Provincial convergence in Spain: a spatial econometric approach

Abstract

This article examines the process of provincial convergence in labour productivity that has taken place in Spain between 1985 and 2002. In order to quantify the influence of space on the convergence process, it applies a spatial econometric approach, concluding that although spatial effects do indeed exist, they do not seem to be too relevant for the aforementioned process.

Acknowledgement

The author would like to thank A. Maza for his useful comments and suggestions.

Notes

See, for instance, García Greciano et al. (1995), Villaverde (1996), and Villaverde and Sánchez-Robles (1998). More recent work of interest includes, among others, Goerlich and Mas (2001).

A detailed account of the most commonly used convergence indicators is provided by Villaverde (2004). Generally speaking, β-convergence has been more popular with macroeconomists while σ-convergence has been mainly the focus of regional economists.

An analysis that illustrates spatial econometrics can be seen in Moreno and Vayá (2002), among others.

All computations have been carried out by using the SpaceStat 1.91 software, by Luc Anselin.

This indicator is used to test the null hypothesis that the variable analysed is distributed randomly in space.

The robust test LM-LE is not rejected at the 95% level, so we conclude that there is no substantive autocorrelation. In contrast, the test LM-ERR and its robust LM-EL throw up p-values of less than 0.05, which indicates that the null hypothesis is rejected (absence of spatial autocorrelation) in the residuals. It is concluded, therefore, that the equation of β-convergence estimated previously presents spatial dependence in the residuals. When, as in our case, there is residual autocorrelation, the estimations of the parameters are, like in a temporal context, inefficient although unbiased; as a result, statistical inference is not reliable.

Manipulating Equation 2 (see Toral, 2002; or Anselin, 2003) allows us to obtain the following equation, in which the third and fourth terms on the right-hand side refer to the aforementioned spatial effects:

where ρ = λ; γ = −λβ.

The fact that the parameter λ is significant and positive confirms what the spatial dependence tests suggested about the ordinary least-squares estimation.

This is a very general result in this type of analysis, as can be seen for example in Rey and Montouri (1999) and Moreno and Vayá (2002).