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.