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Sensitivity Analysis in Unconditional Quantile Effects

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  • Julian Martinez-Iriarte

Abstract

This paper proposes a framework to analyze the effects of counterfactual policies on the unconditional quantiles of an outcome variable. For a given counterfactual policy, we obtain identified sets for the effect of both marginal and global changes in the proportion of treated individuals. To conduct a sensitivity analysis, we introduce the quantile breakdown frontier, a curve that (i) indicates whether a sensitivity analysis is possible or not, and (ii) when a sensitivity analysis is possible, quantifies the amount of selection bias consistent with a given conclusion of interest across different quantiles. To illustrate our method, we perform a sensitivity analysis on the effect of unionizing low income workers on the quantiles of the distribution of (log) wages.

Suggested Citation

  • Julian Martinez-Iriarte, 2023. "Sensitivity Analysis in Unconditional Quantile Effects," Papers 2303.14298, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2303.14298
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    References listed on IDEAS

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    1. Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, July.
    2. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    3. Julian Martinez-Iriarte & YiXiao Sun, 2022. "Identification and Estimation of Unconditional Policy Effects of an Endogenous Binary Treatment: an Unconditional MTE Approach," Working Papers 131, Red Nacional de Investigadores en Economía (RedNIE).
    4. Maximilian Kasy, 2016. "Partial Identification, Distributional Preferences, and the Welfare Ranking of Policies," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 111-131, March.
    5. Julian Martinez-Iriarte & Yixiao Sun, 2020. "Identification and Estimation of Unconditional Policy Effects of an Endogenous Binary Treatment: An Unconditional MTE Approach," Papers 2010.15864, arXiv.org, revised Aug 2024.
    6. Pedro Carneiro & James J. Heckman & Edward Vytlacil, 2010. "Evaluating Marginal Policy Changes and the Average Effect of Treatment for Individuals at the Margin," Econometrica, Econometric Society, vol. 78(1), pages 377-394, January.
    7. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    8. Thomas Lemieux, 2006. "Increasing Residual Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill?," American Economic Review, American Economic Association, vol. 96(3), pages 461-498, June.
    9. Henry S Farber & Daniel Herbst & Ilyana Kuziemko & Suresh Naidu, 2021. "Unions and Inequality over the Twentieth Century: New Evidence from Survey Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(3), pages 1325-1385.
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    Cited by:

    1. Martinez-Iriarte, Julian & Sun, Yixiao, 2024. "Identification and estimation of unconditional policy effects of an endogenous binary treatment: An unconditional MTE approach," Journal of Econometrics, Elsevier, vol. 244(1).
    2. Martínez-Iriarte, Julián & Montes-Rojas, Gabriel & Sun, Yixiao, 2024. "Unconditional effects of general policy interventions," Journal of Econometrics, Elsevier, vol. 238(2).

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