Instrumental Variable Bias with Censored Regressors

This note examines the inconsistency of instrumental variables (IV) estimators when endogenous regressors are censored. Using a bivariate setting, asymptotic bias is character-ized for various types of random censoring and for top-coding and bottom-coding. With independent censoring, expansion bias always occurs, with IV estimates proportionately too large. With dependent censoring, expansion bias typically arises, and we study con-ditions that assure this with top-coding and bottom-coding. We illustrate these structures graphically for the case with random assignment. Various aspects of estimation with censored regressors are discussed. 1