Superseded numbers — canonical-target re-estimation (June 4, 2026)
This analysis note documents a historical run under the earlier validation label. On June 4, 2026 the paper adopted a reproducible, non-circular target (651 always-loser cobidders; frequent-loser flag never used in the label) and re-estimated every result. Where this page conflicts with the paper or the changelog, the paper wins.
AN-004: Baseline cobidder concentration in FL14 stratum¶
Intuition (plain-language)
Do the firms the screen flags cluster on the loser side of adjudicated cartels? In a pooled comparison, yes — FL14 separates cobidders from other always-losers at AUC 0.924, the continuous score at 0.939 (0.5 is a coin flip). But most of that gap is opportunity arithmetic: firms that bid in more tenders mechanically overlap more cartel environments. Strip exposure out by comparing firms within the same opportunity stratum and the AUC falls to 0.7715 — a genuine but modest increment of +0.042 over the exposure-only benchmark of 0.946. So this pooled number is the starting point, not the discrimination headline; everything after it decomposes the signal and tests where it reaches.
Question¶
Does the FL14 stratum contain a disproportionate share of CADE- adjudication-anchored cobidders relative to the always-loser baseline? This is the headline-baseline triage result.
Design¶
- Sample: 16,843 always-loser firms in BEC 2009–2019.
- Outcome: cobidder indicator (1 if firm is in the 193-firm cobidder set from AN-003).
- Specifications:
- FL14 binary: AUC of the FL14 indicator.
- Continuous: AUC of
log(1 + tenders_count). - Evaluation: in-sample baseline; discipline applied separately in AN-005, AN-006, AN-013, and AN-014.
Results¶
Pooled (exposure-inflated) baseline — the starting point, not the headline:
| Score | AUC | 95% CI |
|---|---|---|
| FL14 (binary) | 0.924 | [0.921, 0.926] |
| log(1 + tenders_count) (continuous) | 0.939 | [0.932, 0.946] |
Exposure decomposition — the disciplined reading:
| Quantity | AUC |
|---|---|
| Exposure-only benchmark | 0.946 |
| Within-opportunity-stratum (exposure-stripped) | 0.7715 |
| Genuine increment over exposure-only | +0.042 (DeLong p ≈ 2 × 10⁻⁶) |
The pooled firm-level numbers are exposure-inflated: most of the raw separation is opportunity arithmetic — firms that participate more mechanically overlap more adjudicated cartel environments. The genuine loser-side signal, isolated within the opportunity stratum, is the 0.7715 / +0.042 pair. See AN-027 and AN-028 for the full exposure audit.
Macros: \valAUCFLfirm, \valAUCFLfirmCI, \valAUClogtc,
\valAUClogtcCI.
Figure: pooled baseline cobidder AUC for FL14 binary (0.924, [0.921, 0.926]) and continuous log(1+tenders_count) (0.939, [0.932, 0.946]). Both substantially above the random benchmark (0.5) — but these are exposure-inflated; the exposure-stripped within-stratum AUC is 0.7715.
The cobidder share inside FL14 is 7.1% (\valCobidShareFL), against a
baseline always-loser cobidder rate that is much lower. This corresponds
to the headline 131/193 cobidder recovery in the gatekeeping setup
(AN-012).
Interpretation¶
Both the pooled binary and continuous variants separate cobidders well inside the always-loser pool, but the bulk of that separation is opportunity arithmetic. Once exposure is stripped out, the genuine within-stratum signal is AUC 0.7715 (+0.042 over the 0.946 exposure-only benchmark, DeLong p ≈ 2 × 10⁻⁶) — real but modest. The continuous score is the dominating ranking (AN-011); FL14 is the administrative auditable implementation, not a structural threshold. The pooled baseline numbers are exposure-inflated and inflated relative to operational deployment — the disciplined columns in AN-013 and AN-014, and the exposure decomposition in AN-027/AN-028, are the right reading.