On Understanding the Cyclical Behavior of the Price Level and Inflation

In this paper, we examine the relationship between the price level and output and the inflation rate and output at business-cycle frequencies. In the first part of the paper, we develop a methodological approach to characterizing joint business cycle correlations. In particular, we are interested in providing a characterization of the frequency that a pair of correlation coefficients will occur. We apply this methodology to the contemporaneous correlation between the price level and output and between the inflation rate and output. We apply linear filters to the cyclical components, create a time series and compute the correlations. It is straightforward to construct histograms of the two correlation co-efficients. In the second part, we specify a model economy with a form of rational inattention. In this setting, we perform numerical simulations to determine if the model economy can generate correlations quantitatively similar to those observed in the data. It can.