Regression Discontinuity Design under Self-selection

Regression Discontinuity (RD) design is commonly used to estimate the causal effect of a policy. Existing RD relies on the continuity assumption of potential outcomes. However, self selection leads to different distributions of covariates on two sides of the policy intervention, which violates this assumption. The standard RD estimators are no longer applicable in such setting. We show that the direct causal effect can still be recovered under a class of weighted average treatment effects. We propose a set of estimators through a weighted local linear regression framework and prove the consistency and asymptotic normality of the estimators. We apply our method to a novel data set from Microsoft Bing on Generalized Second Price (GSP) auction and show that by placing the advertisement on the second ranked position can increase the click-ability by 1.91%.