论文标题
经验可能性的协变量调整，用于回归不连续设计
Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs
论文作者
论文摘要
本文提出了一种多功能协变量调整方法，该方法将协变量平衡直接纳入回归不连续性（RD）设计中。新的经验熵平衡方法通过使用熵平衡权重来重新授予标准的本地多项式RD估计器，从而使kullback-leibler与均匀权重的差异最小化，同时满足协变量平衡约束。我们的估计器可以作为经验可能性估计值进行配制，该估计值可以有效地合并从协变量平衡条件中正确指定的过度识别矩限制的信息，因此具有渐近方差，而没有协变量的标准估计器的渐近差异。我们揭开了Calonico，Cattaneo，Farrell和Titiunik（2019）基于回归的协变量估算器的渐近效率提高，因为它们的估计量与我们的渐近方差相同。如果使用对协变量功能施加的更强大的协变量约束来计算我们的熵平衡权重，则可以从平衡筛分空间之间进行进一步提高效率。然后，我们证明我们的方法从经验可能性估计和推理中享有有利的二阶特性：估计器具有很小的（有限的）非线性偏差，基于可能性比率的置信度集合可以采用简单的分析校正，可用于提高覆盖范围的准确性。我们信心集的覆盖范围准确性是可靠的，与对协变量平衡条件的轻微扰动，这种情况可能发生在数据污染和误指定为协变量的“未受影响”结果之类的情况下。提出的协变量调整的熵平衡方法适用于其他与RD相关的设置。
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.
