The Performance of Empirical Likelihood and Its Generalizations
Guido W. Imbens, Richard H. Spady · Cambridge University Press eBooks · 2005
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. INTRODUCTION This paper has two parts. In the first part, 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 apparently 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 .