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

The stability of the solution path in a macroeconomic model implies that it admits a Wold representation. This Wold representation can be estimated semi‐parametrically by local projections and used to estimate the model's parameters by minimum distance techniques even when the stochastic process for the solution path is unknown or unconventional. We name this two‐step estimation procedure “projection minimum distance” and investigate its statistical properties for the broad class of models where the mapping between Wold coefficients and parameters is linear. This includes many situations with likelihood score functions nonlinear in the parameters that would otherwise require numerical optimization routines.