Empirical Likelihood Ratio Tests of Conditional Moment Restrictions With Unknown Functions

This article introduces empirical likelihood ratio tests for conditional moment models in which the unknown parameter contains infinite-dimensional components. We allow unknown functions to be included in the conditional moment restrictions. We discusses (1) the limiting distribution of the sieve conditional empirical likelihood ratio (SCELR) test statistic for functionals of parameters under the null hypothesis and local alternatives; and (2) the limiting distribution of the SCELR test statistic for conditional moment restrictions (a consistent specification test) under the null hypothesis and local alternatives. A Monte Carlo study examines finite sample performance. We then apply these tests in an empirical application to construct confidence intervals for Engel curves and test restrictions on the curves.