For 132 candidates whose self-sponsored poll was preceded by an independent poll in the same race (median gap 10 days), the within-candidate jump from preceding-independent to self-sponsored error is +6.70 pp (t=5.21). The most intuitive counter to "self-sponsor when leading".
Results
Table: Within-candidate jump from preceding-independent to self-sponsored poll
| Metric | Value |
|---|---|
| Self-sponsored polls preceded by ≥1 independent poll | n = 132 |
| Median time gap (days) | 10 |
| Mean error in self-sponsored polls | +7.64 pp |
| Mean error in preceding independent polls | +0.93 pp |
| Mean within-candidate jump (self − pre-indep) | +6.70 pp |
| Standard deviation of the jump | 14.77 |
| Share of jumps > 0 | 74% |
| One-sample t-test (H0: jump = 0) | t = 5.21 |
(from build/table/regressions.csv)
Table: Tight-window restriction (gap ≤ 14 days)
| Metric | Value |
|---|---|
| Observations | n = 77 |
| Mean within-candidate jump | +6.43 pp |
| One-sample t-test | t = 3.96 |
| Share of jumps > 0 | 77% |
(from build/table/regressions.csv)
Interpretation
This is the cleanest test of the "candidate commissions when privately believing they're leading" alternative. The comparator is the SAME candidate in the SAME race within a median 10-day window — the only thing that changes between the two polls is who's paying. Two predictions disagree:
- Slant interpretation: self-sponsored polls inflate the candidate by ~7 pp regardless of where they actually stand → predicts +7 pp jump.
- Self-sponsor-when-leading interpretation: candidates commission only when their private belief about leading shifts → predicts the preceding independent poll should already show the candidate high (both measuring the same private peak) → predicts ~0 jump.
The data picks the slant interpretation:
- Jump magnitude: +6.70 pp, t = 5.21, 74% positive — the preceding-independent baseline does not anticipate the self-sponsored number.
- Convergence across designs: ~identical to the within-candidate FE coefficient (+7.75) and the race-week FE coefficient (+6.95). Three independent design strategies converging on +6–7 pp is the load-bearing robustness fact for the paper's main claim.
- Baseline is centered: mean error in the preceding independent polls is +0.93 pp — essentially zero — so the independent-poll baseline is not biased on average. (Different from the SP-only prototype, where the independent baseline ran −12.55 pp because of selection on which candidates had matched independent + self-sponsored polls. At all-Brazil scale, the baseline is centered.)
- Robust to tight window: restricting to gaps ≤ 14 days (n = 77) yields +6.43 pp, t = 3.96, 77% positive — magnitude survives.
Confidence rationale (green). The within-candidate, within-race, median-10-day-window design rules out the most natural selection story (self-sponsor when leading) directly. Three independent specifications converge on the same +6–7 pp magnitude, the tight-window cut leaves the estimate intact, and the independent-poll baseline is centered rather than negatively selected. The placebo discriminates between slant and selection without relying on additional modeling assumptions.
Follow-ups
- The 132-observation placebo is not panel — it's one observation per candidate. A panel version (multiple self-sponsored polls per candidate × multiple independent polls per candidate) would tighten the SE further but doesn't change the qualitative reading.
- The Channel A vs B decomposition can be re-run on the placebo sample once methodology features are extracted, to see whether the within-candidate jump is itself decomposable into design and residual.