Estimation of Linear Regression Models from Bid-Ask Data by a
Spread-Tolerant Estimator

This research was supported by the National Science Foundation.

Oliver Linton

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 nonlinear, and indeed the criterion function itself is non-smooth. We establish its asymptotic properties using the approach of Pakes and Pollard (1989). We compare the estimator with mid-point OLS.

Key Words: Bid-ask spread; Censored data; Linear regression.
JEL Classification Numbers: C13,C24.