The classical dichotomy predicts that all of the time-series variance in the aggregate real exchange rate is accounted for by non-traded goods in the consumer price index (CPI) basket because traded goods obey the Law of One Price. In stark contrast, Engel (1999) claimed the opposite: that traded goods accounted for all of the variance. Using micro-data and recognizing that final good prices include both the cost of the goods themselves and local, non-traded inputs into retail such as labor and retail space, our work re-establishes the conceptual value of the classical dichotomy. We also carefully show the role of aggregation, consumption expenditure weighting and assignment of covariance terms in the differences between our findings and those of Engel.