Testing conditional moment restriction models using empirical likelihood[Efficient estimation of models with conditional moment restrictions containing unknown functions]

SummaryAn empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with nonlinear endogenous covariates, with and without heteroscedastic errors and non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit studentization. A simulation study shows that the observed size is close to the nominal level, unlike alternative empirical likelihood approaches. It also offers a major advantage over two-stage least-squares, because the relationship between endogenous and instrumental variables does not need to be known. An empirical likelihood model specification test is also proposed.