Currency Unions, Product Introductions, 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 very well within currency unions for tens of thousands of goods sold by each of the retailers, implying good-level real exchange rates often 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 the common currency per se, and not simply the lack of nominal volatility, is important in reducing cross-country price dispersion. Second, we derive a new decomposition that shows that good-level real exchange rates in our data predominantly reflect 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. Further, these 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