Generalized Method Of Moments Model Research Articles

DETECTING LACK OF IDENTIFICATION IN GMM

One of the key assumptions of the standard linear instrumental variables (IV) model is that the instruments and endogenous variables are correlated. This is the identification assumption, without which the usual IV estimator is neither consistent nor asymptotically normal. If the correlation between the instruments and the endogenous variables is nonzero, but slight, then the conventional Gaussian asymptotic theory for the IV model can nevertheless provide a very poor approximation to the actual sampling distribution of estimators and test statistics. Recognizing the identification assumption on which the IV model relies, it is quite common in the applied literature to test for instrument relevance by a first-stage F-test. The null hypothesis is one of a total lack of identification. A rejection of this hypothesis by no means implies that issues of weak instruments can be ignored (Staiger and Stock, 1997). But a failure to reject this hypothesis is a strong indication of identification difficulties. The firststage F-test is an important and useful diagnostic in the IV model. The generalized method of moments (GMM) model (Hansen, 1982) nests the linear IV model as a special case. Not surprisingly, analogous issues arise in this model. Researchers have found that, in many contexts, the conventional Gaussian asymptotic theory provides a poor approximation to the sampling distribution of GMM estimators and test statistics. There are many possible reasons why this could happen, but they include identification problems. However, I am aware of no test of the identification condition in the nonlinear-inparameters GMM model in the existing literature. This paper proposes such a

Confidence intervals in generalized method of moments models

We consider the construction of confidence intervals for parameters characterized by moment restrictions. In the standard approach to generalized method of moments (GMM) estimation, confidence intervals are based on the normal approximation to the sampling distribution of the parameters. There is often considerable disagreement between the nominal and actual coverage rates of these intervals, especially in cases with a large degree of overidentification. We consider alternative confidence intervals based on empirical likelihood methods which exploit the normal approximation to the Lagrange multipliers calculated as a byproduct in empirical likelihood estimation. In large samples such confidence intervals are identical to the standard GMM ones, but in finite samples their properties can be substantially different. In some of the examples we consider, the proposed confidence intervals have coverage rates much closer to the nominal coverage rates than the corresponding GMM intervals.