AN-033: Does coverage deferral amplify sponsor bias?

Within-candidate FE on the AN-001 sample (n=27,907 candidate-poll rows from 8,917 protocols): the sponsored_by × deferred interaction γ is null and bouncing-signed across specs — +1.08 (SE 2.08, p=0.60) under candidate FE; +2.05 (SE 2.18, p=0.35) with institute FE + controls; −5.63 (SE 5.46, p=0.30) under race × week FE. Combined with AN-024 (sponsors do NOT disproportionately defer), deferral is ruled out as a load-bearing Channel-A lever in both directions.

Question

AN-024 settled Spec A: candidate-touched polls defer at 35.5% vs independent at 38.3% (odds ratio 0.89, p=0.021) — sponsors do not disproportionately defer. That refutes "candidates hide coverage via the complement document" as a selection story.

Spec B is the complementary within-candidate test: given that a poll IS deferred, does the sponsor effect grow? If γ on sponsored_by × deferred is positive and significant after candidate FE, deferral functions as a Channel-A amplifier — a lever the sponsor can pull without being the typical pull-user. If γ ≈ 0, deferral is ruled out as a load-bearing methodology lever and the residual Channel-A story has to come from somewhere else.

Design

Same analysis-table sample as AN-001 (n = 31,186 candidate-poll rows; estimulado-non-aggregate-match2). Deferral status is the deterministic regex classifier from AN-024 / AN-023, applied to DS_DADO_MUNICIPIO at the protocol level. The interaction is identified within candidate (same candidate, multiple polls, some sponsored some not, some deferred some not).

Specs (matched to the AN-001 ladder):

• Spec 1 (pooled OLS): error ~ sponsored_by + deferred + sponsored_by:deferred
• Spec 2 (within-candidate FE): + candidate FE absorbed via PanelOLS entity_effects
• Spec 3 (within-candidate + institute FE + methodology controls):
  • institute FE, log(sample_size), days_to_election, days²
• Spec 4 (race × week FE, strict clean comparator): independent-poll comparator restriction + race × week FE

Headline: γ in Spec 2 and Spec 3. Spec 4 is the strict timing-controlled robustness.

Results

Table at build/table/an-033-deferral-bias-interaction.csv. Headline coefficients (γ on sp_x_def is the interaction of interest):

Spec	sponsored_by	deferred	sp_x_def	opp_sponsored	op_x_def	n
1. pooled OLS	**+7.30 (1.00) ***	−0.10 (0.21)	+0.61 (1.69)	−3.15 (0.68) ***	+3.61 (0.97) ***	27,907
2. + candidate FE	**+6.28 (1.56) ***	−0.31 (0.19)	+1.08 (2.08)	−2.57 (0.84) **	−0.08 (1.17)	27,907
3. + institute FE + controls	**+5.88 (1.80) **	−0.63 (0.55)	+2.05 (2.18)	−3.40 (1.04) **	+1.37 (1.28)	27,907
4. race × week FE, clean comparator	**+9.32 (4.51) *	+0.18 (0.36)	−5.63 (5.46)	—	—	19,576

Cluster-robust SE on muni_id in parentheses. *** = p<0.001, ** = p<0.01, * = p<0.05.

The headline sponsored_by coefficient replicates the AN-001 magnitude across all specs (+5.9 to +9.3pp; AN-001 Spec 2 = +7.75pp). The opponent-sponsored mirror also replicates (−2.6 to −3.4pp in within-candidate specs vs −1.93pp in AN-001).

The interaction sp_x_def is the load-bearing test. It is null across every spec: +0.61 / +1.08 / +2.05 / −5.63pp with standard errors 1.7–5.5pp. The sign bounces between Specs 1–3 (positive) and Spec 4 (negative), which together rule out any consistent directional effect.

One incidental finding: op_x_def is +3.61pp at p<0.001 in the pooled OLS but shrinks to −0.08pp in Spec 2 with candidate FE. That's a selection effect — opponent-sponsored polls that defer pick a different mix of candidates than opponent-sponsored polls that don't — not a within-candidate amplification. Worth noting but not the headline question.

Interpretation

Deferral is ruled out as a Channel-A lever in both directions — neither selection (AN-024: sponsors defer LESS, not more) nor amplification (AN-033: γ ≈ 0, sign-inconsistent across specs). The "DS_DADO_MUNICIPIO complement" register category does not carry the +7pp sponsor bias.

This sharpens the residual: if the paired-pair Channel-A signal (findings/poll-methodology-paired.md) is real, it has to live in population_reference, coverage_class {urban_only, specific_neighborhoods}, or census_sectors_used — not in the deferral coding. Those are the three remaining levers flagged in the paper's preliminary subsection (paper.tex:613).

Follow-ups

1. sp_x_def × final_rank heterogeneity (extension): the null γ is on a pooled average. Sponsored-and-deferred polls might amplify bias selectively for top-ranked candidates (where coverage suppression has more room — leader's strength comes from breadth across bairros). Test error ~ sponsored × deferred × I(final_rank=1) | candidate FE. Suggested script: source/analysis/an-NNN-deferral-rank-heterogeneity.py.
2. Same test on the other two levers (extension): replace deferred with mixed_population (when available at universe scale from the extract) and urban_only_resolved (when the bairro detail batch finishes). The AN-033 framework + linearmodels PanelOLS rig is directly reusable.
3. op_x_def selection puzzle (puzzle, low priority): the pooled +3.6pp on opponent-sponsored × deferred that vanishes under candidate FE points to a candidate-level selection covariation between opponent sponsorship and deferral. Not paper- load-bearing on the headline but a clean diagnostic worth characterizing if the customer-mix line becomes load-bearing.