This paper uses a dynamic factor model for the quarterly changes in consumption goods' prices to separate them into three components: idiosyncratic relative-price changes, aggregate relative-price changes, and changes in the unit of account. The model identifies a measure of "pure" inflation: the common component in goods' inflation rates that has an equiproportional effect on all prices and is uncorrelated with relative price changes at all dates. The estimates of pure inflation and of the aggregate relative-price components allow us to re-examine three classic macro-correlations. First, we find that pure inflation accounts for 15-20% of the variability in overall inflation, so that most changes in inflation are associated with changes in goods' relative prices. Second, we find that the Phillips correlation between inflation and measures of real activity essentially disappears once we control for goods' relative-price changes. Third, we find that, at business-cycle frequencies, the correlation between inflation and money is close to zero, while the correlation with nominal interest rates is around 0.5, confirming previous findings on the link between monetary policy and inflation.