It takes (more than) a moment: estimating trade flows with superstar exporters

Understanding producers' selection into exporting and its consequences for micro-founded gravity estimation calls for an in-depth analysis of the interplay between aggregate exports and the distribution of producers' productivity. Yet, knowledge about such interplay is still rather limited from both a theoretical and an empirical standpoint. We supplement this knowledge by studying how different moments of the distribution of producers' productivity affect the trade elasticity, and in turn how shocks that alter those moments in different ways may have different impacts on aggregate exports. We first show that, to obtain an unbiased measure of that elasticity, gravity regressions have to account not only for the share of producers that export, but also for their productivity premium relative to all producers. This is particularly important when the share is small and the premium is large, that is, when aggregate exports are driven by few overperforming 'superstar exporters'. We then assess how aggregate exports react to shocks entailing the same change in the first moment of the distribution of producers' productivity, but different changes in its higher moments. Our empirical results confirm that taking into full consideration the productivity premium of exporters and the occurrence of 'superstar exporters' is crucial to correctly explain and predict the response of aggregate exports to different productivity shocks.