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.