Sponsor effect shrinks with race-level public visibility, but the linear interaction is statistically indistinguishable from zero at this sample size. Within-cand FE: β_sponsored = +7.43 pp on 24,868 rows. Adding the interaction β_sponsored × log(polls_in_race_demeaned): β_sponsored = +7.24, β_interaction = −0.78 pp per log-unit (SE 0.96, p = 0.42). Adding firm FE to control for the market-quality confound: β_interaction = −1.29 (SE 1.04, p = 0.22). Tertile split: β_sponsored is +6.78 in the low-visibility tertile (median 3 polls/race), +10.46 in medium (median 7 polls/race), and +4.93 in high (median 24 polls/race; p = 0.011). Direction is consistent with the reputational-pressure-via-visibility mechanism (highest-visibility tertile has the lowest β; the cross-tertile range is −1.85 pp from low to high and the linear coefficient implies roughly −3 pp across the 10× visibility range), but the linear test does not reach conventional significance on the universe sample. The non-monotone medium-tertile spike dilutes the linear estimate. Reading: weakly supportive of the reputation mechanism, not a tight identification.
Question
Section 6's synthesis claims that reputation acts as the binding quality-control constraint that disclosure rules do not. AN-018 documents the firm-size discipline correlationally; AN-059 shows firm selection is not the mechanism. But the chain from reputational pressure to sponsor-effect shrinkage has not been tested directly. The natural test: in races with more polls and more public scrutiny, the same firm's sponsor effect should be smaller because the comparison across pollsters is more visible.
Design
source/analysis/an-060-race-visibility.py:
- Load
build/assemble/cand_poll.parquet. - Compute race-level visibility = distinct protocols per muni; take the log and demean across the analysis sample.
- Three nested specs:
- Spec A:
error ~ sponsored | cand FE(headline replicate). - Spec B:
error ~ sponsored + sponsored × log_polls_in_race_dm | cand FE. - Spec C: Spec B plus firm FE via
other_effects=["institute"]to isolate within-firm variation in the interaction.
- Spec A:
- Tertile split by visibility for narrative clarity.
Results
Interaction estimates
| Spec | β_sponsored | β interaction (per log-unit) | p (interaction) |
|---|---|---|---|
| A: cand FE | +7.43 (SE 1.12) | — | — |
| B: + interaction | +7.24 (SE 1.09) | −0.78 (SE 0.96) | 0.42 |
| C: + firm FE | +7.63 (SE 1.11) | −1.29 (SE 1.04) | 0.22 |
Direction is consistent with the reputational-visibility prediction: within firm, a one-log-unit increase in race-level polling intensity is associated with a 1.29 pp drop in the sponsor coefficient. The implied range over the 10× visibility variation in the sample is about −3 pp. The interaction does not reach conventional significance at the universe sample size, with p ≈ 0.22 on the cleanest specification.
Visibility tertile cross-check
| tertile | median polls/race | n rows | n sponsored | β_sponsored | p |
|---|---|---|---|---|---|
| low | 3 | 8,338 | 231 | +6.78 | <0.001 |
| medium | 7 | 8,395 | 72 | +10.46 | <0.001 |
| high | 24 | 8,135 | 31 | +4.93 | 0.011 |
The high-visibility tertile (state capitals and large metros) shows the lowest sponsor effect, consistent with the reputational discipline story. The medium tertile spikes to +10.46, which dilutes the linear interaction.
Interpretation
The pattern is directionally supportive but not statistically tight on the linear specification. The cross-tertile contrast (low +6.78 vs high +4.93) is real but the medium-tertile spike at +10.46 suggests the relationship is not monotone in log(polls_in_race) at universe scale.
Plausible interpretation of the medium-tertile spike: medium-visibility races (mid-size municipalities with multiple competing pollster firms) generate enough campaign stakes for sponsors to invest in polls yet not enough public scrutiny to constrain them. Small municipalities have low stakes and no scrutiny; large metros have high stakes and strong scrutiny.
The result is weak supporting evidence for the reputational mechanism, not a tight identification. It belongs in the synthesis as directional confirmation, with the caveat that the linear interaction is statistically indistinguishable from zero.
Follow-ups
- Continuous news-coverage measure. A sharper visibility proxy would be number of news mentions of polls in a race (Folha / Estado coverage). Substantially more work to construct and probably moves a noisy interaction to a tighter one.
- Aggregator inclusion as visibility proxy. Firms whose polls are aggregated by poll-of-polls outlets (e.g., a curated reputation list) versus those that are not.
- Race-week visibility rather than race visibility. The visibility relevant for any single poll is the comparison window around its field date, not the race's total polling over the whole cycle. Possible refinement.