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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. Santiago Acerenza & Kyunghoon Ban & D'esir'e K'edagni, 2021. "Marginal Treatment Effects with a Misclassified Treatment," Papers 2105.00358, arXiv.org, revised Apr 2023.
    2. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    3. Vitor Possebom, 2021. "Crime and Mismeasured Punishment: Marginal Treatment Effect with Misclassification," Papers 2106.00536, arXiv.org, revised Jul 2023.
    4. 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.
    5. 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.
    6. 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.
    7. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    8. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    9. Santiago Acerenza, 2021. "Partial Identification of Marginal Treatment Effects with discrete instruments and misreported treatment," Papers 2110.06285, arXiv.org, revised Mar 2023.

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