Empirical Balancing (Likelihood) Covariate Adjustment for Regression Discontinuity Designs
Holder： Jun Ma（Renmin University of China）
Time：2024-04-11 15:10-17:00
Location：Room 217, Guanghua Building 2
Abstract:
This paper proposes a versatile covariate adjustment method that directly incorporates covariate balance in regression discontinuity (RD) designs. The new empirical entropy balancing method reweights the standard local polynomial RD estimator by using the entropy balancing weights that minimizes the Kullback–Leibler divergence from the uniform weights while satisfying the covariate balance constraints. Our estimator can be formulated as an empirical likelihood estimator that efficiently incorporates the information from the covariate balance condition as correctly specified over-identifying moment restrictions, and thus has an asymptotic variance no larger than that of the standard estimator without covariates. We demystify the asymptotic efficiency gain of Calonico, Cattaneo, Farrell, and Titiunik (2019)’s regression based covariate-adjusted estimator, as their estimator has the same asymptotic variance as ours. Further efficiency improvement is possible if our entropy balance weights are computed using stronger covariate balance conditions that are imposed on functions in sieve spaces of covariates. Then we show our method enjoys favorable second-order properties carried over from empirical likelihood estimation and inference. Our estimator has a small (bounded) nonlinearity bias and the likelihood ratio based confidence set admits a simple analytical correction that can be exploited to improve coverage accuracy. The coverage accuracy of our confidence set is robust against slight perturbation to the covariate balance condition, which may happen in cases such as data contamination and misspecified “unaffected” outcomes used as covariates. The proposed entropy balancing approach for covariate adjustment is applicable to other RD related settings.
About the Speaker:
Jun Ma is an associate professor at School of Economics, Renmin University of China. He conducts research in econometrics. His research interests include empirical likelihood, nonparametric / semiparametric econometrics, econometrics of auctions and causal inference. His research work appears in journals such as Journal of Econometrics and Journal of Business & Economic Statistics etc. He has been principal investigator and co-investigator of NSFC projects.
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