pith. sign in

arxiv: 2604.07604 · v1 · submitted 2026-04-08 · 💰 econ.EM · stat.ME

Assessing Sensitivity to IV Exclusion and Exogeneity without First Stage Monotonicity

Paul Diegert , Matthew A. Masten , Alexandre Poirier This is my paper

Pith reviewed 2026-05-10 16:58 UTC · model grok-4.3

classification 💰 econ.EM stat.ME
keywords instrumental variablessensitivity analysisexclusion restrictionexogeneityidentified setslinear programmingpotential outcomesaverage treatment effects
0
0 comments X

The pith

Identified sets for potential outcome distributions and average treatment effects are derived as linear programs under nonparametric relaxations of IV exclusion and exogeneity without monotonicity.

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 assess the sensitivity of instrumental variable estimates to violations of the exclusion and exogeneity assumptions. It derives identified sets for the marginal distributions of potential outcomes and for functionals such as average treatment effects. These sets arise as solutions to linear programs under a broad class of nonparametric relaxations that allow arbitrary treatment effect heterogeneity. The approach requires no monotonicity condition on the first stage. Computationally tractable estimation procedures are provided even for infinite-dimensional cases, and the methods are applied to data on peer effects in movie viewership with weather as a candidate instrument.

Core claim

Under a broad class of nonparametric relaxations of the exclusion and exogeneity assumptions, the identified sets for the marginal distributions of potential outcomes and their functionals such as average treatment effects are characterized as the solutions to linear programs; this characterization holds without any first-stage monotonicity requirement and accommodates arbitrary heterogeneity in treatment effects.

What carries the argument

The linear program whose feasible set encodes the relaxed exclusion and exogeneity conditions as linear constraints on the joint distribution of observables and unobservables, thereby characterizing the identified set for the potential outcome distributions.

Load-bearing premise

The chosen class of nonparametric relaxations must be structured so that the resulting identified-set problem remains expressible as a linear program.

What would settle it

In simulated data generated from a known data-generating process with specified violations of exclusion and exogeneity, the linear-program bounds fail to contain the true average treatment effect.

Figures

Figures reproduced from arXiv: 2604.07604 by Alexandre Poirier, Matthew A. Masten, Paul Diegert.

Figure 1
Figure 1. Figure 1: Left: Example identified set for pY (x) = (pY (x, 0), pY (x, 1)) under no exogene￾ity assumptions. Right: corresponding linear program minimizing/maximizing the ATE = pY (x, 0)(1 − pZ) + pY (x, 1)pZ. H0 × H1 is a Cartesian product of intervals, so appropriately evaluating ΓATE at the lower/upper bounds of the intervals in (4) will yield sharp bounds for it. The same approach can be used to obtain sharp bou… view at source ↗
Figure 2
Figure 2. Figure 2: Left: Empty identified set under exogeneity and exclusion. Right: Nonempty [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example identified sets for different sensitivity parameter values. Relaxation is [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example identified set and minimization/maximization of the ATE under a sensi [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Distributional bounds. These plots show the bounds on the cumulative distribution [PITH_FULL_IMAGE:figures/full_fig_p031_5.png] view at source ↗
read the original abstract

Exclusion and exogeneity are core assumptions in instrumental variable (IV) analyses, but their empirical validity is often debated. This paper develops new sensitivity analyses for these assumptions. Our results accommodate arbitrary heterogeneity in treatment effects and do not impose any monotonicity requirements on the first stage. Specifically, we derive identified sets for the marginal distributions of potential outcomes and their functionals, like average treatment effects, under a broad class of nonparametric relaxations of the exclusion and exogeneity assumptions. These identified sets are characterized as solutions to linear programs and have desirable theoretical properties. We explain how to estimate these solutions using computationally tractable methods even when the linear program is infinite-dimensional. We illustrate these methods with an empirical application to peer effects in movie viewership, using weather as a potentially imperfect instrument.

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.

Referee Report

1 major / 2 minor

Summary. The paper develops new sensitivity analyses for the IV exclusion and exogeneity assumptions. It derives identified sets for the marginal distributions of potential outcomes and functionals such as average treatment effects under a broad class of nonparametric relaxations of these assumptions, without imposing first-stage monotonicity or restricting treatment effect heterogeneity. The identified sets are characterized as solutions to linear programs with desirable theoretical properties, and the paper provides computationally tractable estimation methods even for infinite-dimensional programs. An empirical illustration uses weather as a potentially imperfect instrument for peer effects in movie viewership.

Significance. If the central results hold, the work offers a practical and flexible framework for assessing robustness of IV inferences to core assumption violations in settings with arbitrary heterogeneity. The linear-programming characterization, avoidance of monotonicity, and emphasis on tractable estimation for infinite-dimensional cases are notable strengths that could facilitate wider adoption in applied work. The approach derives the sets directly from the relaxed assumptions rather than post-hoc fitting, which supports its internal coherence.

major comments (1)
  1. [§3] §3 (main identification results): The claim that the relaxations remain nonparametric yet yield tractable linear programs requires explicit discussion of how the identified sets vary with the precise functional form of the relaxation class; without this, it is difficult to assess whether the reported sets are robust or sensitive to analyst choices in the class definition.
minor comments (2)
  1. [Abstract] The abstract refers to 'desirable theoretical properties' of the identified sets; enumerating the key properties (e.g., sharpness, convexity) in one sentence would improve readability.
  2. [Empirical Application] In the empirical application, the motivation for weather as an instrument could include a brief discussion of plausible channels for exclusion violations to ground the sensitivity exercise.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment and the recommendation for minor revision. The point raised about Section 3 is well taken, and we will incorporate additional discussion to clarify the dependence of the identified sets on the specific form of the relaxation class.

read point-by-point responses

  1. Referee: [§3] §3 (main identification results): The claim that the relaxations remain nonparametric yet yield tractable linear programs requires explicit discussion of how the identified sets vary with the precise functional form of the relaxation class; without this, it is difficult to assess whether the reported sets are robust or sensitive to analyst choices in the class definition.

    Authors: We agree that explicit discussion is warranted. Our framework defines a broad class of nonparametric relaxations parameterized by the analyst (e.g., via bounds on the violation of exclusion or exogeneity), and the linear program is solved conditional on the chosen class. Different functional forms of the class—such as alternative norms or support restrictions on the violation—will in general produce different identified sets, which is a feature of the sensitivity analysis rather than a limitation. To address the concern directly, we will add a paragraph (or short subsection) in Section 3 that (i) states how the identified sets are constructed as a function of the class, (ii) provides simple comparative examples illustrating variation across common choices of the relaxation, and (iii) notes that the computational methods remain applicable regardless of the specific form. This revision will make the dependence transparent without altering the core results. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives identified sets for marginal distributions of potential outcomes and functionals such as ATEs as solutions to linear programs under nonparametric relaxations of IV exclusion and exogeneity assumptions, without first-stage monotonicity. This is a standard partial identification exercise in which the sets are obtained directly from the stated assumptions via LP duality or optimization; no quoted step shows a fitted parameter renamed as a prediction, a self-definitional loop, or a load-bearing result that reduces to an unverified self-citation. The empirical illustration is presented separately from the theoretical characterization, and the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central results rest on the existence of a broad class of nonparametric relaxations of exclusion and exogeneity that still permit linear-program characterization; no free parameters, axioms, or invented entities are mentioned in the abstract.

pith-pipeline@v0.9.0 · 5432 in / 1119 out tokens · 45397 ms · 2026-05-10T16:58:27.340721+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    Aliprantis, C. D. and K. C. Border (2006): Infinite Dimensional Analysis: A Hitchhiker's Guide, Springer, 3rd ed

    work page 2006

  2. [2]

    Altonji, J. G., T. E. Elder, and C. R. Taber (2005): An evaluation of instrumental variable strategies for estimating the effects of catholic schooling, Journal of Human Resources, 40, 791--821

    work page 2005

  3. [3]

    (2009): Assessing the credibility of instrumental variables inference with imperfect instruments via sensitivity analysis, Journal of Applied Econometrics, 24, 325--337

    Ashley, R. (2009): Assessing the credibility of instrumental variables inference with imperfect instruments via sensitivity analysis, Journal of Applied Econometrics, 24, 325--337

    work page 2009

  4. [4]

    Ashley, R. A. and C. F. Parmeter (2015): Sensitivity analysis for inference in 2SLS/GMM estimation with possibly flawed instruments, Empirical Economics, 49, 1153--1171

    work page 2015

  5. [5]

    Balke, A. and J. Pearl (1997): Bounds on treatment effects from studies with imperfect compliance, Journal of the American Statistical Association, 92, 1171--1176

    work page 1997

  6. [6]

    Basit, M. A., M. A. Latif, and A. S. Wahed (2023): Sensitivity Analysis for Causal Effects in Observational Studies with Multivalued Treatments, arXiv preprint arXiv:2308.15986

    work page arXiv 2023

  7. [7]

    Molchanov, and F

    Beresteanu, A., I. Molchanov, and F. Molinari (2012): Partial identification using random set theory, Journal of Econometrics, 166, 17--32

    work page 2012

  8. [8]

    (1959): Espaces topologiques: fonctions multivoques, Collection universitaire de math \'e matiques, Dunod

    Berge, C. (1959): Espaces topologiques: fonctions multivoques, Collection universitaire de math \'e matiques, Dunod

    work page 1959

  9. [9]

    Border, K. C. (1985): Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press

    work page 1985

  10. [10]

    Bound, J., D. A. Jaeger, and R. M. Baker (1995): Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak, Journal of the American Statistical Association, 90, 443--450

    work page 1995

  11. [11]

    Christensen, T. and B. Connault (2023): Counterfactual sensitivity and robustness, Econometrica, 91, 263--298

    work page 2023

  12. [12]

    Conley, T. G., C. B. Hansen, and P. E. Rossi (2012): Plausibly exogenous, The Review of Economics and Statistics, 94, 260--272

    work page 2012

  13. [13]

    (2024): A unified approach for assessing sensitivity to violations of causal assumptions, Working paper

    Duarte, G. (2024): A unified approach for assessing sensitivity to violations of causal assumptions, Working paper

    work page 2024

  14. [14]

    Fisher, F. M. (1961): On the cost of approximate specification in simultaneous equation estimation, Econometrica, 29, 139--170

    work page 1961

  15. [15]

    Flores, C. and X. Chen (2018): Average Treatment Effect Bounds with an Instrumental Variable: Theory and Practice, Springer

    work page 2018

  16. [16]

    Frandsen, B. R., L. J. Lefgren, and E. C. Leslie (2023): Judging Judge Fixed Effects, American Economic Review, 113, 253--277

    work page 2023

  17. [17]

    Freyberger, J. and M. A. Masten (2019): A practical guide to compact infinite dimensional parameter spaces, Econometric Reviews, 38, 979--1006

    work page 2019

  18. [18]

    Gallen, T. and B. Raymond (2023): Broken Instruments, Working paper

    work page 2023

  19. [19]

    Gilchrist, D. S. and E. G. Sands (2016): Something to Talk About: Social Spillovers in Movie Consumption, Journal of Political Economy, 124

    work page 2016

  20. [20]

    Hotz, V. J., C. H. Mullin, and S. G. Sanders (1997): Bounding causal effects using data from a contaminated natural experiment: Analysing the effects of teenage childbearing, The Review of Economic Studies, 64, 575--603

    work page 1997

  21. [21]

    (2014): Sensitivity checks for the local average treatment effect, Economics Letters, 123, 220--223

    Huber, M. (2014): Sensitivity checks for the local average treatment effect, Economics Letters, 123, 220--223

    work page 2014

  22. [22]

    Imbens, G. W. and J. D. Angrist (1994): Identification and estimation of local average treatment effects, Econometrica, 62, 467--475

    work page 1994

  23. [23]

    K \'e dagni, D. and I. Mourifi \'e (2020): Generalized instrumental inequalities: testing the instrumental variable independence assumption, Biometrika, 107, 661--675

    work page 2020

  24. [24]

    (2021): The identification region of the potential outcome distributions under instrument independence, Journal of Econometrics, 225, 231--253

    Kitagawa, T. (2021): The identification region of the potential outcome distributions under instrument independence, Journal of Econometrics, 225, 231--253

    work page 2021

  25. [25]

    Kline, P. and A. Santos (2013): Sensitivity to missing data assumptions: Theory and an evaluation of the US wage structure, Quantitative Economics, 4, 231--267

    work page 2013

  26. [26]

    (2012): Instrumental variables regressions with uncertain exclusion restrictions: A Bayesian approach, Journal of Applied Econometrics, 27, 108--128

    Kraay, A. (2012): Instrumental variables regressions with uncertain exclusion restrictions: A Bayesian approach, Journal of Applied Econometrics, 27, 108--128

    work page 2012

  27. [27]

    (2018): Bounding average treatment effects using linear programming, Empirical Economics, 1--41

    Laff \'e rs, L. (2018): Bounding average treatment effects using linear programming, Empirical Economics, 1--41

    work page 2018

  28. [28]

    --- -.1pt --- -.1pt --- (2019): Identification in models with discrete variables, Computational Economics, 53, 657--696

    work page 2019

  29. [29]

    Lechicki, A. and A. Spakowski (1985): A note on intersection of lower semicontinuous multifunctions, Proceedings of the American Mathematical Society, 95, 119--122

    work page 1985

  30. [30]

    Shaikh, and E

    Machado, C., A. Shaikh, and E. Vytlacil (2019): Instrumental variables and the sign of the average treatment effect, Journal of Econometrics, 212, 522--555

    work page 2019

  31. [31]

    Manski, C. F. (1983): Closest empirical distribution estimation, Econometrica: Journal of the Econometric Society, 305--319

    work page 1983

  32. [32]

    --- -.1pt --- -.1pt --- (1990): Nonparametric bounds on treatment effects, American Economic Review P&P, 80, 319--323

    work page 1990

  33. [33]

    --- -.1pt --- -.1pt --- (2003): Partial Identification of Probability Distributions, Springer

    work page 2003

  34. [34]

    Masten, M. A. and A. Poirier (2018): Identification of treatment effects under conditional partial independence, Econometrica, 86, 317--351

    work page 2018

  35. [35]

    --- -.1pt --- -.1pt --- (2020): Salvaging Falsified Instrumental Variable Models, arXiv:1812.11598v3

    work page arXiv 2020

  36. [36]

    --- -.1pt --- -.1pt --- (2021): Salvaging falsified instrumental variable models, Econometrica, 89, 1449--1469

    work page 2021

  37. [37]

    --- -.1pt --- -.1pt --- (2023): Choosing exogeneity assumptions in potential outcome models , The Econometrics Journal, 26, 327--349

    work page 2023

  38. [38]

    Mellon, J. (2025): Rain, Rain, Go Away: 194 Potential Exclusion-Restriction Violations for Studies Using Weather as an Instrumental Variable, American Journal of Political Science, 69, 881--898

    work page 2025

  39. [39]

    Santos, and A

    Mogstad, M., A. Santos, and A. Torgovitsky (2018): Using instrumental variables for inference about policy relevant treatment parameters, Econometrica, 86, 1589--1619

    work page 2018

  40. [40]

    Nunn, N. and L. Wantchekon (2011): The slave trade and the origins of mistrust in Africa, American Economic Review, 101, 3221--52

    work page 2011

  41. [41]

    (1995): On the testability of causal models with latent and instrumental variables, in Proceedings of the Eleventh conference on Uncertainty in artificial intelligence, 435--443

    Pearl, J. (1995): On the testability of causal models with latent and instrumental variables, in Proceedings of the Eleventh conference on Uncertainty in artificial intelligence, 435--443

    work page 1995

  42. [42]

    Ramsahai, R. R. (2012): Causal bounds and observable constraints for non-deterministic models, Journal of Machine Learning Research, 13, 829--848

    work page 2012

  43. [43]

    (2015): Rainfall and Conflict: A Cautionary Tale, Journal of Development Economics, 115, 62--72

    Sarsons, H. (2015): Rainfall and Conflict: A Cautionary Tale, Journal of Development Economics, 115, 62--72

    work page 2015

  44. [44]

    Small, D. S. (2007): Sensitivity analysis for instrumental variables regression with overidentifying restrictions, Journal of the American Statistical Association, 102, 1049--1058

    work page 2007

  45. [45]

    Swanson, S. A., M. A. Hern \'a n, M. Miller, J. M. Robins, and T. Richardson (2018): Partial identification of the average treatment effect using instrumental variables: Review of methods for binary instruments, treatments, and outcomes, Journal of the American Statistical Association, 113, 933--947

    work page 2018

  46. [46]

    (2006): A distributional approach for causal inference using propensity scores, Journal of the American Statistical Association, 101, 1619--1637

    Tan, Z. (2006): A distributional approach for causal inference using propensity scores, Journal of the American Statistical Association, 101, 1619--1637

    work page 2006

  47. [47]

    (2019): Partial identification by extending subdistributions, Quantitative Economics, 10, 105--144

    Torgovitsky, A. (2019): Partial identification by extending subdistributions, Quantitative Economics, 10, 105--144

    work page 2019

  48. [48]

    van Kippersluis, H. and C. A. Rietveld (2017): Pleiotropy-robust Mendelian randomization, International Journal of Epidemiology, 47, 1279--1288

    work page 2017

  49. [49]

    --- -.1pt --- -.1pt --- (2018): Beyond plausibly exogenous, The Econometrics Journal, 21, 316--331

    work page 2018

  50. [50]

    Young, H. P. (2009): Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence, and Social Learning, The American Economic Review, 99, 1899--1924

    work page 2009

  51. [51]

    Zhao, Q., D. S. Small, and B. B. Bhattacharya (2019): Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap, Journal of the Royal Statistical Society Series B: Statistical Methodology, 81, 735--761

    work page 2019