AN-029: Money-controlled selection test for the two-mechanism interpretation

Money does NOT drive the rank gradient in self-sponsoring. The AN-027 two-mechanism interpretation of safe-race rank-1 over-commissioning as 'resourcing without strategic need' is REFUTED on the literal money-control test. Baseline rank-2 vs rank-1 gap is −3.6 pp tight / −3.6 pp mid / −6.8 pp wide; under log(revenue) control it moves to −3.6 / −3.6 / −6.6 — essentially unchanged across all margin tertiles. log(revenue) main effect is +0.23 pp per log-unit (p=0.16 pooled); rank × log(revenue) interactions are all <0.012 pp / log-unit and insignificant (p>0.17). The cross-margin pattern (rank-1 dominance largest in safe races) is robust to money control. Substantive read: the safe-race rank-1 over-commissioning is real but is NOT explained by campaign-finance revenue. Alternative resourcing channels (campaign sophistication, party support, fixed-cost crossing of the polling-affordability threshold) remain candidates; pure-money resourcing as a stand-alone mechanism is not supported.

Hypothesis: H6: β peaks at the M+1 viability cutoff (coordination)
Confidence: yellow
Type: descriptive

Design

Sample: Per-candidate cohort: 2024 prefeitos running in races with ≥1 poll. n_cohort=8,225, n_self=428. Self-sponsoring indicator from `sponsored_by==1` in the project panel; campaign-finance revenue from receita_2024.csv aggregated by SQ_CANDIDATO (99.8% match rate), bridged to politico_id via candidato.csv. Median revenue R$146,788.
Specification: Linear-probability OLS: I[self_sponsored=1] ~ C(rank_bin, ref=1) [× log_receita] + C(muni_id) — three specs (A baseline, B + log_receita, C + rank × log_receita interactions). Cluster-robust SE at muni. Stratified by race_margin tertile.
Comparator: Reference rank = 1. Margin tertiles via qcut(race_margin, 3).
Cluster: muni
Weights: none
Notes: Final-rank framing (consistent with AN-026 / AN-029 user-spec). The AN-027 rank-at-commission version is a separate test deferred as a follow-up.

Script: source/analysis/an-029-money-controlled-selection.py
Target: build/table/money_controlled_selection.csv
Status: interpreted · 2026-06-02
Created: 2026-06-02

Question

AN-027 / AN-028 proposed a two-mechanism story for the AN-026 selection finding: in TIGHT races runners-up over-commission for coordination-demand reasons; in WIDE races leaders over-commission because they have resources to spend on non-strategic uses (donor signaling, GOTV planning). AN-029 tests the resourcing leg directly: does adding campaign-finance revenue as a control attenuate the safe-race rank-1 dominance while preserving the tight-race rank patterns?

Results

Money-controlled selection: rank-2 coefficient pre/post money + log(revenue) slope by tertile

Rank coefficients (vs rank-1 reference) — Spec A baseline vs Spec B with log(revenue)

Stratum	Term	A baseline (pp)	B + log(revenue) (pp)	Δ
All margins	rank-2	−4.76***	−4.69***	+0.07
	rank-3	−6.91***	−6.57***	+0.34
	rank-4	−8.76***	−8.21***	+0.55
	rank-5+	−10.60***	−9.78***	+0.82
	log(revenue)	—	+0.23 (p=0.16)	—
Tight margin	rank-2	−3.61**	−3.60**	+0.01
	rank-3	−6.44***	−6.24**	+0.20
	rank-4	−10.36***	−10.04***	+0.32
	rank-5+	−14.27***	−13.78***	+0.49
	log(revenue)	—	+0.17 (p=0.65)	—
Mid margin	rank-2	−3.63**	−3.56**	+0.07
	rank-3	−6.68***	−6.27***	+0.41
	rank-4	−7.52***	−6.79***	+0.73
	rank-5+	−8.62***	−7.55***	+1.07
	log(revenue)	—	+0.28 (p=0.14)	—
Wide margin	rank-2	−6.78***	−6.59***	+0.19
	rank-3	−7.57***	−7.02***	+0.55
	rank-4	−7.91***	−7.07***	+0.84
	rank-5+	−6.66***	−5.33**	+1.33
	log(revenue)	—	+0.30 (p=0.25)	—

Race FE (muni) absorbed in all specs. n_cohort = 8,225, n_self = 428.

Spec C — rank × log(revenue) interactions

All four interaction coefficients are small (≤+0.012 pp / log-unit) and all insignificant (p ∈ [0.17, 0.99]). Money does not operate differentially across ranks. The rank-1 main effect of log(revenue) in spec C is −0.003 pp / log-unit (p = 0.76), so there's no evidence that rank-1 candidates' self-sponsoring is more responsive to money than other ranks'.

Interpretation

Money is not the resourcing channel. The rank gradient is essentially unchanged after adding log(revenue) as a control — across all margin tertiles, after race FE, and whether money is modeled as a linear control or interacted with rank. The log(revenue) coefficient itself is positive but small (+0.2 to +0.3 pp per log-unit) and statistically insignificant except as a weak overall signal.

Cross-margin pattern survives. The safe-race rank-1 dominance (rank-2 vs rank-1 gap = −6.8 pp wide vs −3.6 pp tight) is real, robust, and not attenuated by money. The tight-vs-wide difference in rank gradient is therefore not the "money channel" but something else.

The AN-027 / AN-028 interpretation (safe-race leaders commission for resourcing reasons) is REFUTED on its literal money-revenue form. The AN-027 finding (rank-2 over-commissioning in tight races under rank-at-commission framing) is a separate test that this iteration didn't address — it uses final_rank, not rank-at-commission, per the user-specified scope.

What could drive safe-race rank-1 dominance if not money? Plausible alternatives the AN-029 design doesn't separate:

Campaign sophistication — well-organized campaigns commission polls regardless of marginal need; well-organized campaigns also tend to win safe races. Revenue is a noisy proxy for sophistication.
Polling fixed cost — a real poll costs ~R$50k–200k, which is a fixed cost. Above some threshold of revenue, more money doesn't buy more polls. The continuous log(revenue) control mis-specifies this; a threshold indicator might bind differently.
Party institutional inertia — established parties have in-house pollsters and standard practices that commission polls on behalf of their candidates, independent of the candidate's own revenue.
Selection on candidate quality — competent candidates win AND commission polls; rank-1 over-commissioning is then a quality confound, not a strategic-incentive one.

The companion paper should pick one or two of these to operationalize rather than letting "resourcing" stand as an ungrounded label.

Caveats:

Revenue is valor_receita_total summed across all receita_2024 line items per candidate, including in-kind, party transfers, etc. Some of these are mechanically tied to party support rather than candidate-side fundraising capacity.
The LPM specification absorbs muni effects but doesn't account for selection into running for prefeito; the self-sponsoring rate conditional on running is the outcome.
Final-rank coding (per user spec) — the AN-027 rank-at-commission framing would give a different baseline pattern. A clean money-control test on the AN-027 rank-at-commission cohort is the natural follow-up.

Follow-ups

Rank-at-commission + money control (extension, highest paper value): re-run AN-029 using rank-at-commission (from AN-028's date_start anchor) instead of final_rank. The tight-race rank-2 over-commissioning that AN-027 documented under rank-at-commission should survive money control if the coordination story holds — but AN-029 hasn't tested this directly yet.
Threshold-based money control (extension): replace log(revenue) with an indicator for "revenue above the cost of one polling contract" (~R$50k or ~R$100k). If polls have fixed costs, the relevant question is whether the candidate crossed the threshold, not the marginal log-revenue slope.
Campaign sophistication proxies (blind spot): try alternative resourcing measures — number of paid staff, advertising spend, in-kind contributions — and see if any attenuates the rank gradient where log(revenue) doesn't.
Decisions.md candidate (framing update): AN-029 is a null on the resourcing interpretation. If this finding becomes load-bearing for the companion paper's section on selection mechanisms, the "two-mechanism" framing from AN-027/028 needs revision and should be flagged as a decisions.md entry: drop "resourcing" as a stand-alone mechanism; report safe-race rank-1 over-commissioning as an unexplained selection fact that future work needs to mechanize.