The ecological fallacy in a time series context: evidence from Spanish regional unemployment rates

Abstract

The ecological fallacy (EF) is a common problem regional scientists have to deal with when using aggregated data in their analyses. Although there is a wide number of studies considering different aspects of this problem, little attention has been paid to the potential negative effects of the EF in a time series context. Using Spanish regional unemployment data, this paper shows that EF effects are not only observed at the cross-section level, but also in a time series framework. The empirical evidence obtained shows that analytical regional configurations are the least susceptible to time effects relative to both normative and random regional configurations, while normative configurations are an improvement over random ones.

Appendix: The Theil index

The Theil index has been computed as follows:

$$ T = {\sum\limits_{p = 1}^n {\frac{{u_{p} }} {U}} }\log {\left[ {\frac{{u_{p} /U}} {{1/n}}} \right]} $$

where n is the number of provinces (47), u _p is the provincial unemployment rate indexed by p, and U represents the Spanish unemployment rate $U = {\sum\nolimits_{p = 1}^n {u_{p} } }.$

Overall inequality can be completely and perfectly decomposed into a between-group component T ^′_g and a within-group component (T ^w_g ) Thus: T = T ^′_g  + T ^w_g With $T^{'}_{{\text{g}}} = {\sum\limits_{i = 1}^m {\frac{{U{}_{i}}} {U}\log {\left[ {\frac{{U_{i} /U}} {{n_{i} /n}}} \right]}} }$ where i indexes regions, with n _i representing the number of provinces in group i, and U _i the unemployment rate in region i, and $T^{{\text{W}}}_{{\text{g}}} = {\sum\limits_{t = 1}^m {\frac{{U_{i} }} {U}{\sum\limits_{p = 1}^{n_{i} } {\frac{{u_{{ip}} }} {{U_{i} }}} }\log {\left[ {\frac{{u_{{ip}} /U_{i} }} {{1/n_{i} }}} \right]}} },$ where each provincial unemployment rate is indexed by two subscripts: i for the unique region to which the province belongs, and subscript p, where, in each region, p goes from 1 to n _i .