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

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 $$\beta $$ β -convergence equations. First, we show how aggregation of spatial data can generate a problem of bias in the OLS estimator of $$\beta $$ β -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 $$\beta $$ β -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.