A Tale of Two Tails: Productivity Distribution and the Gains from Trade

I use firm-level data to show that neither the Log-normal nor the Pareto distribution can approximate the shape of the productivity distribution along the entire support. While the former underpredicts the thickness of the right tail, the latter does not capture the shape of the left one. Using empirical distribution as a benchmark, I show that such inaccuracies lead to sizable errors in the estimates of the gains from trade in models featuring firm selection. I propose using a mixed distribution which models the left tail as Log-normal and right tail as Pareto and produces negligible errors in quantitative analysis.