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AN-026: Persistent-pair coordination screen, class-conditional

Intuition (plain-language)

Another collusion check: do the same pairs of firms keep meeting more than chance, once you condition on product class? Raw clustering rejects randomness, but conditioning on CADMAT class makes the 'persistent meeting' pattern disappear — it is market segmentation (firms specialize in product lines), not coordination. Stable before and after the policy.

Question

The Bajari-Ye T1 screen in AN-015 detects raw pair-coordination clustering — observed counts of frequent co-bidding pairs exceed a permutation null. A natural question: how much of that clustering is bidder coordination vs market segmentation (the same firms repeatedly meet because they specialize in the same CADMAT product class)? A class-conditional permutation null answers this directly: shuffle firm labels within CADMAT class, breaking firm-auction associations within class while preserving class-level firm-bid counts. The residual clustering after class conditioning is what bears on coordination.

Design

  • Sample: BEC Pregão bid logs spanning March 2018; firms with ≥5 bids in the stratum; CADMAT product class as conditioning variable; 4 cells (non-pharma / pharma × pre / post).
  • Variation: persistent-pair clustering relative to a class-conditional permutation null.
  • Specification: \(B = 200\) permutation replicates. Three test statistics:
  • \(T_1\): max pair co-bidding count in the stratum.
  • \(T_2\): 99th percentile of the pair co-bidding distribution.
  • \(T_3\): count of firm pairs co-bidding in ≥5 auctions ("persistent pairs").
  • Outcomes: observed statistic, class-conditional null mean, one-sided \(p\)-value.

Results

Persistent-pair screen, class-conditional null (tab_collusion_screen_pair_classcond.tex):

Stratum \(N_{\mathrm{cls}}\) \(T_1\) obs \(T_1\) null \(T_1\) \(p\) \(T_2\) obs \(T_2\) null \(T_2\) \(p\) \(T_3\) obs \(T_3\) null \(T_3\) \(p\)
Non-pharma Pre 47 1220 769.4 <0.001 131.4 60.5 <0.001 5733 6057.3 1.000
Non-pharma Post 47 1059 871.8 <0.001 102.0 52.3 <0.001 6048 6071.1 0.730
Pharma Pre 2 1428 1104.1 <0.001 606.1 328.3 <0.001 2294 3070.4 1.000
Pharma Post 3 1100 1005.2 <0.001 312.1 164.8 <0.001 2676 3170.9 1.000

Output: v7-jpube-tight/output/tables/tab_collusion_screen_pair_classcond.tex.

Interpretation

\(T_1\) and \(T_2\) reject the class-conditional null in every cell. The maximum pair co-bidding count and the 99th-percentile of the distribution both exceed the within-class permutation null at \(p<0.001\). There IS pair-clustering beyond what within-class random shuffling produces.

\(T_3\) does NOT reject in any cell. The "persistent pair" signature — firm pairs co-bidding in ≥5 auctions — sits at or below the class-conditional null mean in all 4 cells: - Non-pharma Pre: 5733 observed vs 6057.3 null (obs below null; \(p = 1.000\)). - Non-pharma Post: 6048 vs 6071.1 (\(p = 0.730\)). - Pharma Pre: 2294 vs 3070.4 (obs well below null; \(p = 1.000\)). - Pharma Post: 2676 vs 3170.9 (\(p = 1.000\)).

Reading. The raw \(T_1\) / \(T_2\) clustering picked up by the unconditional Bajari-Ye in AN-015 partly survives class conditioning — there is real within-class clustering. But the persistent-meeting signature (\(T_3\)) is fully absorbed by class segmentation: firms repeatedly co-bid because they specialize in the same CADMAT class, not because they coordinate.

Cross-period stability. This is the load-bearing reading for H:no-collusion-confound: the \(T_3\) result is invariant across the policy break. Non-pharma: 5733 → 6048; pharma: 2294 → 2676 — increases in both cells, but within the null distribution in both. Whatever "coordination" is present is stable across the cutoff — not generated by the policy shock.

Caveat — pharma cell sizes. Pharma has \(N_{\mathrm{cls}} = 2\) (pre) and 3 (post) — very small number of conditioning classes. The within-class permutation has limited variation in pharma; conclusions in pharma are weaker than in non-pharma.

Confidence: yellow. The class-conditional test is informative beyond the unconditional Bajari-Ye — it isolates segmentation from coordination, and the persistent-pairing signature dissolves under conditioning. The yellow caveat is the small pharma cell (\(N=2\) or 3 classes) and the absence of a within-firm coordination test (which would require strategic-bid-level analysis, not just pair counts).

Follow-ups

  • Schurter test as separate AN: the third leg of the screen battery (v7-jpube-tight/scripts/59_collusion_screen_schurter.R) is reported only in aggregate in AN-015; a separate AN would document its test-statistic distribution.
  • Anchor variant: tab_collusion_screen_anchor.tex reports a pair-anchored variant that ties pairs to specific reference firms — useful for identifying which firms drive the unconditional \(T_1\) rejection.
  • Pharma class expansion: re-run with finer pharma sub-classes (drug therapeutic class) to expand \(N_{\mathrm{cls}}\) in pharma and tighten inference.