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Regression Discontinuity Design under Self-selection

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Document pages: 53 pages

Abstract: In Regression Discontinuity (RD) design, self-selection leads to differentdistributions of covariates on two sides of the policy intervention, whichessentially violates the continuity of potential outcome assumption. Thestandard RD estimand becomes difficult to interpret due to the existence ofsome indirect effect, i.e. the effect due to self selection. We show that thedirect causal effect of interest can still be recovered under a class ofestimands. Specifically, we consider a class of weighted average treatmenteffects tailored for potentially different target populations. We show that aspecial case of our estimands can recover the average treatment effect underthe conditional independence assumption per Angrist and Rokkanen (2015), andanother example is the estimand recently proposed in Frölich and Huber(2018). We propose a set of estimators through a weighted local linearregression framework and prove the consistency and asymptotic normality of theestimators. Our approach can be further extended to the fuzzy RD case. Insimulation exercises, we compare the performance of our estimator with thestandard RD estimator. Finally, we apply our method to two empirical data sets:the U.S. House elections data in Lee (2008) and a novel data set from MicrosoftBing on Generalized Second Price (GSP) auction.

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