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The Annals of Regional Science

Erschienen in:

18.02.2016 | Original Paper

The role of spatial scale in regional convergence: the effect of MAUP in the estimation of \(\beta \)-convergence equations

verfasst von: Alberto Díaz Dapena, Esteban Fernández Vázquez, Fernando Rubiera Morollón

Erschienen in: The Annals of Regional Science | Ausgabe 2/2016

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Abstract

Empirical analysis of regional convergence is normally based on data collected at a geographical scale corresponding to states or large regions (NUTS-2 or NUTS-3 for the case of Europe). However, it could be more realistic to consider that the dynamics generating economic growth take place at a smaller spatial scale. Potential heterogeneity across local areas might be not correctly quantified if the analysis is made at an aggregated geographical scale, which produces the so-called modifiable areal unit problem (MAUP). The objective of this paper is to explore to which extent MAUP has an effect on convergence analysis, in particular in the empirical estimation of \(\beta \)-convergence equations. First, we show how aggregation of spatial data can generate a problem of bias in the OLS estimator of \(\beta \)-convergence equations from cross-sectional data, as well as inflating its variance. Second, by means of a numerical simulation, we quantify the effect of geographical aggregation on the estimates of \(\beta \)-convergence. Our experiment is based on real spatial structures of aggregated and disaggregated data for different countries, and it numerically illustrates how a modification in the spatial scale has a significant effect on this type of studies.

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Additionally, the zoning effect refers to the shape of the spatial units and the problem that a modification of their shape can also change any empirical result. However, in this paper we just pay attention to the problem of aggregation.

Also see Rey and Montouri (1999) and Janikas and Rey (2005).

For a recent review of advanced estimation strategies, see Elhorst et al. (2010).

A similar exercise could be done for conditional \(\beta \)-convergence equations just by adding more regressors to this basic equation. We have opted for working with this simple case for the sake of simplicity, but the main conclusions in terms of the effects of aggregation on its estimation, however, would hold.

For the sake of clarity in the exposition, in the remaining of this section we refer to the matrix of potential regressors \({\varvec{X}}\) included as explanatory variables in the specification of a general \(\beta \)-convergence equation. Absolute \(\beta \)-convergence equation only considers initial values \({\varvec{y}}_{\mathbf{0}}\) in matrix \({\varvec{X}}\).

The positive or negative sign of the bias depends on the aggregation schemes represented on matrices \({\varvec{G}}\) and \({\varvec{H}}\)—because of the per capita nature of the dependent and explanatory variables—and it is not straightforward, since their elements are influenced by the population dynamics of the spatial units aggregated into larger regions. The issue of the logarithmic transformation adds more complexity to the study of the bias. Details are provided in the “Appendix”.

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Titel: The role of spatial scale in regional convergence: the effect of MAUP in the estimation of -convergence equations
verfasst von: Alberto Díaz Dapena
Esteban Fernández Vázquez
Fernando Rubiera Morollón
Publikationsdatum: 18.02.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: The Annals of Regional Science / Ausgabe 2/2016
Print ISSN: 0570-1864
Elektronische ISSN: 1432-0592
DOI: https://doi.org/10.1007/s00168-016-0750-0

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