Asymptotically Perfect and Relative Convergence of productivity.

In this paper we measure the extent to which countries are converging in per capita productivity levels. We formally define convergence in a time series analytical context, derive the necessary and sufficient conditions and introduce a cluster analytical procedure that enables us to distinguish several convergence clubs. The results obtained with this procedure indicate that convergence might not be such a widespread phenomenon as suggested by the results of standard cross sectional growth regressions. Instead, we find a large number of relatively small convergence clubs. Furthermore, a comparison of our empirical results with those obtained from a Monte Carlo simulation for a diverging sample reveals that our results do not significantly differ from that of the case in which log per capita productivity levels are independent random walks around linear deterministic trends. In order to show that our results are consistent with those obtained using cross country growth regressions we show that the negative correlation between initial productivity levels and subsequent productivity growth can also be the result of a divergent sample. Hence, our time series analytical results suggest that there is much less convergence of productivity levels and productivity growth rates than previously found using cross sectional procedures.