An approximated exponentially tilted empirical likelihood estimator of moment condition models

This study proposes an approximated estimator for moment condition models. Our estimator approximates the exponentially tilted empirical likelihood (ETEL) estimator in Schennach (2007) by using a second-order approximation of implied probabilities (IPs) for the exponential tilting (ET). The resulting approximated ETEL estimator generates positive IPs. As the nested optimization of ETEL and EL is avoided, it is computationally simple. It is second-order asymptotically equivalent to the EL estimator. In particular, it has the same O(n−1) bias as EL. It also has the same O(n−2) variance as EL. Like ET and ETEL estimators, it is n convergent under model misspecification, while the EL estimator may not be.