With this work we try to present a non linear model for Portugal based on the new economic geography. We built the model taking into account an analyse about the agglomeration process in Portugal, using the New Economic Geography models, in a non linear way . In a non linear way, of referring, as summary conclusion, that with this work the existence of increasing returns to scale and low transport cost, in the Portuguese regions, was proven and, because this, the existence of agglomeration in Portugal.new economic geography; non linear models; Portuguese regions

Martinho, Vítor João Pereira Domingues

English

Research Papers in Economics

  1 
A NON LINEAR MODEL OF THE NEW ECONOMIC GEOGRAPHY 
FOR PORTUGAL 
 
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  
 
With this work we try to present a non linear model for Portugal based on the new economic geography. 
We built the model taking into account an analyse about the agglomeration process in Portugal, using the New 
Economic Geography models, in a non linear way . In a non linear way, of referring, as summary conclusion, that 
with this work the existence of increasing returns to scale and low transport cost, in the Portuguese regions, was 
proven and, because this, the existence of agglomeration in Portugal 
 
Keywords: new economic geography; non linear models; Portuguese regions. 
 
1.  INTRODUCTION 
 
To built the model, we mainly aimed to analyze the process of agglomeration across regions (NUTS II) of 
Portugal,  using  non  linear  models  of  New  Economic  Geography,  in  particular,  developments  considered  by 
(1)Krugman (1991), (2)Thomas (1997), (3)Hanson (1998) and (4)Fujita et al. (2000). We will also try to compare 
the results obtained by the empirical models developed by each of these authors ((5)Martinho, 2011a). 
In a theoretical context, it is intended to explain the complementarily of clustering models, associated 
with  the  New  Economic  Geography,  and  polarization  associated  with  the  Keynesian  tradition  ((6)Martinho, 
2011b). 
 
2.  THE BASE NON LINEAR MODEL 
 
Taking in to account the procedures referred in Martinho (2011a), we use the Krugman (1991), Thomas 
(1997) and Fujita et al. (2000) equations, respectively, as following (reduced and linearized): 
 
it
j
d
jt jt
j
d
jt jt
it
ij
ij
e w Y
e w Y
w  
  

  

 















 


 

 
 


) log(
) log(
) log(
) 1 (
1
1 1
) 1 (
1
1 , (1) 
 
 
 
it
j
d
jt jt jt
j
d
jt jt jt
it
ij
ij
e w H Y
e w H Y
w  
  


 

 
  


 

 
 















 


 


 

 

 
    

) log(
) log(
) log(
) 1 (
1
1
) 1 )( 1 (
1
1 ) 1 (
1
) 1 (
1 ) 1 )( 1 ( 1 ) 1 (
1 , (2)                                
 
   
it
j
ijt jt jt
j
ijt jt jt
it
T w Y
T w Y
w  
 

 

 















 


 


 
 


) log(
) log(
) log(
) 1 (
1
1
1 1
) 1 (
1
1
, (3) 
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 
  In these equations, Yi is the income in region i, wi the wage in region i and dij is the distance between 
each pair of locations. Hi the supply of housing in the region i and Tij transport costs between regions i and j. The 
parameters to be estimated, these models are   the elasticity of substitution between manufactured goods,    
the share of expenditure on manufactured goods and   the transport costs to send a unit of manufactured goods 
in a unit distance. 
i  , 
i   and 
i   are error terms. 
 
3.  THE NON LINEAR MODEL 
 
Analysis of the results, obtained in the estimations, it appears that these are slightly different for the 
reduced equations of the three models considered, with the estimates made with the equation of the Thomas 
model present statistically better results. Possibly because it is an equation to work harder and thus beyond the 
centripetal forces of agglomeration, consider also the centrifugal forces of anti-agglomeration by immobile factors. 
Anyway, the results obtained with the estimates of the three equations confirm some importance, but small, of the 
transport costs, given the low values of the parameter  . Looking at the increasing returns to scale, calculating, 
as noted, the value  ) 1 /(    , it appears that this is always greater than one, reflecting the fact that there were 
increasing returns in the Portuguese regions in this period. It should be noted also that the parameter values   
are unreasonably high in all three estimations, however, as stated there is a tendency for these values that fall 
around the unit in most empirical work. 
 
4. THE DATA USED 
 
Considering the variables of the model presented previously, and the availability of statistical information, 
we used the following data at regional level: temporal data from 1987 to 1994 for the five regions (NUTS II) in 
mainland  Portugal  and  for  the  various  manufacturing  industries  existing  in  these  regions,  from  the  regional 
database of Eurostat statistics (Eurostat Regio of Statistics 2000). 
 
5. CONCLUSIONS 
 
In light of what has been said above, we can conclude, with the non linear models, the existence of 
agglomeration processes in Portugal (around Lisboa e Vale do Tejo) in the period 1987 to 1994, given the low 
transport costs, what was shown by the  ) 1 /(     and the  ) 1 (     values obtained in the estimations made 
with the reduced forms of the models presented above. On other hand, there are increasing returns to scale in 
manufacturing in the Portuguese regions.  
Finally, is important to refer the importance of the transportation costs in explaining the spatial issues, 
reinforced by the fact that the estimates made with the seven NUTS II Portugal (including Madeira and Açores) 
present values much worse than when considering only the five NUTS II. What makes sense, since the real wage 
developments do not follow the increase in transport costs from the continent for these two Portuguese islands. 
 
6. REFERENCES 
 
1. P. Krugman. Increasing Returns and Economic Geography. Journal of Political Economy, 99, 483-499 (1991). 
2.  A.  Thomas.  Increasing  Returns,  Congestion  Costs  and  the  Geographic  Concentration  of  Firms.  Mimeo, 
International Monetary Fund, 1997. 
3.  G.  Hanson.  Market  Potential,  Increasing  Returns,  and  Geographic  concentration.  Working  Paper,  NBER, 
Cambridge, 1998. 
4. M. Fujita; P. Krugman and J.A. Venables. The Spatial Economy: Cities, Regions, and International Trade. MIT 
Press, Cambridge, 2000. 
5. V.J.P.D. Martinho. The importance of increasing returns to scale in the process of agglomeration in Portugal: A 
non linear empirical analysis. MPRA Paper 32204, University Library of Munich, Germany (2011a). 
6.  V.J.P.D.  Martinho.  Regional  agglomeration  in  Portugal:  a  linear  analysis.  MPRA  Paper  32337,  University 
Library of Munich, Germany (2011b). 
7. A. Marshall. Principles of Economics. Macmillan, London 1920. 
 
 
 
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. 

Increasing Returns and Economic Geography.

Increasing Returns, Congestion Costs and the Geographic Concentration of Firms. Mimeo, International Monetary Fund,

Market Potential, Increasing Returns, and Geographic concentration. Working Paper,

Principles of Economics.

Regional agglomeration in Portugal: a linear analysis.

The importance of increasing returns to scale in the process of agglomeration in Portugal: A non linear empirical analysis.

The Spatial Economy: Cities, Regions, and International Trade.

A non linear model of the new economic geography for Portugal

A non linear model of the new economic geography for Portugal

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