Asymptotically perfect and relative convergence of productivity

In this paper we examine the extent to which countries are converging in pe r capita productivity levels. We propose to use cluster analysis in order t o allow for the endogenous selection of converging countries. We formally d efine convergence in a time series analytical context, derive the necessary and sufficient conditions for convergence, and introduce a cluster analyti cal procedure that distinguishes several convergence clubs by testing for t hese conditions using a multivariate test for stationarity. We rind a large number of relatively small convergence clubs, which suggests that converge nce might not be such a widespread phenomenon. Copyright (C) 2000 John Wile y & Sons, Ltd.