The anticipation to policy changes overstates the estimated elasticity of substitution, the most important parameter in international trade. Standard identification of this parameter uses tariff variation from Free Trade Agreements (FTA) and assumes that trade flows equal their consumption. However, FTAs eliminate tariffs gradually through announced phaseouts. This allows firms to delay their purchases until tariff cuts are effective while consuming their inventories. Indeed, during NAFTA’s staged tariff reductions, imports experienced sizable anticipatory slumps followed by liberalization bumps. A trade model with inventories replicates these dynamics and illustrates that consumed imports provide unbiased estimates of the elasticity of substitution. We propose an empirical measure of consumed imports validated through Monte Carlo simulations. Application to the data shows that using imports instead of consumed imports overestimates the annual elasticity by 68%, the average elasticity by 16%, and increases the ratio of the long- to short-run response from 2 to 3.5.