We study the purchasing power parity (PPP) puzzle in a multi-sector, two-country, sticky-price model. Across sectors, firms differ in the extent of price stickiness, in accordance with recent microeconomic evidence on price setting in various countries. Combined with local currency pricing, this leads sectoral real exchange rates to have heterogeneous dynamics. We show analytically that in this economy, deviations of the real exchange rate from PPP are more volatile and persistent than in a counterfactual one-sector world economy that features the same average frequency of price changes, and is otherwise identical to the multi-sector world economy. When simulated with a sectoral distribution of price stickiness that matches the microeconomic evidence for the U.S. economy, the model produces a half-life of deviations from PPP of 39 months. In contrast, the half-life of such deviations in the counterfactual one-sector economy is only slightly above one year. As a by-product, our model provides a decomposition of this difference in persistence that allows a structural interpretation of the different approaches found in the empirical literature on aggregation and the real exchange rate. In particular, we reconcile the apparently conflicting findings that gave rise to the "PPP Strikes Back debate" (Imbs et al. 2005a,b and Chen and Engel 2005).

We provide evidence on three mechanisms that can reconcile frequent individual price changes with sluggish aggregate price dynamics. To that end, we estimate a semistructural model that can extract information about real rigidities and the distribution of price stickiness from aggregate data. Hence, the model can also speak to the debate about the aggregate implications of sales. Our estimates indicate large real rigidities and substantial heterogeneity in price stickiness. Moreover, the cross-sectional distribution of price stickiness implied by aggregate data is in line with an empirical distribution obtained from microprice data that factors out sales and product substitutions.