  In many applications common in testing for convergence the number of
cross-sectional units is large and the number of time periods are few. In these
situations asymptotic tests based on an omnibus null hypothesis are
characterised by a number of problems. In this paper we propose a multiple
pairwise comparisons method based on an a recursive bootstrap to test for
convergence with no prior information on the composition of convergence clubs.
Monte Carlo simulations suggest that our bootstrap-based test performs well to
correctly identify convergence clubs when compared with other similar tests
that rely on asymptotic arguments. Across a potentially large number of
regions, using both cross-country and regional data for the European Union, we
find that the size distortion which afflicts standard tests and results in a
bias towards finding less convergence, is ameliorated when we utilise our
bootstrap test.
