Technology spillovers and International Borders:

Transcription

1 Technology spillovers and International Borders: (A Spatial Econometric Analysis) Amjad Naveed & Nisar Ahmad Department of Border Region Studies University of Southern Denmark January 2013 Abstract The borders of EU are open for the movement of resources but still there can be some strong negative effects of international borders on productivity and knowledge spillovers compared to the internal regional borders. These negative effect could be due to language barriers, cultural differences, local rules and regulation, legal issues, property rights etc. These effects of international borders have economic significance that need to be controlled for analyzing the regional knowledge spillovers. This aspect related to international borders has not been fully taken into account in the literature related to technology spillovers. In this study, we specifically test international border effect on technology and knowledge spillovers. The study implements extended versions of spatial econometric models like Spatial Autoregressive model (SAR) and Spatial Durbin Model (SDM). The results show that there exist close link between productivity and knowledge stock. The productivity effect of both technology and knowledge spillovers are significant for neighbouring regions within the country, while the neighbour regions across international border have statistically insignificant spillovers effect on productivity. JEL Codes: C23, O49, O52, R15 Keywords: Total factor productivity, Knowledge spillovers, European regions, Spatial econometrics, Extended Spatial Durbin Model. 1

2 1 Introduction Regions across international borders characterize differences in institutions, policies and regulations that have economic significance. On the contrary, regions within same country are clearly more integrated: they have more synchronized business cycles, they engage in more extensive risk-sharing, they trade more with each other, their growth rates converge faster, and their inflation rates are more similar (Anderson and van Wincoop, 2001). The borders of EU are open for the movement of resources but still there can be some strong negative effects of international borders on productivity and knowledge spillovers compared to the internal regional borders. For example, these negative effects can be due to language barriers, cultural differences, local rules and regulation, legal issues, property rights etc. These negative effects of international borders have economic significance that need to be controlled for analyzing the regional spillovers. If we assume that there is negative effect of borders then ignoring it will overestimate the spillover effect of technology across international borders and underestimate across regions within country. Neoclassical economic theory has focused on differences in factor endowments across countries (Solow, 1957). However, less attention has been given to the possibility of differences in technology. There is evidence in the literature showing that countries differ in terms of technology and productivity. For example, Islam (1995) and Islam (2003) reported the large differences in productivity among very large sample of countries, while others have shown different rate of technology adoption and differences in human capital stock and institutional quality etc., (see for example, Nelson and Phelps (1965), Acemoglu et al. (2006), Comin et al. (2006) and Comin and Hobijn (2009)). Literature on technology spillovers focuses on the spillover of knowledge across regions, and countries (see, for example, Gong and Keller (2003), Coe and Helpman (1995)). Some recent studies have focused on spillover across firms (see for example, Fischer et al. (2006), Los and Verspagen (2000), Griliches and Mairesse (1983)), and spillover across industries (see, for example, Scherngell et al. (2007), Verspagen (1997), Goto and Suzuki (1989), Griliches and Lichtenberg (1984)). Most of the earlier empirical studies have ignored the issue of spatial dependence except some recent studies (see for example, LeSage and Fischer (2012), Fischer et al. (2007), Scherngell et al. (2007), Bottazzi and Peri (2003), Elhorst (2003) and Bottazzi and Peri (2000)). These studies have shown that geographic location does matter for regional growth performance. Technological advances in one region will affect its neighbouring regions through spillover effect. The methodological point of view, ignoring the spatial aspect will create two problems, spatial dependence and spatial heterogeneity. Ignoring spatial dependence violates the basic assumptions of least square estimates which causes 2

3 the results to be biased and inconsistent, while spatial hetrogenity causes the instability or nonstationarity of economic relationships over space (see for example, Arbia et al. (2005), and Anselin (1988)). In the existing literature on technology spillovers, the spatial dependence related to international borders is ignored. The studies mentioned above have included only overall spatial dependence of the neighbouring regions. They do not differentiate the spatial dependence between the neighbour region within the same country and the neighbour region across the international borders. 1 In the current study, we examine technology spillovers by controlling two types of spatial dependences specific to internal and international borders respectively. Few studies in general have incorporated two types of spatial dependences, (Lacombe (2004), Badinger and Egger (2011)). For example, Lacombe (2004) examined two types of spatial dependences, first, between counties within a state and second, between counties in adjacent states for the US. The study analyzed the effect of public policy like Aid to Families with Dependent Children and Food Stamp payment on female headed household and female labour force participation. The results show that there is strong spatial dependence for both within state and between states that confirms the biasedness and inconsistency of least square estimates. However, these studies though do not consider technology spillovers. The aim of current the study is to identify the impact of international borders on knowledge spillovers that spread across regions in EU. The neighbour regions are divided into two categories. First is Internal Regions, defined as neighbour regions within the same country and second is Border Regions, defined as neighbour regions across the international borders. Then for each type of regions, two types of spillovers are analyzed i.e. Local Spillovers, (measured as spatial lag of independent variable(knowledge)) and Global Spillovers, (measured as spatial lag of the dependent variable (technology)). 2 The important contribution of this paper is to identifying the border effect on technology and knowledge spillovers, which not has been fully discussed in the literature related to technology and knowledge spillovers. Table 1 summarizes the division of regions and their spillovers respectively. We used European Patent Office(EPO)application stock as a measure of the knowledge spillover and total factor productivity (TFP) as a measure of technology. The study implements extended versions of spatial econometric models like Spatial Autoregressive model (SAR) and Spatial Durbin Model (SDM) by using maximum likelihood method of estimation. The extended versions of SAR and SDM models simultaneously incorporate two types 1 Some trade studies have shown that trade reduces significantly between region across international borders; see for example Millimet and Osang (2007) and Krugman et al. (2011). 2 Local and global spillovers are analyzed for both internal and border regions. 3

4 Table 1: Regions and Spillovers Internal Region Border Regions Local Spillovers Spatial lag of Knowledge Spatial lag of Knowledge (independent variable weighted by (independent variable weighted by internal neighbour regions) border neighbour regions) Global Spillovers Spatial lag of Technology Spatial lag of Technology ( dependent variable weighted by (dependent variable weighted by internal neighbour regions) border neighbour regions) of neighbouring regions internal and border. NUTS-2 level regional data of EU is used for the analysis. The regions in NUTS-2 level are varying in size and widely viewed as the most appropriate unit for modelling and analysis. 3 The final database consists of 204 regions for 16 EU countries over the period of Among these 204 EU regions, 86 regions share a border of a region in a neighbouring country. These regions are important to identify the border effect of the spillovers among EU countries. The results show that there exist close link between productivity and knowledge stock. The productivity effect of both technology and knowledge spillovers are significant for neighbouring regions within the country, while the neighbour regions across international border have statistically insignificant spillovers effect on productivity. The remainder of the paper is organized as follows. Section 2 reviews some of the earlier studies related to the current study. Section 3 presents the empirical model which relates total factor productivity as an approximation of technology to the region s knowledge stock by using Cobb Douglas production function. This section also explains the spatial econometrics methodology used in the paper. Section 4 describes the data and provides detailed about construction of variables, capital stock, knowledge stock and the TFP index. Section 5 reports the estimation results. The last section of the paper offers some concluding remarks. 2 Literature Review There is a considerable debate in the literature about technology and its spillover. In this section we will review some important studies in the literature related to the current study. A country level panel study by Madsen (2007) on technology spillover and total factor productivity (TFP) convergence found that knowledge spillovers is an important contributing factor behind the TFP convergence among OECD countries. The study was conducted 3 For detail see, Fischer et al. (2006), Fischer et al. (2007),and LeSage and Fischer (2012)etc. 4

5 without incorporating the spatial dimension of the countries, but gives an important evidence of spillovers. A study by Coe and Helpman (1995) focuses on the analysis that a country s productivity level not only depends on domestic R&D capital stock but also on R&D capital stocks of foreign trade partners. Their sample consists of 21 OECD countries plus Israel during the period of 1971 to By using pooled data they found that both domestic and foreign R&D capital stocks have important effects on total factor productivity. More specifically, their results explain that the countries with larger share of import to GDP have stronger effect of foreign R&D capital stocks on their domestic productivity. It concludes that more open economies can get larger productivity benefits from foreign R&D capital stock than less open economies.there exists the evidences of spillovers across borders but without differentiating it s effect from internal and border regions. Another study based on 15 Korean manufacturing industries by Kwon (2003) analyzed the role of R&D on total factor productivity during the period of They tested the hypothesis that productivity in one industry depends not only on its own R&D but also on R&D of other neighbouring industries. Furthermore, they also performed a comparative analysis of the role of R&D spillover effects in advanced economies with developing countries. The main finding of this study is that the rate of return to own R&D in Korea is higher than that in the developed countries, but the rate of return to R&D spillovers is less than advanced economies. A study by Scherngell et al. (2007) highlights the contribution of research and development on regional productivity that spread across manufacturing industries. They used a panel of 203 NUTS-2 regions covering 15 EU countries over the period of According to their results interregional knowledge spillovers and their productivity effects are geographically localised. Furthermore, there exists some level of heterogeneity across industries with evidence that two industries (electronics, and chemical industries) produce interregional knowledge spillovers that have significant positive effect on productivity. Moreover, the study also confirms the presence of spatial dependence in the disturbance term. Both spatial dependence and spillover effect exists from neighbouring regions at industry level. In a different type of study by LeSage and Fischer (2012) analyzed the dynamic and static knowledge externalities on regional TFP for 198 regions of 15 EU countries at NUTS- 2 level. Where, dynamic externalities are related to the prior period knowledge and current level of innovation, while static refers to current period scale only. The study resulted in three important findings. First, regional TFP depends on its own knowledge capital (direct 5

6 impact), as well as that of other nearby regions (static externalities). Second, direct impacts are important, but externalities (knowledge spillover effects) are more important. Because they found that external effects are three times the magnitude of the direct effects. Third, a productivity effect from neighbouring knowledge stocks is important for technological dimension which they attribute to the notion of dynamic externalities. In summary they found that dynamic externalities may have a larger magnitude of impact than static externalities and there exists spatial dependence between productivity and knowledge stock at regional level. Liberto and Usai (2010) tested TFP convergence at regional level for EU countries. This study is based on 199 regions in EU 15 plus two countries Norway and Switzerland over the period of They used different estimation procedure, like LSDV, Spatially corrected LSDV and GMM Arellano and Bond method, for the robustness of the results. Their results confirms that there is persistent level of TFP heterogeneity exists across EU regions. They also found that distance is increasing between high growth and low growth regions. Furthermore, the finding suggests that there is increment in the cluster of low growth TFP regions. Overall there is no convergence in TFP but spatial dependence exists in EU regions. It is important to analyze why there is cluster of low growth TFP regions. Fischer et al. (2007) analyzed the interregional knowledge on TFP for the panel of 203 EU regions over the period of They used random effect panel data with spatial error model. They measured the knowledge elasticity effect within regional Cobb-Douglas production function framework, with special focus on knowledge spillover. The results of their study show that region s total factor productivity not only depend on its own knowledge capital, but also on cross-regional knowledge. There is spatial dependence, as distance decreases the spillover effect increases but that distance do not incorporate the borders between the EU regions. A study by Elhorst (2010) used SDM to incorporate both the spatial lag of independent variables and spatial lag of dependent variable. The paper is based on new introductory book on spatial econometrics by LeSage and Pace (2009).The study mentioned two reasons for using the spatial Durbin model. First, it is the only means of producing unbiased coefficient estimates, even if the true data-generation process is a spatial lag, spatial error, Kelejian-Prucha or spatial Durbin error model. Second, it produces both global and local spillover effects. Moreover, it does not impose prior restrictions on the magnitude of these effects. Therefore, we will also apply the extended version of a spatial durbin model in the current study for analyzing the local and global spillovers. The above literature highlights the importance of technology spillover across regions. But 6

7 these studies do not differentiate between internal regional spillovers (spillover from neighbouring regions with in the country) and spillover spillovers from border regions (neighbouring regions across the international border). In the present study we are focusing on these issues in detail. 3 Methodology In this section we will develop our methodology to address our empirical question. We will start with regional Cobb Douglas production function and then we will discuss spatial econometric analysis with reference to the neighbouring regions in the same country and for neighbouring regions across international borders. 3.1 Technological Production Function We start with the traditional neoclassical Cobb Douglas type production function for region i. Q i = AL α i C β i e(ɛ i) (3.1) Where Q is output for region i, L is the labour stock of the regions, C is a measure of the physical capital stock and ɛ is the error term. α and β, are the elasticities of output with respect to labor and captial respectively. Following Griliches (1979), and Griliches (1986), if we add the stock of knowledge (or innovations) K in the above production function then we have, Q i = AL α i C β i Kγ i eɛ i (3.2) Where γ is elasticity with respect to the stock of knowledge (innovations) in region i. Many studies have shown that the innovation in particular region is not only effected by the innovation in that region but also the innovations in its neighbouring regions. 4 If we assume that knowledge of neighbouring regions j also affect (spillovers to i) the productivity in region i, then the above production function can be written as follows, Q i = AL α i C β i Kγ i γ 1 Kj e ɛ i (3.3) i j K= W K 4 For detail see Fischer et al. (2006), LeSage and Fischer (2012), Fischer et al. (2007). 7

8 Where K is the stock of knowledge in all neighbouring region j, W is spatial weight matrix representing neighbour regions and γ 1 is elasticity with respect to stock of knowledge (innovations) in neighbouring region j. It is also known as local spillovers in the literature. Earlier studies, mentioned in section 2, have assumed that the spillovers effect of knowledge and technology from neighbouring region is homogeneous for internal and border regions. Some other studies related to trade and labour mobility have found the negative effect of borders but as for as we know no study has explored the border effect associated to knowledge and technology spillovers. 5 If there is negative affect of international borders on spillovers then we might be underestimating the spillovers effect for internal regions and overestimating the effect for border regions. Identifying the border effect is important addition in the literature. Therefore, if we allow the hetrogenous spillovers effect of knowledge for internal and border regions then the production function can be written as follows, Where, Q i = AL α i C β i Kγ i γ 1 γ 2 K i j K= W 1 K K= W 2 K j,a Kj,b e ɛ i (3.4) K is the stock of knowledge (innovations) in the neighbouring regions j within the same country and K is stock of knowledge (innovations) in the neighbouring regions across international borders.w 1 is the spatial weight matrix representing neighbour regions with in the same country and W 2 is the spatial weight matrix representing neighbour regions across the borders. α, β, γ, γ 1 and γ 2 are the elasticities of output with respect to labour, capital, innovations in the same region, innovations in the neighbouring regions within the country and innovations in the neighbouring regions across the international border respectively. 6 ɛ is the error term. If we divide the equation (3.4) by factor share weighted physical capital and labour, then after taking log transformation we have; ln(q i ) αln(l i ) βln(c i ) = ln(a) + γk i + γ 1 Kj,a +γ 2 Kj,b +ɛ i (3.5) we are expecting that the elasticities γ, γ 1 and γ 2 will be different and need to be tested. According to Solow (1957) residual, total factor productivity (TFP) is given as follows: ln(q i ) αln(l i ) βln(c i ) = T F P i (3.6) 5 See for example, Millimet and Osang (2007) and Krugman et al. (2011). 6 a and b representing the neighbour regions with in the country and across the international borders respectively. 8

9 If we assume ln(a) = a and substitute for TFP in equation (3.5) then we obtain the following equation for estimation purpose: T F P i = a + γk i + γ 1 Kj,a +γ 2 Kj,b +ɛ i (3.7) The detail about construction of TFP, physical capital stock, and knowledge stock is given in section 4. For spatial analysis we have to use the weighted TFP as regressors. The discussion on spatial econometric models is presented in next section. 3.2 Spatial Dependence in Technology As we are dealing with the data which is distributed into pre-defined spatial regions. One can observe that technological advancement in one can be affected by the technological advancement in neighbouring regions. We start this concept by the statement of Tobler (1970) Everything is related to everything else, but closer things more so. Simply we can say what happens in one region is related to what happens in neighbouring regions but the regions with in the country matters more than the regions across the international borders due to various reasons. 7 Spatial Autocorrelation is an assessment of the correlation of a variable in reference to spatial location of the variable. Anselin et al. (1996) define positive spatial correlation by high or low values tending to cluster in space for a random variable and negative spatial correlation by the locations then to be surrounded by neighbours with very dissimilar values. If there is any systematic pattern in the spatial distribution of a variable Y, it is said to be spatially auto-correlated. Random pattern in spatial distribution exhibits no spatial autocorrelation. But the level of spatial autocorrelation could be different for internal and border regions. For example, if Y i and Y j are realization of random variable Y index by spatial location (i, j), then we have spatial autocorrelation if Corr[Y i, Y j ] 0 Tests for Spatial Dependence The first step before applying any spatial model is to test the spatial autocorrelation. Does the data exhibit the spatial autocorrelation or not? There are number of statistical tests that can be used to detect the presence of spatial autocorrelation in the residuals from a least-squares model( for detail discussion see Anselin (1988) and LeSage (1998)). The 7 The reasons could be language barriers, cultural differences, local rules and regulation, legal issues, property rights etc. 9

10 popular test in spatial econometrics is Moran (1996) I test that can be used for particular data set X (or residual). I = R Σ i Σ j W ij Σ i Σ j W ij (X i X)(X j X) Σ i (X i X) 2 I = R N Σ i (X i X)W ij Σ i (X j X) Σ i (X i X) 2 (3.8) Where N = Σ i Σ j W ij and R is the number of spatial unit indexed by i, and j. X is the variable of interest, X is mean of X and W is spatial weight matrix. Null hypothes is: no spatial autocorrelation and Moran s I statistics is asymptotically normal. The detail of other tests are given in appendix. Weight Matrix Which regions are spatial neighbours of a given region? Weight matrix is used to define the spatial neighbours. W ij = 1 or 0 W ij = W ij / W ij (row standardization) In a simple binary weight matrix the elements of the neighbour is equal to 1 if regions i and j are neighbour of one another and zero otherwise. The diagonal elements of W matrix are zero, which implies that we do not have the circular specification that region j on the left is influenced by the same region j on the right. There are number of ways to construct the weight matrix define by LeSage (1998) and Arbia et al. (2005). 8 In the current study we use Contiguity-based neighbourhood to define the neighbours of a particular region since we want to identity the effect of international borders. After defining neighbour and construction of weight matrix, we are in a position to focus on spatial econometrics. 3.3 Spatial Autoregressive (SAR) and Spatial Durbin Models (SDM) The basic SAR model is formulated in the following equation. Y = ρw Y + Xβ + µ (3.9) Where Y (n 1) is a vector of endogenous variable that represents technology in the current study. X is (n k) matrix of exogenous variables which includes knowledge stocks, some dummy variables for language and location, parameter β is (k 1) vector and µ is iid(0, σ 2 I) vector of disturbance term. W is spatial weight (n n) matrix (typically with zero diagonal), ρ is autoregressive parameter and W Y combined is a spatial lag of Y variable. If 8 See appendix for detail. 10

11 ρ is equal to zero then OLS is a special case of SAR model. The presence of Y on both sides means correlation between errors and regressors and the resulting estimates from OLS will be biased and inconsistent. As LeSage (1998) point out two problems that arises when sample data has a locational component. First is spatial dependence between the observations (already discussed above) and second is spatial heterogeneity in the relationships we are modelling. 9 One can easily find the reduced form for estimation. Y = ρw Y + Xβ + µ Y ρw Y = Xβ + µ Y = (1 ρw ) 1 Xβ + (1 ρw ) 1 µ Now consider (1 ρw ) 1. If ρ < 0, then this can be extended as power series, (1 ρw ) 1 Xβ = 1 + ρw + ρ 2 W 2 Xβ + ρ 3 W 3 Xβ + (3.10) Think of the series W, W 2 and W 3 etc. W is the spatial weights of the neighbours of a given region. W 2 is the weights of the neighbours of the neighbours, W 3 is the weights of the neighbours of the neighbours of the neighbours, etc. So (1 ρw ) 1 Xβ is the sum of a series of decreasing influences of the entire spatial units, means decreasing intensity as we move further away from the center. This known as Global Spillovers from neighbour regions. The model is non-linear and reduced form of the model can be estimated by using maximum likelihood method. When we add the spatial lag of the dependent variable Y (for global spillovers) as well as a spatial lag of the explanatory variables matrix X (for local spillovers) into the traditional least-squares model, then it is known as the Spatial Durbin Model (SDM) as given below. 10 Y = ρw Y + βx + γw X + µ (3.11) Where ρ (autoregressive parameter) captures the effect of global spillovers and γ (parameter of spatial independent variable) captures the effect of local innovation (knowledge spillover from neighbouring region). 9 Spatial heterogeneity refers to variation in relationships over space, for detail see LeSage (1998). 10 Apart from potential problems of multicollinearity (recall that row-wise, X and WX are for different regions because the diagonal elements of W are zero), this model poses no problems for us. 11

12 3.4 Extended Versions of SAR and SDM Models In current study we are using the extended versions of the basic SAR and SDM models which incorporate two types of spatial dependences. First, spatial dependence through neighbouring regions within the country, represented by W 1 weight matrix. Second, spatial dependence through neighbouring region across international borders represented by W 2. The attractiveness of using two weight matrices is that we can analyze the policies and spatial dependence that varies across countries. Furthermore, it is also important to explore the net border erffect in spatial dependence as border effects differs over intranational and international prospectives. The extended SAR model with two weight matrices can be represented by the following equation. Y = ρ 1 W 1 Y + ρ 2 W 2 Y + βx + µ (3.12) Where, Y is (n 1) vector of dependent variable representing technology, W 1 and W 2 are (n n) spatial weight matrices, ρ 1 and ρ 2 are spatial parameters. X is (n k) matrix of exogenous variables and µ is traditional disturbance term. If ρ 1 and ρ 2 are zero then traditional linear model is appropriate. There are two important motivations for using two different matrices discussed by LeSage and Pace (2012). First is that additional weight matrix capture more elaborate types of nonspatial dependence. Second motivation is the mistaken belief that change in the spatial weight matrix will change the marginal effect estimates and inferences. A small change in the W will not affect the marginal effects estimates and inference and hence spillover associated with additional weight matrix can be separately analyzed. In order to analyze the specific border effect it is very important to use two different weight matrices. The reduced from of the extended SAR model with two matrices can be derived as follows: Y = ρ 1 W 1 Y + ρ 2 W 2 Y + Xβ + µ Y ρ 1 W 1 Y ρ 2 W 2 Y = Xβ + µ Y = (1 ρ 1 W 1 ρ 2 W 2 ) 1 Xβ + (1 ρ 1 W 1 ρ 2 W 2 ) 1 µ (3.13) The maximum likelihood method is required to estimate the parameters of extended SAR model in the following form: 12

13 Y ρ 1 W 1 Y ρ 2 W 2 Y = Xβ + µ u = (1 ρ 1 W 1 ρ 2 W 2 )Y Xβ L(β, σ, ρ 1, ρ 2 ) = (2πσ 2 ) n 2 1 ρ 1 W 1 ρ 2 W 2 exp( 1 2σ 2 µµ) (3.14) The extended version of SDM model with two types of weight matrices can be represented by the following equation. Y = ρ 1 W 1 Y + ρ 2 W 2 Y + βx + γ 1 W 1 X + γ 2 W 2 X + µ (3.15) Where β captures the effect of regional stock of knowledge, parameters γ 1 captures the effect of knowledge stock in neighbouring region with in the country, γ 2 captures the effect of knowledge stock in neighbouring region across the borders, ρ 1 captures the effect of technology in neighbouring region with in the country and ρ 2 captures the effect of technology in neighbouring region across the borders. The summary of the terminologies used for spillovers is shown in table 1 and also figure in appendix. 4 Data and Variables This section explain the construction of important variables we use in this study i.e. capital stock, knowledge stock (derived from European Patent Office (EPO)), and Total Factor Productivity (TFP) index. Beside that we used language dummy for common language (Germon speaking) countries which allow us to analyze the impact of language on spillovers across borders, we also used the scandinavian dummy for analysing the impact of scandinavian countries. Furthermore, we used GDP per capita, labour force, populatioan, investment share to GDP in the construction of capital stock and TFP index. Our cross sectional database consists of 16 EU countries and 204 regions at NUTS-2 level, over the period of 1999 to Among these 204 EU regions there are 86 regions that share the border of neighbour countries. 11 These regions are important to analyze the cross border effect among countries. The NUTS-2 level that is adopted by the European Commission for their evaluation of regional growth process. These regions vary in size and widely viewed as the most appropriate unit for modelling and analysis purposes. The Appendix describes the complete sample of regions used in this study. We used two important sources for database. First is Cambridge Econometrics and second is Eurostat. 11 The map of regions used in this study are reported in the Appendix figure 2 and figure 3. 13

14 Construction of Capital Stock There are several methods to compute capital stock. The detail discussion can be found in Neruh and Dhareshwar (1993) and King and Levine (1994). The first method is known as direct method, which consists of an evaluation of the stock of physical capital through direct surveys. This method is more expensive, and it may not provide the accurate measure in the presence of disinformation on rental and second hand prices. The second method is uses the actual book values of capital items. This method is also not appropriate, since it depends on the actual book values of capital items which are sensitive to the tax schedules of individual countries. The third method is indirect perpetual inventory method which is used in this study. The data on physical capital stock is not available for all the regions and years, but gross fixed capital formation is. Therefore, by using perpetual inventory method, we generate the capital stock variable. 12 Construction of Knowledge (Innovation) Stock For knowledge or innovation stock, the R&D expenditure were the most common choice among empirical researchers, but suffers from the problem of double counting because of special fiscal rules in favor of R&D spending (Fischer et al., 2006). Therefore, we use patent counts as a proxy for the knowledge or innovation stocks as it is more closely related to a stock of knowledge than R&D expenditures. 13 The patents data were derived from EPO which provides the information on the inventors share, his or her name and address, the company or institution to which property rights have been assigned, citations to previous patents, and a description of the device. The data on EPO is not available in stock form. Therefore, for each region i, patent stocks were derived from the patent data, using the perpetual inventory method. Following Caballero and Jaffe (1993) and LeSage and Fischer (2012), we used a constant depreciation rate 12 percent that corresponds to the rate of knowledge obsolescence in the United States for the year For initializing the EPO we use the same way as physical capital. 14 Measurement of Total Factor Productivity The technology growth cannot be measured directly, but using the growth accounting method, we can measure it indirectly as the growth of unobservable factor i.e., growth of residual of total factor productivity (TFP). There are basically two methodologies to compute the total factor productivity i.e. the growth accounting and the regression based method. The growth accounting is an empirical method, which decomposes the growth rate of output to 12 For details see Neruh and Dhareshwar (1993) and King and Levine (1994). 13 For detail see Robbins (2006), Fischer et al. (2006) and Fischer et al. (2007). 14 We are thankful to Dr.Timo Friedel Mitze for giving access to the EPO data and for helping us generating EPO variable. 14

15 its components such as growth in inputs and the technological progress (TFP growth). The regression method involves econometric estimation but this method lacks time variations in factor shares and the total factor productivity. Therefore, we prefer to use growth accounting approach for this study. Consider the following aggregate production function: Y t = F (A t, K t, L t ) (4.1) Here Y t, A t, K t, and L t are output, technology, capital and labor respectively. If the technology is Hicks-neutral then we can write production function as follows, and Y t = A t F (K t, L t ) (4.2) A t = Y t /F (K t, L t ) (4.3) The after taking log and differentiating it with time we will get: ln(a t /A t 1 ) = ln(y t /Y t 1 ) F kk t ln(k t /K t 1 ) F ll t ln(l t /L t 1 ) (4.4) Y t Y t In the above equation coefficients of each growth rates are the respective shares or elasticities. Total share of labor and capital must be equal to one and if share of capital equal to α then share of labor will be (1 α) labor. The above equation then can be written as follows, ln(a t /A t 1 ) = ln(y t /Y t 1 ) αln(k t /K t 1 ) (1 αln(l t /L t 1 ) (4.5) The above equation is used to construct the TFP for this study Summary of Weight Matrices We are using contiguity based weight matrix to define neighbourhood as described in section 3. The summary of the weight matrix with their number of links (neighbours) are reported in table 1. There are 924 neighbour links in total and out of them 182 links are related to international borders for 86 border regions. The remaining 742 links are for regions within the same countries Solow (1957) used this method to calculate total factor productivity for American manufacturing sector and concluded that more than 80 percent of the growth is due to the technical progress. 16 The links of neighbour regions are shown in Appendix figure 4. 15

16 Table 2: Weight Matrices Summary Neighbour Definition Non-zero links Average links Internal Regions Border Regions All Regions Results This section describes the results related to technology spillovers and international borders. The dependent variable is technology (measured by Total Factor Productivity) and the independent variables include stock of knowledge (innovation), its spatial lag and spatial lag of technology. 17 There are two types of spillovers analyzed in this study. First is the knowledge spillover that is captured through spatial lag of knowledge stock (also known as local spillovers) and second is technology spillovers that is captured through spatial lag of dependent variable (also known as global spillovers). Before estimating any spatial model we have to tests the spatial dependence. In particular, four different tests for spatial dependence are considered (described already in section 4). The first is the general purpose Moran s I test which does not admit an explicit alternative hypothesis to contrast the null. The other three tests are LM, LR and Wald that consider the spatial models as an alternative to the hypothesis of spatial independence (Arbia et al., 2005). In computing all these tests we assumed contiguity based weight matrix. The results of Moran s I, LM, LR and Wald tests are presented in Table 1. Where Y represents TFP and X is stock of knowledge (EPO), W is a weight matrix for all neighbour regions, W 1 is a weight matrix for neighbour regions with in the country and W 2 is a weight matrix for neighbour regions across the borders only. All tests lead to the rejection of the null hypothesis except for the border regions. These results give the strong indication of spatial dependence in the residuals, which means we have to consider the spatial Models as alternative specifications to the classical linear regression model. Another important signal from these tests is that border regions are not spatially dependent. After testing the spatial dependence we are in a position to employ the spatial analysis. The cross-sectional results of the spatial models for year 2008 are reported in table 3 together with their t-values. 18 First column reports the results of conventional regression 17 We also used language dummy for German and a dummy variable for Scandinavian countries. 18 We also have estimated the same models separately from 1999 to 2010 and the results are available on request. 16

17 Table 3: Test Results of Spatial Depedence Moran I M-I-Statistics P-Value (Y, c, W ) (Y, c, W 1 ) (Y, c, W 2 ) LM value P-Value χ 2 at 1% (Y, X, W ) (Y, X, W 1 ) (Y, X, W 2 ) LR value P-Value χ 2 at 1% (Y, X, W ) (Y, X, W 1 ) (Y, X, W 2 ) Wald value P-Value χ 2 at 1% (Y, X, W ) (Y, X, W 1 ) (Y, X, W 2 ) model (OLS) as a benchmark to compare the possible bias with other estimates. The remaining results from column 2 to 9 are based on spatial models. 19 These models are estimated via maximum likelihood methods using pseudo likelihood definition and the approximate non-linear maximization method. The results from OLS regression show that own regional knowledge stock (EPO) affects productivity and the parameter estimate is statistically significant with value However, these results are not reliable since there is spatial dependence in the residuals. Column 2 and 3 reports the results of SAR and SDM models for all regions respectively. The SAR and SDM specification are estimated based on equation 3.12 and 3.14 respectively. In SAR model, the parameter estimate of own knowledge stock is slightly improved to 0.48 compared to OLS estimate. The coefficient of spatial autocorrelation (ρ) is statistically significant with the value of 0.44, which confirms the impact of global technology spillovers. In order to captures the local knowledge spillover we estimated SDM model reported in column 3. The estimate for local knowledge spillover is which is highly significant, suggesting that the innovation in neighbouring region significantly affect the productivity level of any region. 19 The available software (MATLAB) allows the SAR, SEM, SDM and Extended SAR and ESDM models. We are thankful to Dr.James P. LeSage and Dr.Donald J. Lacombe for providing the spatial econometrics toolbox for estimating Extended SAR and SDM models. Some of them are available on 17

18 Table 4: Estimation results Year 2008: Technological transfer and International borders Spatial Auto-Regressive Model Extended Spatial Models Variables All Regions Internal Regions Border Regions (W 1 &W 2 ) OLS SAR SDM SAR SDM SAR SDM ESAR ESDM constant (5.290) -(4.032) -(5.452) -(4.233) -(5.378) -(5.358) -(5.358) -(4.401) -(5.858) EPO (4.220) (3.429) (0.966) (3.599) (1.010) (4.274) (4.274) (3.666) (0.923) W EP O (4.293) W 1 EP O (4.006) (4.072) W 2 EP O (1.044) (1.049) ρ(all neighbours) (5.995) (5.984) ρ 1 (Internal Regions) (6.763) (6.835) (7.159) (7.440) ρ 2 (Boder Regions) (0.761) -(0.761) -(0.644) -(0.416) SAR: Spatial Auto Regressive Model SDM: Spatial Durbin Model ESAR: Extended Spatial Auto Regressive Model SDM: Extended Spatial Durbin Model Bold value represent significance at 1% level of significance 18

19 In the same SDM model the spatial autocorrelation coefficient is also significant with the value of 0.434, again confirms the global technology spillover. However, the estimate of own knowledge stock becomes statistically insignificant when we add the spatial lag of knowledge stock variable. One possible reason could be that multiple spillovers come from neighbour regions that affect more than own regional knowledge stock. This result is consistent with earlier studies, e.g., LeSage and Fischer (2012) also found that the external knowledge effect is three times bigger than own knowledge stock on productivity. 20 Another possibility could be that there is higher effect of inter-regional knowledge on productivity than its own stock of knowledge due to the free and easy mobility of resources across the regions within the same country. It also confirms the importance of innovation in neighbour regions. In order to identify the impact of knowledge and technology spillovers for neighbour region within the same country and for neighbour regions across international borders, we estimated models separately for internal and border regions, which is an important contribution of this study. The columns 4 and 5 reports the results for internal regions (neighbour regions within the same country) based on SAR and SDM respectively. The parameter estimate of global technology spillovers is 0.443, which is almost same as estimated for all regions in column 2 but the estimate of own knowledge stock is slightly improved to The results of SDM for internal regions show that the productivity effect of local knowledge spillover is and global technology spillover is The effect of global technology spillover is almost same for internal regions compared to those we obtained in SDM for all regions. Moreover, the local knowledge spillover is higher than own regional knowledge stock. This is also consistent with the results we obtained for all regions in SDM specification. The column 6 and 7 reports the results for border regions (neighbour regions across the international borders). According to the results of SAR model the estimate of global technology spillover is statistically insignificant; this means that there is a no technological spillovers from border regions. The results of SDM specification show that both knowledge and technology spillovers are statistically insignificant for border regions, which also confirms the strong effect of borders. Another important contribution of the current study is that we are simultaneously identifying the spillovers from internal and border regions. The results of extended version of SAR (ESAR) and extended version of SDM (ESDM) models are reported in columns 8 and 9, which are based on equation 3.15 and The important aspect of these models is that we are using two weight matrices (W1 and W2) in one single model. Estimating the spatial model with two weight matrices will help us to identify the effect of international 20 For detail see Scherngell et al. (2007),Fischer et al. (2006) and Fischer et al. (2007). 19

20 borders on productivity. According to the results of ESAR model the estimate of productivity effect of own regional stock of knowledge is 0.493, which is statistically significant. In this specification there are two global spillovers i.e. internal and border spillovers. First, the parameter estimate of global technology spillovers from internal neighbouring regions is 0.46, which means that there are technology spillovers from internal regions. However, the parameter estimate for border regions is but it is statistically insignificant, which shows the negative effect of border on technology spillovers. It is also consistent with SAR model for border regions reported in column 6. In the final specification i.e. ESDM model, we have two types for both knowledge and technology spillovers. The two types for local knowledge spillovers are internal knowledge spillovers and border knowledge spillovers. Similarly, there are the two types of global technology spillovers. The parameter estimate of the local internal knowledge stock is and it is statistically significant, while the parameter estimate of the local border spillovers is statistically insignificant. It means that knowledge spillovers only from internal regions affect productivity. Moreover, the effect of own regional stock of knowledge is statistically insignificant as we found in other specifications. Similarly, we have two types of global technology spillovers for both internal and border regions. The parameter estimate of global technology spillover from internal neighbouring regions is but the same parameter estimate for border region is statistically insignificant. Again these results also confirms that border strongly obstructing both knowledge and technology spillovers. This is a new evidence and important contribution in the empirical literature of technology spillovers. This result is also consistent with the findings in trade literature where researchers found a strong negative effects of international borders (see e.g., Millimet and Osang (2007) and Krugman et al. (2011)). To test the robustness of the results we also did the same analysis separately for each year from 1999 to The results of ESDM model for some selected years are reported in table By visualizing the results of table 4 it is clear that the average estimates from the year 1999 to 2010, the productivity effect of local knowledge spillover is significant for internal neighbour regions but not for the border neighbour regions. Similarly, results related to global technology spillovers are significant for internal neighbour regions and insignificant for the border neighbour regions. It shows the robustness of the results for different time periods. 21 We estimated all the models for all the years and the results can be provided on request. 20

21 Table 5: Extended Spatial Durbin Models for the years variables constant (5.858) -(4.013) -(5.934) -(5.874) EPO (0.923) (3.098) (0.957) (0.931) W 1 EP O (4.072) (4.480) (4.089) (4.075) W 2 EP O (1.049) (0.570) (1.103) (1.059) ρ 1 (Internal Regions) (7.440) (16.456) (7.369) (7.427) ρ 2 (Boder Regions) (0.416) -(0.291) -(0.460) -(0.423) Log-Liklihood

22 6 Summary and Conclusion The main aim of this study is to identify the impact of international borders on knowledge spillovers and technology spillovers among EU regions. The study implements spatial econometric models like SAR (spatial autoregressive), SDM (spatial durbin model) and extended versions of these basic models. The extended models simultaneously identify the effect of internal and border regions. We use EPO stock as a measure of R&D to capture the knowledge spillover effect on regional productivity. Our cross sectional database of 16 EU countries consisting 204 regions at NUTS-2 level, over the period of Among these 204 EU regions there are 86 regions that share international border. Our model is based on regional Cobb-Douglas production function. The results of current study show that there exist close link between productivity and knowledge stock. The regional productivity depends on local knowledge stocks from the internal region and does not depend on the stock of knowledge from border regions. Similarly, there exists global technology spillover from the internal neighbouring regions but not from the border neighbouring region. These findings provide a substantial evidence for the role of internal regional (local) knowledge spillovers and internal (global) technology spillovers as the important factors contributing to the regional productivity growth. The finding also confirms that the neighbour region across the international border contributes nothing to the regional productivity growth though the effect is often not significant. Even though, there is free movement of resources like labor and capital etc. but still there are strong effect of borders on technology and knowledge transfer. 22

23 7 References References Acemoglu, Daron, Philippe Aghion, and Fabrizio Zilibotti, Distance to Frontier, Selection, and Economic Growth, Journal of the European Economic Association, , 4 (1), Anderson, James E. and Eric van Wincoop, Borders, Trade and Welfare, Working Paper 8515, National Bureau of Economic Research October Anselin, Luc, Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, 1988., Anil K. Bera, Raymond Florax, and Mann J. Yoon, Simple diagnostic tests for spatial dependence, Regional Science and Urban Economics, February 1996, 26 (1), Arbia, Giuseppe, Roberto Basile, and Gianfranco Piras, Using Spatial Panel Data in Modelling Regional Growth and Convergence, ISAE Working Papers 55, ISAE - Institute for Studies and Economic Analyses - (Rome, ITALY) August Badinger, Harald and Peter Egger, Estimation of higherorder spatial autoregressive crosssection models with heteroscedastic disturbances, Papers in Regional Science, , 90 (1), Bottazzi, Laura and Giovanni Peri, Innovation and Spillovers: Evidence from European Regions, Technical Report and, Innovation and spillovers in regions: Evidence from European patent data, European Economic Review, August 2003, 47 (4), Caballero, Ricardo J. and Adam B. Jaffe, How High are the Giants Shoulders: An Empirical Assessment of Knowledge Spillovers and Creative Destruction in a Model of Economic Growth, in NBER Macroeconomics Annual 1993, Volume 8 NBER Chapters, National Bureau of Economic Research, Inc, August 1993, pp Coe, David T. and Elhanan Helpman, International R&D spillovers, European Economic Review, May 1995, 39 (5),

24 Comin, Diego A., Bart Hobijn, and Emilie Rovito, World Technology Usage Lags, NBER Working Papers 12677, National Bureau of Economic Research, Inc November Comin, Diego and Bart Hobijn, Lobbies and Technology Diffusion, The Review of Economics and Statistics, December 2009, 91 (2), Elhorst, J., Applied Spatial Econometrics: Raising the Bar, Spatial Economic Analysis, 2010, 5 (1), Elhorst, J. Paul, Unconditional maximum likelihood estimation of dynamic models for spatial panels, Technical Report Fischer, Manfred M., Thomas Scherngell, and Eva Jansenberger, The Geography of Knowledge Spillovers between High-Technology Firms in Europe - Evidence from a Spatial Interaction Modelling Perspective, Geographical Analysis, May 2006, 38 (5), ,, and Martin Reismann, Cross-region Spillovers and total factor productivity: Eurpean evidence using spatial panel data model, VUE Working Papers, Institute for Economic Geography and GIScience- (Vienna University of Economics and BA, Vienna, Austria) August Gong, Guan and Wolfgang Keller, Convergence and polarization in global income levels: a review of recent results on the role of international technology diffusion, Research Policy, June 2003, 32 (6), Goto, Akira and Kazuyuki Suzuki, R&D Capital, Rate of Return on R&D Investment and Spillover of R&D in Japanese Manufacturing Industries, The Review of Economics and Statistics, November 1989, 71 (4), Griliches, Zvi, Issues in Assessing the Contribution of Research and Development to Productivity Growth, Bell Journal of Economics, Spring 1979, 10 (1), , Productivity, R&D, and the Basic Research at the Firm Level in the 1970 s, American Economic Review, March 1986, 76 (1), and Frank R. Lichtenberg, R&D and Productivity Growth at the Industry Level: Is There Still a Relationship?, in R & D, Patents, and Productivity NBER Chapters, National Bureau of Economic Research, Inc, February 1984, pp

25 and Jacques Mairesse, Comparing productivity growth: An exploration of french and U.S. industrial and firm data, European Economic Review, 1983, 21 (1-2), Islam, Nazrul, Growth Empirics: A Panel Data Approach, The Quarterly Journal of Economics, November 1995, 110 (4), , Productivity Dynamics in a Large Sample of Countries: A Panel Study, Review of Income and Wealth, , 49 (2), King, R. J. and R. Levine, Capital Fundamentalism Economic developmnet and Economic Growth, Carnegie-Rochester Conference Series on Public Policy Krugman, P., M. Obstfeld, and M. Melitz, International Economics: Theory & Policy, Student Value Edition, Prentice Hall, Kwon, Hyeog Ug, Measuring the Rate of Return to R&D, Interindustry R&D Spillovers in Korean Manufacturing Industries, Hitotsubashi Journal of Economics, June 2003, 44 (1), Lacombe, Donald J., Does Econometric Methodology Matter? An analysis of Public Poicy Using Spatial Econometric Techniques, Geographical Analysis, April 2004, 36 (2), LeSage, James P., ECONOMETRICS: MATLAB toolbox of econometrics functions, Statistical Software Components, Boston College Department of Economics December and Manfred M. Fischer, Estimates of the Impact of Static and Dynamic Knowledge Spillovers on Regional Factor Productivity, International Regional Science Review, January 2012, 35 (1), LeSage, James P and R Kelley Pace, Pitfalls in higher order model extensions of basicspatial regression methodology, Working Paper LeSage, J.P. and R.K. Pace, Introduction to Spatial Econometrics Statistics: Textbooks and Monographs, CRC Press, Liberto, Adriana Di and Stefano Usai, TFP convergence across European regions: a comparative spatial dynamics analysis, Technical Report Los, Bart and Bart Verspagen, R&D spillovers and productivity: Evidence from U.S. manufacturing microdata, Empirical Economics, 2000, 25 (1),

26 Madsen, Jakob B., Technology spillover through trade and TFP convergence: 135 years of evidence for the OECD countries, Journal of International Economics, July 2007, 72 (2), Millimet, Daniel L. and Thomas Osang, Do state borders matter for U.S. intranational trade? The role of history and internal migration, Canadian Journal of Economics, February 2007, 40 (1), Moran, P. A. P., The interpretation of statistical maps, Journal of the Royal Statistical Society, 1996, B (10), Nelson, Richard R. and Edmond S. Phelps, Investment in Humans, Technological Diffusion and Economic Growth, Technical Report Neruh, V. and A. Dhareshwar, A New Database on Human Physical Capital Stock: Source, Methodology and Results, Revista Analisis Economico, 1993, 8 (1), Robbins, Carol, The Impact of Gravity-Weighted Knowledge Spillovers on Productivity in Manufacturing, The Journal of Technology Transfer, , 31 (1), Scherngell, Thomas, Manfred M. Fischer, and Martin Reismann, Total factor productivity effects of interregional knowledge spillovers in manufacturing industries across Europe, Romanian Journal of Regional Science, December 2007, 1 (1), Solow, Robert M., Technical Change and the Aggregate Production Function, Review of Economics and Statistics, August 1957, 39, Tobler, W., Acomputer movie simulating urban growth in the Detroit region, Economic Geography Supplement, 1970, 46, Verspagen, Bart, Estimating international technology spillovers using technology flow matrices, Review of World Economics (Weltwirtschaftliches Archiv), , 133 (2),

27 8 Appendix List of Country and Region Names at Nuts-2 level : Austria (AT-9): AT11(Burgenland), AT12 (Niedersterreich), AT13 (Wien), AT21 (Krnten), AT22 (Steiermark), AT31 (Obersterreich), AT32 (Salzburg), AT33 (Tirol), AT34 (Vorarlberg). Belgium (BE-11): BE10 (Rgion de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest), BE21 (Prov. Antwerpen), BE22 (Prov. Limburg (B)), BE23 (Prov. Oost-Vlaanderen), BE24 (Prov. Vlaams Brabant), BE25 (Prov. West-Vlaanderen), BE31 (Prov. Brabant Wallon), BE32 (Prov. Hainaut), BE33 (Prov. Lige), BE34 (Prov. Luxembourg (B)), BE35 (Prov. Namur). Switzerland (CH-7): CH01 (Lake Geneva region), CH02 (Espace Mittelland), CH03 (Northwestern Switzerland), CH04 (Zurich), CH05 (Eastern Switzerland), CH06 (Central Switzerland), CH07 (Ticino). Germany (DE-39): Stuttgart, Karlsruhe, Freiburg, Tbingen, Oberbayern, Niederbayern, Oberpfalz, Oberfranken, Mittelfranken, Unterfranken, Schwaben, Berlin, Brandenburg - Nordost, Brandenburg - Sdwest, Bremen, Hamburg, Darmstadt, Gieen, Kassel, Mecklenburg-Vorpommern, Braunschweig, Hannover, Lneburg, Weser-Ems, Dsseldorf, Kln, Mnster, Detmold, Arnsberg, Koblenz, Trier, Rheinhessen-Pfalz, Saarland, Chemnitz, Dresden, Leipzig, Sachsen-Anhalt, Schleswig- Holstein, Thringen. Denmark (DK-5): Hovedstaden, Sjlland, Syddanmark, Midtjylland, Nordjylland Spain (ES-15): Galicia, Principado de Asturias, Cantabria, Pais Vasco, Comunidad Foral de Navarra, La Rioja, Aragn, Comunidad de Madrid, Castilla y Len, Castilla-la Mancha, Extremadura, Catalua, Comunidad Valenciana, Andalucia, Regin de Murcia. Finland (FL-4): It-Suomi, Etel-Suomi, Lnsi-Suomi, Pohjois-Suomi. France (FR-22): le de France, Champagne-Ardenne, Picardie, Haute-Normandie, Centre, Basse-Normandie, Bourgogne, Nord - Pas-de-Calais, Lorraine, Alsace, Franche-Comt, Pays de la Loire, Bretagne, Poitou-Charentes, Aquitaine, Midi-Pyrnes, Limousin, Rhne-Alpes, Auvergne, Languedoc- Roussillon, Provence-Alpes-Cte d Azur, Corse. Irland (IE-2): 27

28 Border-Midlands and Western, Southern and Eastern. Italy (IT-20): Piemonte, Valle d Aosta/Valle d Aoste, Liguria, Lombardia, Provincia Autonoma Trento, Veneto, Friuli-Venezia Giulia, Emilia-Romagna, Toscana, Umbria, Marche, Lazio, Abruzzo, Molise, Campania, Puglia, Basilicata, Calabria, Sicilia, Sardegna. Luxumburg (LU-1): Luxumburg. Netherlands (NL-12): Groningen, Friesland, Drenthe, Overijssel, Gelderland, Flevoland, Utrecht, Noord-Holland, Zuid-Holland, Zeeland, Noord-Brabant, Limburg. Norway (NO-7): Oslo, Hedmark, Sr-stlandet, Agder og Rogaland, Vestlandet, Trndelag, Nord-Norge. Portugal (PT-5): Norte, Algarve, Centro, Lisboa, Alentejo. Sweden (SE-8): Stockholm, stra Mellansverige, Smland med arna, Sydsverige, Vstsverige, Norra Mellansverige, Mellersta Norrland, vre Norrland. UK (UK-37): Tees Valley and Durham, Northumberland-Tyne and Wear, Cumbria, Cheshire, Greater Manchester, Lancashire, Merseyside, East-Yorkshire and Northern-Lincolnshire, North Yorkshire, South Yorkshire, West Yorkshire, Derbyshire and Nottinghamshire, Leicestershire, Rutland and Northants, Lincolnshire, Herefordshire, Worcestershire and Warks, Shropshire and Staffordshire, West Midlands, East Anglia, Bedfordshire, Hertfordshire, Essex, Inner London, Outer London, Berkshire, Bucks and Oxfordshire, Surrey, East and West Sussex, Hampshire and Isle of Wight, Kent, Gloucestershire, Wiltshire and Bristol/Bath area, Dorset and Somerset, Cornwall and Isles of Scilly, Devon, West Wales and The Valleys, East Wales, Eastern Scotland, South Western Scotland, North Eastern Scotland, Highlands and Islands, Northern Ireland. 28

29 Tests for Spatial Dependence LM Test LM test which is based on the least-squares residuals e and the spatial weight matrix W. The LM statistic takes the following form: LM = (1/T )[éw e] 2 has χ 2 distribution (8.1) where T = tr(w + Ẃ ) W LR Test The LR (Likelihood Ratio) test is based on the difference between the log likelihood from the spatial model and the log likelihood from a least-squares regression. The statistics can be written as follow, LR = 2(Likelihood (unrestricted) Likelihood (restricted) ) has χ 2 distribution (8.2) Wald Test Another test for spatial autocorrelation is also based on residual and weight matrix define as follows, W ald = λ 2 [t 2 + t 3 (1/n)(t 1 2)] has χ 2 distribution (8.3) where t 1 = tr(w B 1 ) t 2 = tr((w B 1 ) 2 ) t 2 = tr((w B 1 ) )(W B 1 ) B = (I n λw ) Other Definitions of Weight Matrix (LeSage (1998) and Arbia et al. (2005)): 1-Linear contiguity means that two sites s i and s j are neighbours if they share (part of) a common eastern or western border. 2-Critical cut-off neighbourhood means two sites s i and s j are said to be neighbours if, 0 < d ij < d with d ij the appropriate distance adopted, and d representing the critical 29

30 cut-off. 3-Nearest neighbour means two sites s i and s j are said to be neighbours if, d ij = Min(d ik ) i, j. 4-Contiguity-based neighbourhood means that two polygons indexed by s i ands j are said to be neighbours if they share a common boundary. 5-Rook contiguity mean two regions are neighbours if they share (part of) a common border (border is longer than the snap distance on any side) with the region of interest. 6-Bishop Contiguity mean two regions are spatial neighbours if they meet at a point (if border is shorter than the snap distance), or one region share a common vertex with the region of interest. 7-Queen Contiguity means two regions are neighbours in the sense if they share any part of a common border, no matter how short (one region share a common side or vertex with the regions of interest).in the current study we use Queen Contiguity to define the neighbours of a particular region since we want to identity the effect of international borders. 30

31 Figure 1: Terminologies used for spillovers 31

32 Figure 2: 14 EU Countries plus Norway and Switzerland 32

33 Figure 3: 86 Border Regions 33