On Testing Conditional Sigma – Convergence*

In a cross‐section where the initial distribution of observations differs from the steady‐state distribution and initial values matter, convergence is best measured in terms of σ ‐convergence over a fixed time period. For this setting, we propose a new simple Wald test for conditional σ ‐convergence. According to our Monte Carlo simulations, this test performs well and its power is comparable with the available tests of unconditional convergence. We apply two versions of the test to conditional convergence in the size of European manufacturing firms. The null hypothesis of no convergence is rejected for all country groups, most single economies, and for younger firms of our sample of 49,646 firms.