Gmm Estimation In Econometrics

Recent applications in economics include many that base estimation on the method of moments. The generalized method of moments departs from a set of model based moment equations, E [m(y,, x,, f)] = 0, where the set of equations specifies a relationship known to hold in the population. We used one of these in the preceding paragraph. The least squares estimator can be motivated by noting that the essential assumption is that E [x, (y, - xi f)] = 0. The estimator is obtained by seeking a parameter estimator, b, which mimics the population result; (1/n)^i [x, (y, - xib)] = 0. This is, of course, the

20Practitioners might note, recent developments in commercial software have produced a wide choice of "mixed" estimators which are various implementations of the maximum likelihood procedures and hierarchical Bayes procedures (such as the Sawtooth program (1999)). Unless one is dealing with a small sample, the choice between these can be based on convenience. There is little methodological difference. This returns us to the practical point noted earlier. The choice between the Bayesian approach and the sampling theory method in this application would not be based on a fundamental methodological criterion, but on purely practical considerations—the end result is the same.

normal equations for least squares. Note that the estimator is specified without benefit of any distributional assumption. Method of moments estimation is the subject of Chapter 18, so we will defer further analysis until then.

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