The Performance of Empirical Likelihood and Its Generalizations [chapter]

Guido W. Imbens, Richard H. Spady, Donald W. K. Andrews, James H. Stock
Identification and Inference for Econometric Models  
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 having an MSE that exceeds OGMM's by an additional term of order (M ¡1)=N, i.e. the degree of overidenti¯cation divided by sample size. In contrast, any 2-step GMM estimator has an additional bias relative to OGMM of order (M ¡ 1)=N and
more » ... order (M ¡ 1)=N and an additional MSE of order (M¡1) 2 =N: Consequently GEL must be expected to dominate 2-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.
doi:10.1017/cbo9780511614491.011 fatcat:3jl6fova75cizefbboiqtcckbi