Bias From Censored Regressors

We study the bias that arises from using censored regressors in estimation of linear models. We present results on bias in ordinary least aquares (OLS) regression estimators with exogenous censoring and in instrumental variable (IV) estimators when the censored regressor is endogenous. Bound censoring such as top-coding results in expansion bias, or effects that are too large. Independent censoring results in bias that varies with the estimation method-attenuation bias in OLS estimators and expansion bias in IV estimators. Severe biases can result when there are several regressors and when a 0-1 variable is used in place of a continuous regressor.