The Performance of Empirical Likelihood and its Generalizations


Imbens G, Spady R. The Performance of Empirical Likelihood and its Generalizations. Identification and Inference for Econometric Models, Essays in Honor of Thomas Rothenberg, Cambridge University Press. 2005.
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We calculate higher-order asymptotic biases and mean-squared errors (MSE) for a simple model with a sequence of moment conditions. In this setup, generalized empirical likelihood (GEL) and infeasible optimal GMM (OGMM) have the same higher-order biases, with GEL apparently having an MSE that exceeds OGMM's by an additional term of order (M - 1)/N, i.e. the degree of overidentification divided by sample size. In contrast, any two-step GMM estimator has an additional bias relative to OGMM of order (M - 1)/N and an additional MSE of order (M-1)^2/N. Consequently, GEL must be expected to dominate two-step GMM. In our simple model all GEL's have equivalent next higher order behavior because generalized third moments of moment conditions are assumed to be zero; we explore in further analysis and simulations the implications of dropping this assumption.

Last updated on 07/06/2012