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TESTING FOR UNOBSERVED HETEROGENEOUS TREATMENT EFFECTS WITH OBSERVATIONAL DATA

Published online by Cambridge University Press:  28 April 2022

Yu-Chin Hsu ,
Ta-Cheng Huang  and
Haiqing Xu
Yu-Chin Hsu
Affiliation:
Academia Sinica, National Central University, National Chengchi University, and National Taiwan University
Ta-Cheng Huang*
Affiliation:
National University of Singapore
Haiqing Xu
Affiliation:
University of Texas at Austin
*
Address correspondence to Ta-Cheng Huang, Global Asia Institute, National University of Singapore, Singapore; e-mail: tchuang@nus.edu.sg.
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Abstract

Unobserved heterogeneous treatment effects have been emphasized in the recent policy evaluation literature (see, e.g., Heckman and Vytlacil (2005, Econometrica 73, 669–738)). This paper proposes a nonparametric test for unobserved heterogeneous treatment effects in a treatment effect model with a binary treatment assignment, allowing for individuals’ self-selection to the treatment. Under the standard local average treatment effects assumptions, i.e., the no defiers condition, we derive testable model restrictions for the hypothesis of unobserved heterogeneous treatment effects. Furthermore, we show that if the treatment outcomes satisfy a monotonicity assumption, these model restrictions are also sufficient. Then, we propose a modified Kolmogorov–Smirnov-type test which is consistent and simple to implement. Monte Carlo simulations show that our test performs well in finite samples. For illustration, we apply our test to study heterogeneous treatment effects of the Job Training Partnership Act on earnings and the impacts of fertility on family income, where the null hypothesis of homogeneous treatment effects gets rejected in the second case but fails to be rejected in the first application.

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Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 3 , June 2023 , pp. 582 - 622
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

The authors are grateful to the Editor (Peter C.B. Phillips), the Co-Editor (Yoon-Jae Whang), three anonymous referees, Jason Abrevaya, Qi Li, Xiaojun Song, and Quang Vuong for valuable comments and suggestions, which have considerably improved the presentation of the paper. Yu-Chin Hsu gratefully acknowledges the research support from the Ministry of Science and Technology of Taiwan (MOST2628-H-001-007, MOST110-2634-F-002-045), Academia Sinica Investigator Award of Academia Sinica (AS-IA-110-H01), and Center for Research in Econometric Theory and Applications (110L9002) from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education of Taiwan. Ta-Cheng Huang is indebted to Qi Li for his continued inspiration, guidance, and support. Haiqing Xu would like to dedicate this paper to the memory of Professor Halbert White.

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