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AN-028: Exposure-stratum balance — cobidders vs reference classes

Intuition (plain-language)

Are cobidders just the highest-volume frequent losers wearing a different label? Across seven dimensions — tenders, unique winners crossed, repeat-buyer share, pair density, CADE-facing share, portfolio HHI, number of item groups — they separate from other FLs at effect sizes Cohen's d 0.19–1.00. The distinctness is multi-dimensional, which matters: if it were one-dimensional (just volume) the screen would carry no information beyond a bid counter. AN-041 then asks which dimensions survive once volume is matched away.

Question

Within the always-loser stratum, are cobidders distinguishable from non-cobidder FLs along dimensions other than raw participation volume? The exposure question for H3 is: if we hold the stratum fixed and ask whether cobidders look like other FLs, do we see them collapse into a homogeneous "high-volume losers" pool? The standardized-diff battery says no — they remain distinct across multiple dimensions.

Design

  • Sample: always-loser firms in BEC 2009–2019, partitioned:
  • Cobidders: 191 firms (a subset of FL).
  • FL_non_cobidder: 2,544 firms (other FL14 firms).
  • AL_non_FL: 14,108 firms (always-loser, but below FL14 cutoff).
  • winner_other: 24,561 firms (with at least one win).
  • Dimensions (7):
  • tenders_count: participation intensity.
  • unique_winners: count of distinct winners crossed.
  • share_repeat_5: share of buyers with ≥5 repeat interactions.
  • pairs_at_least_5: number of cobidder pairs with ≥5 shared tenders.
  • share_facing_direct_cade: share of tenders where a direct CADE defendant participated.
  • item_group_HHI: portfolio concentration HHI.
  • n_item_groups: number of distinct item groups.
  • Statistic: Cohen's d (standardized mean difference) and Wilcoxon rank-sum p-value.

Results

Cohen's d of cobidders vs each reference class, across 7 dimensions:

Dimension vs FL_non_cobidder vs AL_non_FL vs winner_other
tenders_count +0.67 +4.63 −0.13
unique_winners +1.00 +7.10 −0.23
share_repeat_5 −0.38 +1.33 −0.56
pairs_at_least_5 +0.19 +3.15 −0.29
share_facing_direct_cade +0.46 +0.36 +0.42
item_group_HHI +0.39 −1.09 +0.30
n_item_groups −0.32 +3.18 −0.60

All Wilcoxon p-values < 0.05; most < 10⁻¹⁰ — the differences are highly significant given the cobidder N = 191.

Key reading on the vs FL_non_cobidder column (the within-FL14 test that matters for H3):

  • Cobidders bid in ~2× more tenders (d = 0.67) and cross ~2× more unique winners (d = 1.00) than non-cobidder FLs. Within the FL stratum, cobidders still have higher participation intensity.
  • Cobidders are 8× more likely to face a direct CADE defendant in a tender (1.46% vs 0.17%; d = 0.46).
  • Cobidders operate in more concentrated product portfolios (HHI 0.380 vs 0.288; d = 0.39).
  • Cobidders are in fewer item groups (7.6 vs 9.5; d = −0.32) — consistent with focal-portfolio cover bidding.

Source: output/theory_bridge/standardized_diffs.csv.

AN-028 standardized differences heatmap

Figure: Cohen's d heatmap of cobidders vs three reference classes (rows) × 7 dimensions (columns). Red = cobidder higher; blue = lower. Values capped at ±2 for color scale; the ⁺ marks cells where the true d exceeds the cap (vs AL_non_FL: d up to 7.1 for unique winners). Cobidder vs FL_non_cobidder is the within-FL row that matters for H3 / H5: d in 0.19–1.00 range across most dimensions.

Interpretation

The balance battery answers a key exposure-discipline question: "are cobidders just the highest-participation always-losers?"

The answer is no. Within the FL14 stratum (i.e., conditional on already being a frequent loser):

  1. Cobidders have higher tenders_count and unique_winners (d 0.67 and 1.00) — the participation margin still discriminates within FL.
  2. Cobidders have more focal portfolios (HHI d 0.39, n_item_groups d −0.32) — qualitative difference in operations.
  3. Cobidders are 8× more likely to face direct CADE defendants in a tender (d 0.46) — a structural feature of cartel exposure, not a volume artifact.
  4. Cobidders have lower repeat-buyer shares (d −0.38) — they do not display the "stable supplier" profile of non-cobidder FLs.

For H:exposure-discipline, this means: the FL14 cutoff alone is NOT what concentrates the signal. Even after fixing the always-loser stratum, cobidders remain distinguishable along seven economically meaningful dimensions. The signal carries past volume conditioning.

For H:cobidder-profile-distinct, this is the formal balance table that supports the §5 economic profile of cartel-adjacent losers. AN-008 and AN-009 quote selected numbers from this table; this AN documents the full battery.

Follow-ups

  • Stratify the balance table by procurement modality (Convite vs Pregão).
  • Re-run on the audit-disciplined sample (AN-014 OOF folds).
  • Match cobidders to non-cobidder FLs on tenders_count and re-run the balance test — does the remaining signal collapse if we explicitly match on volume? (this is the strongest within-data audit possible for H3).
  • Add macros \valDiffTendersFL (0.67), \valDiffUniqueFL (1.00), \valDiffCadeFaceFL (0.46), \valDiffHHIFL (0.39) to the macro pipeline.