arXiv 21 Aug 2020 · Econometrics · 1 citations (OpenAlex)
arXiv:2008.09263 · PDF · DOI · OpenAlex · Extracted main text
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 minimize 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 from balancing over sieve spaces is possible if our entropy balancing weights are computed using stronger covariate balance constraints that are imposed on functions of covariates. We then show that our method enjoys favorable second-order properties from empirical likelihood estimation and inference: the estimator has a small (bounded) nonlinearity bias, and the likelihood ratio based confidence set admits a simple analytical correction that can be used 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Dong, Y. and A. Lewbel (2015) Identifying the effect of changing the policy threshold in regression discontinuity models | 1.000 | 7 | 4 | 100% |
| 2 | Calonico, S., M. D. Cattaneo, and M. H. Farrell (2020) Optimal bandwidth choice for robust bias corrected inference in regression discontinuity designs | 1.000 | 6 | 3 | 100% |
| 3 | Hyytinen, A., J. Meriläinen, T. Saarimaa, O. Toivanen, and J. Tukiai… (2018) When does regression discontinuity design work? evidence from random election outcomes | 1.000 | 6 | 3 | 100% |
| 4 | Chan, K. C. G., S. C. P. Yam, and Z. Zhang (2016) Globally efficient nonparametric inference of average treatment effects by empirical balancing calibration weighting | 1.000 | 5 | 3 | 100% |
| 5 | Krei, A. and C. Rothe (2022) Inference in regression discontinuity designs with high-dimensional covariates | 0.928 | 4 | 3 | 100% |
| 6 | Calonico, S., M. D. Cattaneo, and R. Titiunik (2014) Robust nonparametric confidence intervals for regression-discontinuity designs | 0.928 | 4 | 3 | 100% |
| 7 | Frölich, M. and M. Huber (2019) Including covariates in the regression discontinuity design | 0.928 | 4 | 3 | 100% |
| 8 | Noack, C., T. Olma, and C. Rothe (2021) Flexible Covariate Adjustments in Regression Discontinuity Designs | 0.874 | 15 | 2 | 100% |
| 9 | Newey, W. K. and R. J. Smith (2004) Higher order properties of GMM and generalized empirical likelihood estimators | 0.874 | 9 | 2 | 100% |
| 10 | Ben-Michael, E., A. Feller, D. A. Hirshberg, and J. R. Zubizarreta (2021) The balancing act in causal inference | 0.874 | 5 | 2 | 100% |
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arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Covariate Adjustment in Regression Discontinuity Designs | 0.405 | 1 | 1 |