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How does military coercion affect the trade policies governments adopt in times of peace? Because international bargaining is conducted “in the shadow of power” (Powell 1999), weaker states may liberalize to appease militarily powerful trade partners and avoid costly conflict. This setting raises an inference problem. Namely, are trade policies chosen for their desirable domestic effects (preferences) or to prevent war with affected foreign governments (power)? Here, I build and calibrate a structural model of trade policy under threat that allows me to disentangle these incentives. Once calibrated to data, the model allows me to measure governments’ underlying trade policy preferences and the magnitude of policy appeasement attributable to latent military coercion. It can also be used to conduct counterfactual experiments – such as assessing the international economic effects of U.S. military retrenchment or Chinese military expansion. These exercises shed light on how Powell’s “shadow of power” affects international economic exchange, and how expectations about exchange affect governments’ military strategies.