H:direct-defendants-null — The frequent-loser binary flag does not order direct CADE defendants

A loser-side screen built from persistent zero-win participation should not order direct CADE defendants — these are legal anchors that typically include the designated winners of the rotation, who are not zero-win firms. A null AUC against direct defendants is therefore a scope boundary by design, not a failure: it marks the edge of what a cheap award-layer ranking can reach, and it disciplines the rest of the paper against any "cartel-detector" reading.

Intuition (plain-language)

Direct CADE defendants in procurement cartels are typically the winners of the rotation, not the systematic losers. A loser-side binary flag — built on persistent zero-win participation — cannot order winners, and the data confirm this (AUC ≈ 0.49, indistinguishable from random). Participation volume, by contrast, ranks defendants moderately above chance (0.66–0.70), because heavy participants are easier to flag generically. The binary null is the predicted finding: it is a scope boundary by design, not a failure. It defines what the flag claims to do (concentrate forensic priority toward adjudication-anchored losers) and what it doesn't claim to do (identify ringleaders). This is the anti-claim that disciplines the rest of the paper.

Evidence strength: Strong (on the binary flag). AUC of the binary FL flag against direct CADE defendants ≈ 0.491 [0.461, 0.520]; indistinguishable from random and stable across raw, OOF, and temporal-holdout regimes. The continuous participation score ranks defendants moderately above chance (0.658 full / 0.695 strict) — volume is generically informative; the loser-side binary flag is not. D4 mechanistic check: only 14.9% of direct defendants are always-losers; their median win rate is 0.261, whereas cobidders — being always-losers — have win rate ≡ 0 by construction. The binary null is the predicted finding — the loser-side flag misses win-heavy defendants by design.

Theory

The cartel theory underlying the loser-side construction \citep{marshall2012economics,clark2021collusion} predicts heterogeneous roles: winners take the contract, cobidders manufacture competition. A participation-intensity score over zero-win firms cannot order winners by construction. If the score did order direct defendants, it would either be picking up opportunity volume rather than loser-side exposure, or the "cheap-signal" framing of the paper would be wrong.

Prediction

AUC of the frequent-loser binary flag against direct CADE defendants ≈ 0.50 (random); the continuous participation score, by contrast, may rank defendants moderately above chance because volume is generically informative.

Competing prediction

Generic-detector reading. If the binary flag had general predictive power for cartel membership, AUC against direct defendants would be substantially above 0.50, contradicting the reach-and-limits map: a cheap award-layer flag concentrates loser-side priority, it does not detect cartelists. (Participation volume ranking defendants moderately above chance — 0.66–0.70 — is consistent with the map: volume is generic, the loser-side binary flag is the scope-bounded object.)

Case evidence

Direct CADE defendants in 2009–2019 procurement-cartel adjudications include firms identified as designated winners or coordinators in the legal record. The cobidder set is constructed excluding direct defendants by design — see §2.3 of the manuscript.

Empirical test

• Outcome: direct-defendant indicator (1 if firm is a direct CADE defendant).
• Variation: position in the FL stratum vs other firms in BEC.
• Specification: AUC of the score s = log(1+T) (and FL14) over the full firm panel, with direct defendants as the positive class.
• Identification: same as H:cobidder-concentration, but with a different positive label.

Data requirements and limitations

Requires CADE × BEC CNPJ-root link. Limitation: the test is constructive — it asks whether the score fails on a target it was not designed to detect. A null result is the predicted finding under the loser-side scope.

Evidence

Analysis	Bearing	Status	Key takeaway
AN-007 (direct-defendant AUC)	Direct	done	Binary FL flag AUC = 0.491 [0.461, 0.520] — random; continuous participation score 0.658 (full) / 0.695 (strict) — volume generically informative
AN-018 (D4 winner-heavy)	Supports	done	14.9% of direct defendants are always-losers; median win rate 0.261
AN-014 (leakage audit)	Supports	done	Direct-defendant AUC stays at 0.51 across raw/OOF/temporal — null is regime-invariant

Open tests

• Decomposition of direct-defendant pool into roles (declared winner, coordinator, other) and AUC by role.
• Sensitivity to alternative direct-defendant definitions.