2023 Fiscal Year Research-status Report
New Developments in Regression Discontinuity Designs: Covariates Adjustment and Coverage Optimal Inference
| Project/Area Number |
21K01419
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| Research Institution | University of Tsukuba |
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Principal Investigator |
YU ZHENGFEI 筑波大学, 人文社会系, 准教授 (40774758)
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| Project Period (FY) |
2021-04-01 – 2025-03-31
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| Keywords | Regression discontinuity / Covariate adjustment / Balancing estimator / Efficiency / Empirical likelihood |
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| Outline of Annual Research Achievements |
This year's research proposes a balancing approach for covariate-adjusted estimation of the treatment effect parameter in the Regression discontinuity (RD) model.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. The entropy balancing estimator can be formulated as an empirical likelihood estimator that efficiently incorporates the information from the covariate balance condition as over-identifying moment restrictions, and thus has an asymptotic variance no larger than that of the standard estimator without covariates. Further efficiency improvement is also possible by balancing functions of covariates over a linear sieve space. The proposed 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.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Following the advice of journal editors and referees, this year's research improves the initially proposed covariate adjustment method for RD in several aspects: first, I propose an entropy balancing estimator for RD which resembles the entropy
balancing method in the literature on average treatment effect(ATE) estimation under unconfoundedness. Second, the proposed estimation procedure no longer involves nuisance parameters. Third, further efficiency gain is possible if the covariate balance conditions are imposed on functions of the covariates.
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| Strategy for Future Research Activity |
This project is going to extend the empirical balancing method for covariate adjustment beyond the standard regression discontinuity (RD) model. Specifically, it also applies to covariate-adjusted estimation of the treatment effect derivative and nonlinear RD estimators for limited dependent variables. In general, one can start with the standard estimator (without covariates) for a parameter of interest in an RD-related context and then replace its standard uniform weights with the balancing weights. The balancing weights are computed using the covariates only, and are independent of the standard estimator. The balancing approach proposed in the project can also be cast in a more general framework: the risk minimization problem that trades off between imbalance and complexity.
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