Trend inflation, firms' backward-looking behavior, and inflation gap persistence

In the macroeconomics literature, it is often believed that inflation persistence can be attributed to variations in the Federal Reserve's long-run inflation target rather than to firms' backward-looking pricing behavior. With this in mind, this paper investigates the need for a role of firms' backward-looking behavior in accounting for inflation persistence after trend inflation is eliminated from the inflation rate. Our findings are twofold. First, the observed low contemporaneous correlation and reverse dynamic correlation between the output gap and the inflation gap cannot be replicated by a standard dynamic stochastic general equilibrium (DSGE) model incorporating the purely forward-looking New Keynesian Phillips Curve (NKPC) and trend inflation. When the NKPC is replaced with its hybrid version, the DSGE model does provide a reasonable description of the observed joint dynamic correlation between the output and the inflation gaps. Second, the second moments of key macroeconomic variables are best explained by the hybrid NKPC emphasizing both firms' forward- and their backward-looking behaviors. These results dispute the view that trend inflation is able to replace the role of firms' backward-looking behavior in generating inflation persistence.