Estimation and inference by the method of projection minimum distance

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