A tale of two correlations: Evidence and theory regarding the phase shift between the price level and output

We examine the relationship between the price level and output at business-cycle frequencies. In the postwar period, there is evidence of a phase shift between the price level and output. Such a phase shift is manifested in the price level being countercyclical and the inflation rate being procyclical or acyclical, depending on the detrending method used. Our examination takes three approaches. First, we apply bootstrapping methods to characterize the two correlations, though the methodology could easily be extended to any set of facts. Second, we specify a model economy with forecast heterogeneity, showing numerically that this model economy can match the observed pair of correlations. Third, we apply robust control theory, deriving conditions in which the price level is countercyclical and the inflation rate is procyclical.