Identification and Auto-debiased Machine Learning for Outcome Conditioned Average Structural Derivatives
结果条件平均结构导数的识别与自动去偏机器学习AI 解读 ↓
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结果条件平均结构导数的识别与自动去偏机器学习
- 研究问题
- 如何刻画连续处理的边际变化对处于不同结果分布位置人群的平均效应，并连接无条件分位数及分布政策效应？
- 方法与思路
- 作者在一般非可分模型下定义结果条件平均结构导数，以条件外生性识别，构造自动去偏估计并研究自助法一致推断。
- 材料陈述的贡献
- 摘要称，建立该参数与若干反事实分布效应的关系，并证明所提估计量根号样本量一致、渐近正态及达到半参数效率界。
- 阅读关注点
- 应核对结果条件群体的定义、结构导数存在条件、条件外生性及支持限制，以及参数等价关系和一致推断的具体范围。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审或期刊接收未核实；摘要未列完整正则条件，按结果位置分组的含义需与分位数效应区分。
原文摘要
This paper proposes a new class of heterogeneous causal quantities, named \textit{outcome conditioned} average structural derivatives (OASD) in a general nonseparable model. OASD is the average partial effect of a marginal change in a continuous treatment on the individuals located at different parts of the outcome distribution, irrespective of individuals' characteristics. OASD combines both features of ATE and QTE: it is interpreted as straightforwardly as ATE while at the same time more granular than ATE by breaking the entire population up according to the rank of the outcome distribution. One contribution of this paper is that we establish some close relationships between the \textit{outcome conditioned average partial effects} and a class of parameters measuring the effect of counterfactually changing the distribution of a single covariate on the unconditional outcome quantiles. By exploiting such relationship, we can obtain root-$n$ consistent estimator and calculate the semi-parametric efficiency bound for these counterfactual effect parameters. We illustrate this point by two examples: equivalence between OASD and the unconditional partial quantile effect (Firpo et al. (2009)), and equivalence between the marginal partial distribution policy effect (Rothe (2012)) and a corresponding outcome conditioned parameter. Because identification of OASD is attained under a conditional exogeneity assumption, by controlling for a rich information about covariates, a researcher may ideally use high-dimensional controls in data. We propose for OASD a novel automatic debiased machine learning estimator, and present asymptotic statistical guarantees for it. We prove our estimator is root-$n$ consistent, asymptotically normal, and semiparametrically efficient. We also prove the validity of the bootstrap procedure for uniform inference on the OASD process.