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Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects

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  • Shoya Ishimaru

    (Hitotsubashi University)

Abstract

This study proposes an econometric framework to interpret and empirically decompose the difference between instrumental variables (IV) and ordinary least squares (OLS) estimates given by a linear regression model when the true causal effects of the treatment are nonlinear in treatment levels and heterogeneous across covariates. I show that the IV-OLS coefficient gap consists of three estimable components: the difference in weights on the covariates, the difference in weights on the treatment levels, and the difference in identified marginal effects that arises from endogeneity bias. Applications of this framework to return-to-schooling estimates demonstrate the empirical relevance of this distinction in properly interpreting the IV-OLS gap.

Suggested Citation

  • Shoya Ishimaru, 2024. "Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects," The Review of Economics and Statistics, MIT Press, vol. 106(2), pages 505-520, March.
    • Handle: RePEc:tpr:restat:v:106:y:2024:i:2:p:505-520
    DOI: 10.1162/rest_a_01169
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    Cited by:

    1. Xie, Jian & Yuan, Song, 2025. "The cultural origins of family firms," Journal of Comparative Economics, Elsevier, vol. 53(1), pages 1-24.
    2. Galofré-Vilà, Gregori, 2023. "Spoils of War: The Political Legacy of the German hyperinflation," Explorations in Economic History, Elsevier, vol. 88(C).
    3. Bjerk, David J., 2025. "Understanding IV Versus OLS Estimates of Treatment Effects and the Coefficient Difference Check," IZA Discussion Papers 18274, Institute of Labor Economics (IZA).
    4. Patrinos, Harry Anthony, 2025. "Returns to education in Greece: Causal evidence from the 1977 labor market survey," GLO Discussion Paper Series 1674, Global Labor Organization (GLO).
    5. He, Xiaoyu & Zheng, Yawen & Chen, Yiwen, 2025. "Weapons and influence: Unpacking the impact of Chinese arms exports on the UNGA voting alignment," European Journal of Political Economy, Elsevier, vol. 87(C).
    6. Klaus Ackermann & Sefa Awaworyi Churchill & Russell Smyth, 2023. "Broadband Internet and Cognitive Functioning," The Economic Record, The Economic Society of Australia, vol. 99(327), pages 536-563, December.
    7. Tymon Sloczynski & Tymon Słoczyński, 2021. "When Should We (Not) Interpret Linear IV Estimands as LATE?," CESifo Working Paper Series 9064, CESifo.
    8. Shoya Ishimaru, 2021. "What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence," Papers 2103.12374, arXiv.org, revised Sep 2025.

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