Principles of System Identification

Estimation Methods: Part I 355

that they can accommodate more moment conditions than necessary, i.e., the over-identified case.

Furthermore, where the distribution of the data is known, GMM can be computationally lighter than

the MLE counterparts. In general, these estimators yield asymptotically normal, consistent, but not

necessarily efficient estimates. Efficiency (asymptotic) is achieved only with an appropriate choice

of the weighting matrix W . These characteristics are similar to that of a weighted least-squares

method as shall learn shortly. The optimal choice of the weighting matrix will also be detailed at

that point of discussion. Interestingly, GMM also contains the methods of generalized least squares

and maximum likelihood estimation, which ...