Estimation and Inference by the Method of Projection Minimum Distance : An Application to the New Keynesian Hybrid Phillips Curve

In most macroeconomic models, the stability of the solution path implies that the system is covariancestationary and hence admits a Wold representation. The ability to estimate this Wold representation semi-parametrically by local projections (Jordà, 2005), even when the process for the solution path is unknown or unconventional, can be exploited to estimate the model’s parameters by minimum distance techniques. We label this two-step estimation procedure “projection minimum distance” (PMD) and formally investigate its statistical properties in models where the mapping between Wold coefficients and parameters is linear even though the likelihood score function is nonlinear in the parameters, which traditionally requires numerical routines to maximize the likelihood. As an illustration of the practicalities of PMD estimation, we reexamine estimates of the New Keynesian Hybrid Phillips curve by providing ample Monte Carlo evidence and an empirical reassessment of Fuhrer and Olivei (2005). •