摘要翻译：
本文为异构因果效应模型中的仪器效度测试提供了一个通用框架。一般化包括治疗可以是多值的（和有序的）或无序的情况。基于一系列可测性的含义，我们提出了一个非参数测试，并证明了它是渐近尺寸控制的和一致的。由于问题的非标准性质，测试统计量是基于一个非光滑映射来构造的，这造成了技术上的复杂性。我们给出了一个推广的连续映射定理和一个推广的delta方法，这可能是独立的兴趣，以建立测试统计量在零点下的渐近分布。然后我们扩展了Fang和Santos(2018)提出的bootstrap方法来逼近该渐近分布，并构造了测试的临界值。与文献中的测试相比，我们的测试可以应用于更广泛的环境中，并可能实现功耗的提高。通过仿真，证明了该测试在有限样本上表现良好。我们回顾了Card(1993)的实证研究，并使用他们的数据来证明所提出的测试在实践中的应用。我们表明，如果治疗变粗，一个有效的多值治疗工具可能不会继续有效。
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英文标题：
《Instrument Validity for Heterogeneous Causal Effects》
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作者：
Zhenting Sun
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最新提交年份：
2021
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  This paper provides a general framework for testing instrument validity in heterogeneous causal effect models. The generalization includes the cases where the treatment can be multivalued (and ordered) or unordered. Based on a series of testable implications, we propose a nonparametric test which is proved to be asymptotically size controlled and consistent. Because of the nonstandard nature of the problem in question, the test statistic is constructed based on a nonsmooth map, which causes technical complications. We provide an extended continuous mapping theorem and an extended delta method, which may be of independent interest, to establish the asymptotic distribution of the test statistic under null. We then extend the bootstrap method proposed by Fang and Santos (2018) to approximate this asymptotic distribution and construct a critical value for the test. Compared to the tests in the literature, our test can be applied in more general settings and may achieve power improvement. Evidence that the test performs well on finite samples is provided via simulations. We revisit the empirical study of Card (1993) and use their data to demonstrate application of the proposed test in practice. We show that a valid instrument for a multivalued treatment may not remain valid if the treatment is coarsened.
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PDF链接：
https://arxiv.org/pdf/2009.01995