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Over the past twenty years, U.S. import prices have become less responsive to the exchange rate. We propose that a significant portion of this decline is a result of increased trade integration. To illustrate this effect, we develop an open economy DGE model in which trade occurs along both the intensive and extensive margins. The key element we introduce into this environment is strategic complementarity in price setting. As a result, a firm's pricing decision depends on the prices set by its competitors. This feature implies that a foreign exporter finds it optimal to vary its markup in response to shocks that change the exchange rate, insulating import prices from exchange rate movements. With increased trade integration, exporters have become more responsive to the prices of their competitors and this change in pricing behavior accounts for a significant portion of the observed decline in the sensitivity of U.S import prices to the exchange rate.
Gust et al. (Tue,) studied this question.