Product Introductions, Currency Unions, and the Real Exchange Rate

We use a novel dataset of online prices of identical goods sold by four large global retailers in dozens of countries to study good-level real exchange rates and their aggregated behavior. First, in contrast to the prior literature, we demonstrate that the law of one price holds perfectly within currency unions for thousands of goods sold by each of the retailers, implying good-level real exchange rates equal to one. Prices of these same goods exhibit large deviations from the law of one price outside of currency unions, even when the nominal exchange rate is pegged. This clarifies that it is the common currency per se, rather than the lack of nominal volatility, that results in the lack of cross-country differences in the prices of these goods. Second, we use a novel decomposition to show that most of the cross-sectional variation in good-level real exchange rates reflects differences in prices at the time products are first introduced, as opposed to the component emerging from heterogeneous passthrough or from nominal rigidities during the life of the good. In fact, international relative prices measured at the time of introduction move together with the nominal exchange rate. This stands in sharp contrast to pricing behavior in models where all price rigidity for any given good is due simply to costly price adjustment for that good.