Second order expansions of estimators in nonparametric moment conditions models with weakly dependent data

Abstract This paper considers estimation of nonparametric moment conditions models with weakly dependent data. The estimator is based on a local linear version of the generalized empirical likelihood approach, and is an alternative to the popular local linear generalized method of moment estimator. The paper derives uniform convergence rates and pointwise asymptotic normality of the resulting local linear generalized empirical likelihood estimator. The paper also develops second order stochastic expansions (under a standard undersmoothing condition) that explain the better finite sample performance of the local linear generalized empirical likelihood estimator compared to that of the efficient local linear generalized method of moments estimator, and can be used to obtain (second order) bias corrected estimators. Monte Carlo simulations and an empirical application illustrate the competitive finite sample properties and the usefulness of the proposed estimators and second order bias corrections.