Relative Goods' Prices, Pure Inflation, and the Phillips Correlation

This paper uses a dynamic factor model for the quarterly changes in consumption goods' prices to separate them into three independent components: idiosyncratic relative-price changes, a low-dimensional index of aggregate relative-price changes, and an index of equiproportional changes in all inflation rates, that we label "pure" inflation. The paper estimates the model on U.S. data since 1959, and it presents a simple structural model that relates the three components of price changes to fundamental economic shocks. We use the estimates of the pure inflation and aggregate relative-price components to answer two questions. First, what share of the variability of inflation is associated with each component, and how are they related to conventional measures of monetary policy and relative-price shocks? We find that pure inflation accounts for 15-20% of the variability in inflation while our aggregate relative-price index accounts most of the rest. Conventional measures of relative prices are strongly but far from perfectly correlated with our relative-price index; pure inflation is only weakly correlated with money growth rates, but more strongly correlated with nominal interest rates. Second, what drives the Phillips correlation between inflation and measures of real activity? We find that the Phillips correlation essentially disappears once we control for goods' relative-price changes. This supports modern theories of inflation dynamics based on price rigidities and many consumption goods.