We show the importance of a dynamic aggregation bias in accounting for the PPP puzzle. We prove that the aggregate real exchange rate is persistent because its components have heterogeneous dynamics. Established time series and panel methods fail to control for this. Using Eurostat data, we find that when heterogeneity is taken into account, the estimated persistence of real exchange rates falls dramatically. Its half-life, for instance, may fall to as low as eleven months, significantly below the "consensus view" of three to five years.