A semi-parametric empirical likelihood approach for conditional estimating equations under endogenous selection

Abstract

The estimation and inference for conditional estimating equations models with endogenous selection, are considered. The approach takes into account possible endogenous selection which may lead to a selection bias. It can be used for a wide range of statistical models not covered by the model-based sampling theory. Endogeneity can be either part of the selection or within the covariates. It is particularly well suited for models with unknown heteroscedasticity, uncontrolled confounders and measurement errors. It will not be necessary to model the relationship between the endogenous covariates and the instrumental variables, which offers major advantages over two-stage least-squares. The approach proposed has the advantage of being based on a fixed number of constraints determined by the size of the parameter.