We built a model analyzing, through cross-section estimation methods, the influence of spatial effects in the productivity conditional convergence in the economic sectors of NUTs III of mainland Portugal between 1995 and 2002. Taking into account the estimation results, it is stated once again that the indications of convergence are greater in industry, and it can be seen that spatial spillover effects, spatial lag and spatial error, do not condition the convergence of productivity in the several economic sectors of Portuguese region in the period under consideration.endogenous growth theory; spatial econometrics; Portuguese Regions

Martinho, Vítor João Pereira Domingues

English

Research Papers in Economics

 
A SPATIAL MODEL BASED ON THE ENDOGENOUS GROWTH 
THEORY 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 
 
We built a model analyzing, through cross-section estimation methods, the influence of spatial effects in 
the productivity conditional convergence in the economic sectors of NUTs III of mainland Portugal between 1995 
and 2002. Taking into account the estimation results, it is stated once again that the indications of convergence 
are  greater  in  industry, and  it  can  be  seen  that  spatial spillover effects, spatial  lag  and  spatial  error,  do  not 
condition the convergence of productivity in the  several economic sectors of Portuguese region in the period 
under consideration.  
 
Keywords: endogenous growth theory; spatial econometrics; Portuguese Regions 
  
1. INTRODUCTION 
 
There  are  few  known  studies  concerning  conditional  productivity  convergence  with  spatial  effects. 
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 of endogenous growth. Abreu et al. 
(2004) have investigated the spatial distribution of the rates of total productivity growth of factors using exploratory 
analyses of spatial data and other techniques of spatial 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”. They have also found high indications of positive spatial autocorrelation at the level of the total factor 
productivity, which has increased throughout the period of 1960 to 2000. This result could indicate a tendency to 
clustering with time.  
There is, on the other hand, a variety of studies analysing conditional product convergence with spatial 
effects.  Armstrong  (1995)  has  defended  that  the  evidence  of  convergence  across  European  countries  as 
mentioned by Barro and Sala-i-Martin is due to the omission of spatial autocorrelation in their 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 across Chinese provinces in the period from 1985 to 2000 
and found indications that there had been absolute convergence during the periods of 1985 to 2000 and 1985 to 
1990. He has also found evidence that conditional convergence had been seen in the sub-period of 1990 to 1995, 
with signs of spatial dependency across adjacent provinces. Arbia et al. (2004) have studied the convergence of 
gross domestic 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  spatial  dependency  considerably 
improved the rates of convergence. Lundberg (2004) has tested the hypothesis of conditional convergence with 
spatial effects between 1981 and 1990 and, in contrast to previous results, found no clear evidence favouring the 
hypothesis  of  conditional  convergence.  On  the  contrary,  the  results  foresaw  conditional  divergence  across 
municipalities  located  in  the  region  of  Stockholm  throughout  the  period  and  for  municipalities  outside  of  the 
Stockholm region during the 1990s. 
This study seeks to test conditional productivity convergence (using as a proxy the product per worker) 
for  each  of  the  economic  sectors  of  regions  (NUTs  III)  of  mainland  Portugal  from  1995  to  2002,  through 
techniques of cross-section spatial econometrics.  
 
  2. MODEL OF CONDITIONAL CONVERGENCE WITH SPATIAL EFFECTS 
 
  Bearing in mind the theoretical considerations, what is presented next is the model used to analyse 
conditional productivity convergence with spatial effects, at a sector and regional level in mainland Portugal: 
   
it i it ij i it P b p W P P T        0 0 log ) / log( ) / 1 ( , with  0    e  0                     (1) 
 
In  this  equation  (1)  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 convergence coefficient,    is the autoregressive spatial coefficient 
(of the spatial lag component) and   is the error term (of the spatial error component, with,        W ). The 
Alert! This author has published many duplicate versions of very similar papers with slightly 
different titles, but without an appropriate notice. This may apply to this contribution, too.  
indices i, j and t, represent the regions under study, the neighbouring regions and the period of time respectively. 
 
  3. DATA ANALYSIS 
 
The data referring to gross growth value at base prices and employment were obtained in the Regional 
Accounts of the National Statistics Institute. To carry out the cross-section estimations, the GeoDa
1 software was 
used.  
     
  4. LINEAR MODEL  
 
The  productivity  convergence  is  only  seen  in  industry  and  we  do  not  found  signs  of  spatial  effects 
influence in the convergence of that variable in the several economic sectors. 
 
  5. CONCLUSIONS 
 
  This  study  has  sought  to  test  the  convergence  of  productivity  for  each  of  the  economic  sectors 
(agriculture, industry, services and the totality of services) across the 28 regions (NUTs III) of mainland Portugal 
in the period of 1995 to 2002, with spillover effects, spatial lag and spatial error. To do so, cross-section estimates 
(with average temporal values) have been carried out with the OLS and ML estimation methods, following the 
specification procedures indicated by Florax et al. (2003) who suggest that models are first tested with the OLS 
method, to test what is the better specification (spatial lag or spatial error) and then the spatial lag or spatial error 
is estimated with the ML method. 
  As far as cross-section estimates are concerned, it can be seen that sector by sector the tendency for 
productivity convergence is greatest in industry. With reference to spatial autocorrelation it is also confirmed that 
this possibly exists in agriculture and services, when taking into account the LM tests. 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 the consideration of these spatial effects does not significantly alter 
the results obtained previously with the OLS estimation. 
   
6. REFERENCES 
 
Abreu, M.; Groot, H.; and Florax, R. (2004). Spatial Patterns of Technology Diffusion: An Empirical Analysis 
Using TFP. ERSA Conference, Porto. 
Arbia, G. and Piras, G. (2004). Convergence in per-capita GDP across European regions using panel data 
models extended to spatial autocorrelation effects. ERSA Conference, Porto. 
Fingleton, B. (2001). Equilibrium and Economic Growth: Spatial Econometric Models and Simulations. 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. 
Lundberg, J. (2004). Using Spatial Econometrics to Analyze Local Growth in Sweden. ERSA Conference, Porto. 
Sandberg, K. (2004). Growth of GRP in Chinese Provinces : A Test for Spatial Spillovers. ERSA Conference, 
Porto. 
 
                                                 
1 Available at http://geodacenter.asu.edu/ 
Alert! This author has published many duplicate versions of very similar papers with slightly 
different titles, but without an appropriate notice. This may apply to this contribution, too. 

Convergence in per-capita GDP across European regions using panel data models extended to spatial autocorrelation effects. ERSA Conference,

A spatial model based on the endogenous growth theory for Portugal

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics