The Sign of a Mean Regression: Characterisation, Estimation and Applications

Abstract

There exist a number of important applications in which interest centers on the sign rather than the overall shape of a mean regression. These include certain decision-making problems as well as the problems of calibration and econometric equation inversion. We show that the sign of a mean regression for Y may be viewed as a generalisation of a quantile regression for the sign of Y. This characterisation is used to construct three related estimators that require only a very weak specification condition for the estimated model's sign to be consistent for the regression's sign. The relative merits of each estimator are discussed and simulations are used to study one of the estimators.

Keywords: Regression sign, regression zeros, robust consistent estimation, quantile regression, decision rule estimation, calibration, econometric equation inversion

JEL Classification: C13, C14, C25, C44, G11.