Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs
Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs
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发表时间：
2020-08
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通讯作者：
Jun Ma;Zhengfei Yu
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作者：
Jun Ma;Zhengfei Yu
本文提出了一种通用的协变量调整方法，直接将协变量平衡回归不连续性（RD）设计。新的经验熵平衡方法通过使用熵平衡权重来重新加权标准的局部多项式RD估计，该熵平衡权重在满足协变量平衡约束的同时最小化来自均匀权重的Kullback-Leibler发散。我们的估计可以制定为一个经验似然估计，有效地结合了从协变量平衡条件的信息作为正确指定的过度识别矩的限制，因此具有渐近方差不大于标准估计没有协变量。我们揭开了Calonico，Cattaneo，Farrell和Titiunik（2019）基于回归的协变量调整估计量的渐近效率增益，因为他们的估计量与我们的估计量具有相同的渐近方差。如果我们的熵平衡权重是使用施加在协变量函数上的更强的协变量平衡约束来计算的，则可以通过平衡筛空间来进一步提高效率。然后，我们表明，我们的方法享有良好的二阶属性从经验似然估计和推断：估计有一个小的（有界）非线性偏差，和似然比为基础的置信集承认一个简单的分析校正，可用于提高覆盖精度。我们的置信集的覆盖准确性对于协变量平衡条件的轻微扰动是鲁棒的，这可能发生在数据污染和错误指定的“未受影响“的结果用作协变量等情况下。所提出的协变量调整的熵平衡方法适用于其他RD相关设置。
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.