H:exposure-discipline — Cobidder concentration survives exposure-disciplined placebos

A raw co-bidding association could reflect opportunity-set exposure — firms active in the same products, buyers, years, and modalities as CADE defendants mechanically have more chances of appearing near those legal anchors. The hypothesis is that the FL ranking still concentrates cobidders after the exposure margin is disciplined away by participation-volume placebos and audits within tighter opportunity sets.

Intuition (plain-language)

The headline result might be an artifact — perhaps the screen just identifies firms that bid a lot, and high-volume firms happen to cluster around CADE cases by mechanical overlap (same products, buyers, periods). Several audits discipline this: a formal sham permutation rejects the volume-only null at 32 standard deviations, a leakage audit preserves AUC above 0.85, a universe-scope matrix rules out generic-detector readings. The observed signal is not explained by any within-data artifact family we can test.

Evidence strength: Partial (strongly supported). Four converging audit chains, all strong within the BEC × CADE data: (i) Formal sham permutation (AN-005): B = 2,000 volume-matched permutations; sham AUC distribution mean 0.500, SD 0.013, q99 0.531, max 0.547. Observed 0.924 is ~32 sham SDs above the mean; permutation p < 1/2,000 = 0; rejects volume-only null at 99%. (ii) Leakage audit (AN-014): raw item-level 0.995 → OOF firm-level 0.891 [0.887, 0.894] → temporal firm-level 0.864 [0.858, 0.870]. Attenuation 0.10–0.13, residual AUC

sham distribution. (iii) Universe-anchored stratum scope (AN-027): 8-row meta-table confirms the score targets only what the framing predicts. Crucial row 4: participation count on all BEC vs direct CADE = 0.383 — below 0.5, the score actively repels winner-heavy defendants. No "generic detector" reading possible. (iv) Exposure-stratum balance (AN-028): within the FL14 stratum, cobidders distinct from non-cobidder FLs at Cohen's d 0.19–1.00 across 7 dimensions; not driven by volume alone. Promotion to 🟢 (Confirmed) requires independent replication on a non-BEC procurement panel — see the H3 page commentary section on why within-data exhaustion (however strong) does not satisfy the bar.

Theory

Exposure-disciplined comparisons are the cartel-screening equivalent of opportunity-controlled placebos: they ask whether the observed concentration would arise mechanically from where firms bid, independent of how they bid. The discipline isolates the signal from the volume \citep{conley2016detecting,kawai2022detecting}.

Prediction

Cobidder concentration inside the FL stratum should remain elevated when:

• the FL score is recomputed on a participation-matched placebo sample ("sham FL"); and
• cobidder classification is restricted to firms within the same (product × buyer × year × modality) opportunity sets as direct CADE defendants.

Competing prediction

Mechanical exposure. If concentration falls to baseline under either discipline, the result reduces to opportunity-set overlap rather than a behavioral signal. The hypothesis predicts robustness; the placebo predicts attenuation.

Case evidence

The exposure construction uses the same product × buyer × year × modality strata that procurement-cartel cases typically operate in (see manuscript, §2.3).

Empirical test

• Sham FL: random reassignment of the FL label among always-losers, preserving the marginal distribution; recompute AUC and compare to observed.
• Exposure-adjusted audit: restrict the cobidder benchmark to firms in the same exposure stratum and recompute concentration.
• Outcome: AUC against the cobidder set in each discipline.

Data requirements and limitations

Requires the BEC LANCES panel and the (product × buyer × year × modality) exposure key. Limitation: the exposure stratum is defined by observed participation, which itself can be affected by cartel behavior; the audit disciplines exposure but does not separately identify cartel-driven participation distortions.

Evidence

Analysis	Bearing	Status	Key takeaway
AN-005 (sham FL placebo, formal)	Direct	done	B=2,000 permutation; sham mean 0.500 SD 0.013; observed 0.924 = 32 σ above; p < 1/2,000
AN-014 (leakage audit D3)	Direct	done	Raw 0.995 → OOF 0.891 → temporal 0.864; attenuation 0.10–0.13
AN-027 (universe-anchored scope matrix)	Direct	done	8-row meta-table; row 4 (participation count vs direct CADE) = 0.383, below random
AN-028 (within-FL standardized diffs)	Direct	done	Cobidders distinct from non-cobidder FLs at d 0.19–1.00 across 7 dimensions
AN-006 (exposure + timing)	Supports	done	Strict ex ante firm AUC 0.767 [0.734, 0.800]

Open tests

• Sensitivity to exposure-stratum definition (coarser vs finer cells).
• Decomposition of attenuation by modality.
• Volume-matched cobidder vs non-cobidder-FL test — done (AN-041): matching on tenders_count (SMD 0.49 → 0.00), the within-stratum concentration is not a volume artifact (HHI d +0.47, repeat-spread −0.56 hold or strengthen; bid-dispersion sub-signal collapses to n.s.).

Why not 🟢 Confirmed?

The within-data evidence is strong at the audit level: sham permutation rejects at p < 1/2,000 (32 σ above null), the leakage audit preserves AUC > 0.85, the universe matrix shows row-by-row scope discipline, and the standardized-diff battery rules out within-stratum volume artifact. By the rubric of audit-survival claims, H3 is near-exhaustive.

So why not 🟢? Two artifact families remain untested by any within-data audit:

1. Data-generating process artifacts. BEC missingness, CNPJ-root collision (only 8 digits → possible aggregation across distinct firms with shared root), and CADE adjudication completeness bias. These are not "audits" but structural properties of the data lake. No within-data permutation can rule them out.

2. Selection on CADE adjudication. The cobidder set is defined relative to the CADE adjudications that exist in 2009–2019. If CADE selects which cartels to adjudicate non-randomly (e.g., easier cases, larger-impact cases, politically prominent cases), the loser-side signal could be tracking that selection rather than cartel-adjacent behavior in general.

Both can only be ruled out by replication on a non-BEC panel (ComprasNet federal, another state's e-procurement, or another country's data) with an independent cartel anchor. Until that exists, H3 stays at Partial (strongly supported), consistent with the project-wide rule documented in findings/index.md.