Per-pollster β regressed on candidate-sponsored share gives slope = +13.58 (unweighted) / +6.28 (n-weighted), both positive but underpowered (p=0.40 / 0.47, n=11). Direction matches the reputation-equilibrium prediction; the two highest-volume firms (IIP, Census) sit near β=0 against the strict monotone version.
Results
Sample: 11 institutes with ≥ 5 self-sponsored polls AND non-degenerate cluster-robust SE (> 0.1).
Table: β regressed on candidate-sponsored share
| Regression | Slope on candidate_share |
SE | p | R² |
|---|---|---|---|---|
| OLS (unweighted) | +13.58 pp per 100% | 15.39 | 0.40 | 0.08 |
| WLS (weighted by n_self) | +6.28 pp per 100% | 8.34 | 0.47 | 0.06 |
(from build/table/pollster_customer_mix.csv)
Table: Auxiliary single-share regressions
| Spec | Coefficient | SE | p |
|---|---|---|---|
| β ~ share_media_only | γ_m = −17.50 | 13.52 | 0.27 |
| β ~ share_pollster_self_only | γ_p = −22.16 | 16.80 | 0.18 |
(from build/table/pollster_customer_mix.csv)
All four directional signs match the theory (positive on
candidate_share, negative on media / pollster-self share). None
clears significance at n=11.
Table: Per-pollster β distribution by customer-share band
| Pattern | Institutes |
|---|---|
| Low candidate-share (≤25%), low/negative β | Verita (+0.5), Ver Pesquisa (−5.0), Paraná (−10.5), Estimativa (−4.9), AR7 (−4.0) |
| Mid candidate-share (25–50%), positive β | Mendonça (+4.7), Gerais (+3.0), Opinar (+8.9), Promidia (+2.1) |
| Mid candidate-share, negative β outlier | Eva Francieli (−9.4) |
| High candidate-share (≥50%), high β | Intenção (+30.3, n=5 — noisy) |
| High candidate-share, near-zero β | IIP (−0.5, n=66) and Census (−2.8, n=72) |
(from build/table/per_pollster_beta.csv)
Interpretation
- Direction is right, power is thin. Magnitudes are plausible (a 100-pp candidate-share gap predicts a 6-14 pp β gap, comparable to the headline +8). But n=11 institutes is too thin for any slope to clear significance.
- IIP/Census anomaly is the empirical story. The two highest-volume firms (n_total = 412 and 263 respectively) sit near β = 0 despite high candidate-share. This is consistent with the theory's secondary prediction — high-volume firms are more disciplined because more reputation is at stake — but against the strict monotone primary prediction (high candidate-share → high β).
- Plot tells the textured story. The figure at
build/figure/pollster_beta_vs_customer_mix.pdfshows monotone-positive at the low-to-mid share range, but the IIP/Census points pull the WLS slope down. The bivariate analysis can't disentangle customer-mix from volume.
Confidence rationale (yellow). Directional signs across four specifications all match theory and magnitudes are economically plausible, but n=11 institutes leaves every slope far from significance, and the IIP/Census pattern complicates the strict monotone prediction. Real signal, but verdict has to wait for the 2022 panel extension.
Follow-ups
- 2022 cycle extension is the natural next step (queued in
docs/todo.md). Doubles the pollster panel and — more importantly — gives within-pollster-over-time identification: did a pollster's β change between 2022 and 2024 when their customer composition shifted? Pure cross-section can't separate equilibrium sorting from causal customer-mix effects. - Volume control: include
log(n_total)in the regression to separate volume effects from customer-mix. Underpowered now; feasible once n_pollsters doubles via 2022. - Shrunken-β estimator: replace per-pollster OLS β with a hierarchical / random-effects estimator that pools toward the grand mean for small-n firms. Would tighten the slope test.