On the Estimation of Selection Models when Participation is Endogenous and Misclassified

This chapter presents a Bayesian analysis of the endogenous treatment model with misclassified treatment participation. Our estimation procedure utilizes a combination of data augmentation, Gibbs sampling, and Metropolis–Hastings to obtain estimates of the misclassification probabilities and the treatment effect. Simulations demonstrate that the proposed Bayesian estimator accurately estimates the treatment effect in light of misclassification and endogeneity.