SPATIAL DATA ANALYSIS BASED ON THE KEYNESIAN AND CONVERGENCE THEORIES FOR PORTUGAL
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SPATIAL DATA ANALYSIS BASED ON THE KEYNESIAN AND CONVERGENCE THEORIES FOR PORTUGAL Vítor João Pereira Domingues Martinho Escola Superior Agrária, Instituto Politécnico de Viseu, Quinta da Alagoa, Estrada de Nelas, Ranhados, 3500 - 606 VISEU Centro de Estudos em Educação, Tecnologias e Saúde (CI&DETS) Portugal e-mail: vdmartinho@esav.ipv.pt ABSTRACT: This study analyses the data of the Portuguese regions, for the several economic sectors, basedon the Keynesian theory and on the spatial econometrics instruments. To analyse the data, by usingMoran I statistics, it is stated that productivity is subject to a positive spatial autocorrelation, above allin services. The total of all sectors present, also, indicators of being subject to positive autocorrelationin productivity. This study analyses, yet, the data of the Portuguese regions, for the different sectors,based on the convergence theories and on the spatial econometrics instruments. To analyse the data,Moran’s I statistics is considered, and it is stated that productivity is subject to positive spatialautocorrelation, above all, in agriculture and services. Industry and the total of all sectors presentindications that they are subject to positive spatial autocorrelation in productivity. Keywords: Spatial Econometric; Verdoorn Law; Convergence Theories Portuguese Regions.
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1. Introduction The influence of neighbouring locations (parishes, councils, districts, regions, etc) in thedevelopment of a particular area, through the effects of spatial spillovers, is increasingly considered inmore recent empirical studies, a fact which has been highlighted by Anselin (2002a). Anselin (1988and 2001) and Anselin and Bera (1998), who refer to the inclusion of spatial effects as being importantfrom an econometric point of view. If the underlying data arises from processes which include aspatial dimension, and this is omitted, the estimators are either biased and inconsistent or inefficientdepending on whether the error or the lag model is the underlying data generating process. Following on from these studies, the development of productivity of a particular region, forexample, can be influenced by the development of productivity in neighbouring regions, throughexternal spatial factors. The existence or non-existence of these effects can be determined through anumber of techniques which have been developed for spatial econometrics, where Anselin, amongothers, in a number of studies has made a large contribution. Paelinck (2000) has brought a number oftheoretical contributions to the aggregation of models in spatial econometrics, specifically concerningthe structure of parameters. Anselin (2002b) considered a group of specification tests based on themethod of Maximum Likelihood to test the alternative proposed by Kelejian and Robinson (1995),related to perfecting the spatial error component. Anselin (2002c) has presented a classification ofspecification for models of spatial econometrics which incorporates external spatial factors. Anselin(2002d) has reconsidered a number of conceptual matters related to implementing an explicit spatialperspective in applied econometrics. Baltagi et al. (2003) has sought to present improvements inspecification tests (testing whether the more correct specification of models is with the spatial lagcomponent or the spatial error component) LM (Lagrange Multiplier), so as to make it more adaptableto spatial econometrics. Anselin et al. (1996) has proposed a simple, robust diagnostic test, based onthe OLS method, for the spatial autocorrelation of errors in the presence of spatially lagged dependentvariables and vice-versa, applying the modified LM test developed by Bera and Yoon (1993). This testwas, also, after proposed by Florax et al. (2003). This study seeks to test Verdoorn’s Law (using product per worker as a proxy forproductivity) for each of the economic sectors of regions (NUTs III) of mainland Portugal from 1995to 1999 and from 2000 to 2005, through techniques of cross-section spatial econometrics. There are few known studies concerning conditional productivity convergence with spatialeffects. Fingleton (2001), for example has found spatial correlation at the level of productivity when,using data from 178 regions of the European Union, he introduced spillover effects in a model ofendogenous growth. Abreu et al. (2004) have investigated the spatial distribution of the rates of totalproductivity growth of factors using exploratory analyses of spatial data and other techniques ofspatial econometrics. The sample consists of 73 countries and covers the period from 1960 to 2000.They have found significant spatial correlation in the rates of total factor productivity growth,indicating that high and low values tend to concentrate in space, forming the so-called “clusters”. Theyhave also found high indications of positive spatial autocorrelation at the level of the total factorproductivity, which has increased throughout the period of 1960 to 2000. This result could indicate atendency to clustering with time. There is, on the other hand, a variety of studies analysing conditional product convergencewith spatial effects. Armstrong (1995) has defended that the evidence of convergence across Europeancountries as mentioned by Barro and Sala-i-Martin is due to the omission of spatial autocorrelation intheir analysis and bias resulting from the selection of European regions. Following on, Sandberg(2004), for example, has examined the hypothesis of absolute and conditional convergence acrossChinese provinces in the period from 1985 to 2000 and found indications that there had been absoluteconvergence during the periods of 1985 to 2000 and 1985 to 1990. He has also found evidence thatconditional convergence had been seen in the sub-period of 1990 to 1995, with signs of spatialdependency across adjacent provinces. Arbia et al. (2004) have studied the convergence of grossdomestic product per capita among 125 regions of 10 European countries from 1985 to 1995,considering the influence of spatial effects. They concluded that the consideration of spatialdependency considerably improved the rates of convergence. Lundberg (2004) has tested thehypothesis of conditional convergence with spatial effects between 1981 and 1990 and, in contrast toprevious results, found no clear evidence favouring the hypothesis of conditional convergence. On the
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contrary, the results foresaw conditional divergence across municipalities located in the region ofStockholm throughout the period and for municipalities outside of the Stockholm region during the1990s. This study seeks to test conditional productivity convergence (using as a proxy the product perworker) for each of the economic sectors of regions (NUTs III) of mainland Portugal from 1995 to2002, through techniques of cross-section spatial econometrics. 2. Data description The GeoDa programme was used to analyse the data, obtained from the National StatisticsInstitute, and to carry out the estimations used in this study. GeoDa1 is a recent computer programmewith an interactive environment that combines maps with statistical tables, using dynamic technologyrelated to Windows (Anselin, 2003a). In general terms, functionality can be classified in sixcategories: 1) Manipulation of spatial data; 2) Transformation of data; 3) Manipulation of maps; 4)Construction of statistical tables; 5) Analysis of spatial autocorrelation; 6) Performing spatialregressions. All instructions for using GeoDa are presented in Anselin (2003b), with someimprovements suggested in Anselin (2004). The analysis sought to identify the existence of Verdoorn’s relationship by using Scatterplotand spatial autocorrelation, the Moran Scatterplot for global spatial autocorrelation and Lisa Maps forlocal spatial autocorrelation. In this analysis of data the dependent variable of the equation used to testVerdoorn’s Law is presented in average growth rates for the period considered for cross-sectionanalysis. About the convergence analysis, we use the product per worker as proxy of the productivity ofwork in the period 1995 to 2002 in the various economic sectors of the regions (NUTs III) of mainlandPortugal. The data analysis is carried out while considering, in the various economic sectors, thevalues of the productivity ratio of each of the regions under consideration, in relation to averageproductivity in mainland Portugal. It also seeks to identify the existence of spatial autocorrelation byusing Moran Scatterplots for over all spatial autocorrelation and LISA Maps for local spatialautocorrelation. 2.1. Analysis of cross-section data for Verdoorn law The eight (Figure I and II) Scatterplots presented below allow an analysis of the existence of acorrelation between growth of productivity and product growth under Verdoorn’s Law, for each of theeconomic sectors (agriculture, industry, services and the total of all sectors) of Portuguese NUTs III(28 regions), with average values for the period 1995 to 1999 and from 2000 to 2005.1 Available at http://geodacenter.asu.edu/
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a) Agriculture b) Industry c) Services d) All sectors Note: PRO = Productivity; QUA = Product.Figure I: “Scatterplots” of Verdoorn’s relationship for each of the economic sector (cross-section analysis, 28 regions, 1995-1999) a) Agriculture b) Industry c) Services d) All sectors Note: PRO = Productivity; QUA = Product.Figure II: “Scatterplots” of Verdoorn’s relationship for each of the economic sector (cross-section analysis, 28 regions, 2000-2005) To analyse the Scatterplots we confirm what is defended by Kaldor, or, in other words,Verdoorn’s relationship is stronger in industry (a sign of being the sector with the greatest scaledincome, although the underlying value is far too high) and weaker in other economic sectors (anindication that these sectors have less scaled income). Although agriculture is an exception here (sincethere is evidence of quite high scaled income, which is contrary to what was expected when
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considering the theory), due to the restructuring which it has undergone since Portugal joined the EEC,with the consequent decrease in population active in this sector which is reflected in increasedproductivity. The eight (Figure III and IV) Moran Scatterplots which are presented below concerning thedependent variable (average growth rates of productivity in the period 1995 to 1999 and from 2000 to2005), constructed by the equation of Verdoorn’s Law, show Moran’s I statistical values for each ofthe economic sectors and for the totality of sectors in the 28 NUTs in mainland Portugal. The matrixWij used is the matrix of the distances between the regions up to a maximum limit of 97 Km. Thisdistance appeared to be the most appropriate to the reality of Portuguese NUTs III, given the diversevalues of Moran’s I obtained after various attempts with different maximum distances. For example,for services which, as we shall see, is the sector where the Moran’s I has a positive value (a sign ofspatial autocorrelation), this value becomes negative when the distances are significantly higher than97 Km, which is a sign that spatial autocorrelation is no longer present. On the other hand, theconnectivity of the distance matrix is weaker for distances over 97 Km. Whatever the case, the choiceof the best limiting distance to construct these matrices is always complex. a) Agriculture b) Industry c) Services d) Total of sectors Note: W-PRO = Spatially lagged productivity; PRO = Productivity.Figure III: “Moran Scatterplots” of productivity for each of the economic sectors (cross-section analysis, 28 regions, 1995-1999)
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a) Agriculture b) Industry c) Services d) Total of sectors Note: W-PRO = Spatially lagged productivity; PRO = Productivity.Figure IV: “Moran Scatterplots” of productivity for each of the economic sectors (cross-section analysis, 28 regions, 2000-2005) Would be good if we had more observations, but is difficult to find to a finer spatial unity.Anyway the results obtained are consistent with the Portuguese reality taking into account anotherworks about regional growth. An analysis of the Moran Scatterplots demonstrates that it is principally in services that aglobal spatial autocorrelation can be identified and that there are few indicators that this is present inthe totality of sectors, since Moran’s I value is positive. Below is an analysis of the existence of local spatial autocorrelation with eight LISA Maps(Figure V and VI), investigated under spatial autocorrelation and its significance locally (by NUTsIII). The NUTs III with “high-high” and “low-low” values, correspond to the regions with positivespatial autocorrelation and with statistical significance, or, in other words, these are cluster regionswhere the high values (“high-high”) or low values (“low-low”) of two variables (dependent variableand lagged dependent variable) are spatially correlated given the existence of spillover effects. Theregions with “high-low” and “low-high” values are “outliers” with negative spatial autocorrelation. Insum, this LISA Maps find clusters for the dependent variable and lagged dependent variable.
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a) Agriculture b) Industry c) Services d) Total of sectors Note:Figure V: “LISA Cluster Map” of productivity for each of the economic sectors (cross-section analysis, 28regions, 1995-1999) a) Agriculture b) Industry c) Services d) Total of sectors Note:Figure VI: “LISA Cluster Map” of productivity for each of the economic sectors (cross-section analysis, 28regions, 2000-2005) Upon analysing the Lisa Cluster Maps above (Figure V), confirms what was seen with theMoran Scatterplots, or, in other words, only in the services with high values in the region aroundGreater Lisbon and low values in the Central region is there positive spatial autocorrelation. Thesefigures also show some signs of positive spatial autocorrelation in all sectors, specifically with highvalues in the Greater Lisbon area and with low values in the Central Alentejo. Of not is the fact thatindustry presents signs of positive autocorrelation with high values in the Baixo Vouga in the Central
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region. In the second period (2000 to 2005) we can see differents situations what was expected,because the evolution of the Portuguese economy context was influenced by others factors, namely thecommon currency. 2.2. Analysis of cross-section data for Verdoorn lawThe four Scatterplots, (showing the relation between the growth of productivity and initial productivityfor each of the sectors) presented below, allow for an analysis of productivity convergence for each ofthe economic sectors of the Portuguese NUTs III, with average values for the period 1995 to 2002. a) Agriculture b) Industry c) Services d) Total of sectors Note: PRO = Productivity; PDE = Initial productivity.Figure I: Scatterplots of absolute convergence of productivity for each of the economic sectors (cross-sectionanalysis, 28 regions) Analysing the four figures above confirms what has been previously shown, or, in otherwords, industry is the only economic sector which shows greater tendencies for absolute convergence. The four Moran Scatterplots (showing the relationship between the dependent variable and thespatially redundant dependent variable) which are presented below, show Moran’s I statistical valuesfro each of the economic sectors and for the total of sectors of the 28 NUTs for mainland Portugalfrom 1995 to 2002. The matrix Wij used is the matrix of the distances between the regions up to amaximum limit of 97 Km. This distance appeared to be the most appropriate to the reality ofPortuguese NUTs III, given the signs of spatial autocorrelation encountered, (with an analysis of thedata, bearing in mind namely Moran’s I statistics, and with the estimation results carried out) in theanalysis of robustness and behaviour of the various matrices of distance when considering alternativepossibilities of maximum distances. For example, for agriculture and services which, as we shall see,are the sectors where the signs of autocorrelation are strongest, these indications cease to exist whenthe distances are significantly higher than 97 Km. On the other hand, the connectivity of the distancematrix is weaker for distances over 97 Km. Whatever the case, the choice of the best limiting distanceto construct these matrices is always complex.
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a) Agriculture b) Industry c) Services d) Total of sectors Note: W-PRO = Spatially redundant productivity; PRO = Productivity.Figure II: “Moran Scatterplots” of productivity for each of the economic sectors (cross-section analysis, 28regions) An analysis of the Moran Scatterplots shows that it is only in agriculture and services that theexistence of global spatial autocorrelation can be seen in productivity and that there are fewindications of the same occurring in industry, since Moran’s I value is positive.. Figure III analyses the existence of local spatial autocorrelation with four LISA Maps,investigated under spatial autocorrelation and its significance locally (by NUTs III). The NUTs IIIwith “high-high” and “low-low” values, correspond to the regions with positive spatial autocorrelationand with statistical significance, or, in other words, these are cluster regions where the high values(“high-high”) or low values (“low-low”) of two variables (dependent variable and redundantdependent variable) are spatially correlated given the existence of spillover effects. The regions with“high-low” and “low-high” values are “outliers” with negative spatial autocorrelation
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a) Agriculture b) Industry c) Services d) Total of sectors Note:Figure III: “LISA Cluster Map” of productivity for each of the economic sectors (cross-section analysis, 28regions) Analysing the LISA Cluster Maps above confirms what has been verified by the MoranScatterplots, or, in other words, the indications of positive spatial autocorrelation are highest inagriculture and services. Agriculture shows signs of positive spatial correlation with high values inGreater Lisbon, around Greater Lisbon and the Alentejo and low values in the Centre-North region.Services present high values for the two variables in the Baixo Alentejo and low values in the regionaround Greater Lisbon. There are also some signs of positive spatial autocorrelation in these figuresfor industry and the total of sectors, more specifically with high values in some NUTs III of theCentral region. In consideration of what has previously been referred to, spatial spillover effects interms of productivity are non-existent in the North and the Algarve. This can be seen with high valuesin the Centre for industry and the total of sectors and with low values for agriculture. High values canbe seen in Lisbon and Vale do Tejo for agriculture and low values for services. Positive spatialautocorrelation in the Alentejo can be seen with high values for agriculture and services. These signsof positive spatial autocorrelation as described for each of the economic sectors included in variousNUTs III could be an indication of sector similarities in productive structure in each of the strips ofland, given the example of the existence of spatial spillover effects for agriculture in the Alentejo. 3. Conclusions Considering the analysis of the cross-section data previously carried out, based on theKeynesian Theory, it can be seen, for the first period, that productivity (product per worker) is subjectto positive spatial autocorrelation in services (with high values in the Lisbon region and low values inthe Central region) and in all sectors (with high values in the Lisbon region and low values in theCentral Alentejo) and also in industry (although this sector has little significance, since high values areonly found in the NUT III Baixo Vouga of the Central Region). Therefore, the Lisbon region clearlyhas a great influence in the development of the economy with services. On the other hand, whatKaldor defended is confirmed or, in other words Verdoorn’s relationship is stronger in industry, since
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this is a sector where growing scaled income is most expressive. For the second period the data andthe results are different, what is waited, because the context in Portugal is distinct and in our point ofview the indicators are better. In the first period, industry is one of the sectors with less spatialspillover effects in mainland Portugal and which has the greatest growing scaled income, because thiswe could conclude that the development of the national economy does not have a very favourableinternal outlook with these results. So, it would be advisable to favour economic policies seeking tomodernise industrial structures in Portugal, so that industry can benefit from spillover effects, as seenin services, what happened in the second period. Considering the analysis of the cross-section data previously carried out, based on theconvergence theories, it can be seen that productivity (product per worker) is subject to positive spatialautocorrelation in agriculture and services (with Greater Lisbon, curiously, showing the greatestspatial spillover effects in agriculture than in services). Industry and the total of all sectors also showsome signs of spatial autocorrelation. Also of note is the fact that the region surrounding Lisbon andthe Alentejo will clearly have a great influence in the development of the economy with agriculture.On the other hand, it can be stated that the tendency for absolute productivity convergence is greatestin industry. 4. ReferencesAbreu, M.; Groot, H.; and Florax, R. (2004). Spatial Patterns of Technology Diffusion: AnEmpirical Analysis Using TFP. ERSA Conference, Porto.Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers,Dordrecht, Netherlands.Anselin, L. (2001). Spatial Econometrics. In: Baltagi (eds). A Companion to TheoreticalEconometrics. Oxford, Basil Blackwell.Anselin, L. (2002a). Spatial Externalities. Working Paper, Sal, Agecon, Uiuc.Anselin, L. (2002b). Properties of Tests for Spatial Error Components. Working Paper, Sal, Agecon,Uiuc.Anselin, L. (2002c). Spatial Externalities, Spatial Multipliers and Spatial Econometrics. WorkingPaper, Sal, Agecon, Uiuc.Anselin, L. (2002d). Under the Hood. Issues in the Specification and Interpretation of SpatialRegression Models. Working Paper, Sal, Agecon, Uiuc.Anselin, L. (2003a). An Introduction to Spatial Autocorrelation Analysis with GeoDa. Sal, Agecon,Uiuc.Anselin, L. (2003b). GeoDaTM 0.9 User’s Guide. Sal, Agecon, Uiuc.Anselin, L. (2004). GeoDaTM 0.9.5-i Release Notes. Sal, Agecon, Uiuc.Anselin, L.; Bera A.K.; Florax, R.; and Yoon, M.J. (1996). Simple Diagnostic Tests for SpatialDependence. Regional Science and Urban Economics, 26, pp: 77-104.Anselin, L. and Bera, A. (1998). Spatial Dependence in Linear Regression Models with anIntroduction to Spatial Econometrics. In: A. Ullah and D. Giles (eds), Handbook of Applied EconomicStatistics, New York: Marcel Dekker.Arbia, G. and Piras, G. (2004). Convergence in per-capita GDP across European regions usingpanel data models extended to spatial autocorrelation effects. ERSA Conference, Porto.Baltagi, B.H.; Song, S.H.; and Koh, W. (2003). Testing panel data regression models with spatialerror correlation. Journal of Econometrics, 117, pp: 123-150.Bera, A. and Yoon, M. (1993). Specification testing with locally misspecified alternatives.Econometric Theory, 9, pp: 649-658.Fingleton, B. (2001). Equilibrium and Economic Growth: Spatial Econometric Models andSimulations. Journal of Regional Science, 41, pp: 117-147.Florax, R.J.G.M.; Folmer, H.; and Rey, S.J. (2003). Specification searches in spatial econometrics:the relevance of Hendry´s methodology. ERSA Conference, Porto.Kelejian, H.H. and Robinson, D.P. (1995). Spatial correlation: A suggested alternative to theautoregressive models. In: Anselin, L. and Florax, R.J. (eds). New Directions in Spatial Econometrics.Springer-Verlag, Berlin.
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Lundberg, J. (2004). Using Spatial Econometrics to Analyze Local Growth in Sweden. ERSAConference, Porto.Paelinck, J.H.P. (2000). On aggregation in spatial econometric modelling. Journal of GeographicalSystems, 2, pp: 157-165.Sandberg, K. (2004). Growth of GRP in Chinese Provinces : A Test for Spatial Spillovers. ERSAConference, Porto.
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