ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")

Many macroeconomic models (including the NKPC - "New Keynesian" Phillips Curve) involve hybrid equations, in which some variables depend on both their lags and leads. Hybrid models have produced conflicting empirical results: GMM (respectively ML) estimation find the forward- looking component to be large (small). A rationalization for this conflict is provided, allowing for two kinds of misspecifications (omitted dynamics and measurement error): we show analytically in a simple DGP that the GMM (ML) estimator overstates (understates) the size of the forward-looking component. Monte-Carlo experiments indicate this result has some generality. We use these findings to rationalize discrepancies observed in NKPC estimates.