We built a model analyzing, through cross-section estimation methods, the influence of spatial effects in the conditional product convergence in the parishes’ economies of mainland Portugal between 1991 and 2001 (the last year with data available for this spatial disaggregation level). Taking into account the estimation results, it is stated that there are not indications of convergence (the population is in the littoral of Portugal) and it can be seen that spatial spillover effects, spatial lag (capturing spatial autocorrelation through a spatially lagged dependent variable) and spatial error (capturing spatial autocorrelation through a spatially lagged error term) condition the convergence of product of Portuguese parishes in the period under consideration.endogenous growth theory; spatial econometrics; Portuguese context

Martinho, Vítor João Pereira Domingues

English

Research Papers in Economics

  1 
A SPATIAL MODEL BASED ON THE ENDOGENOUS GROWTH 
THEORY FOR PORTUGAL. ANOTHER APPROACH 
 
Vitor João Pereira Domingues Martinho 
 
Unidade de I&D do Instituto Politécnico de Viseu 
Av. Cor. José Maria Vale de Andrade 
Campus Politécnico 
3504 - 510 Viseu 
(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 conditional product convergence in the parishes’ economies of mainland Portugal between 1991 and 2001 
(the last year with data available for this spatial disaggregation level). Taking into account the estimation results, it 
is stated that there are not indications of convergence (the population is in the littoral of Portugal) and it can be 
seen  that  spatial  spillover  effects,  spatial  lag  (capturing  spatial  autocorrelation  through  a  spatially  lagged 
dependent  variable) and spatial  error  (capturing  spatial autocorrelation through a  spatially  lagged error  term) 
condition the convergence of product of Portuguese parishes in the period under consideration.  
 
Keywords: endogenous growth theory; spatial econometrics; Portuguese context. 
 
1. INTRODUCTION 
 
There  are  some  known  studies  concerning conditional  convergence  with  spatial  effects.  (1)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. (2)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. 
(3)NijKamp (2007) analyses spatial disparities, differences in regional growth and productivity and discuss their 
driving  forces.  In  this  paper  starting  from  traditional  regional  growth  theory,  it  introduces  next  findings  from 
location and agglomeration theory, including infrastructure and network modelling, with a particular emphasis on 
spatial accessibility. Innovation, entrepreneurship and knowledge are addressed, too, and interpreted as critical 
success conditions for modern regional development. Next, elements from endogenous growth theory and the 
new economic geography are introduced.  
There is, on the other hand, a variety of studies analysing conditional product convergence with spatial 
effects. Armstrong 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, (4)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. (5)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. (6)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 product convergence (using as a proxy the population, following the 
new economic geography theory, because the persons are potential workers and consumers, so where we have 
more  persons  we  have  more  product)  for  the  parishes  economies  of  mainland  Portugal  from  1991  to  2001, 
through techniques of cross-section spatial econometrics.  
 
  2. MODEL OF CONDITIONAL CONVERGENCE WITH SPATIAL EFFECTS 
 
  Bearing in mind the theoretical considerations about conditional convergence, what is presented next is 
the model used to analyse conditional product convergence with spatial effects, at parishes’ level in mainland 
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.   2 
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 the product, p is the rate of growth of product 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 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 population were obtained in the censos (population data) of the National Statistics 
Institute. To carry out the cross-section estimations, the GeoDa
1 software was used (7)(Anselin 2010).  
   
4. THE LINEAR MODEL 
 
  This part of the study will examine the specification procedures of (8)Florax et al. (2003) and will firstly 
examine through OLS estimates, the relevance of proceeding with estimate models with spatial lag and spatial 
error components, with recourse to LM specification tests. 
  The results confirm to what has been previously seen, or, in other words, product diverged in Portugal 
between 1991 and 2001. Convergence/divergence in the product will be conditioned by spillover effects, spatial 
error, according to the LM tests.  
    
 
  5. CONCLUSIONS 
 
  This study has sought to test the convergence of product across the 4052 parishes of mainland Portugal 
in the period of 1991 to 2001, with spillover effects, spatial lag and spatial error. To do so, cross-section estimates 
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. 
Considering the analysis of the data and the estimation results previously carried out, it can be seen that 
product is subject to positive spatial autocorrelation and that the product diverged between 1991 and 2001 in 
Portugal. This is a preoccupant situation, because we are the population all in the littoral and no people in the 
interior. 
     
 
6. REFERENCES 
 
1.  B.  Fingleton.  Equilibrium  and  Economic  Growth:  Spatial  Econometric  Models  and  Simulations.  Journal  of 
Regional Science, 41, 117-147 (2001).  
2. M. Abreu; H. Groot; and R. Florax. Spatial Patterns of Technology Diffusion: An Empirical Analysis Using TFP. 
ERSA Conference, Porto 2004. 
3. P. Nijkamp. Regional Development as Self-Organized Converging Growth. 2nd Central European Conference 
in Regional Science – CERS, Košice 2007. 
4. K. Sandberg. Growth of GRP in Chinese Provinces : A Test for Spatial Spillovers. ERSA Conference, Porto 
2004. 
5. G. Arbia and G. Piras. Convergence in per-capita GDP across European regions using panel data models 
extended to spatial autocorrelation effects. ERSA Conference, Porto 2004. 
6. J. Lundberg. Using Spatial Econometrics to Analyze Local Growth in Sweden. ERSA Conference, Porto 2004. 
7. L. Anselin. Thirty years of spatial econometrics. Papers in Regional Science, 89, 3-25 (2010).  
8. R.J.G.M Florax.; H. Folmer; and S.J. Rey. Specification searches in spatial econometrics: the relevance of 
Hendry´s methodology. ERSA Conference, Porto 2003. 
                                                 
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,

Equilibrium and Economic Growth: Spatial Econometric Models and Simulations.

Growth of GRP in Chinese Provinces : A Test for Spatial Spillovers. ERSA Conference,

Regional Development as Self-Organized Converging Growth. 2nd

Spatial Patterns of Technology Diffusion: An Empirical Analysis Using TFP. ERSA Conference,

Specification searches in spatial econometrics: the relevance of Hendry´s methodology. ERSA Conference,

Thirty years of spatial econometrics.

Using Spatial Econometrics to Analyze Local Growth in Sweden. ERSA Conference,

A spatial model based on the endogenous growth theory for Portugal. Another approach

A spatial model based on the endogenous growth theory for Portugal. Another approach

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