Covariate Measurement Error in Endogenous Stratified Samples

Abstract

In this paper we propose a general framework to deal with the presence of covariate mea-surement error in endogenous stratifield samples. Using Chesher’s (2000) methodology, we develop approximately consistent estimators for the parameters of the structural model, in the sense that their inconsistency is of smaller order than that of the conventional estimators which ignore the existence of covariate measurement error. The approximate bias corrected estimators are obtained by applying the generalized method of moments (GMM) to a modifeld version of the moment indicators suggested by Imbens and Lancaster (1996) for endogenous stratified samples. Only the specification of the conditional distribution of the response vari-able given the latent covariates and the classical additive measurement error model assumption are required, the availability of information on both the marginal probability of the strata in the population and the variance of the measurement error not being essential. A score test to detect the presence of covariate measurement error arises as a by-product of this approach. Monte Carlo evidence is presented which suggests that, in endogenous stratified samples of moderate sizes, the modified GMM estimators perform well.