Pitfalls in Interpreting Tests of Backward-Looking Pricing in New Keynesian Models

A finding that lagged inflation helps explain the behavior of current inflation in Phillips-curve-type specifications is generally thought to imply a departure from optimality in the pricing behavior of firms. Popular explanations either involve some fraction of firms using a backward-looking rule of thumb when setting prices or invoke irrational forecasting of expected inflation. However, when one generates data from a Taylor-style staggered contracting model and bases tests of forward-looking pricing behavior on a Calvo model, such tests produce significant coefficients on lagged inflation even though all firms are rational and forward looking. This means that interpreting the significance of a coefficient on lagged inflation in a pricing equation may be subtler than is currently realized.