Changes-in-Changes for Ordered Choice Models with Underreporting

Cenchen Liu; Daniel Gutknecht

Changes-in-Changes for Ordered Choice Models with Underreporting

T0 review · 0 major / 2 minor · reviewed 2026-05-24 · grok-4.3

Challenge this review Download PDF Read on arXiv ↗

Pith's one-line read Nonparametric bounds recover quantile treatment effects for ordered outcomes when underreported.

desk verdict The paper gives sharp nonparametric bounds on distributions and QTEs for underreported ordered outcomes inside a discrete CiC model that admits a threshold-crossing representation. read the letter →

arxiv 2401.00618 v4 submitted 2024-01-01 econ.EM

Daniel Gutknecht , Cenchen Liu This is my paper

classification econ.EM

keywords changes-in-changesunderreportingorderedoutcomesquantiletreatmenteffectsnonparametricboundsdifference-in-differencesdiscretechoicemodels

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper establishes a difference-in-differences framework for discrete ordered outcomes that suffer from underreporting, common in surveys of stigmatized behaviors. It demonstrates that a discrete changes-in-changes model admits an equivalent threshold-crossing representation. From this equivalence, nonparametric bounds are derived for the factual and counterfactual outcome distributions and the quantile treatment effects. The bounds are shown to be sharp uniformly across outcome levels under additional support conditions, with estimation and inference procedures proposed.

What carries the argument

The discrete Changes-in-Changes model and its equivalent threshold-crossing representation, which supports the derivation of bounds on distributions under underreporting.

What would settle it

In a setting with observed true outcomes, if the true quantile treatment effect lies outside the estimated bounds, this would contradict the validity or sharpness of the bounds.

Watch

Extended reading notes

Core claim

For a discrete Changes-in-Changes model that admits an equivalent threshold-crossing representation, nonparametric bounds are derived for the counterfactual and factual outcome distributions as well as for the associated quantile treatment effects when outcomes are underreported. These bounds are sharp uniformly across outcome levels under additional support conditions.

Load-bearing premise

The discrete changes-in-changes model admits an equivalent threshold-crossing representation along with the support conditions needed for uniform sharpness of the bounds.

Editorial extensions

If this is right

Nonparametric bounds can be placed on the outcome distributions and quantile treatment effects accounting for underreporting.
The bounds achieve sharpness uniformly across all outcome levels given the support conditions.
Estimation procedures and bootstrap inference allow implementation of the bounds in practice.
A semiparametric extension to the underreporting model enables point identification of distributional treatment effects.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The framework may apply to other contexts involving misreported categorical data in longitudinal studies.
Ignoring underreporting in standard models could distort estimates of policy effects on behaviors like substance use.
Empirical checks on the support conditions would determine when the sharp bounds apply in specific datasets.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

The main takeaway is that this work extends the changes-in-changes setup to ordered discrete outcomes that suffer from underreporting, deriving nonparametric bounds on the factual and counterfactual distributions plus the associated quantile treatment effects. The bounds are claimed to be sharp uniformly across levels once support conditions hold, and the authors also sketch a semiparametric version that can deliver point identification. They apply the method to the effect of recreational marijuana legalization on 8th-grade consumption in several states. That combination of discrete CiC, underreporting, and sharp bounds does not appear in the cited literature, so the extension is new on its face. The application is a sensible test case because self-reported data on sensitive behaviors routinely involve concealment. The estimation and bootstrap procedures are described at a high level and look like standard adaptations. The central modeling step is showing that the discrete CiC model admits an equivalent threshold-crossing representation; if that step is clean, the rest follows from the usual bounding logic under the stated support restrictions. The soft spot is that we only have the abstract, so it is impossible to verify whether the representation holds without extra restrictions that would limit applicability, or whether the sharpness proof is tight. The support conditions needed for uniform sharpness could turn out to be demanding in typical survey data. Nothing in the description suggests circularity or invented parameters. This is aimed at applied microeconomists who work with ordered survey outcomes and difference-in-differences. A reader who needs tools for measurement error in discrete treatment effects would find it useful. It is coherent enough on its own terms to merit a serious referee who can check the derivations and the practical bite of the assumptions.

Referee Report

0 major / 2 minor

Summary. The paper develops a Difference-in-Differences framework for discrete, ordered outcomes subject to underreporting. For a discrete Changes-in-Changes model that admits an equivalent threshold-crossing representation, nonparametric bounds are derived for the counterfactual and factual outcome distributions as well as for the associated quantile treatment effects. These bounds are shown to be sharp uniformly across outcome levels under additional support conditions. Estimation and bootstrap inference procedures are proposed, and a semiparametric underreporting model is considered for point identification. The framework is applied to investigate the impact of recreational marijuana legalization on the consumption behavior of 8th-grade students.

Significance. If the derivations hold, this work makes a useful contribution to the treatment effects literature by extending Changes-in-Changes methods to ordered outcomes with underreporting, a common feature of survey data on stigmatized behaviors. The nonparametric bounds and sharpness result under support conditions allow for robust analysis without parametric restrictions on the underreporting process. The semiparametric point-identification extension and the proposed estimation/bootstrap procedures enhance applicability, while the marijuana legalization application illustrates policy relevance.

minor comments (2)

[Abstract] Abstract: the description of the support conditions required for uniform sharpness could be stated more explicitly to help readers assess applicability.
The threshold-crossing representation equivalence (mentioned in the abstract) would benefit from a brief intuitive discussion of how the discrete CIC maps to the latent index model before the bounds derivation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged · score 2.0 of 10

Minor self-citation; central derivation self-contained

full rationale

The paper states that a discrete Changes-in-Changes model admits an equivalent threshold-crossing representation, from which nonparametric bounds on counterfactual/factual distributions and quantile treatment effects are derived under support conditions for sharpness. No equations reduce a prediction to a fitted input by construction, no load-bearing uniqueness theorem is imported via self-citation, and no ansatz is smuggled. The derivation chain is independent of the target results and relies on stated model assumptions plus external support conditions. This matches the default expectation of no significant circularity (score 0-2).

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the threshold-crossing equivalence for the discrete CiC model and on support conditions that deliver uniform sharpness; these are domain assumptions standard in ordered choice and DiD settings but not independently verified here.

assumptions (2)

domain assumption discrete Changes-in-Changes model admits an equivalent threshold-crossing representation
Invoked explicitly in the abstract as the starting point for deriving the bounds.
domain assumption additional support conditions hold that make the nonparametric bounds sharp uniformly across outcome levels
Required for the sharpness result stated in the abstract.

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Cite this review

Pith. "Pith review of Changes-in-Changes for Ordered Choice Models with Underreporting." pith.science (2026). https://pith.science/paper/2401.00618

@misc{pith2026240100618,
  author       = {Pith},
  title        = {Pith review of: Changes-in-Changes for Ordered Choice Models with Underreporting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2401.00618}},
  note         = {Machine review of arXiv:2401.00618}
}

read the original 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.

Figures

Figures reproduced from arXiv: 2401.00618 by the authors.

**Figure 1.** Stylized CiC Model Y ∗ 1t (0), t ∈ {0, 1} Y ∗ 0t (0), t ∈ {0, 1} 1 0 1 0 FY ∗ 11(0) FY ∗ 10(0) FY ∗ 11(1) Group g = 1 Distributions Group g = 0 Distributions FY ∗ 01(0) FY ∗ 00(0) ∆CiC ∆CiC y ∗ q q ′ Note: The figure is a stylized example of a CiC model where the curves in blue denote the marginal distribution functions FY ∗ gt(0)(·) of the counterfactual latent outcome Y ∗ gt(0), g ∈ {0, 1} and t ∈ {0, 1}, with the… view at source ↗

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We develop a Difference-in-Differences framework for discrete, ordered outcomes subject to underreporting... derive nonparametric bounds for the counterfactual and factual outcome distributions as well as for the associated quantile treatment effects
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Y*gt(0) = ηgt(Xgt) + λgt(Xgt)εgt... CiC model if and only if η11(x) − λ11(x)/λ10(x) η10(x) = η01(x) − λ01(x)/λ00(x) η00(x) and λ11(x)/λ10(x) = λ01(x)/λ00(x)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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Pith tools

Reviewed May 24, 2026 · model on record in the stance chip above.

[1] [1]

Anderson, D. M., B. Hansen, and D. I. Rees (2015). Medical marijuana laws and teen marijuana use. American Law and Economics Review\/ 17\/ (2), 495–528

work page 2015

[2] [2]

Arellano, M. and S. Bonhomme (2017). Quantile selection models with an application to understanding changes in wage inequality. Econometrica\/ 85 , 1--28

work page 2017

[3] [3]

Corradi, and D

Arulampalam, W., V. Corradi, and D. Gutknecht (2017). Modeling heaped duration data: An application to neonatal mortality. Journal of Econometrics\/ 200\/ (2), 363--377

work page 2017

[4] [4]

McMillan, and J

Assun c ao, J., R. McMillan, and J. Murphy (2023). Optimal environmental targeting in the A mazon rainforest. Review of Economic Studies\/ 90 , 1608--1641

work page 2023

[5] [5]

Athey, S. and G. Imbens (2006). Identification and inference in nonlinear difference-in-differences models. Econometrica\/ 74\/ (2), 431--497

work page 2006

[6] [6]

Brinkman, J. and D. Mok-Lamme (2019). Not in my backyard? Not so fast. The effect of marijuana legalization on neighborhood crime. Regional Science and Urban Economics\/ 78 , 1--23

work page 2019

[7] [7]

Brown, S., M. N. Harris, P. Srivastava, and X. Zhang (2018). Modelling illegal drug participation. Journal of the Royal Statistical Society (Series A)\/ 181\/ (1), 133--154

work page 2018

[8] [8]

Caudill, S. B. and F. G. Mixon (2005). Analysing misleading discrete responses: A logit model based on misclassified data. Oxford Bulletin of Economics and Statistics\/ 67\/ (1), 105--113

work page 2005