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AN-041: Volume-matched cobidder audit — does within-FL distinctness survive holding tenders_count fixed?

Intuition (plain-language)

The hardest skeptical test of the profile: pair each cobidder with a non-cobidder frequent loser that bids in the same number of tenders, then re-measure the gaps. Most distinctness survives and some grows — product specialization and bidding-close-to-winner strengthen once volume is equalized, meaning volume had been masking them. One signal dies honestly: the elevated bid dispersion of AN-031 turns out to be a pure volume artifact. The cobidder type is real, but it is about what and how they bid, not merely how much.

Question

AN-028 (seven participation dimensions, Cohen's d 0.19–1.00) and AN-031 (bid-level median gap-to-winner, d = −0.28) document that cobidders are distinct from non-cobidder FLs. But cobidders also participate in ~1.8× more tenders. Several of those dimensions — unique_winners, pairs_at_least_5, n_item_groups — mechanically grow with the number of bids. The question for H5 is whether the distinctness is anything beyond participation volume. Does it survive matching cobidders to non-cobidder FLs on tenders_count?

Design

  • Sample. Within-FL always-loser stratum, cobidder (treated, N = 190) vs FL non-cobidder (control, N = 2,542), direct CADE defendants removed from both classes so the treated group is the cover-bidder type, not adjudicated principals. Bid-level metrics on firms with ≥ 5 usable losing bids.
  • Matching variable. tenders_count (= total_participations), the single volume axis the docs flag as the confound.
  • M1 — PS nearest-neighbour. 1:1 on the logit propensity score of tenders_count, caliper 0.2 SD, no replacement. This is the "PS matching on tenders_count" the H5/H3 Open-tests ask for.
  • M2 — CEM. Coarsened exact matching on tenders_count deciles, weighted, as a functional-form-free robustness estimator.
  • Outcome. Cohen's d (pooled SD) and Wilcoxon rank-sum recomputed inside the matched sample, compared to the raw (unmatched) d. A dimension whose |d| holds or grows is distinct beyond volume; one that collapses toward zero was a volume artifact.

Results

Balance. Cobidders bid in 1.8× more tenders than controls (mean 136.7 vs 76.8; raw SMD 0.489). M1 matching equalizes volume almost exactly (122.4 vs 122.2; SMD 0.002), retaining 186/190 cobidders. The 4 unmatched cobidders are off-support — high-volume cobidders with no FL non-cobidder bidding as much, which is itself evidence that the upper volume tail is cobidder-specific. CEM SMD 0.114.

Standardized differences (Cohen's d: cobidder vs FL non-cobidder).

Dimension Kind d raw d M1 (PS) d M2 (CEM) Wilcoxon p (M1) Verdict
item_group_HHI product specialization +0.396 +0.466 +0.409 6.1 × 10⁻⁹ survives, strengthens
share_repeat_5 winner-pair spread −0.386 −0.563 −0.487 3.3 × 10⁻⁷ survives, strengthens
median_gap_to_winner bid proximity to winner −0.261 −0.246 −0.202 6.6 × 10⁻⁴ survives (mild attenuation)
n_item_groups breadth (volume-ish) −0.315 −0.579 −0.423 — survives, strengthens
unique_winners volume-mechanical +1.007 +0.370 +0.531 — mostly volume; residual +0.37
pairs_at_least_5 volume-mechanical +0.197 −0.216 −0.100 — sign flips; was volume
sd_gap_to_winner bid dispersion +0.157 +0.051 +0.122 0.87 collapses — volume artifact
mean_gap_to_winner bid proximity −0.142 −0.192 −0.104 — survives (weak)
p75_gap_to_winner bid proximity −0.133 −0.137 −0.086 — survives (weak)
share_facing_direct_cade circular +0.534 +0.593 +0.592 — excluded (tautological)

Interpretation

The profile distinctness is not a volume artifact. The three headline non-volume dimensions — product-portfolio concentration (item_group_HHI), winner-pair spread (share_repeat_5), and bid proximity to the winner (median_gap_to_winner) — all survive volume matching, and the two participation-portfolio dimensions strengthen once volume is equalized. Matching makes the controls high-volume FL non-cobidders; the fact that the gap widens means participation volume was partially masking the distinctness, not generating it. M1 and M2 agree on every sign.

The cover-bidder profile that survives is "specialist broker", not "repeat colluder". Cobidders concentrate in a narrower set of product groups (HHI up, n_item_groups down) while spreading across more distinct winners with lower concentration in any single repeat-pair (share_repeat_5 down, unique_winners up). This is the opposite of a naive "bids repeatedly against the same winner" reading and should be described as product specialization with broad winner exposure.

Two honest casualties. (1) The bid-dispersion elevation reported in AN-031 (sd_gap d = +0.15) does not survive PS matching (d = +0.05, p = 0.87) — it was a volume artifact and should be dropped from the distinctness claim. (2) unique_winners attenuates from a very large d = 1.01 to +0.37; most of the "crosses more winners" gap is volume, with a modest residual.

One dimension excluded. share_facing_direct_cade (d ≈ +0.53–0.59) is circular: cobidders are defined as always-losers that bid alongside direct CADE defendants, so this dimension is tautological and carries no information about distinctness.

This audit isolates the participation-volume confound only. It is a matched descriptive comparison, not a causal identification of cobidder status; the distinctness is associational and single-source (BEC × CADE).

Bearing on hypotheses

  • H:cobidder-profile-distinct (H5). Resolves the headline Open-test affirmatively for product specialization, winner-pair spread, and bid-proximity; refutes the bid-dispersion sub-signal. The earlier reading that within-FL distinctness "is largely a volume effect" is too strong: the profile distinctness survives volume matching. H5's remaining limits are the mechanism-heterogeneity negative (AN-032) and the first-time-FL channel (AN-021), not the profile distinctness — keep H5 Mixed but on revised grounds.
  • H:exposure-discipline (H3). Strengthens: the within-stratum concentration documented in AN-028 is not driven by participation volume.

Follow-ups

  • Bid-timing and inter-bid-interval moments under the same volume match — a second behavioral channel beyond gap-to-winner would lift the bid-conduct claim above a single residual.
  • Multivariate matched logit (cobidder on HHI + gap + repeat, holding tenders_count) to confirm the dimensions are jointly, not just marginally, distinct.
  • Cross-jurisdiction replication (ComprasNet) — the same volume-matched profile on a non-BEC panel is the path to promoting H5 distinctness beyond single-source.
  • Macros for the manuscript: \valVMHHId (= +0.47), \valVMRepeatd (= −0.56), \valVMGapd (= −0.25), \valVMSdGapd (= +0.05, ns), \valVMBalRaw (= 0.49), \valVMBalMatched (= 0.00) if §5 cites the audit.