要旨：　Exclusion and shape restrictions are crucial for defining causal effects, understanding individual heterogeneity, and interpreting estimators in potential outcome models. This paper is concerned with characterizing the empirical content of such restrictions. To date, the testable implications of these restrictions have been studied on a case-by-case basis within a limited set of models. Using a novel graph-based representation of the model, we provide a systematic approach to deriving sharp testable implications of general support restrictions. We illustrate the proposed approach in simulations and an empirical application.

アブストラクト：
独立な高次元確率ベクトルの和の成分の最大値として与えられる統計量の分布の近似は、高次元パラメータに対する仮説検定や一様信頼区間の構成を行う上で重要な役割を果たす。V. Chernozhukov, D. ChetverikovおよびK. Katoらによる近年の研究によって、そのような最大値統計量の分布に対する正規型の近似やブートストラップ近似は、次元がサンプル数よりもはるかに大きいような超高次元の設定においても適当なモーメント条件下で正当化できることが明らかにされた。一方で、データの歪度がある程度大きい場合、スチューデント化を行わない場合であっても、高次元の設定では3次モーメントまでマッチさせるようなブートストラップ近似の方が正規型の近似よりも有限標本でのパフォーマンスが優れていることが数値実験によって観察されているが、既存の理論的結果はこのことを説明できない。本報告では、漸近展開を用いることでこの現象が理論的に説明できることを示す。特に、母集団の共分散行列が一定の条件を満たす場合、次元がサンプル数よりも大きい状況では3次モーメントまでマッチさせるようなブートストラップ近似がスチューデント化せずとも2次の精度を持つというblessing of dimensionality phenomenonが現れる。

Abstract: The exclusion restriction plays a key role in the identification of LATE (Imbens & Angrist (1994), Angrist, Imbens & Rubin (1996)). We discuss a particularly ubiquitous way in which the exclusion restriction would seem to be generically violated. We argue that this form of violation is not addressed in the many applications that rely on this influential framework. We characterize the bias that this particular violation gives rise to and, more constructively, discuss how to use the particular structure of the violation along with milder assumptions and additional data to restore identification. We provide sharper bounds by exploiting the specific structure of the exclusion restriction violation we uncover. Further, with an additional assumption which is plausible in many empirical settings, we restore point identification of LATE. We illustrate with examples and discuss why this violation is likely present in most existing empirical applications. We discuss how our arguments naturally extend to other IV settings where the LATE parameter is commonly invoked, such as randomized controlled trials with imperfect compliance and fuzzy regression discontinuity designs. Moving beyond LATE, we also consider how the same problems and solution ideas apply to identification of the MTE profile and more structural “Roy” models of treatment effects.

要旨：　In the evaluation of social programs, it is often difficult to conduct randomized controlled experiments due to non-compliance; therefore the local average treatment effect (LATE) is commonly applied. However, the LATE identifies the average treatment effect only for a subpopulation known as compliers and requires the monotonicity assumption. Given these limitations of the LATE, this paper proposes a nonparametric strategy to identify the causal effects for larger populations (such as the ATT and ATE) and to remove the monotonicity assumption in the cases of non-compliance. Our strategy utilizes two types of auxiliary observations, one is an outcome before assignment and the other is a treatment before assignment. These observations do not require specially designed experiments, and are likely to be observed in baseline surveys of the standard experiment or panel data. We show the results for the random assignment and those of multiply robust representations in the case where the random assignment is violated. We then present details of the GMM estimation and testing methods which utilize over-identified restrictions. The proposed strategy is illustrated by empirical examples which revisit the studies by Thornton (2008), Gerber et al. (2009), and Beam (2016), as well as the data set from the Oregon Health Insurance Experiment and that from an experimental data on marketing in a private sector.

Workshop on Recent Advances in Econometrics3