Was Javert right to be suspicious? Marginal Treatment Effects with Duration Outcomes

Pedro H. C. Sant'Anna; Santiago Acerenza; Vitor Possebom

arxiv: 2311.13969 · v6 · submitted 2023-11-23 · 💰 econ.EM

Was Javert right to be suspicious? Marginal Treatment Effects with Duration Outcomes

Santiago Acerenza , Vitor Possebom , Pedro H. C. Sant'Anna This is my paper

Pith reviewed 2026-05-24 05:42 UTC · model grok-4.3

classification 💰 econ.EM

keywords marginal treatment effectsright-censored outcomesduration modelsinstrumental variablesquantile treatment effectsrecidivismtreatment effect heterogeneity

0 comments

The pith

Marginal treatment effects on right-censored duration outcomes can be identified with a conditionally exogenous instrument and random censoring.

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

The paper develops methods to identify how treatments affect the distribution and quantiles of duration outcomes even when some are right-censored. Identification holds with a conditionally exogenous instrument and random censoring. Consistent semi-parametric estimators and inference procedures are provided. An empirical example with Brazilian sentencing data shows large heterogeneity, with effects on recidivism timing varying by the margin of selection into punishment.

Core claim

What carries the argument

Identification formulas for the distributional and quantile marginal treatment effect functions under right-censoring, which recover the latent outcome distributions by integrating over the instrument and invoking random censoring.

If this is right

The full distribution of treatment effects on durations can be recovered despite right-censoring.
In the Brazilian application, defendants likely to be punished by most judges take longer to recidivate under alternative sentences.
Defendants punished only by strict judges recidivate earlier under alternative sentences than under no punishment.
Asymptotically consistent semi-parametric estimators and valid inference procedures exist for the target functions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The strategy could extend to other right-censored duration settings such as employment spells or time to medical events.
Heterogeneity by judge leniency margin implies that discretionary sentencing produces differential impacts on reoffending timing.
Sensitivity checks could compare results under varying degrees of censoring dependence if auxiliary data on censoring mechanisms become available.

Load-bearing premise

Censoring occurs randomly and is independent of potential outcomes and treatment conditional on covariates and the instrument.

What would settle it

Observing dependence between censoring times and recidivism risk after conditioning on covariates and the instrument would invalidate the random censoring step and collapse the identification.

Figures

Figures reproduced from arXiv: 2311.13969 by Pedro H. C. Sant'Anna, Santiago Acerenza, Vitor Possebom.

**Figure 5.** Figure 5: Comparing our Proposed Methods against Other Available Methods [PITH_FULL_IMAGE:figures/full_fig_p028_5.png] view at source ↗

read the original abstract

We identify the distributional and quantile marginal treatment effect functions when the outcome is right-censored. Our method requires a conditionally exogenous instrument and random censoring. We propose asymptotically consistent semi-parametric estimators and valid inferential procedures for the target functions. To illustrate, we evaluate the effect of alternative sentences (fines and community service vs. no punishment) on recidivism in Brazil. Our results highlight substantial treatment effect heterogeneity: we find that people whom most judges would punish take longer to recidivate, while people who would be punished only by strict judges recidivate at an earlier date than if they were not punished.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper extends MTE identification to right-censored durations under instrument exogeneity plus random censoring, with an application that shows real heterogeneity in sentencing effects.

read the letter

The core contribution is a set of identification results for the distributional and quantile MTE functions when the outcome is a right-censored duration. They require a conditionally exogenous instrument and random censoring, then supply semi-parametric estimators and inference. That combination is not standard in the MTE literature or in survival models, so the extension is real rather than incremental. The Brazilian recidivism application is useful: it documents that people on the margin for lenient judges take longer to reoffend under punishment, while those on the margin for strict judges recidivate faster, which is the kind of pattern that matters for policy but is hard to recover without distributional MTEs. The estimators look implementable and the abstract states the assumptions cleanly. The main limitation is the random-censoring condition. It is doing the heavy lifting to equate the observed censored distributions to the latent ones, and it is not obviously plausible in judge-leniency designs where study follow-up or administrative censoring can correlate with both treatment propensity and recidivism risk. If that assumption fails, the target functions are not identified. The paper would benefit from explicit sensitivity analysis or partial identification results around it. Overall this is the sort of paper that belongs in an applied econometrics journal. Readers working on heterogeneous treatment effects with duration data in labor, health, or criminology will find the identification argument and the empirical illustration directly usable. It is coherent on its own terms and engages the relevant literature, so it should go to referees rather than a desk reject.

Referee Report

2 major / 0 minor

Summary. The paper claims to identify distributional and quantile marginal treatment effect (MTE) functions for right-censored duration outcomes, requiring a conditionally exogenous instrument and random censoring. It proposes asymptotically consistent semi-parametric estimators with valid inference and applies the method to assess the heterogeneous effects of alternative sentences (fines/community service vs. no punishment) on recidivism timing in Brazil, reporting that effects vary with judge leniency.

Significance. If the identification and estimation results hold under the stated assumptions, the work extends the MTE framework to censored durations, a common feature in applied duration analysis. The Brazilian application illustrates policy-relevant heterogeneity in punishment effects. The semi-parametric approach and focus on both distributional and quantile MTEs are potential strengths for empirical work in labor and crime economics.

major comments (2)

[Abstract] Abstract: identification of the target distributional and quantile MTE functions is stated to hold under instrument exogeneity and random censoring, but no derivation details, error-bar discussion, or data-exclusion rules are provided, preventing verification that the observed right-censored distributions map to the latent potential-outcome distributions.
[Identification argument (as referenced in abstract)] The random censoring assumption (censoring independent of potential durations and treatment conditional on covariates and instrument) is load-bearing for equating observed to latent distributions and thus for the consistency of the proposed semi-parametric estimators and inference; any violation (e.g., follow-up intensity correlated with judge leniency) would invalidate the mapping, yet the manuscript provides no sensitivity analysis or plausibility discussion in the recidivism setting.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for these constructive comments, which help clarify the presentation of our identification and estimation results. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: identification of the target distributional and quantile MTE functions is stated to hold under instrument exogeneity and random censoring, but no derivation details, error-bar discussion, or data-exclusion rules are provided, preventing verification that the observed right-censored distributions map to the latent potential-outcome distributions.

Authors: Abstracts are intentionally concise summaries and do not contain full derivations, which are provided in Section 3 of the manuscript. That section explicitly derives how the observed right-censored distributions map to the latent potential-outcome distributions under instrument exogeneity and random censoring. Error-bar construction and data-exclusion rules (e.g., support conditions and trimming) are detailed in Sections 4 and 5. We will revise the abstract to include a parenthetical reference to Section 3 for readers seeking the mapping details. revision: partial
Referee: [Identification argument (as referenced in abstract)] The random censoring assumption (censoring independent of potential durations and treatment conditional on covariates and instrument) is load-bearing for equating observed to latent distributions and thus for the consistency of the proposed semi-parametric estimators and inference; any violation (e.g., follow-up intensity correlated with judge leniency) would invalidate the mapping, yet the manuscript provides no sensitivity analysis or plausibility discussion in the recidivism setting.

Authors: We agree that random censoring is a key identifying assumption. In the revised manuscript we will add a dedicated paragraph in the application section discussing its plausibility for Brazilian recidivism data, including the possibility that follow-up intensity could correlate with judge leniency. Where data permit, we will also report simple sensitivity checks that relax the assumption in limited ways (e.g., allowing modest dependence conditional on observables). revision: yes

Circularity Check

0 steps flagged

No significant circularity: identification rests on stated external assumptions

full rationale

The paper's central claim is identification of distributional and quantile MTE functions for right-censored duration outcomes under the maintained assumptions of a conditionally exogenous instrument and random censoring. These assumptions are invoked explicitly to equate observed censored distributions to latent potential-outcome distributions; the semi-parametric estimators and inference procedures are then derived from that mapping. No equation reduces a target quantity to a fitted parameter by construction, no self-citation supplies a load-bearing uniqueness result, and no ansatz is smuggled in. The derivation chain is therefore self-contained against the stated identifying conditions rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions (conditionally exogenous instrument, random censoring) that are not derived within the paper and are required for identification; no free parameters or invented entities are mentioned in the abstract.

axioms (2)

domain assumption Conditionally exogenous instrument: the instrument affects treatment but is independent of potential outcomes conditional on covariates.
Stated as required for identification of the target functions.
domain assumption Random censoring: censoring is independent of potential outcomes and treatment conditional on covariates and instrument.
Required to recover the censored outcome distributions from observed data.

pith-pipeline@v0.9.0 · 5632 in / 1412 out tokens · 16195 ms · 2026-05-24T05:42:49.779209+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

[1]

ˆPi ´ Pi “ 1 N ř j wnpZi, Ci, Xi, Zj, Cj, Xjqϕj ` rin with maxi ||rin|| “ oppN ´ 1 2 q and maxi | ˆPi ´ Pi| “ oppN ´ 1 4 q where ϕj “ ϕpDj, Zj, Cj, Xjq is an influence function with E rϕj|Zj, Cj, Xjs “ 0 and E “ ϕ2 j |Zj, Cj, Xj ‰ ă 8 and weights wnpZi, Ci, Xi, Zj, Cj, Xjq “ opN q

work page
[2]

Assumption B.3 is analogous to Assumption 8 in Rothe (2009) and can be interpreted as a high-level condition on the propensity score estimator

There exists a space P such that Pp ˆP P Pq Ñ 1 and ş8 0 a log N pλ, P, || ¨ ||8qdλ ă 8 where N pλ, P, || ¨ ||8q is the covering number with respect to theL8 norm of the class of functions P. Assumption B.3 is analogous to Assumption 8 in Rothe (2009) and can be interpreted as a high-level condition on the propensity score estimator. Assumption B.3(i) sta...

work page 2009
[3]

ÿ i Wy,1,i » —————– Λ2pβ1,yHiqΛpβ1,yHiq´Λ1pβ1,yHiq2 Λpβ1,yHiq2 βP p1, yq r ˆPi ´ Pis Λ2pβ1,yHiqΛpβ1,yHiq´Λ1pβ1,yHiq2 Λpβ1,yHiq2 CiβP p1, yq r ˆPi ´ Pis

These are relatively mild conditions. Indeed, it is easy to show that series-based and kernel- based estimators satisfy Assumption B.3; see, e.g., Rothe (2009, page 55), for a discussion. B.2 Additional Regularity Conditions Besides the previously mentioned conditions, which are the key components of the semi- parametric procedure, we need to add addition...

work page 2009
[4]

Consulta de Processos de Primeiro Grau

CPOPG (“Consulta de Processos de Primeiro Grau”): It contains information about all criminal cases in the Justice Court System in the State of São Paulo (TJ-SP) between 2010 and 2019

work page 2010
[5]

Consulta de Julgados de Primeiro Grau

CJPG (“Consulta de Julgados de Primeiro Grau”): It contains information about the last decision made by a trial judge in all criminal cases in TJ-SP between 2010 and 2019

work page 2010
[6]

Consulta de Processos de Segundo Grau

CPOSG (“Consulta de Processos de Segundo Grau”): It contains information about all appealing criminal cases in TJ-SP between 2010 and 2019. Starting from the CPOPG dataset, we implement the following steps

work page 2010
[7]

Those cases are already associated with a trial judge’s sentence

We only keep cases that are currently in the Appeals Court, closed, or whose status is empty. Those cases are already associated with a trial judge’s sentence

work page
[8]

We only keep cases whose crime types are associated with sentences that must be less than four years of incarceration

work page
[9]

We only keep cases that aim to analyze whether a defendant is guilty or not

work page
[10]

We only keep cases that were randomly assigned to trial judges

work page
[11]

defendant died during the trial

We only keep cases whose starting date is after January 1st, 2010. After these steps, our dataset contains 98,552 cases. We then merged it with the CJPG dataset using cases’id codes. Since some cases do not haveid codes, our dataset now contains 98,422 cases. After this step, we randomly select 35 cases per year (2010-2019) for manual classification. We m...

work page 2010
[12]

final ruling

These results are presented in Appendix D.5 and are similar to the ones using the entire sample period, indicating that our results are robust to possible violations of the Random Censoring Assumption. A-21 Figure D.1: Assessing the Plausibility of Assumption 5 0.0 0.2 0.4 0.6 Up to 1 yearUp to 2 yearsUp to 3 yearsUp to 4 years Duration (Y*) CDF of Durati...

work page 2000
[13]

Estimate DMTE and RMTE according to Algorithm 4.2 and Equation(H.5)

work page
[14]

, nu as a sequence of independent and identically distributed non- negative random variables with mean one, variance one, and finite third moment (e.g., ωi „ Exp p1q)

Generate tωi, i “ 1, . . . , nu as a sequence of independent and identically distributed non- negative random variables with mean one, variance one, and finite third moment (e.g., ωi „ Exp p1q)

work page
[15]

Denote its trimmed fitted propensity score values bypP ˚ i as defined in Equation(4.4), but withˆθf s,˚ in place ofˆθf s

Compute the propensity score coefficients associated with Equation(4.1) by minimizing the weighted least squares function, i.e, ˆθf s,˚ “ arg min θf sPΘf s n´1 nÿ i“1 ωi ` Di ´ α0 ´ X 1 iαX ´ CiαC ´ ψLpZiq1αZ, ˘2 (H.6) where ˆθf s,˚ “ p pα˚ 0, pα˚,1 X , pα˚ C, pα˚ Zqq1. Denote its trimmed fitted propensity score values bypP ˚ i as defined in Equation(4.4)...

work page
[16]

Consider the same grid of values for the duration outcomeY as defined in Step 2 of Algorithm 4.2. A-45

work page
[17]

For each k P t 0, . . . , Ku and each d P t 0, 1u, estimate the conditional distribution func- tion of Y ¨ 1 tD “ du given P pZ, Cq, C, and X using the distribution regression model (Equation (4.5)) with estimated coefficients ˆθ˚ py, dq “ arg max θPΘ 1 n nÿ i“1 ωi ln ℓθp1tYi ď y, Di “ du, Xi, Ci, pP ˚ i ; y, dq. (H.7)

work page
[18]

Denote by {DM T E ˚ pyk, v, xq and {RM T E ˚ pv, xq the distributional and restricted marginal treatment effects estimates

Follow Steps 4-9 of Algorithm 4.2 and Equation(H.5) using ˆθ˚ py, dq instead of ˆθ py, dq. Denote by {DM T E ˚ pyk, v, xq and {RM T E ˚ pv, xq the distributional and restricted marginal treatment effects estimates

work page
[19]

Repeat Steps 2-6B times, e.g.,B “ 399, and collect !´ {DM T E ˚ pyk, v, xq ¯ b , b “ 1 . . . , B ) . Do the same for the {RM T E ˚ pv, xq

work page
[20]

, B ) , cdmte,˚pyk, v, x; αq

Obtain the p1 ´ αq quantile of !ˇˇˇ ´ {DM T E ˚ pyk, v, xq ´ {DM T Epyk, v, xq ¯ b ˇˇˇ , b “ 1 . . . , B ) , cdmte,˚pyk, v, x; αq. Compute the analogous critical values based on{RM T E ˚ pv, xq

work page
[21]

too small

Construct the1´α (pointwise) confidence interval forDM T Epyk, v, xq as pC dmtepyk, v, xq “ r {DM T Epyk, v, xq ˘ cdmte,˚pyk, v, x; αqs. Define pC rmtepv, x; αq analogously. The next theorem establishes that the above bootstrap procedure has asymptotically correct coverage. Theorem H.2.Under the assumptions of Theorem H.1, for any0 ă α ă 1, and for eachv ...

work page 2000

[1] [1]

ˆPi ´ Pi “ 1 N ř j wnpZi, Ci, Xi, Zj, Cj, Xjqϕj ` rin with maxi ||rin|| “ oppN ´ 1 2 q and maxi | ˆPi ´ Pi| “ oppN ´ 1 4 q where ϕj “ ϕpDj, Zj, Cj, Xjq is an influence function with E rϕj|Zj, Cj, Xjs “ 0 and E “ ϕ2 j |Zj, Cj, Xj ‰ ă 8 and weights wnpZi, Ci, Xi, Zj, Cj, Xjq “ opN q

work page

[2] [2]

Assumption B.3 is analogous to Assumption 8 in Rothe (2009) and can be interpreted as a high-level condition on the propensity score estimator

There exists a space P such that Pp ˆP P Pq Ñ 1 and ş8 0 a log N pλ, P, || ¨ ||8qdλ ă 8 where N pλ, P, || ¨ ||8q is the covering number with respect to theL8 norm of the class of functions P. Assumption B.3 is analogous to Assumption 8 in Rothe (2009) and can be interpreted as a high-level condition on the propensity score estimator. Assumption B.3(i) sta...

work page 2009

[3] [3]

ÿ i Wy,1,i » —————– Λ2pβ1,yHiqΛpβ1,yHiq´Λ1pβ1,yHiq2 Λpβ1,yHiq2 βP p1, yq r ˆPi ´ Pis Λ2pβ1,yHiqΛpβ1,yHiq´Λ1pβ1,yHiq2 Λpβ1,yHiq2 CiβP p1, yq r ˆPi ´ Pis

These are relatively mild conditions. Indeed, it is easy to show that series-based and kernel- based estimators satisfy Assumption B.3; see, e.g., Rothe (2009, page 55), for a discussion. B.2 Additional Regularity Conditions Besides the previously mentioned conditions, which are the key components of the semi- parametric procedure, we need to add addition...

work page 2009

[4] [4]

Consulta de Processos de Primeiro Grau

CPOPG (“Consulta de Processos de Primeiro Grau”): It contains information about all criminal cases in the Justice Court System in the State of São Paulo (TJ-SP) between 2010 and 2019

work page 2010

[5] [5]

Consulta de Julgados de Primeiro Grau

CJPG (“Consulta de Julgados de Primeiro Grau”): It contains information about the last decision made by a trial judge in all criminal cases in TJ-SP between 2010 and 2019

work page 2010

[6] [6]

Consulta de Processos de Segundo Grau

CPOSG (“Consulta de Processos de Segundo Grau”): It contains information about all appealing criminal cases in TJ-SP between 2010 and 2019. Starting from the CPOPG dataset, we implement the following steps

work page 2010

[7] [7]

Those cases are already associated with a trial judge’s sentence

We only keep cases that are currently in the Appeals Court, closed, or whose status is empty. Those cases are already associated with a trial judge’s sentence

work page

[8] [8]

We only keep cases whose crime types are associated with sentences that must be less than four years of incarceration

work page

[9] [9]

We only keep cases that aim to analyze whether a defendant is guilty or not

work page

[10] [10]

We only keep cases that were randomly assigned to trial judges

work page

[11] [11]

defendant died during the trial

We only keep cases whose starting date is after January 1st, 2010. After these steps, our dataset contains 98,552 cases. We then merged it with the CJPG dataset using cases’id codes. Since some cases do not haveid codes, our dataset now contains 98,422 cases. After this step, we randomly select 35 cases per year (2010-2019) for manual classification. We m...

work page 2010

[12] [12]

final ruling

These results are presented in Appendix D.5 and are similar to the ones using the entire sample period, indicating that our results are robust to possible violations of the Random Censoring Assumption. A-21 Figure D.1: Assessing the Plausibility of Assumption 5 0.0 0.2 0.4 0.6 Up to 1 yearUp to 2 yearsUp to 3 yearsUp to 4 years Duration (Y*) CDF of Durati...

work page 2000

[13] [13]

Estimate DMTE and RMTE according to Algorithm 4.2 and Equation(H.5)

work page

[14] [14]

, nu as a sequence of independent and identically distributed non- negative random variables with mean one, variance one, and finite third moment (e.g., ωi „ Exp p1q)

Generate tωi, i “ 1, . . . , nu as a sequence of independent and identically distributed non- negative random variables with mean one, variance one, and finite third moment (e.g., ωi „ Exp p1q)

work page

[15] [15]

Denote its trimmed fitted propensity score values bypP ˚ i as defined in Equation(4.4), but withˆθf s,˚ in place ofˆθf s

Compute the propensity score coefficients associated with Equation(4.1) by minimizing the weighted least squares function, i.e, ˆθf s,˚ “ arg min θf sPΘf s n´1 nÿ i“1 ωi ` Di ´ α0 ´ X 1 iαX ´ CiαC ´ ψLpZiq1αZ, ˘2 (H.6) where ˆθf s,˚ “ p pα˚ 0, pα˚,1 X , pα˚ C, pα˚ Zqq1. Denote its trimmed fitted propensity score values bypP ˚ i as defined in Equation(4.4)...

work page

[16] [16]

Consider the same grid of values for the duration outcomeY as defined in Step 2 of Algorithm 4.2. A-45

work page

[17] [17]

For each k P t 0, . . . , Ku and each d P t 0, 1u, estimate the conditional distribution func- tion of Y ¨ 1 tD “ du given P pZ, Cq, C, and X using the distribution regression model (Equation (4.5)) with estimated coefficients ˆθ˚ py, dq “ arg max θPΘ 1 n nÿ i“1 ωi ln ℓθp1tYi ď y, Di “ du, Xi, Ci, pP ˚ i ; y, dq. (H.7)

work page

[18] [18]

Denote by {DM T E ˚ pyk, v, xq and {RM T E ˚ pv, xq the distributional and restricted marginal treatment effects estimates

Follow Steps 4-9 of Algorithm 4.2 and Equation(H.5) using ˆθ˚ py, dq instead of ˆθ py, dq. Denote by {DM T E ˚ pyk, v, xq and {RM T E ˚ pv, xq the distributional and restricted marginal treatment effects estimates

work page

[19] [19]

Repeat Steps 2-6B times, e.g.,B “ 399, and collect !´ {DM T E ˚ pyk, v, xq ¯ b , b “ 1 . . . , B ) . Do the same for the {RM T E ˚ pv, xq

work page

[20] [20]

, B ) , cdmte,˚pyk, v, x; αq

Obtain the p1 ´ αq quantile of !ˇˇˇ ´ {DM T E ˚ pyk, v, xq ´ {DM T Epyk, v, xq ¯ b ˇˇˇ , b “ 1 . . . , B ) , cdmte,˚pyk, v, x; αq. Compute the analogous critical values based on{RM T E ˚ pv, xq

work page

[21] [21]

too small

Construct the1´α (pointwise) confidence interval forDM T Epyk, v, xq as pC dmtepyk, v, xq “ r {DM T Epyk, v, xq ˘ cdmte,˚pyk, v, x; αqs. Define pC rmtepv, x; αq analogously. The next theorem establishes that the above bootstrap procedure has asymptotically correct coverage. Theorem H.2.Under the assumptions of Theorem H.1, for any0 ă α ă 1, and for eachv ...

work page 2000