Empirical likelihood estimation and consistent tests with conditional moment restrictions

This paper is about efficient estimation and consistent tests of conditional moment restrictions. We use unconditional moment restrictions based on splines or other approximating functions for this purpose. Empirical likelihood estimation is particularly appropriate for this setting, because of its relatively low bias with many moment conditions. We give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size. We also give results for generalized empirical likelihood, generalized method of moments, and nonlinear instrumental variable estimators.