Convergence analysis for hierarchical longitudinal data

Convergence analysis is typically envisaged either from a macro or a micro perspective. However, empirical tests tend to ignore that the two levels are often “nested” in a hierarchy. Building on hierarchical growth curve modelling, we propose an approach to convergence analysis that allows contemporaneous inference on macro and micro-convergence. Compared to the classic linear convergence analysis, the suggested methodology provides a more flexible alternative to model heterogeneity and validate the results for possible Galton's fallacy. We illustrate the approach in two empirical examples, one considering convergence across European regions and countries and the other across Italian firms and regions. In the European case, we find that the evidence of convergence depends on the choice of cross-sectional sample. Evidence on convergence in Italy applies only to part of the temporal sample and, therefore, is not robust to Galton's fallacy. Our analysis returns more robust results on the convergence process and allows better inference for policy intervention. We can envisage that this approach will find increasing applications in the future, as disaggregated data becomes available and heterogeneity becomes an increasingly prominent feature in economic modelling.