Tests for Convergence Clubs

In many applications common in testing for convergence the number of cross-sectional units is large and the number of time periods are few. In these situations tests which are founded upon an omnibus null hypothesis are characterised by a number of problems. In this paper we consider a broad class of tests of convergence based on multivariate time series and panel data methodologies, and track a gradual progression away from tests based on an omnibus null, to sequential tests and tests that are founded upon multiple pairwise comparisons. In a previous study Corrado, Martin and Weeks (2005) test for regional convergence across the European Union allowing for an endogenous selection of regional clusters using a multivariate test for stationarity. Given that the time series are relatively short, there are potential problems in basing inference on asymptotic results for stationarity tests. To circumvent this problem we bootstrap the stationarity test and explore the robustness of the cluster outcomes. In general our results show that the size distortion which afficts the asymptotic tests, and resulting in a bias towards finding less convergence, is resolved when we apply the bootstrap generated critical values. To interpret the composition of the resulting convergence clusters, the latter are tested against a variety of possible groupings suggested by recent theories and hypotheses of regional growth and convergence.