Estimation and Inference by the Method of Projection Minimum Distance

A covariance-stationary vector of variables has a Wold representation whose coefficients can be semiparametricallyestimated by local projections (Jordà, 2005). Substituting the Wold representationsfor variables in model expressions generates restrictions that can be used by the method of minimumdistance to estimate model parameters. We call this estimator projection minimum distance(PMD) and show that its parameter estimates are consistent and asymptotically normal. In manycases, PMD is asymptotically equivalent to maximum likelihood estimation (MLE) and nests GMMas a special case. In fact, models whose ML estimation would require numerical routines (such asVARMA models) can often be estimated by simple least-squares routines and almost as efficiently byPMD. Because PMD imposes no constraints on the dynamics of the system, it is often consistent inmany situations where alternative estimators would be inconsistent. We provide several Monte Carloexperiments and an empirical application in support of the new techniques introduced.