Strategy-Proof Estimations for Simple Regression

In this paper we propose a whole class of estimators ("clockwise repeated median estimators" or CRM) for the simple regression model that are immune to manipulation by the agents generating the data.Although strategic considerations affecting the stability of the estimated parameters in regression models have already been studied (the Lucas critique), few efforts have been made to designestimators that are incentive compatible.We find that some well-known robust estimators proposed in the literature like the resistant line method are included in our family. Finally, we also undertake a Monte Carlo study to compare thedistribution of some estimators that are robust to data anipulation with the OLS estimators under some specific data manipulation process.