Unobserved heterogeneity in the productivity distribution and the gains from trade

Finding a good parametric approximation to the productivity distribution is a problem of general interest. This paper argues that heterogeneity in productivity is best captured by finite mixture models (FMMs). FMMs build on the existence of unobserved subpopulations in the data. As such, they are generally consistent with models of firm dynamics differing between groups of firms and allow for a very flexible distribution fit. Relative to commonly used parametric alternatives, we find that FMMs are the only distributions able to provide a sufficiently good fit to the data. A gains from trade exercise with Portuguese data reveals that only FMMs approximate the "true" gains reasonably well.