New trade models, new welfare implications

We show that endogenous firm selection provides a new welfare margin for heterogeneous firm models of trade (relative to homogeneous firm models). Under some parameter restrictions, the trade elasticity is constant and is a sufficient statistic for welfare, along with the domestic trade share. However, even small deviations from these restrictions imply that trade elasticities are variable and differ across markets and levels of trade costs. In this more general setting, the domestic trade share and endogenous trade elasticity are no longer sufficient statistics for welfare. Additional empirically observable moments of the micro structure also matter for welfare.