Testing the convergence hypothesis: A comment

In a recent paper Lichtenberg (1994) proposes a test of the convergence hypothesis that the variance of productivity across countries decreases over time. He argues that the ratio of the variance in the first period to that in the last period of the time series is F-distributed bur overlooks the dependency between these two variances. As a consequence, probabilities of committing a type II error of incorrectly rejecting the convergence hypothesis are large. This problem manifests most strongly in short time periods. Lichtenberg, for example, rejects the convergence hypothesis for a data set of 22 OECD countries over the 1960-1985 period. Using two alternative test statistics, we claim that there is strong empirical evidence for convergence in that time period.