Treatment Effect Analyses through Orthogonality Conditions Implied by a Fuzzy Regression Discontinuity Design, with Two Empirical Studies1

This study proposes a new estimator for estimating a treatment effect in one particular fuzzy regression discontinuity (RD) setting, in which the treatment effect is homogeneous on the support of an assignment variable and the treatment assignment is exogenous conditional on that assignment variable. The estimator is constructed using orthogonality conditions and can be easily implemented by an instrumental variable (IV) estimation procedure. We use Monte Carlo experiments to show that the proposed estimator can substantially reduce the bias in estimating the treatment effect caused by misspecifying the regression model of the observed outcome. We also use two empirical studies to demonstrate the advantages of our proposed estimator over alternative estimators. Furthermore, we use the first empirical study to highlight a connection between our proposed estimator and propensity-score matching estimators. The second empirical study emphasizes that the proposed estimator can work in a fuzzy RD setting where the cutoff point is either unknown or not exactly known.