This paper tests for output convergence across n = 51 economies, employing the definition of Pesaran [Journal of Econometrics 138, 312–355 (2007)]. The definition requires output gaps to be stationary around a constant mean. But when all n(n − 1)/2 pairs of log per capita output gaps are considered, this results in more than 1,000 unit root tests to be conducted. Hence, because of the ensuing multiplicity of the testing problem, a nontrivial number of output gaps will be falsely declared to be stationary when each of the n(n − 1)/2 hypotheses is tested at some conventional level like 5%. To solve the problem, we employ recent multiple testing techniques that allow us to bound the expected fraction of false rejections at a desired level. Monte Carlo results illustrate the usefulness of the techniques. The empirical results show that the data do not support the notion of output convergence after controlling for multiplicity.
