as well as by LMH. The null hypothesis is nonstationarity for LLC as well as IPS and stationarity for LMH. Table1shows test statistics and p-values in parenthesis for an individual and time trend. Turning to the null hypothesis of nonstationarity, the LLC and IPS testing procedure do not reject the null hypothesis and therefore confirm nonstationarity for all variables at least at the 10% level in the case of two lags. If there is one lag, the results for the domestic R&D capital stock and foreign R&D capital stock by equation (4) are somehow mixed. Especially for the domestic R&D capital stock, both testing procedure reject nonstationarity. However, turning to the null hypothesis of stationarity, the LMH testing procedure confirms unit roots and nonstationarity for the entire set of data. Given the results in Table1by LMH and by LLC and IPS, especially for two lags, I conclude the all variables are nonstationary. Considering the EC model first, the testing procedure uses the lagged error correction term and analyzes statistical significance by means of the usual t-statistics of the EC model. The t-statistics are significantly different from zero for all , both test statistics reject the null hypothesis and confirm cointegration. Test statistics from[START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] are somehow mixed. Especially for the case of endogenous regressors with respect to the errors, test statistics DF , test results do not reject the null hypothesis of no cointegration for equation (

	Pedroni (2004)
	Test Results for Unit Roots
	o r F o r
	P P
	e e
	e r e r
	R e v R e v
	i e i e	Deleted: 1995
	w w
	model specifications, equation (2) with (4) in combination with technology intensity measures
	(5)-(7), showing that the error term is stationary. Turning to the tests of no cointegration by
	18 19

[Table 1]

Test Results for Cointegration

Once confirmed that the variables are nonstationary and before turning to the empirical results, a regression containing all variables must have a stationary error term in to avoid spurious results. Test procedures based on the EC model as well as on test statistics from Pedroni (2004) and

[START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF]

are in Table 2. * DF and * t

  instead of LP as the dependent variable. Second, I use randomly created weights by Monte Carlo Simulation to calculate foreign R&D capital stocks and to respond toKeller's

	I apply TFP
		Deleted: However, the k
	F o r
	P
	e
	e r
	R e v	Deleted:
	i e
	w
	24

Table Deleted :

 Deleted

	7 is low compared to the corresponding coefficient (0.139) in Table
	F o r
	P
	e
	e r
	R e v
	i e
	w
	26

  (A.3). I calculate the average as well as the annual average growth rate of R&D expenditure by the period, in cases where the OECD has published R&D data in the Main Science and Technology Database. The expected flow is the first year for which the data is available as proposed by

	R&D Capital Stock Data
	By the use of BERD expenditure flows, R&D benchmark stocks ( d i S 0 , for	i	=	18 ,..., 1	) are cal-
	culated according equation
	F o r
	P
	e
	e r
	R e v
	i e
			w
					4)
					32

  The benchmark for FDI inflow stocks ( F PPP). The country and time-invariant depreciation rate is assumed to 10%. TableA.2 lists figures in million current US$ for 14 OECD countries.

	ures into million constant US$ (
	F o r
	P
	e
	e r
	R e v
	i e
		w
	f S , i 0 ,	for	i	=	14 ,..., 1	) for
	each country follows equation (A.3). A R&D deflator as well as PPP data converts FDI fig-
						33

  The benchmark relates to the year 1980 for all countries except for Germany and Sweden with 1981 as the benchmark year. Figures are calculated following equation (A

	Table A.2: FDI Inflow Stock Data
	(FDI Inflow in million current US$)
	FDI Inflow Data	FDI Expected Inflow	FDI Stock
	Available Avg.Growth	Period	Avg.Growth Ann.Growth Exp. Flow	Benchmark
	Australia 1980-2001 97967.582
	Notes:

Table B .1: Unit Root Tests by Levin, Lin and Chu (2002) a ; Im, Peseran and Shin (2003)

 B The null hypothesis is nonstationarity while the alternative hypothesis is that all individual series are stationary with identical (individual) first order autoregressive coefficients. The null hypothesis is nonstationarity while the alternative hypothesis is that some individual series are stationary with identical (individual) first order autoregressive coefficients.

													b
	(Annual data for 18 countries for equation (8)/(9) and for 14 countries for equation (10) from 1981-2001)
	Individual and Time: LLC, Lag (1)	LLC, Lag (2)	IPS, Lag (1)	IPS, Lag (2)
	(8)/(9):	b	M	log	S	f	,	M	-0.403 (0.343)	2.636 (0.996)	-1.04 (0.15)	-0.232 (0.592)
	(10):	log	f S ,	F					3.423 (1)	5.224 (1)	1.54 (0.938)	2.567 (1)
	Notes: Test statistics converge asymptotically to a standard normal distribution. The p-values are in paren-
	theses.

a b

Table B .2: Cointegration Tests by Pedroni (2004) a and Kao (1999) b ; Patent-, Trade-and FDI-Related Spillover Effects

 B (Pooled data for 18 countries for equation (

Table B .3: Labor Productivity Estimation Results for G7 and Non-G7 OECD Countries by DOLS; Patent-, Trade-and FDI-Related Spillover Effects; Depreciation Rate: 5%

 B Test statistics converge asymptotically to a standard normal distribution. The p-values are in parentheses. a Two test statistics are given by Pedroni (2004) based on a pooled Phillips and Perron type test with the null hypothesis of no cointegration. Regressors are assumed to be strictly exogenous. Residuals are derived from an OLS estimation. b[START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] presents four Dickey-Fuller type test statistics with the null hypothesis of no cointegration. (Pooled data for 18 countries for equation (

	DF		1.79 (0.037)	1.787 (0.037)	-2.552 (0.01)	-2.57 (0.01)
	t DF		1.617 (0.05)	1.612 (0.05)	-2.273 (0.01)	-2.294 (0.01)
	DF	*	-2.075 (0.02)	-2.043 (0.02)	-8.074 (0)	-8.144 (0)
	t DF	*	-0.803 (0.211)	-0.797 (0.213)	-3.133 (0)	-3.144 (0)
	Notes: While DF and	t DF are based on the assumption of strict exogeneity of the regressors,	* DF and	t DF	*
	account for endogeneity with respect to the errors. Residuals are derived from an OLS estimation.
				F o r
					P
					e
					e r
						R e v
							i e	Deleted: 1995
							(12) w
						)/(11)
	Pedroni (2004)				Deleted: 1995
	1 PC	-7.314 (0)	-7.304 (0)	-16.839 (0)	-16.864 (0)
	PC	2	-7.138 (0)	-7.128 (0)	-16.434 (0)	-16.457 (0)
	Kao (1999)
							34

Deleted: 1995 Deleted: 1995 Page 34 of 39 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  The bias corrected t-statistics (p-values) of the coefficients (of the cointegration-tests) are reported in parentheses. * (**) [***] denotes that the coefficient is significantly different from zero at a 10% (5%) [1%] level. All equations include unreported, country-specific constants. The variable G7 acts as a dummy variable, which is equal to one for the seven major countries and zero for the Non-G7 OCED countries. Assumption: Lag (2) and Lead (2). Two test statistics are given by Pedroni (2004) based on a pooled Phillips and Perron type test with the null hypothesis of no cointegration. Regressors are assumed to be strictly exogenous. Residuals are derived from an OLS estimation. b[START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] presents four Dickey-Fuller type test statistics with the null hypothesis of no cointegration. While DF account for endogeneity with respect to the errors. Residuals are derived from an OLS estimation.

		Submitted Manuscript
	Tables
		Deleted: 1995
	DOLS: S log G7 log d P S f S , log M S b log F f S , log 2 R Cointegration-Test: d M f , Pedroni (2004) a 1 PC 2 PC	)/(11) 0.039 (1.475) 0.133 (3.415)*** 0.084 (3.637)*** 0.065 (8.413)*** 0.92 F o r P e e r R e v i e w (12) 0.104 (2.83)*** 0.04 (1.543) 0.141 (1.535) 0.137 (3.522)*** 0.129 (2.903)*** 0.079 (3.356)*** -0.05 (-0.16) -0.012 (-0.083) 0.065 (7.855)*** 0.706 0.923 o 0.104 (2.842)*** 0.145 (1.569) 0.144 (3.2)*** 0.693 F r P e -7.346 (0) -7.35 (0) -16.657 (0) -16.71 (0) -7.168 (0) -7.173 (0) -16.256 (0) -16.31 (0) e r
	b No. of Observation Kao (1999) DF t DF * DF * t DF t DF are based on the assumption of strict exogeneity of the regressors, 1.741 (0.04) 1.742 (0.04) -2.684(0) 1.516 (0.06) 1.518 (0.06) -2.342 (0.01) -2.162 (0.02) -2.128 (0.02) -8.229 (0) -0.867 (0.193) -0.857 (0.196) -3.18 (0) 378 378 294 R e v i -2.681 (0) -2.392 (0.01) -8.342 (0) -3.211 (0) 294 e Notes: DF and w
		36

a * DF and * t

Table 1 : Unit Root Tests by Levin, Lin and Chu (2002)

 1 (Annual data for 18 countries from 1981-2001; Observations: 342 with lag (1); Observations: 324 with lag (2) Test statistics converge asymptotically to a standard normal distribution. The p-values are in parentheses. a The null hypothesis is nonstationarity while the alternative hypothesis is that all individual series are stationary with identical (individual) first order autoregressive coefficients. b The null hypothesis is nonstationarity while the alternative hypothesis is that some individual series are stationary with identical (individual) first order autoregressive coefficients. c The null hypothesis is trend stationarity for LMH while the alternative hypothesis is nonstationarity. Assumption: Error term is heteroskedastic across units and serially correlated over time.

	Individual and Time: LLC, Lag (1)	LLC, Lag (2)	IPS, Lag (1)	IPS, Lag (2)	LMH
	log	LP									1.245 (0.89)	3.199 (1)	-0.147 (0.44)	0.259 (0.60)	10.574 (0)
	log	S	d									-4.814 (0)	2.775 (1)	-5.71 (0)	-0.772 (0.22)	8.07 (0)
	(4):	log	f S ,	P					-8.403 (0)	7.972 (1)	3.587 (1)	3.005 (1)	8.914 (0)
	(4)/(6):	b	P	log	S	f	,	P	3.150 (1)	3.802 (1)	2.623 (1)	1.844 (0.97)	8.741 (0)
	(4)/(7):	b	P	log	S	f	,	P	-1.11 (0.13)	-1.358 (0.08)	-0.085 (0.466)	-0.7 (0.24)	10.163 (0)
	Notes:

a ; Im, Peseran and Shin (2003) b ; Hadri (2000) c

Table 2 : Cointegration Tests by the EC Model

 2 Two test statistics are given by Pedroni (2004) based on a pooled Phillips and Perron type test with the null hypothesis of no cointegration. Regressors are assumed to be strictly exogenous. Residuals are derived from an OLS estimation.

	Patent-Related Spillover Effects
	(Pooled data for 18 countries from 1981-2001)
	Equation:	(2) with (4)/(5)	(2) with (4)/(6)	(2) with (4)/(7)
	EC-Model:
	t-statistics of the EC-	-3.62 (0)	-3.74 (0)	-3.63 (0)
	modell
	Pedroni (2004):
	1 PC	-7.579 (0)	-6.286 (0)	-7.510 (0)
	PC	2	-7.397 (0)	-6.135 (0)	-7.329 (0)
	Kao (1999):
	DF		1.462 (0.07)	2.697 (0)	1.603 (0.05)
	t DF		1.404 (0.08)	2.583 (0)	1.4 (0.08)
	DF	*	-2.619 (0)	-0.504 (0.3)	-2.388 (0.01)
	t DF	*	-0.93 (0.176)	-0.202 (0.42)	0.936 (0.175)
						* DF account for t
	endogeneity with respect to the errors. Residuals are derived from an OLS estimation.

a , Pedroni (2004) b and Kao (1999) c ; Notes: Test statistics converge asymptotically to a standard normal distribution. The p-values are in parentheses.

a The first step is to estimate long-run equilibrium values in levels by removing units as well as time effects (transformation for a two-way fixed effects model). The resulting residuals (i.e., error correction term) are used in the second step to estimate the EC model. The t-statistic from the EC model indicates whether the lagged error correction term is significantly different from zero or not. A cointegration relationship amongst variables exits if the t-statistics is significant. Assumption: Lag (1). b c

[START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF]

presents four Dickey-Fuller type test statistics with the null hypothesis of no cointegration. While DF and t DF are based on the assumption of strict exogeneity of the regressors, * DF and

Table 3 : Labor Productivity Estimation Results by OLS with Bias Correction, FM-OLS and DOLS; Patent-Related Spillover Effects

 3 The bias corrected t-statistics are in parentheses. * (**) [***] denotes that the coefficient is significantly different from zero at a 10% (5%) [1%] level. All equations include unreported, country-specific constants. Assumptions for DOLS: Lag (2) and Lead (2).

	(Pooled data for 18 countries from 1981-2001)
	Equation:				(2) with (4)/(5)	(2) with (4)/(6)	(2) with (4)/(7)
	OLS with Bias Correction:
	log	S	d					0.081 (2.796)***	0.194 (6.436)***	0.119 (4.519)***
	b	P	log	S	f	,	P	0.221 (6.496)***	0.430 (1.353)	0.041 (6.322)***
	R	2								0.674	0.616	0.6735
	FM-OLS:
	log	S	d					0.078 (2.558)**	0.2 (6.299)***	0.116 (4.210)***
	b	P	log	S	f	,	P	0.219 (6.133)***	0.505 (1.514)	0.041 (5.947)***
	R	2								0.668	0.613	0.667
	DOLS:
	log	S	d					0.099 (2.58)***	0.19 (4.792)***	0.129 (3.737)***
	b	P	log	S	f	,	P	0.174 (3.90)***	0.449 (1.078)	0.036 (4.248)***
	R	2								0.652	0.6	0.631
	No. of Observation	378	378	378
	Notes:

Table 4 : Labor Productivity Estimation Results for G7 and Non-G7 OECD Countries by DOLS; Patent-Related Spillover Effects

 4 (Pooled data for 18 countries from 1981-2001) The bias corrected t-statistics (p-values) of the coefficients (of the cointegration-tests) are in parentheses. * (**) [***]

	Equation:			(3) with (4)/(5)	(3) with (4)/(6)	(3) with (4)/(7)
	DOLS:
	log	S	d					0.107 (2.89)***	0.158 (4.217)***	0.117 (3.613)***
	G7		log	S	d	0.144 (1.568)	0.204 (2.25)**	0.196 (2.294)**
	b	P	log	S	f	,	P	0.139 (3.072)***	0.629 (1.644)	0.032 (4.014)**
	R	2								0.683	0.657	0.68
	Cointegration-Test:
	Pedroni (2004)	a
	1 PC						-7.314 (0)	-6.664 (0)	-7.783 (0)
	PC	2						-7.138 (0)	-6.504 (0)	-7.596 (0)
	No. of Observation	378	378	378
	Notes:

  The bias corrected t-statistics (p-values) of the coefficients (of the cointegration-tests) are in parentheses. * (**) [***]

										(12)
										)/(11)
	DOLS:
	log	S	d					0.107 (2.89)***	0.104 (2.85)***	0.044 (1.658)*	0.045 (1.689)*
	G7	log	S	d		0.144 (1.568)	0.138 (1.515)	0.128 (3.225)***	0.131 (3.305)***
	log	f S ,	P			0.139 (3.072)***	0.125 (2.819)*** 0.085 (3.574)***	0.082 (3.405)***
	b	M	log		S	f	,	M	-0.008 (-0.025)	0.003 (0.019)
	log	f S ,	F			0.062 (8.403)***	0.062 (7.838)***
	R	2							0.683	0.657	0.919	0.92
	No. of Observation:	378	378	294	294
	Notes:

Table 6 : Unit Root Tests by Levin, Lin and Chu (2002)

 6 The null hypothesis is nonstationarity while the alternative hypothesis is that all individual series are stationary with identical (individual) first order autoregressive coefficients. b The null hypothesis is nonstationarity while the alternative hypothesis is that some individual series are stationary with identical (individual) first order autoregressive coefficients.

	Individual and Time:	LLC, Lag (1)	LLC, Lag (2)	IPS, Lag (1)	IPS, Lag (2)
	TFP:
	log	TFP	0.209 (0.58)	2.531 (1)	-1.278 (0.1)	-0.319 (0.37)
	Random Shares:
	log	f S ,	P	-4.814 (0)	-0.576 (0.28)	-5.71 (0)	-4.46 (0)
	Non Aggregation-Bias:
	log	f S ,	P	-1.533 (0.063)	1.614 (0.95)	-1.343 (0.09)	1.397 (0.92)

a ; Im, Peseran and Shin (2003) b (Annual data for 18 (13) countries from 1981-2001) Notes: Test statistics converge asymptotically to a standard normal distribution. The p-values are in parentheses. a

Table 7 : Productivity Estimation Results for G7 and Non-G7 OECD Countries by DOLS; Patent-Related Spillover Effects

 7 (Pooled data for 18 (13) countries from 1981-2001) The bias corrected t-statistics (p-values) of the coefficients (of the cointegration-tests) are in parentheses. * (**) [***]

								TFP	Random Shares	Non Aggregation-Bias
	Equation:		(3) with (4)/(5)	(3) with (4)/(5)	(3) with 4/(5)
	Dependent Variable:	log TFP	log LP	log LP
	DOLS:
	log	S	d			0.171 (4.94)***	0.134	0.14 (3.51)***
	G7		log	S	d	0.155 (1.5)	0.146	0.218 (2.46)***
	log		f S ,	P		-0.01 (-0.26)	0.085	0.023 (1.7)*
	R	2						0.64	0.69	0.67
	Cointegration-Test:
	Kao (1999)	a
	DF						1.739 (0.04)	-0.636 (0.26)	1.963 (0.02)
	t DF					1.56 (0.06)	-0.704 (0.24)	1.751 (0.04)
	DF		*				-1.4 (0.08)	-6.158 (0)	-1.776 (0.04)
	t DF	*				-0.57 (0.28)	-2.244 (0.01)	-0.72 (0.24)
	No. of Observation	273	378	378
	Notes:

[START_REF] Coe | International R&D spillovers[END_REF] assume a Cobb-Douglas functional form with constant returns and define TFP as output divided by input factors according to their elasticity. To keep the analysis comparable, I assume aggregated output produced by a single input factor.

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

The reader is referred to the paper for further details and discussions.

The 18 OECD countries are respectively: Australia, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Netherlands, Norway, Spain, Sweden, United Kingdom, and USA.

See Appendix (A) for an analytical derivation as well as TableA.1 for further information.

Given depreciation rates for capital stocks between 5% and 15% used in comparable studies, I also run regressions assuming a depreciation rate of 5%. As expected, the results do not change and the main conclusions remain valid. TableB.3 in Appendix (B) lists the results.

University/ New York and CIDE Institution/ Mexico City with special thanks to Jonathan Eaton and to David Mayer-Foulkes and Cermeño Bazán Rodolfo for helpful comments. I also would like to thank two anonymous referees for their remarks. Financial support from the German Science Foundation (DFG) as well as the German Academic Exchange Service (DAAD) is gratefully acknowledged.

Appendix (A) lists specific details on assumptions and methods of calculation. Appendix (B) lists further estimates and tables. All data and calculations are available upon request.

(A) Assumptions and Methods of Calculation

To convert flow figures into stock variable, I use the perpetual inventory method. Suppose the following relationship between steady state stock variable * S and its flow value * F : The last column is the total number of foreign patent applications received by the country in the corresponding row. The United States, for example, is the dominating source of submitted foreign patents followed by Germany and Japan, whereas the number of received foreign patents ranks Spain followed by the UK and Denmark in the first place. Source: Industrial Property Statistics Publication B Part I by WIPO


Marta Pascual
email: marta.pascual@unican.es

David Cantarero
email: david.cantarero@unican.es

INTERGENERATIONAL HEALTH MOBILITY: AN EMPIRICAL APPROACH BASED ON THE ECHP

Keywords: Intergenerational health mobility, Health inequalities, ECHP Intergenerational health mobility, health inequalities, ECHP Intergenerational health mobility, health inequalities, ECHP

published or not. The documents may come

INTRODUCTION

During the last years, population health has been considered as a fundamental aspect in all countries and one of the most important indicators of life quality. In this way, policy makers have an increased interest in social inequalities in health and on those characteristics of individuals that are related to health. Traditionally, population health has been measured through different indicators such as life expectancy, infant mortality, death rates, disability, self-assessed health, happiness or well being. However, health and its outcomes continue being a complex matter and therefore difficult to measure. By this way, individuals' health has being specified as an individual characteristic function based on different inputs [START_REF] Grossman | On the concept of health capital and the demand for health[END_REF][START_REF] Fuchs | Reflections on the socio-economic correlates of health[END_REF]. Thus, one of the most commonly used indicators of individuals' health status is Self-Assessed Health (SAH) which is classified into five categories reflecting negative health rating (bad or very bad health) versus positive or neutral health ratings (very good, good or fair health). In this sense, there exist important relationships between health and socioeconomic status [START_REF] Salas | On the Empirical Association between Poor Health and Low Socioeconomic Status at Old Age[END_REF][START_REF] Adams | Healthy, wealthy and wise? Tests for direct causal paths between health and socioeconomic status[END_REF], between health and lifestyles [START_REF] Contoyannis | Socio-economic Status, Health and Lifestyle[END_REF] and between public health expenditure and SAH status [START_REF] Rivera | The Effects of Public health spending on Self-Assessed Health status: an ordered probit model[END_REF]. On the other hand, different authors have analysed the links between income and health. [START_REF] Mangalore | Income, health and health care utilization in the UK[END_REF] tests that many social and economic factors influence an individual's probability of having a health problem or making use of health care facilities. [START_REF] Cantarero | Effects of income inequality on population health: new evidence from the European Community Household Panel[END_REF] provide new evidence in order to explore the relationship between income inequality and health in the European Union using aggregate data and panel techniques. [START_REF] Wildman | Health and income inequality: attempting to avoid the aggregation problem[END_REF] discuss the aggregation problem when the relationship between health and income inequality is studied.

However, despite the importance of the study of income and health mobility, few attempts have been made to measure intergenerational mobility in the European Union.

Most of the recent papers are focused on the study of income mobility. Thus, Di Pietro et analysing the relationship between the occupational status of parents and their children. [START_REF] Carmichael | Intergenerational mobility and occupational status in Britain[END_REF] examines the link between parents occupational attainment and that of their children using data from the British Household Panel Survey (BHPS) concluding that individual attainment is strongly influenced by parental status in Britain.

In recent papers, some authors have focused their attention on the dynamics of health [START_REF] Hauck | A longitudinal analysis of mental health mobility in Britain[END_REF][START_REF] Jones | Measurement and Explanations of Socioeconomic Inequality in Health with Longitudinal Data[END_REF]). However, health mobility studies are mainly concerned with the evolution over time of individuals' health 1 .

However, empirical analysis of intergenerational health dynamics has not received much attention although there exists evidence suggesting that sons' reported health depends significantly on the SAH of their parents. In this way, [START_REF] Case | The Lasting Impact of Childhood health and Circumstances[END_REF] suggest that health is a potentially important transmission mechanism for the intergenerational correlation of income and education. These authors find that, controlling for parental income, education and social class, children who have poor health also have significantly lower educational attainment, poorer adult health and lower socio-economic status. More recently, [START_REF] Doyle | The Impact of Parental Income and Education on the Health of their Children[END_REF] have investigated the relationship between key parental characteristics of education and income on child health using data from the Health Survey of England.

In this paper, we will focus on intergenerational health mobility in Spain using the information contained in the European Community Household Panel (ECHP). We will use the econometric framework proposed by [START_REF] Solon | Intergenerational Income Mobility in the United States[END_REF] and Zimmermam (1992) 1 [START_REF] Hauck | A longitudinal analysis of mental health mobility in Britain[END_REF] identify whether individuals within different social and economic strata experience differential mobility over time in their respective mental health distributions using the BHPS. [START_REF] Jones | Measurement and Explanations of Socioeconomic Inequality in Health with Longitudinal Data[END_REF] define an index of health-related income mobility as one minus the ratio by which the concentration index for the joint distribution of longitudinal averages differs from the weighted average of the cross sectional concentration indices. The paper is organised as follows. Section two describes the data sources we have used and characteristics of the variables involved in our analysis together with the principal methodological decisions we have taken. In Section three, we describe intergenerational income health from a theoretical and empirical framework and finally, Section four gives a summary and conclusion.

DATA DESCRIPTION

The source of data used in this paper is taken from the ECHP for Spain. This survey contains data on individuals and households for the European Union countries with eight waves available (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001). It was elaborated for the first time in 1994 and it was composed by 60,500 households (approximately 170,000 individuals). In the case of Spain, the first wave was composed by 7,206 households (23,025 individuals).

The variable we use as a proxy of individual's health status is the SAH that each individual reports of their own health status and the possible responses are ordered qualitatively. Thus, SAH variable is a subjective response to the question "How is your heath in general?" and it takes the values "1" (very good), "2" (good), "3" (fair), "4" (bad) and "5" (very bad).

The ECHP is particularly useful for the study of intergenerational health mobility because it provides data on the socio-economic status of both respondents and their The starting point for this analysis of mobility is the existence of information for the same individuals in eight different periods. Thus, it is possible to study correlations in SAH. As an example, FIGURE 1 shows the distribution of SAH (Sons versus Fathers) for year 2001 2 and it suggests the different pattern of this variable. The sample mean age for sons in the first wave is less than 30 (24.11 years old) while the sample mean for fathers is 55. Obviously, sons are observed at an earlier stage of their life cycle. This fact justifies that their mean SAH is lower and the standard deviation of their SAH is higher. Note that lower SAH means better health.

INTERGENERATIONAL HEALTH MOBILITY: THEORETICAL FRAMEWORK

Although there exist different approximations for the study of income mobility [START_REF] Prais | Measuring Social Mobility[END_REF][START_REF] Shorrocks | The Measurement of Mobility[END_REF][START_REF] Bartholomew | Stochastic Models for Social Process[END_REF][START_REF] Hart | The Dynamics of Earnings, 1963-1973[END_REF], there exist few attempts to measure intergenerational health mobility. In this paper, we analyse the level of dependence on inherited conditions and the potential for intergenerational health mobility in Spain. In particular, we study the link between parents' self-assessed health and that of their children.

The basic model is the following:

i i i h h + = 0 1 , ( 1
)
where i h 1 represents self-assessed health for a son in family i, i h 0 the same variable for his father and the correlation between i h 0 and i h 1 , and i is an error term. However, downward biases in the intergenerational correlations are generated because of the use of 2 Similar results are obtained for the other waves. So, the previous model can be extended incorporating age profiles. Thus, son's SAH in year t can be expressed as:

it it it i it A A h h 1 2 1 1 1 1 1 1 1 + + + + = , ( 2
)
where i A 1 is the age of the son from family i. Also, parent's health status in year s can be expressed as:

is is is i is A A h h 0 2 0 0 0 0 0 0 0 + + + + = , ( 3
)
where is A 0 is the age of the father (or mother) from family i in year s. Combining these equations, individual's observed status in year t can be expressed as a regression function of parent's observed status in year s considering age for both parents and individuals.

However, estimates based on averages of several years of data are preferred over those in a cross-section due to the reduction of the effects of transitory variation in the measured variable [START_REF] Solon | Intergenerational Income Mobility in the United States[END_REF][START_REF] Couch | Intergenerational Correlations in Labor Market Status. A Comparison of the United States and Germany[END_REF]. Thus, taking into account the errors in variables bias, we consider average parent's health status over T years, so the model considered is:

i it i i i it it i it A A A A h h 0 1 2 0 0 0 0 2 1 1 1 1 0 0 1 1 ) ( + + + + + = . (4)
One important aspect is the definition of the individuals' SAH. For the sons we have considered the response to the question "How is your health in general?" and it takes the values "1" (very good), "2" (good), "3" (fair), "4" (bad) and "5" very bad. For the In this way, regression analysis is used through specifying an ordered probit model [START_REF] Greene | Econometric Analysis[END_REF]. Results using STATA 8.0. are shown in TABLE 1. Also, we have tested the specification of the models using a RESET test which suggests that the models are not miss-specified. We can observe that there exists a negative and highly significant relationship between son´s SAH and fathers´ health. Thus, if parent's health is good or very good, the probability of the son´s reporting good or very good health is higher. Furthermore, we are interested in the impact of parental health on child health outcomes (controlling by the age), so we are going to compare these results with those obtained including in the analysis other instrumental variables such as household income and parental educational attainment. In fact, there exists a significant and positive effect of income, with children in poorer families having significantly worse health than children from richer families [START_REF] Case | Economic Status and Health in Childhood: The Origins of the Gradient[END_REF].

Our income variable is equivalised annual net household income adjusted using OECD modified scale to take into account household size and composition. In this sense, we have used household information rendering the component family by using equivalence scales. In this case, we use the logarithm of household´s income (OECD modified scale) taking into account the concavity in the health-income relationship [START_REF] Gravelle | How much of the relation between population mortality and unequal distribution of income is a statistical artefact?[END_REF].

The second group of variables are referred to the maximum level of education completed. In the ECHP, education is classified into three categories based on ISCED (ISCED 3) and third level (ISCED 5-7). Thus, a dummy variable which takes value 1 if parental educational attainment is less than secondary level has been included. The econometric model that has been used to deal with these ordered categorical variables is the ordered probit model. However, the coefficients on the explanatory variables in the ordered probit model have a qualitative interpretation [START_REF] Jones | Applied Econometrics for Health Economists-A practical guide[END_REF].

Thus, a positive coefficient means that an individual is more likely to report a higher category of SAH. That is, worse health. On the other hand, a negative coefficient implies individuals are likely to report good or very good health. TABLES 2-3 show the estimates for the ordered probit model obtained using the method of maximum likelihood estimation. These Tables include coefficients and z-ratios. Thus, the qualitative interpretation is that those individuals whose father report good or very good health are more likely to report good or very good health. So, we will say that there exists "Parents' Health Effect". However, we are also interested in the quantitative implications of these results. So, we have considered a new statistical model in which our dependent is a dichotomy variable which takes a value of 1 if the individual (son or daughter) reports good or very good health. As previously, factors such as age, average parents' health and other instrumental variables (household income and education) could be relevant in explaining whether an individual reports good or very good health. In this way, we will use a latent variable interpretation [START_REF] Jones | Applied Econometrics for Health Economists-A practical guide[END_REF][START_REF] Greene | Econometric Analysis[END_REF] 10 Also, we have calculated marginal effects (for the continuous explanatory variables) and average effects (for the binary explanatory variables). On average the probability of a men whose father reports good or very good health is between 5 percent and 10 percent more than for the reference individual (see TABLE 2). Thus, a high value shows individuals' health is influenced by his/her parents' SAH. On the other hand, a low value indicates a very mobile society in terms of health where individuals' health does not depend on his/her parents' ones. Similar results are obtained when we consider mother-son pairs, father-daughter pairs and mother-daughter pairs.

CONCLUSIONS

Despite the importance of the study of health mobility, few attempts have been made to measure intergenerational mobility not only in the European Union but also in other countries such as United States. In this sense, although there exists a growing and new literature on health mobility, we still know very little about intergenerational health mobility.

Therefore, this paper is concentrated on possible intergenerational correlations measuring the link between an individuals' health and his/her parents'. In this paper, sonfather pairs have been considered and we can conclude that those individuals whose parents report good or very good health are most probably to report better health. So, we will say that there exists "parents health effect".

We have studied the impact of both paternal and maternal influences on child health outcomes testing that individuals' health is influenced by their parents' health. We can conclude that on average, in Spain and using the information contained in the ECHP 11 (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001), the probability of an individual whose father reports good or very good health is between 5 percent and 10 percent more than for the reference individual. Thus, the results obtained suggest that although there exists strong influence between personal characteristics (age, gender and household composition), education level, household income and perceived health status, it should be considered the relationship between individuals' SAH and their parents' SAH.

  2003) examine the intergenerational transmission of socio-economic status using data from the 2000 wave of the Bank of Italy's Survey on Household Income and Wealth and

  individual's health on subsequent years as a measure of long term health status. Following these theoretical and methodological approaches, health mobility can be analysed across socio-economic groups, educational attainment and social class group.

  proxies (for instance, using only single-year measures of health) and because of the characteristics of the data[START_REF] Solon | Biases in the Estimation of Intergenerational Earnings Correlations[END_REF]).

  built a dummy variable which takes value one if fathers' response is good or very good health and zero otherwise.

  than secondary level (ISCED 0-2), second stage of secondary level

  through probit models estimated by maximum likelihood estimation. Results for sons and fathers relationships are presented in TABLES 2 and 3.

  Figure 1 Distribution of SAH: Sons versus Fathers. Country: Spain. Year: 2001

Table 1

 1 Ordered probit model estimation. Dependent variable Son's SAH in 2001.

	Year of				Father's SAH					Father's SAH and instrumental variables
	son's	Two-	Three-	Four-	Five-	Six-	Seven-	Eight-	Two-year	Three-	Four-	Five-	Six-	Seven-	Eight-
	SAH	year	year	year	year	year	year	year	average	year	year	year	year	year	year
		average	average	average	average	average	average	average		average	average	average	average	average	average

Table 2

 2 Probit model estimation. Dependent variable Son's SAH in 2001.

	Year of				Father's SAH					Father's SAH and instrumental variables
	son's	Two-	Three-	Four-	Five-	Six-	Seven-	Eight-	Two-year	Three-	Four-	Five-	Six-	Seven-	Eight-
	SAH	year	year	year	year	year	year	year	average	year	year	year	year	year	year
		average	average	average	average	average	average	average		average	average	average	average	average	average
	1994
		0.4750							0.4354
	1995	(3.29)	0.4042 (2.68)						(2.97)	0.3548 (2.32)
		0.4682		0.6512					0.4179		0.6049
		(3.17)		(3.94)					(2.78)		(3.59)
	1996		0.6571 (4.07)		0.5181 (3.34)					0.6111 (3.72)		0.4777 (3.04)
		0.6727		0.5728		0.5370			0.6344		0.5373		0.4729
		(4.28)		(3.63)		(3.40)			(3.97)		(3.37)		(2.92)
	1997		0.3624 (2.47)		0.6277 (3.90)		0.3033 (1.90)			0.3224 (2.17)		0.5794 (3.51)		0.2472 (1.50)
		0.2068		0.5626		0.3337		0.5239	0.1682		0.5081		0.2863		0.4873
		(1.49)		(3.65)		(2.09)		(2.97)	(1.19)		(3.22)		(1.75)		(2.72)
	1998		0.5021 (3.38)		0.3717 (2.34)		0.4449 (2.63)			0.4569 (3.01)		0.3227 (1.99)		0.4028 (2.34)
		0.4404		0.2233		0.2967			0.3882		0.1669		0.2544
		(3.10)		(1.46)		(1.85)			(2.68)		(1.07)		(1.56)
	1999		0.1914 (1.28)		0.1081 (0.70)					0.1338 (0.87)		0.0613 (0.39)
		0.2940		0.2149					0.2324		0.1760
		(2.02)		(1.38)					(1.55)		(1.11)
	2000		0.1859 (1.24)							0.1391 (0.91)
		0.2332							0.1953
		(1.60)							(1.30)
	2001

Note: z-statistics are in

parentheses Page 17 of 18 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i e w 18Table 3

 3 Probit model estimation. Average Effects Dependent variable Son's SAH in 2001.

	Year of				Father's SAH					Father's SAH and instrumental variables
	son's	Two-	Three-	Four-	Five-	Six-	Seven-	Eight-	Two-year	Three-	Four-	Five-	Six-	Seven-	Eight-
	SAH	year	year	year	year	year	year	year	average	year	year	year	year	year	year
		average	average	average	average	average	average	average		average	average	average	average	average	average
	1994
		0.07160							0.0644
	1995	(3.29)	0.0579 (2.68)						(2.97)	0.0489 (2.32)
		0.0679		0.0892					0.0584		0.0805
		(3.17)		(3.94)					(2.78)		(3.59)
	1996		0.0911 (4.07)		0.0760 (3.34)					0.0822 (3.72)		0.0692 (3.04)
		0.0953		0.0824		0.0804			0.0868		0.0764		0.0682
		(4.28)		(3.63)		(3.40)			(3.97)		(3.37)		(2.92)
	1997		0.0560 (2.47)		0.0919 (3.90)		0.0423 (1.90)			0.0491 (2.17)		0.0812 (3.51)		0.0341 (1.50)
		0.0334		0.0852		0.0463		0.0669	0.0266		0.0736		0.0392		0.0619
		(1.49)		(3.65)		(2.09)		(2.97)	(1.19)		(3.22)		(1.75)		(2.72)
	1998		0.0781 (3.38)		0.0514 (2.34)		0.0588 (2.63)			0.0677 (3.01)		0.0440 (1.99)		0.05302 (2.34)
		0.0715		0.0322		0.0414			0.0600		0.0237		0.0352
		(3.10)		(1.46)		(1.85)			(2.68)		(1.07)		(1.56)
	1999		0.0280 (1.28)		0.0159 (0.70)					0.0193 (0.87)		0.0089 (0.39)
		0.0433		0.0308					0.03367		0.0250
		(2.02)		(1.38)					(1.55)		(1.11)
	2000		0.2724 (1.24)							0.201 (0.91)
		0.0344							0.0283
		(1.60)							(1.30)
	2001
	Note: z-statistics are in parentheses

Page 18 of 18 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

Acknowledgements

The authors would like to acknowledge the help given by the Centre for Health Economics (CHE) of the University of York (United Kingdom). Also, we are very grateful for many helpful comments from the participants in the York Seminars in Health Econometrics (YSHE). This work has been partially supported by the Ministerio de Educación y Ciencia (SEJ2004-02810). Finally, the authors acknowledge the financial support of FUNCAS (Fundación de las Cajas de Ahorros). Responsibility for any remaining error lies solely with the authors.