A Binary IV Model for Persuasion: Profiling Persuasion Types among Compliers

Zeyang Yu

REVIEW 3 major objections 9 minor 35 references

A Binary IV Model for Persuasion: Profiling Persuasion Types among Compliers

T0 review · 3 major / 9 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read In a binary instrumental-variable model with monotone treatment response, the joint distribution of potential outcomes among compliers is point identified, so the shares and covariate profiles of always-voters, never-voters, and mobilised…

desk verdict The theoretical identification results are sound and worth publishing after the empirical section's arithmetic error and the too-narrow sensitivity analysis are fixed. read the letter →

arxiv 2411.16906 v2 pith:E2MAVSEN submitted 2024-11-25 econ.EM

Zeyang Yu This is my paper · ORCID

classification econ.EM MSC 62P20

keywords instrumentalvariablesmonotonetreatmentresponsepersuasioncompliersAbadiekappalocalratesharptestget-out-the-vote

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

This paper asks what an encouragement experiment can reveal about who is actually persuaded, not just how many are moved on average. It shows that under the standard binary Imbens-Angrist instrumental-variable assumptions plus a monotone treatment response, the joint distribution of potential outcomes among compliers is point identified. Because that joint distribution is exactly what separates always-voters, never-voters, and mobilised voters, each latent type's share and its profile in pre-treatment covariates become estimable from the observed data. The paper also gives a sharp test of the identifying assumptions, a sensitivity analysis for the monotone-response assumption, and an application to get-out-the-vote experiments.

What carries the argument

The carrying object is the pair of binary potential outcomes with monotone treatment response, $Y_i(1) \geq Y_i(0)$ almost surely. This restriction removes the demobilised type, so each persuasion type among compliers corresponds to an event whose marginal probability the Imbens-Rubin framework already identifies. The profiling results ride on an extension of Abadie's kappa weighting: Theorem 3.1 shows that any moment of $(Y_i(t), T_i, X_i)$ among compliers is identified, and Theorem 3.2 conditions those moments on the joint potential-outcome type. The test and sensitivity analysis use the same linear structure: cell probabilities are written as linear combinations of unobserved type probabilities, so the assumptions hold exactly when some nonnegative vector $p$ satisfies $A_{obs} p = b$.

What would settle it

A direct check would be a crossover or panel design in which the same individual is observed under both treatment and control: if a non-negligible share have $Y_i(1)=0$ and $Y_i(0)=1$, the monotone-response assumption fails and the point-identification claim collapses. Equivalently, applying the paper's sharp linear-system test to data with a known demobilised subpopulation should reject at a rate above the nominal size.

Watch

Extended reading notes

Core claim

The central discovery is that the joint distribution of potential outcomes among compliers, usually treated as unidentified in instrumental-variable settings, is point identified when the outcome is binary and treatment response is monotone. Proposition 3.1 gives explicit formulas: the share of always-voters among compliers equals $(E[Y_i(1-T_i)|Z_i=0] - E[Y_i(1-T_i)|Z_i=1])/(E[T_i|Z_i=1]-E[T_i|Z_i=0])$, with analogous expressions for never-voters and mobilised compliers. Identification works because monotone treatment response collapses joint types to marginal events: always-voters are those with $Y_i(0)=1$, never-voters are those with $Y_i(1)=0$, and mobilised compliers are the remaining cell. Theorem 3.2 then identifies the conditional expectation of any measurable $g(T_i, X_i)$ given each persuasion type among compliers. The paper also characterises the identifying assumptions sharply as the existence of a nonnegative solution to a linear system and applies the method to the Green et al. (2003) get-out-to-vote experiments.

Load-bearing premise

The load-bearing premise is that no one is dissuaded by the treatment: an individual who would take the action without the treatment also takes it with the treatment, which is what collapses the unobserved joint persuasion types onto identifiable marginal outcome events.

Editorial extensions

If this is right

Researchers can estimate the share of compliers who are always-voters, never-voters, and mobilised voters, and can profile each group by covariates such as partisanship or prior turnout.
The approach extends Abadie's kappa weighting: any moment of the joint distribution of treatment and covariates is identifiable conditional on a persuasion type, not merely for compliers as a whole.
A sharp test reduces the identifying assumptions to checking whether a known linear system has a nonnegative solution, so the validity of the instrument and of monotone treatment response can be jointly tested.
The comparison of persuasion-rate estimands pins down when the commonly used approximated persuasion rate coincides with the local persuasion rate under one-sided non-compliance.
Applied to the Green et al. (2003) experiments, the method estimates that roughly 8% of compliers in the full sample and 14% in Bridgeport were mobilised, with prior-turnout profiles consistent with habit formation.

Reading between the lines

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

The same identification logic would apply to other binary-outcome encouragement settings, such as charitable giving, advertising, or job-training take-up, whenever the treatment plausibly moves outcomes only in one direction.
Because the point-identification result hinges on ruling out demobilised voters, the method is most credible when the treatment lowers the cost of an action; for counter-attitudinal or backfiring treatments, researchers would need the partial-identification version of the same linear-system argument.
The sharp test could be extended to continuous covariates by partitioning the covariate space and using high-dimensional linear-inequality inference, making the specification check practical in observational studies.
The sensitivity analysis suggests a routine robustness practice: report the estimated joint distribution as a function of the allowed share of demobilised compliers, which directly shows how much of the mobilised-voter conclusion depends on the monotone-response assumption.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this is a real but modest theoretical contribution. The key identification result amounts to combining Imbens-Rubin marginal outcome distributions with monotone treatment response to get the joint distribution among compliers, and then extending Abadie's kappa to profile the three persuasion types. That is worth having, and the paper is honest that the MTR assumption does the heavy lifting. The sharp test and sensitivity analysis are useful additions. The appendix proofs look correct, and the writing is clear about what is new relative to Jun-Lee and Comey et al.

The empirical application is where I have real problems. The Bridgeport cost calculation has a straightforward arithmetic inconsistency: the text says 1.6% of mobilised voters are Democrats, or about 28 people, and then uses that to get $1,066 per Democrat. But Table 5 reports a point estimate of 81.3% Democrat among mobilised compliers, and Table 4 says 13.9% of compliers are mobilised. With 1,806 observations and a 27.7% complier share, that gives roughly 0.813 × 0.139 × 0.277 × 1806 ≈ 56 people, not 28. The reported 1.6% and 28 people are off by about a factor of two. This needs to be fixed, and it changes the cost estimate materially.

The sensitivity analysis is also too narrow. It varies the size of the demobilised group and shows how the mobilised share changes in the joint distribution, but it does not trace the effect on the profiling estimands—the Democrat share among mobilised compliers, the number of mobilised Democrats, or the cost per Democrat. Since those are the headline applied results, the fragility under MTR violations is unexamined for exactly the quantities the empirical section advertises. The sharp test did not reject, but non-rejection cannot establish that the demobilised share is zero, and the paper doesn't analyse the power of the test.

None of this undermines the theoretical identification results. Proposition 3.1 is correct, and Theorem 3.2 is a clean extension of Abadie's kappa. The paper deserves a serious referee. My advice is to send it out, but the empirical section needs correction, and a replication package would be appropriate for an applied econometrics journal. I would cite the identification results after the empirical fixes; the policy numbers are not trustworthy as they stand.

Referee Report

3 major / 9 minor

Summary. This paper studies identification in a binary treatment/binary outcome Imbens-Angrist IV model augmented by the monotone treatment response assumption (Yi(1) ≥ Yi(0)). It shows that the joint distribution of potential outcomes among compliers is point identified: the always-voter, never-voter, and mobilised shares are the Imbens-Rubin marginals, and the mobilised share equals the LATE. It extends Abadie's kappa weighting to moments of (Yi(t), Ti, Xi) and, under monotone treatment response, to moments of (Ti, Xi) conditional on always-voter, never-voter, and mobilised compliers. It also proposes a sharp test of the identifying assumptions based on a system of linear inequalities, gives conditions under which the DellaVigna-Gentzkow approximated persuasion rate equals the local persuasion rate, provides a sensitivity analysis for the monotone treatment response assumption, and applies the methods to Green et al. (2003).

Significance. If correct, the main theoretical result is useful and clean: with binary outcomes, monotone treatment response collapses joint persuasion types into marginal potential-outcome events, so the joint distribution among compliers is identified from standard Imbens-Rubin/Abadie results. The extension of Abadie's kappa to treatment-inclusive moments is a genuine contribution, and the proposed sharp test is a real refutation test rather than a fitted verification. The proofs are complete and rely on known external results, with no hidden free parameters in the identification argument. The contribution is somewhat incremental given Jun and Lee (2023) and the acknowledged independent work of Comey et al. (2023), but the paper provides a useful unified treatment and a concrete application.

major comments (3)

[Section 5.2; Tables 4-5] The application's headline cost-effectiveness figures are internally inconsistent. In Bridgeport, Table 4 gives P[Yi(1)=1,Yi(0)=0|C]=0.139 and Table 5 gives P[Democrat=1|Yi(1)=1,Yi(0)=0,C]=0.813. With the first-stage complier share 0.277 and n=1,806 (about 500 compliers), this implies about 56 compliers who are both mobilised and Democrats, or 3.1% of the sample. The text reports exactly this 3.1% and then, one sentence later, reports '1.6%, or around 28 people', apparently multiplying by the 0.5 assignment probability. If the intended estimand is the number of complier-mobilised Democrats actually assigned to treatment (28), that needs to be stated explicitly and the 3.1% number cannot be used as the share of voters mobilised by the experiment without the same qualifier. The cost computation is also not transparent: the stated components ($3,000 + $30 per outreach voter) do not obviously sum to $29,350, and the implied cost per Democrat is roughly $524 if the 56 figure is used instead of $1,066. Please correct the arithmetic and define the target estimand precisely.
[Section 4.3; Table 6; Theorem 3.2] The sensitivity analysis in Table 6 varies the demobilised share P[Yi(1)=0,Yi(0)=1|C] and recomputes the three joint outcome probabilities among compliers, but it never traces the effect of this violation on the profiling estimands emphasised in the application: P[Democrat=1|mobilised,C], the number of mobilised Democrats, or the cost per Democrat. This is a substantive gap because Theorem 3.2's mobilised-cell formula is derived from the identity E[g(z,X)(Y(1)-Y(0))1{C}], and once demobilised individuals (Y(1)=0,Y(0)=1) are allowed, the observed numerator no longer equals E[g(z,X)1{Y(1)=1,Y(0)=0}1{C}]; the profiling ratios are therefore not identified. Table 6 shows the mobilised share rising from 13.9% to 23.9% in Bridgeport at δ=0.10, and the same δ could shift the Democrat share and cost figures by an amount the paper does not quantify. The introductory claim that the paper 'provides a simple sensitivity analysis for the monotone treatment response assumption' should be scoped to the joint outcome distribution, or the analysis should be extended to the Theorem 3.2 estimands.
[Section 4.2; Section 5.3] The sharp test is a joint test of IA-IV plus monotone treatment response, and the paper is careful to state that non-rejection does not verify the assumptions. Since the paper's own Table 6 entertains demobilised shares as large as 0.10, the test's power against such alternatives should be assessed or at least discussed; otherwise the Section 5.3 conclusion that the assumptions are 'not rejected' gives little assurance for the application. Please report the numerical test statistics and subsampling p-values, and ideally a small simulation showing which demobilised shares the test can detect with the Green et al. sample sizes.

minor comments (9)

[Section 4.3; Appendix A.2] The text refers to 'Lemma 3.1' and 'the identification results in Lemma 3.1', but no lemma with that number is stated in the main text; renumber the result or add the lemma statement.
[Appendix A.13] Appendix A.13 refers to 'Theorem 3.3', which is not defined anywhere in the paper; correct the cross-reference.
[Appendix B; Appendix D] Several labels collide: 'Assumption 2.1' is used again in Appendix B.1, 'Proposition 4.1' appears in both the main text and Appendix D, and 'Proposition 2.1' appears in Appendix B.2; renumber the appendix items.
[Section 4.2] The test statistic T_n is defined with a constraint Bp=1, but the matrix B is never introduced; define B as the row vector of ones or write the constraint as the sum of the components of p being one.
[Proposition 4.3] Part (2) of Proposition 4.3 says 'satisfies the restrictions in P0' before P0 is defined in equation (4.2); state the definition of P0 before or inside the proposition.
[Section 4.2] The definition of L_n(t) sums over all N_n = C(n,b) subsamples, which is computationally impossible for n=18,933; state that random subsamples are used in practice and specify their number.
[Section 5.2] The sentence 'we estimate that 3.1% of mobilised voters are also compliers and Democrats' is ambiguous; it should say '3.1% of the Bridgeport sample are mobilised compliers who are Democrats' (or whatever is intended), and a confidence interval for this joint share should be reported given the wide CI for the Democrat share among mobilised compliers.
[Table 6 note] The table note contains 'among compilers' in the last sentence; it should be 'among compliers'.
[Appendix E.1] Proposition 5.1 contains the typo 'rull rank'; it should be 'full rank'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the identification results are derived transparently from stated assumptions and established external results, with no fitted parameter renamed as a prediction and no load-bearing self-citation.

full rationale

The paper's central claim (Proposition 3.1) is a direct derivation from Assumption 2.1: under monotone treatment response and binary outcomes, the joint persuasion-type events collapse to marginal potential-outcome events, so the joint distribution among compliers is built from the Imbens-Rubin/Abadie marginals and the LATE. The proof in Appendix A.2 explicitly reduces each joint probability to a marginal probability or to the Wald estimand, and Proposition 3.2 and Theorem 3.2 then condition Abadie's kappa weights on these identified events. No free parameter is fitted to data in order to produce these results, and the sharp test in Section 4.2 is a refutable linear-programming characterization (Proposition 4.3) rather than a verification of the assumptions. The sensitivity analysis in Section 4.3 transparently varies the violation of monotone treatment response and traces its effect on the identified joint distribution; its restriction to the joint outcome distribution rather than the covariate-profiling estimands is a limitation, not a circular step. The paper contains no self-citations: references to Abadie (2003), Imbens and Rubin (1997), and Jun and Lee (2023) are independent external results, and the author's statement that H0 is refutable but nonverifiable is an honest limitation. The derivation is therefore self-contained and no circularity is present.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The identification results rely on the standard IA IV assumptions (exclusion, exogeneity, first stage, monotonicity in treatment) plus the additional monotone treatment response assumption. The latter is a substantive behavioral restriction that does the main work in reducing the joint distribution of potential outcomes to marginals. The empirical section adds arbitrary cost parameters and a subsample size choice that are not load-bearing for the identification claims.

free parameters (2)

Cost assumptions = $3,000 administrative and $30 per voter outreach
Used only in the illustrative cost-per-Democrat calculation in Section 5.2; not part of the identification results.
Subsample size for sharp test = b_n = n^(2/3)
Implementation choice in Section 5.3 following Bai et al. (2022); does not affect identification.

assumptions (7)

domain assumption Exclusion restriction: Yi(t,z) = Yi(t) for all t,z
Standard instrumental variables assumption; required for observed Y to reveal the relevant potential outcome.
domain assumption Exogenous instrument: Zi independent of (Yi(0), Yi(1), Ti(0), Ti(1), Xi)
Random assignment; used to replace potential outcome means with observed sample moments.
domain assumption Relevant first stage: P[Ti=1|Zi=1] != P[Ti=1|Zi=0]
Needed for the Wald ratios to be well-defined.
domain assumption IV monotonicity: Ti(1) >= Ti(0) a.s.
Ruled out defiers; used in decompositions of complier indicators.
domain assumption Monotone treatment response: Yi(1) >= Yi(0) a.s., with binary outcomes
Ruled out demobilised voters; maps joint persuasion types to marginal potential outcome conditions. This is the paper's key identifying assumption.
domain assumption Support conditions: P[Yi(t)=y, Ti(1)>Ti(0)] > 0 for relevant t,y
Needed so conditional moments are well-defined in Propositions 3.2 and 3.3.
domain assumption The Green et al. (2003) experiments satisfy the IV assumptions and provide valid pre-treatment covariates
Applied in Section 5 to draw empirical conclusions.

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Pith. "Pith review of A Binary IV Model for Persuasion: Profiling Persuasion Types among Compliers." pith.science (2026). https://pith.science/paper/E2MAVSEN

@misc{pith2026241116906,
  author       = {Pith},
  title        = {Pith review of: A Binary IV Model for Persuasion: Profiling Persuasion Types among Compliers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E2MAVSEN}},
  note         = {Machine review of arXiv:2411.16906}
}

read the original abstract

In an empirical study of persuasion, researchers often use a binary instrument to encourage individuals to consume information and take some action. We show that, with a binary Imbens-Angrist instrumental variable model and the monotone treatment response assumption, it is possible to identify the joint distribution of potential outcomes among compliers. This is necessary to identify the percentage of mobilised voters and their statistical characteristic defined by the moments of the joint distribution of treatment and covariates. Specifically, we develop a method that enables researchers to identify the statistical characteristic of persuasion types: always-voters, never-voters, and mobilised voters among compliers. These findings extend the kappa weighting results in Abadie (2003). We also provide a sharp test for the two sets of identification assumptions. The test boils down to testing whether there exists a nonnegative solution to a possibly under-determined system of linear equations with known coefficients. An application based on Green et al. (2003) is provided.

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Reference graph

Works this paper leans on

35 extracted references · 29 canonical work pages

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Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Abadie, A. (2003). Semiparametric instrumental variable estimation of treatment response models. Journal of Econometrics\/ 113\/ (2), 231--263

work page 2003

[2] [2]

Anzia, S. F. (2011). Election timing and the electoral influence of interest groups. Journal of Politics\/ 73\/ (2), 412--427

work page 2011

[3] [3]

Santos, and A

Bai, Y., A. Santos, and A. M. Shaikh (2022). On testing systems of linear inequalities with known coefficients. Working Paper\/

work page 2022

[4] [4]

Balke, A. and J. Pearl (1997). Bounds on treatment effects from studies with imperfect compliance. Journal of the American Statistical Association\/ 92\/ (439), 1171--1176

work page 1997

[5] [5]

Blattman, C. and J. Annan (2016). Can employment reduce lawlessness and rebellion? a field experiment with high-risk men in a fragile state. American Political Science Review\/ 110\/ (1), 1--17

work page 2016

[6] [6]

Chernozhukov, V. and C. Hansen (2004). The impact of 401 (k) participation on the wealth distribution: An instrumental quantile regression analysis. Review of Economics and Statistics\/ 86\/ (3), 735--751

work page 2004

[7] [7]

Comey, M. L., A. R. Eng, and Z. Pei (2023). Supercompliers. arXiv preprint arXiv:2212.14105\/

work page Pith review arXiv 2023

[8] [8]

DellaVigna, S. and M. Gentzkow (2010). Persuasion: empirical evidence. Annual Review of Economics\/ 2\/ (1), 643--669

work page 2010