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Analysis of Spatial Effects in Sectoral Productivity across Portuguese Regions Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Objectives The study analyses, through cross-section estimation methods: the influence of spatial effects in productivity (product per worker) in the NUTs III economic sectors of mainland Portugal from 1995 to 1999 and from 2000 to 2005 (taking in count the availability of data), considering the Verdoorn relationship. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Structure The study is structured in six parts:  after the introduction, in the second part some studies which have already been developed in the area of spatial econometrics, specifically concerning Verdoorn’s Law, are presented;  in the third part some theoretical considerations of spatial econometrics are presented;  in the fourth, the models considered are explained;  in the fifth the data is analysed based on techniques of spatial econometrics developed to explore spatial data;  the sixth presents estimations under Verdoorn’s Law, taking into account spatial effects;  and in the seventh part the main conclusions obtained through this study are presented.  Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Empirical contributions based on spatial effects Concerning Verdoorn’s Law and the effects of spatial lag and spatial error, Bernat (1996), for example, tested Kaldor’s three laws of growth in North American regions from 1977-1990. The results obtained by Bernat clearly supported the first two of Kaldor’s laws and only marginally the third. Kaldor’s laws refer to the following: i) there is a strong link between the rate of growth of national product and the rate of growth of industrial product, in such a way that industry is the motor of economic growth; ii)  The growth of productivity in industry and endogeny is dependent on the growth of output (Verdoorn’s law); iii) There is a strong link between the growth of non-industrial product and the growth of industrial product, so that the growth of output produces externalities and induces the growth of productivity in other economic sectors. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Fingleton and McCombie (1998) analysed the importance of scaled growth income, through Verdoorn’s Law, with spatial lag effects in 178 regions of the European Union in the period of 1979 to 1989 and concluded that there was a strong scaled growth income. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Fingleton (1999), with the purpose of presenting an alternative model between Traditional and New Geographical Economics, also constructed a model with the equation associated to Verdoorn’s Law, augmented by endogenous technological progress involving diffusion by spillover effects and the effects of human capital. Fingleton applied this model (Verdoorn) to 178 regions of the European Union and concluded there was significant scaled growth income with interesting results for the coefficients of augmented variables (variable dependent lagged, rurality, urbanisation and diffusion of technological innovations)) in Verdoorn’s equation.  Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Theoretical considerations about spatial effects Tests: Moran´I tests the global and local spatial autocorrelation; Jarque-Bera tests the stability of parameters; Breuch-Pagan and Koenker-Bassett, in turn, tests for heteroskedasticity ; To find out if there are spatial lag and spatial error components in the models, two robust Lagrange Multiplier tests are used (LME for “spatial error” and LML for “spatial lag”) : In brief, the LME tests the null hypothesis of spatial non-correlation against the alternative of the spatial error model (“lag”) and LML tests the null hypothesis of spatial non-correlation against the alternative of the spatial lag model to be the correct specification.   Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Recommendations of Florax et al. (2003): 1) Estimate the initial model using the procedures using OLS;  2) Test the hypothesis of spatial non-dependency due to the omission spatially redundant variables or spatially autoregressive errors, using the robust tests  LME and LML;  3) If none of these tests has statistical significance, opt for the estimated OLS model, otherwise proceed to the next step,  4) If both tests are significant, opt for spatial lag or spatial error specifications, whose test has greater significance, otherwise go to step 5; 5) If LML is significant while LME is not, use the spatial lag specification;  6) If LME is significant while LML is not, use the spatial error specification.   Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Verdoorn’s model with spatial effects ln(Pit/Pit-1)=a+rho.Wij.pit+b.ln(Qit/Qit-1)+epsilonit,  with a>0 and  0<b<1. In this equation: P is sector productivity; p is the rate of growth of sector productivity in various regions; W is the matrix of distances; b is the Verdoorn coefficient; rho is the autoregressive spatial coefficient (of the spatial lag component); and epsilon is the error term (of the spatial error component);  the indices i, j and t, represent the regions under study, the neighbouring regions and the period of time respectively. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Data analysis   Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Empirical evidence for Verdoorn’s Law, with spatial effects  Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
Conclusions   Considering the analysis of the cross-section data previously carried out, it can be seen that: for the first period, that productivity (product per worker) is subject to positive spatial autocorrelation in services (with high values in the Lisbon region and low values in the Central region) and in all sectors (with high values in the Lisbon region and low values in the Central Alentejo) and also in industry (although this sector has little significance, since high values are only found in the NUT III Baixo Vouga of the Central Region).  therefore, the Lisbon region clearly has a great influence in the development of the economy with services. On the other hand, what Kaldor defended is confirmed or, in other words Verdoorn’s relationship is stronger in industry, since this is a sector where growing scaled income is most expressive .  Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
About the cross-section estimate, it can be seen that: that sector by sector the growing scaled income is much stronger in industry and weaker or non-existent in the other sectors, just as proposed by Kaldor. With reference to spatial autocorrelation, Moran’s I value is only statistically significant in agriculture and services. Following the procedures of Florax et al. (2003) the equation is estimated with the spatial error component for agriculture and the spatial lag component for services, it can be seen that it is only in agriculture that Verdoorn’s coefficient improves with the consideration of spatial effects. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
For the second period the data and the results are different, what is waited, because the context in Portugal is distinct and in our point of view the indicators are better. In the first period, industry is one of the sectors with less spatial spillover effects in mainland Portugal and which has the greatest growing scaled income, because this we could conclude that the development of the national economy does not have a very favourable internal outlook with these results. So, it would be advisable to favour economic policies seeking to modernise industrial structures in Portugal, so that industry can benefit from spillover effects, as seen in services, what happened in the second period.  Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu

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Spatial Econometrics (Presentation in the University of Reading (29-11-2010))

  • 1. Analysis of Spatial Effects in Sectoral Productivity across Portuguese Regions Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 2. Objectives The study analyses, through cross-section estimation methods: the influence of spatial effects in productivity (product per worker) in the NUTs III economic sectors of mainland Portugal from 1995 to 1999 and from 2000 to 2005 (taking in count the availability of data), considering the Verdoorn relationship. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 3. Structure The study is structured in six parts: after the introduction, in the second part some studies which have already been developed in the area of spatial econometrics, specifically concerning Verdoorn’s Law, are presented; in the third part some theoretical considerations of spatial econometrics are presented; in the fourth, the models considered are explained; in the fifth the data is analysed based on techniques of spatial econometrics developed to explore spatial data; the sixth presents estimations under Verdoorn’s Law, taking into account spatial effects; and in the seventh part the main conclusions obtained through this study are presented. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 4. Empirical contributions based on spatial effects Concerning Verdoorn’s Law and the effects of spatial lag and spatial error, Bernat (1996), for example, tested Kaldor’s three laws of growth in North American regions from 1977-1990. The results obtained by Bernat clearly supported the first two of Kaldor’s laws and only marginally the third. Kaldor’s laws refer to the following: i) there is a strong link between the rate of growth of national product and the rate of growth of industrial product, in such a way that industry is the motor of economic growth; ii) The growth of productivity in industry and endogeny is dependent on the growth of output (Verdoorn’s law); iii) There is a strong link between the growth of non-industrial product and the growth of industrial product, so that the growth of output produces externalities and induces the growth of productivity in other economic sectors. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 5. Fingleton and McCombie (1998) analysed the importance of scaled growth income, through Verdoorn’s Law, with spatial lag effects in 178 regions of the European Union in the period of 1979 to 1989 and concluded that there was a strong scaled growth income. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 6. Fingleton (1999), with the purpose of presenting an alternative model between Traditional and New Geographical Economics, also constructed a model with the equation associated to Verdoorn’s Law, augmented by endogenous technological progress involving diffusion by spillover effects and the effects of human capital. Fingleton applied this model (Verdoorn) to 178 regions of the European Union and concluded there was significant scaled growth income with interesting results for the coefficients of augmented variables (variable dependent lagged, rurality, urbanisation and diffusion of technological innovations)) in Verdoorn’s equation. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 7. Theoretical considerations about spatial effects Tests: Moran´I tests the global and local spatial autocorrelation; Jarque-Bera tests the stability of parameters; Breuch-Pagan and Koenker-Bassett, in turn, tests for heteroskedasticity ; To find out if there are spatial lag and spatial error components in the models, two robust Lagrange Multiplier tests are used (LME for “spatial error” and LML for “spatial lag”) : In brief, the LME tests the null hypothesis of spatial non-correlation against the alternative of the spatial error model (“lag”) and LML tests the null hypothesis of spatial non-correlation against the alternative of the spatial lag model to be the correct specification. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 8. Recommendations of Florax et al. (2003): 1) Estimate the initial model using the procedures using OLS; 2) Test the hypothesis of spatial non-dependency due to the omission spatially redundant variables or spatially autoregressive errors, using the robust tests LME and LML; 3) If none of these tests has statistical significance, opt for the estimated OLS model, otherwise proceed to the next step, 4) If both tests are significant, opt for spatial lag or spatial error specifications, whose test has greater significance, otherwise go to step 5; 5) If LML is significant while LME is not, use the spatial lag specification; 6) If LME is significant while LML is not, use the spatial error specification. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 9. Verdoorn’s model with spatial effects ln(Pit/Pit-1)=a+rho.Wij.pit+b.ln(Qit/Qit-1)+epsilonit, with a>0 and 0<b<1. In this equation: P is sector productivity; p is the rate of growth of sector productivity in various regions; W is the matrix of distances; b is the Verdoorn coefficient; rho is the autoregressive spatial coefficient (of the spatial lag component); and epsilon is the error term (of the spatial error component); the indices i, j and t, represent the regions under study, the neighbouring regions and the period of time respectively. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 10. Data analysis Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 11. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 12. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 13. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 14. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 15. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 16. Empirical evidence for Verdoorn’s Law, with spatial effects Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 17. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 18. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 19. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 20. Conclusions Considering the analysis of the cross-section data previously carried out, it can be seen that: for the first period, that productivity (product per worker) is subject to positive spatial autocorrelation in services (with high values in the Lisbon region and low values in the Central region) and in all sectors (with high values in the Lisbon region and low values in the Central Alentejo) and also in industry (although this sector has little significance, since high values are only found in the NUT III Baixo Vouga of the Central Region). therefore, the Lisbon region clearly has a great influence in the development of the economy with services. On the other hand, what Kaldor defended is confirmed or, in other words Verdoorn’s relationship is stronger in industry, since this is a sector where growing scaled income is most expressive . Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 21. About the cross-section estimate, it can be seen that: that sector by sector the growing scaled income is much stronger in industry and weaker or non-existent in the other sectors, just as proposed by Kaldor. With reference to spatial autocorrelation, Moran’s I value is only statistically significant in agriculture and services. Following the procedures of Florax et al. (2003) the equation is estimated with the spatial error component for agriculture and the spatial lag component for services, it can be seen that it is only in agriculture that Verdoorn’s coefficient improves with the consideration of spatial effects. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu
  • 22. For the second period the data and the results are different, what is waited, because the context in Portugal is distinct and in our point of view the indicators are better. In the first period, industry is one of the sectors with less spatial spillover effects in mainland Portugal and which has the greatest growing scaled income, because this we could conclude that the development of the national economy does not have a very favourable internal outlook with these results. So, it would be advisable to favour economic policies seeking to modernise industrial structures in Portugal, so that industry can benefit from spillover effects, as seen in services, what happened in the second period. Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Viseu