Minimally capturing heterogeneous complier effect of endogenous treatment for any outcome variable

Goeun Lee, Jin Young Choi, Myoung Jae Lee

Research output: Contribution to journalArticlepeer-review


When a binary treatment D is possibly endogenous, a binary instrument δ is often used to identify the "effect on compliers."If covariates X affect both D and an outcome Y, X should be controlled to identify the "X-conditional complier effect."However, its nonparametric estimation leads to the well-known dimension problem. To avoid this problem while capturing the effect heterogeneity, we identify the complier effect heterogeneous with respect to only the one-dimensional "instrument score"E (δ|X) for non-randomized δ. This effect heterogeneity is minimal, in the sense that any other "balancing score"is finer than the instrument score. We establish two critical "reduced-form models"that are linear in D D or δ, even though no parametric assumption is imposed. The models hold for any form of Y (continuous, binary, count, ...). The desired effect is then estimated using either single index model estimators or an instrumental variable estimator after applying a power approximation to the effect. Simulation and empirical studies are performed to illustrate the proposed approaches.

Original languageEnglish
Article number20220036
JournalJournal of Causal Inference
Issue number1
Publication statusPublished - 2023 Jan 1

Bibliographical note

Funding Information:
Funding information : Jin-young Choi’s research has been supported by the Hankuk University of Foreign Studies Research Fund of 2023. Myoung-jae Lee’s research has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01007786).

Publisher Copyright:
© 2023 the author(s), published by De Gruyter.


  • complier effect
  • endogenous treatment
  • instrument score
  • instrumental variable estimator
  • propensity score
  • single index model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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