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Changes-in-Changes for Ordered Choice Models with Underreporting

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  • Daniel Gutknecht
  • Cenchen Liu

Abstract

We develop a Difference-in-Differences framework for discrete, ordered outcomes subject to underreporting. Such outcomes commonly arise in self-reported surveys on socially undesirable or stigmatized behaviors, where respondents may conceal their true behavior. For a discrete Changes-in-Changes model that is shown to admit an equivalent threshold-crossing representation, we derive nonparametric bounds for the counterfactual and factual outcome distributions as well as for the associated quantile treatment effects when outcomes are underreported. These bounds are shown to be sharp uniformly across outcome levels under additional support conditions, and we propose suitable estimation and bootstrap inference procedures. In an extension, we also consider a semiparametric underreporting model that allows to point identify and estimate distributional treatment effects. As an application, we investigate the impact of recreational marijuana legalization on the consumption behavior of 8th-grade students in several U.S. states.

Suggested Citation

  • Daniel Gutknecht & Cenchen Liu, 2023. "Changes-in-Changes for Ordered Choice Models with Underreporting," Papers 2401.00618, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2401.00618
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    References listed on IDEAS

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    1. Roger W. Klein & Robert P. Sherman, 2002. "Shift Restrictions and Semiparametric Estimation in Ordered Response Models," Econometrica, Econometric Society, vol. 70(2), pages 663-691, March.
    2. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
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