A pair-wise approach to testing for output and growth convergence

This paper proposes a pair-wise approach to testing for output convergence that considers all N(N-1)/2 possible pairs of log per-capita output gaps across N economies. A general probabilistic definition of output convergence is also proposed, which suggests that all such output gap pairs must be stationary with a constant mean. The approach is compatible with individual output series having unit roots, or other non-stationary common components and does not involve the choice of a reference country in computation of output gaps. It is also applicable when N is large relative to T (the time dimension of the panel). After providing some encouraging Monte Carlo evidence on the small sample properties of the pair-wise test, the test is applied to output series in the Penn World Tables over 1950-2000. Overall, the results do not support output convergence, and suggest that the findings of convergence clubs in the literature might be spurious. However, significant evidence of growth convergence is found, a result which is reasonably robust to the choice of the sample period and country groupings. Non-convergence of log per-capita outputs combined with growth convergence suggests that while common technological progress seems to have been diffusing reasonably widely across economies, there are nevertheless important country-specific factors that render output gaps highly persistent, such that we cannot be sure that the probability for the output gaps to lie within a fixed range will be non-zero.