Regularized empirical likelihood as a solution to the no moment problem: The linear case with many instruments

Abstract

In this paper, we explore the finite sample properties of the generalized empirical likelihood for a continuum, applied to a linear model with endogenous regressors and many discrete moment conditions. In particular, we show that the estimator from this regularized version of GEL has finite moments. It therefore solves the issue regarding the no moment problem of empirical likelihood. We propose a data driven method to select the regularization parameter based on a cross validation criterion, and show that the method outperforms many existing methods when the number of instruments exceeds 20.