Extensions¶
Intuition (plain-language)
A screen that gets used gets gamed — a cartel can rotate its cover bidders or let them win occasionally to duck a fixed threshold. These extensions ask whether the signal holds up anyway: it degrades gracefully rather than collapsing under strategic adaptation, it still discriminates firms it was never trained on, and the headline "83% cost saving" turns out to be one point on a whole frontier an enforcer can dial between investigation cost and how many cartels it catches. Together they describe how the tool would behave in the wild, not just on the historical sample.
This page collects auxiliary analyses that support the paper's screening and architecture results: strategic adaptation, the strict-ex-ante timing battery, population turnover under the temporal split, the structure of the price sign-reversal, and the cost-of-evidence envelope behind the headline 83% reduction.
Scope of this page
Earlier versions of this page reported a structural regime model, classical mechanism diagnostics (M1–M5), and a minimum-bidder-rule channel. Those explorations are not part of the current paper: the construct is positioned as an award-layer screen for forensic triage, not a structural cover-bidding model, and the minimum-bidder-rule interpretation was set aside (the modal asymmetry is reported as scope information, not a positive institutional test). The content below is the portion that carries over to the current framing.
Strategic Adaptation¶
A sophisticated cartel could rotate its cover bidders or let them win occasionally to stay below the threshold, and the threshold-sensitivity analysis suggests some do. Any operational deployment would need periodic recalibration alongside bid-level tools, which is why the staged workflow treats the screen as a first stage rather than a final word. Refreshed thresholds, continuous ranks, capacity-constrained queues, and bunching checks fit the staged enforcement architecture.
Three-Classifier Timing Battery¶
The strict ex ante variant trains the score on progressively earlier windows and evaluates against truly out-of-time targets:
| Classifier | vs cobid_all (FL / continuous) | vs cobid_post2019 (FL / continuous) |
|---|---|---|
| clf_2015 (train 09–15) | 0.791 / 0.851 | 0.786 / 0.854 |
| clf_2017 (train 09–17) | 0.856 / 0.897 | 0.844 / 0.894 |
| clf_2019_full (in-sample ref) | 0.924 / 0.939 | — |
cobid_post2019 is the strict out-of-time target: cobidders linked only to
CADE adjudications closed after 2019, which cannot be in the clf_2015 or
clf_2017 training data. Discrimination preserves AUC 0.79–0.89 even against
this strictly disjoint target. (See AN-029.)
Population Turnover Under the Temporal Split¶
Firm persistence between the 2009–2016 and 2017–2019 panel windows is 8.7% (108 of 1,240 early-period always-loser firms remain in the late period). Market persistence (PBU × item-group) is 12.4%; PBU persistence is 83.5%. The institutional environment (procurers) is stable across the temporal split, while the firm and market populations are essentially fresh. The temporal holdout therefore evaluates a new firm population, not the same firms in different years — which is why the holdout AUC of 0.864 is the honest discrimination reference.
Structure of the Price Sign-Reversal¶
The price sign-reversal under overlap-cell ATT (broad +0.064 → ATT −0.097) is not uniform across item groups. Most groups (12, 13, 14, 29) flip from positive baseline to negative ATT. Item group 37 stays strongly negative across all three specifications (−0.105 broad → −0.126 ATT, p < 10⁻⁶) — the cleanest structural negative. Item group 10 stays positive (+0.107 broad → +0.063 ATT) — the scope boundary at the item-group level. The heterogeneity is predictably structured, not random. The price evidence is reported as scope information, not a damages estimate. (See AN-038.)
Cost-of-Evidence Envelope¶
The headline 83% pool-reduction is a single point on a wider operational envelope. The full architecture × k × regime matrix maps the cost-of-evidence trade-off across four sequencing rules (award-only, bid-only, joint, and sequential award → bid) over several top-k cutoffs and two evaluation regimes (in-sample, temporal holdout).
The canonical gatekeeper result (Section 6): at the top-1,000 cutoff, sequential award → bid scoring recovers 131 of 193 cobidders while opening bid microdata for only 2,000 of 11,676 firms — an 83% footprint reduction at an 8% recall cost relative to full-observability joint scoring. Joint scoring is the full-observability upper bound, not an implementable first-stage policy.
Under temporal holdout the sequential rule's recall is markedly more robust than joint scoring (sequential recall drops ~9% versus joint's ~24% from in-sample to holdout), so the sequential architecture's relative advantage widens in the operationally honest regime. (See AN-034 and AN-035.)
Year-by-Year Stability¶
The broad-sample FL–price association is not an artifact of any single year. As elsewhere on this site, the broad-sample coefficient is a descriptive object; the overlap-restricted ATT reverses sign, and the paper does not rest on either sign of the price coefficient.