Advanced Methods

Intuition (plain-language)

The conceptual move on this page is to be precise about what is being identified. The screen does not estimate guilt or damages; it produces a defensible ranking of forensic priority — an answer to "investigate whom first," not "who is liable." The audit chain then works through every artifact a single dataset could hide (raw volume, overfitting, threshold choice, lucky years) and rules them out one by one. The two things it cannot settle from BEC alone — quirks of the data source and which cartels prosecutors happened to pursue — are exactly what cross-jurisdiction replication is meant to test.

This page collects the methodological machinery that supports the empirical claims in the manuscript but is too heavy for the Robustness and Extensions tabs. It documents the formal audit chain that the current (v20) submission relies on, with cross-references to the AN pages where each result is computed.

Identification under costly observability

The award-layer triage is operationalized as a monotone rank over zero-win firms, not a classifier. The legal-economic object is forensic priority, not liability. The construct identifies participation intensity within the always-loser stratum; that intensity orders cobidder risk, not cartel membership.

Two scope conditions discipline the interpretation:

1. The rank does not detect winner-heavy defendants. AUC against 47 direct CADE defendants is 0.491 [0.461, 0.520] in the full panel (AN-007); 0.506 in the raw item-level evaluation; 0.511 under temporal holdout. The null is regime-invariant.
2. A scope-discipline matrix confirms the rank targets exactly what the loser-side framing predicts and actively repels winner-heavy defendants (AN-027). Raw participation count against direct CADE in the full BEC universe returns AUC 0.383 — below random.

Cobidder labels and adjudication anchors

The validation target is adjudication-anchored exposure: always- loser firms that bid alongside direct CADE defendants in adjudicated cartel environments. Direct defendants are 47 firms; cobidders are 193 firms (AN-003). The cobidder set excludes direct defendants by construction; the 193 figure corrects an earlier 98-cobidder count that resulted from a CNPJ zero-pad bug (v12 audit; locked from v13 onward).

The adjudication-anchored label inherits CADE's selection of which procurement cartels to adjudicate. Cross-jurisdiction replication on a non-BEC panel (see COMPRASNET_PATH_TO_CONFIRMED.md) is the natural test of whether the loser-side concentration generalizes beyond CADE's adjudication choices.

Exposure, leakage, and timing audits

The audit chain disciplines the headline AUC against four artifact families:

Audit	Source AN	Outcome
Volume sham permutation (B = 2,000)	AN-005	Sham AUC mean 0.500, SD 0.013; observed FL14 AUC 0.924 = 32 σ above null; p < 1/2,000
Leakage decomposition (raw → OOF → temporal)	AN-014	0.995 → 0.891 → 0.864; attenuation 0.10–0.13
Timing discipline (strict ex ante)	AN-006, AN-029	Firm AUC 0.767 strict; three-classifier battery preserves AUC 0.79–0.89 against truly out-of-time cobid_post2019
Exposure-stratum balance	AN-028	Within-FL14 cobidder distinctness d 0.19–1.00 across 7 dimensions
Cutoff sweep robustness	AN-025	FL10–FL15 plateau ≥ 0.90; clean inverted-U
Subsample robustness	AN-026	AUC 0.89–0.96 across full/data-rich/low-bid/high-bid
CV precision stability	AN-036	K-fold SD ≤ 0.011
Market persistence (structural OOS)	AN-030	Firm persistence 8.7% between train/test — fresh population

The chain is designed to enumerate the within-data artifact families systematically. Each audit rules out a candidate explanation for the observed concentration.

Sequential gatekeeping and cost-of-evidence

The operational architecture sequences a cheap award-layer triage before a costly bid-layer forensic stage. The architecture and its cost-of-evidence trade-off are documented in:

• AN-010: Imhof full pipeline vs the frequent-loser flag vs the combined model, on the five-fold CV pool (manuscript Table Discrimination at Different Information Costs). Imhof full 0.888; FL flag (binary) 0.921; combined 0.962. Imhof CV-only is chance-level (0.585), so the bid-distribution pipeline needs participation features to reach its headline.
• AN-033: formal DeLong incremental tests. Imhof + FL Δ = +0.096, p = 1.2 × 10⁻²⁶. Shapley decomposition: FL binary marginal beyond continuous tenders is only +0.003 — continuous participation is the load- bearing complement; FL14 is the auditable simplification.
• AN-034: sequential award → bid gatekeeping at Stage-1 K = 2,000 recovers 131 of 193 cobidders (recall 0.679) while opening bid microdata for only 2,000 of 11,676 firms — 17% of the footprint, an 8% recall cost relative to joint scoring.
• AN-035: full cost-of-evidence matrix. Under temporal holdout the sequential rule's recall is markedly more robust than joint scoring (sequential drops ~9% vs joint's ~24% from in-sample to holdout), so the sequential architecture's relative advantage widens in the operationally honest regime.

Adaptive deployment

Static FL14 cutoffs are auditable but invite gaming. The manuscript proposes adaptive deployment alternatives — refreshed thresholds, continuous ranks, capacity-constrained queues, bunching checks — in §7.4. The deployment alternatives are not separately tested; they are part of the legal-economic design framework rather than a robustness claim.

Why not further audits?

The audit chain documented above is essentially exhaustive at the within-data level. Two artifact families remain untestable from BEC alone:

1. Data-generating process artifacts: BEC missingness, CNPJ-root collision, CADE adjudication completeness. Cannot be ruled out by within-data permutation.
2. Selection on CADE adjudication: CADE's choice of which cartels to adjudicate may have stable biases that the BEC-anchor evaluation inherits.

Both can only be ruled out by non-BEC replication. See COMPRASNET_PATH_TO_CONFIRMED.md for the planning document on cross-jurisdiction validation as the R&R revision target.