By Beverly Lapham and Ayman Mnasri
http://d.repec.org/n?u=RePEc:qed:wpaper:1418&r=dge
We develop an open economy monetary model with heterogeneous households which is characterized by incomplete pass-through of exchange rate movements to import prices. Partial pass-through arises in our environment due to the presence of competitive search in international goods’ markets. Under competitive search, agents choose a sub-market in which to exchange goods, where different sub-markets are characterized by different price and trading probability combinations. Preference and policy shocks which induce exchange rate movements cause households to choose a different sub-market for their purchases of traded goods–an extensive margin response. These responses mitigate the direct effect of nominal exchange rate changes on equilibrium traded goods’ prices, thereby generating incomplete exchange rate pass-through to goods’ prices. In the calibrated model, exchange rate pass-through due to foreign shocks ranges between 19% and 62%, which is in the range of import price pass-through estimates for developed economies. Due to risk aversion by households, the magnitude of pass-through depends on the size and direction of the initial shock, making the model consistent with the observed phenomenon of asymmetric pass-through. Importantly, by incorporating household heterogeneity, we are able to examine the role of precautionary savings in affecting pass-through, characterize how pass-through varies across different types of households, and examine the distributional effects of exchange rate movements.
I have always wondered why there is incomplete pass-through. Of course, you can assume various psychological factors, but that is too easy. This paper shows that incomplete pass-through can be the result of complete rationality: markets are segmented, and moving between markets in response to shocks is costly.
NEP-DGE Blog 
There are many papers in the literature where incomplete exchange rate pass-through (ERPT) arises under full rationality. Most of these study environments where firms have market power and optimally adjust their markups in response to exchange rate movements, thereby generating incomplete price movements to exchange rate fluctuations.
This paper analyzes the role of competitive search in explaining incomplete ERPT. Under competitive search, households choose in which markets to shop and markets are characterized by a combination of the price and the probability of acquiring the good. When a shock causes a domestic depreciation, households optimally choose to switch to a market with a lower price at the “cost” that they have a lower probability of acquiring the good. (Moving from one market to another is not actually costly.) This switching to less expensive markets mitigates the impact of the domestic depreciation so there is incomplete ERPT. Novel features here are that markets are competitive and we emphasize the role of household responses to exchange rate movements in generating incomplete ERPT.