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Instrumental Variables Methods With Heterogeneity And Mismeasured Instruments

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  • Chalak, Karim

Abstract

We study the consequences of substituting an error-laden proxy W for an instrument Z on the interpretation of Wald, local instrumental variable (LIV), and instrumental variable (IV) estimands in an ordered discrete choice structural system with heterogeneity. A proxy W need only satisfy an exclusion restriction and that the treatment and outcome are mean independent from W given Z. Unlike Z, W need not satisfy monotonicity and may, under particular specifications, fail exogeneity. For example, W could code Z with error, with missing observations, or coarsely. We show that Wald, LIV, and IV estimands using W identify weighted averages of local or marginal treatment effects (LATEs or MTEs). We study a necessary and sufficient condition for nonnegative weights. Further, we study a condition under which the Wald or LIV estimand using W identifies the same LATE or MTE that would have been recovered had Z been observed. For example, this holds for binary Z and therefore the Wald estimand using W identifies the same “average causal response,” or LATE for binary treatment, that would have been recovered using Z. Also, under this condition, LIV using W can be used to identify MTE and average treatment effects for e.g., the population, treated, and untreated.

Suggested Citation

  • Chalak, Karim, 2017. "Instrumental Variables Methods With Heterogeneity And Mismeasured Instruments," Econometric Theory, Cambridge University Press, vol. 33(1), pages 69-104, February.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:01:p:69-104_00
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    Cited by:

    1. Acerenza, Santiago & Ban, Kyunghoon & Kedagni, Desire, 2021. "Marginal Treatment Effects with Misclassified Treatment," ISU General Staff Papers 202106180700001132, Iowa State University, Department of Economics.
    2. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    3. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    4. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    5. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    6. Chalak, Karim, 2024. "Nonparametric Gini-Frisch bounds," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    8. Santiago Acerenza, 2024. "Partial Identification of Marginal Treatment Effects with Discrete Instruments and Misreported Treatment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 74-100, February.
    9. Vitor Possebom, 2021. "Crime and Mismeasured Punishment: Marginal Treatment Effect with Misclassification," Papers 2106.00536, arXiv.org, revised Jul 2023.
    10. Black, Nicole & Hughes, Robert & Jones, Andrew M., 2018. "The health care costs of childhood obesity in Australia: An instrumental variables approach," Economics & Human Biology, Elsevier, vol. 31(C), pages 1-13.

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