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When countries change most favored nation (MFN) tariffs, partners that trade on MFN terms experience plausibly exogenous tariff changes. Using this variation, we estimate the trade elasticity at short and long horizons with local projections. We find that the elasticity of tariff-exclusive trade flows is −0.76 in the short run, and approximately −2 in the long run. Our long-run estimates are smaller than typical in the literature, and it takes 7 to10 years to converge to the long run, implying that (i) the welfare gains from trade are high and (ii) there are substantial convexities in the costs of adjusting exports. (JEL C51, F13, F14)