Auer, Raphael and Chaney, Thomas (2009) Exchange Rate Pass-Through in a Competitive Model of Pricing-to-Market. Journal of Money, Credit and Banking, 41 (1).

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Abstract

This paper extends the Mussa and Rosen (1978) model of quality pricing
under perfect competition. Exporters sell goods of different qualities to consumers
who have heterogeneous preferences for quality. Production is subject
to decreasing returns to scale and, therefore, supply and the toughness
of competition react to cost changes brought about by exchange rate fluctuations.
First, we predict that exchange rate shocks are imperfectly passed
through into prices. Second, prices of low-quality goods are more sensitive
to exchange rate shocks than prices of high-quality goods. Third, in response
to an exchange rate appreciation, the composition of exports shifts toward
higher quality and more expensive goods. We test these predictions using
highly disaggregated price and quantity U.S. import data and find only weak
empirical evidence in support of our theory.