Projection Minimum Distance: An Estimator for Dynamic Macroeconomic Models
A covariance-stationary vector of variables has a Wold representation whose coefficients can be emiparametrically estimated by local projections (JordÃ , 2005). The parameters of a model can then be estimated from the restrictions the model imposes on the Wold coefficients by the method of minimum distance. 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 unknown model misspecification renders GMM instruments invalid. We provide several Monte Carlo experiments and an empirical application in support of the new techniques introduced.
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