Working Paper: NBER ID: w27424
Authors: Zhuan Pei; David S. Lee; David Card; Andrea Weber
Abstract: Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regression methods. While Imbens and Kalyanaraman (2012) and Calonico, Cattaneo and Titiunik (2014) provide guidance on bandwidth, the sensitivity to polynomial order still poses a conundrum to RD practitioners. It is understood in the econometric literature that applying the argument of bias reduction does not help resolve this conundrum, since it would always lead to preferring higher orders. We therefore extend the frameworks of Imbens and Kalyanaraman (2012) and Calonico, Cattaneo and Titiunik (2014) and use the asymptotic mean squared error of the local regression RD estimator as the criterion to guide polynomial order selection. We show in Monte Carlo simulations that the proposed order selection procedure performs well, particularly in large sample sizes typically found in empirical RD applications. This procedure extends easily to fuzzy regression discontinuity and regression kink designs.
Keywords: Regression Discontinuity; Local Polynomial Regression; Causal Inference
JEL Codes: C21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Polynomial order choice in local polynomial regression (C69) | Treatment effect estimates (C22) |
| Higher-order polynomials (C69) | Smaller asymptotic biases (C51) |
| Higher-order polynomials (C69) | Poorer finite-sample performance (C51) |
| Local linear specification (C51) | Adequate treatment effect estimates when conditional expectation function is close to linear (C51) |
| Higher-order polynomials (C69) | More suitable when conditional expectation function exhibits significant curvature (C51) |
| Optimal polynomial order (C69) | Varies depending on data generating process and sample size (C29) |
| Order selection procedure based on estimated AMSE (C51) | Substantial improvements in MSE and confidence interval coverage rates (C51) |