Empirical Likelihood Based Inference in Conditional Moment Restriction Models

TLDR: This paper proposed an asymptotically efficient method for estimating models with conditional moment restrictions, which generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994).

Abstract: This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our likelihood ratio-type statistic for parametric restrictions does not require the estimation of variance, and achieves asymptotic pivotalness implicitly. The estimation and testing procedures we propose are normalization invariant. Simulation results suggest that our new estimator works remarkably well in finite samples.