Abstract:

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.