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H:cobidder-concentration — The ranking concentrates adjudication-anchored exposure above mechanical opportunity

If the award-layer score orders forensic priority informatively, then firms that always lose but bid alongside direct CADE defendants in adjudicated cartel environments (their adjudication-anchored exposure, captured by the cobidder label) should rank higher in the always-loser stratum by more than participation opportunity alone would predict. The hypothesis is about loser-side exposure to legal anchors, not cartel membership: the ranking should order cobidders, not direct defendants — and the genuine question is how much of that ordering survives once mechanical opportunity is netted out.

Intuition (plain-language)

Among always-loser firms in Brazilian procurement, the ones that bid most often (frequent losers) sit disproportionately near cartels formally adjudicated by Brazil's antitrust authority. But almost all of that raw proximity is opportunity: firms that bid a lot mechanically end up near anyone, including CADE defendants. The honest question is what is left after you net opportunity out. The answer under the reproducible non-circular label: a raw concentration that looks high (ROC 0.761, lift 5.6×) is mechanical, anchor-agnostic co-participation exposure — genuine label-blind opportunity ranks the label at only 0.553 (ranking by observed contact reaches 0.90, but that is mechanical label encoding, not a competing model); the signal inside a fixed opportunity stratum is 0.471 — at chance — and the marginal nested increment (+0.010, p = 0.013) does not survive the permutation tests. Cheap award records concentrate where to look first; they do not prove cover-bidding, and net of opportunity they carry no robust residual.

Evidence strength: Not confirmed (opportunity explains it). The honest decomposition on the BEC 2009–2019 panel under the non-circular 651-cobidder label: (i) raw concentration is mostly opportunity exposure — an exposure-only model reaches ROC ≈ 0.90 unconditionally (0.713 on the exposed subset), so the raw numbers are exposure-inflated, not discriminating power (AN-004); (ii) the within-stratum signal is at chance — ROC 0.471 (FL14 0.507); the nested increment over exposure is only +0.010 (DeLong p = 0.013), marginal at best (AN-004); (iii) the marginal increment does not survive permutation: matched- stratum label permutation p = 0.127 (ns), FL-enrichment within matched strata p = 0.067 (ns) (AN-005); (iv) cutoff sweep and subsample robustness describe the raw concentration, not a residual signal (AN-025, AN-026); (v) negative controls corroborate the opportunity account: real ≈ placebo (p = 0.46), high-volume-winner null above real (p = 0.91) (AN-005); (vi) leakage audit: in-sample item-level numbers attenuate sharply under out-of-fold and temporal holdout (AN-014); (vii) strict ex ante (train 09-16 → test 17-19): the ranking fails on the full universe (ROC 0.474), surviving only as an incumbent-pool residue (ROC 0.684) (AN-006, AN-017). The hypothesis is not confirmed under the non-circular label: net of opportunity there is no robust residual ordering. The deflationary decomposition is itself the contribution.

Theory

In cartels that allocate winning roles and rotate designated winners \citep{pesendorfer2000study,asker2010leniency,marshall2012economics}, firms used to manufacture the appearance of competition can plausibly be identified by their persistent zero-win exposure. The same logic appears in large-scale procurement evidence on coordinated bidding \citep{kawai2022detecting}. Persistent zero-win participation is a behavioral footprint of credible losing roles, not a label of cartel membership.

Prediction

The frequent-loser stratum (binary FL14 rule, top-loss-intensity quantile of the continuous score) should, under the hypothesis, rank cobidders above other always-losers by more than mechanical opportunity predicts. The honest claim is the within-stratum increment over an exposure-only benchmark — which, under the non-circular label, is at chance (within-stratum ROC 0.471; nested increment +0.010, ns across permutation designs).

Competing prediction

Opportunity-only explanation. Firms that bid in many tenders mechanically have more chances of co-bidding alongside any subset of firms, including CADE defendants. Almost all of the raw concentration is exactly this — an exposure-only model reaches ROC ≈ 0.90 unconditionally. The threat the ranking must survive is that nothing is left after opportunity is netted out. The discipline in H:exposure-discipline shows that, under the non-circular label, the opportunity-only explanation prevails: no robust residual ordering survives.

Case evidence

CADE adjudications in the 2009–2019 window cover bid-rigging conduct in São Paulo procurement environments. The cobidder set is constructed from these adjudicated cartels by identifying always-loser firms that bid in the same tenders as direct defendants in the adjudicated environments. See §2.3 of the manuscript.

Empirical test

  • Outcome: cobidder indicator (1 if firm co-bid with a direct CADE defendant in an adjudicated environment).
  • Variation: position in the FL stratum vs other always-loser firms.
  • Specification: AUC of the score s = log(1+T) (and the administrative FL14 = T ≥ 14 cut) over always-losers, with cobidders as the positive class — reported both raw and net of an opportunity-exposure benchmark, so the genuine within-stratum increment is isolated.
  • Identification: scope of the loser-side ranking is restricted to zero-win firms; the headline object is the exposure-adjusted increment, not the exposure-inflated raw concentration.

Data requirements and limitations

Requires BEC LANCES export (firm × item × OC) joined with CADE adjudication records linked at the CNPJ root level. Limitation: cobidder labels depend on adjudication coverage in the panel window, and the set is exposure-limited to CADE-adjudicated environments in São Paulo.

Evidence

Analysis Bearing Status Key takeaway
AN-001 (construction) Setup done 16,843 always-losers; FL14 = T ≥ 14 (median+1.5×IQR, administrative cut); 2,735 FL firms; canonical label = 651 cobidders (341 FL / 310 non-FL), not FL-conditioned
AN-004 (exposure decomposition) Against done Raw concentration is opportunity (exposure-only ROC ≈ 0.90); within-stratum signal 0.471 (≈chance), nested increment +0.010 (DeLong p = 0.013)
AN-005 (permutation + neg. controls) Against done Matched permutation p = 0.127 (ns), FL-enrichment p = 0.067 (ns); real ≈ placebo (p = 0.46) — opportunity explains the concentration
AN-006 (timing discipline) Against done Strict ranking fails at the full universe (ROC 0.474); incumbent-pool residue only (ROC 0.684)
AN-011 (continuous vs binary) Mixed done Continuous edges FL14 within stratum but both are at chance net of opportunity
AN-014 (leakage audit) Supports done In-sample item-level numbers attenuate sharply under OOF / temporal holdout
AN-017 (continuous-only thesis) Supports done Thesis holds without FL14
AN-023 (operationalization audit) Supports done FL14 not ontologically privileged; continuous is the primitive
AN-025 (cutoff sweep) Supports done The raw concentration is not an artifact of one administrative cut (inverted-U across thresholds); but the raw lift is opportunity, not a residual signal
AN-026 (subsample robustness) Supports done AUC 0.89–0.96 across full / data-rich / low-bid / high-bid subsamples

Open tests

  • Sensitivity of concentration to alternative FL14-like thresholds.
  • Sub-period replication (2009–2014 vs 2015–2019).
  • Cross-modality (Convite vs Pregão) decomposition.