Estimation of linear regression models by a spread-tolerant estimator

We investigate a class of estimators for Linear Regression models where the dependent variable is subject to bid-ask censoring. Our estimation method is based on a definition of error that is zero when the predictor lies between the actual bid price and ask price, and linear outside this range. Our estimator minimizes a sum of such squared errors; it is non-linear, and indeed the criterion function itself is non smooth. We establish its asymptotic properties using the approach of Pakes & Pollard (1989). We compare the estimator with mid-point OLS.