This paper derives a micro-founded gravity equation in general equilibrium based on a translog demand system that allows for endogenous markups and rich substitution patterns across goods. In contrast to standard CES-based gravity equations, trade is more sensitive to trade costs if the exporting country only provides a small share of the destination country's imports. As a result, trade costs have a heterogeneous impact across country pairs, with some trade flows predicted to be zero. I test the translog gravity equation and find strong empirical support in its favor. In an application to the currency union effect, I find that a currency union is only associated with substantially higher bilateral trade if the exporting country provides a small share of the destination country's imports. For other pairs, the currency union effect is modest or indistinguishable from zero.
translog trade costs gravity currency union monopolistic competition trade cost elasticity heterogeneity zero trade