Pricing-to-market, trade costs, and international relative prices

International relative prices across industrialized countries show large and systematic deviations from relative purchasing power parity. We embed a model of imperfect competition and variable markups in a quantitative model of international trade. We find that when our model is parameterized to match salient features of the data on international trade and market structure in the US, it can reproduce deviations from relative purchasing power parity similar to those observed in the data because firms choose to price-to-market. We then examine how pricing-to-market depends on the presence of international trade costs and various features of market structure.