Robust Small Sample Accurate Inference in Moment Condition Models

Abstract

Procedures based on the Generalized Method of Moments (GMM) (Hansen, 1982) are basic tools in modern econometrics. In most cases, the theory available for making inference with these procedures is based on first order asymptotic theory. It is well-known that the (first order) asymptotic distribution does not provide accurate p-values and confidence intervals in moderate to small samples. Moreover, in the presence of small deviations from the assumed model, p-values and confidence intervals based on classical GMM procedures can be drastically affected (nonrobustness). Several alternative techniques have been proposed in the literature to improve the accuracy of GMM procedures. These alternatives address either the first order accuracy of the approximations (information and entropy econometrics (IEE)) or the nonrobustness (Robust GMM estimators and tests). In this paper, we propose a new alternative procedure which combines robustness properties and accuracy in small samples. Specifically, we combine IEE techniques as developed in Imbens, Spady, Johnson (1998) to obtain finite sample accuracy with robust methods obtained by bounding the original orthogonality function as proposed in Ronchetti and Trojani (2001). This leads to new robust estimators and tests in moment condition models with excellent finite sample accuracy. Finally, we illustrate the accuracy of the new statistic by means of some simulations for three models on overidentifying moment conditions.Exponential tilting, Generalized method of moments, Information and entropy econometrics, Monte Carlo, Robust tests, Saddlepoint techniques