H:ipv-clock-admissible — Pregão drop-out prices admit the IPV-clock interpretation as willingness-to-supply observations

The structural decomposition rests on a single maintained restriction: that losing-bidder drop-out prices in the BEC Pregão can be read as type-specific willingness-to-supply observations under an independent private values clock model. If drop-outs are produced by strategic collusive rotation, by budget exhaustion, by sniping considerations, or by non-truthful early exits, the interpretation as cost draws breaks down and the decomposition becomes a price-formation re-weighting exercise rather than a structural counterfactual.

Intuition (plain-language)

The entire structural exercise rests on one reading: in a descending-clock reverse auction, the price at which a losing firm drops out is the lowest price it would accept — its cost. If that reading holds, drop-outs reveal each firm's willingness to supply and the decomposition is a genuine cost-based counterfactual. If firms instead drop out for strategic reasons (collusion, sniping, budget limits), the numbers become a price-formation re-weighting exercise rather than structural primitives. This is the load-bearing assumption of the paper.

Evidence strength: Partial (toward Supports). The IPV-clock interpretation is now disciplined on five independent margins, each addressing a different deviation from the IPV benchmark. (i) Censoring (Turnbull NPMLE, AN-013): exclusion share 74% (non-pharma) and 82% (pharma) under the most-agnostic winner treatment — same direction as baseline. (ii) Auction-level scale shocks (AN-014): Krasnokutskaya correction with ICCs 0.36–0.59 leaves the decomposition intact; a Gaussian-copula relaxation with within-auction cost correlation up to ρ_c=0.3 drifts the exclusion share by <5 pp and the total effect by <10%. (iii) Cross-modality discipline (AN-019): Convite GPV vs Pregão drop-out recoveries line up in the key pharma non-SME cell. (iv) Bidder coordination (AN-015): Conley-Decarolis close-pair shares and Bajari-Ye T1 ratios both stable or falling post-cutoff — no differential-coordination shock. (v) Exit-at-cost itself (paper §6.2, Online Appendix OA-C): the sharpest version of the threat is bounded directly. Following Haile–Tamer (2003), exits are treated as bounds on cost rather than costs; a markup common to all bidders cancels in the decomposition differences, so only a type-differential markup can overturn the ordering. In the worst case (SME costs pushed below exits, non-SMEs at face value, entry held fixed) the exclusion-dominant ordering survives a differential markup up to 0.29 of the exit price in non-pharmaceuticals and the entire [0, 0.30] grid in pharmaceuticals — a reversal would require SMEs to leave ~30% more surplus unbid than non-SMEs at every auction, in the direction that already biases against the finding. The diagnostics do not prove IPV; they show the conclusion survives bounded departures from it, and is not mechanically produced by the most obvious deviations. Yellow remains appropriate — the convergence of five margins is the strongest within-project discipline, but cross-jurisdictional replication is the only path beyond it.

Theory

In a benchmark IPV clock auction, the weakly-dominant strategy for each bidder is to remain active until the price clock crosses the bidder's private cost (Vickrey 1961; Milgrom and Weber 1982). The losing exit price therefore equals the bidder's cost (or willingness to supply at the auction scale). Haile and Tamer (2003) extend this to ascending auctions with weaker restrictions, providing bounds on the underlying value distribution from observed exits. Athey and Haile (2002) survey nonparametric conditions under which ascending-auction exit data identify the type-conditional cost distributions. The IPV-clock reading is therefore well-supported in theory; the empirical question is whether it survives the specific features of BEC Pregão (re-bidding, time pressure, observable competitor exits).

Prediction

The structural decomposition \((S_1, S_2, S_3)\) should survive (i) a cross-modality check against a GPV recovery from Convite first-price bids; (ii) the auction-level Krasnokutskaya-style heterogeneity correction with reasonable ICC magnitudes; (iii) classical bid-rigging screens (Bajari-Ye, Schurter, pair classification) that show no shift in bidder coordination across the policy break; and (iv) a direct relaxation of exit-at-cost itself — treating exits as Haile–Tamer bounds and bounding how large a type-differential exit markup the exclusion-dominant ordering can absorb. Convergence across these margins would upgrade this hypothesis from "Not yet tested" to "Supports".

Competing prediction

Collusive cover-bidding. If the post-policy SME pool exhibits more coordinated cover-bidding than the pre-policy pool (perhaps because the fewer eligible firms repeatedly meet each other), drop-outs no longer reveal costs. The post-policy \(S_3\) would then be a strategically suppressed exit distribution rather than a structural cost distribution. The collusion screens are the load-bearing rule-out; H:no-collusion-confound is the joint disciplinary check.

Setting evidence

BEC Pregão records every bid in the event log, including losing drop-outs. The auction format is a digital English-reverse: the clock moves downward, firms can re-bid until they exit, and final-state prices are observed. Documentation in docs/data.md confirms the structural sample comes from these event logs.

Empirical test

• Cross-modality check: GPV inversion of Convite first-price bids in the same product cells, compared to the Pregão drop-out recovery.
• Heterogeneity correction: Krasnokutskaya method-of-moments variance decomposition; auction-level ICCs reported by cell.
• Collusion screens: Bajari-Ye, Schurter, and pair-classification tests applied to pre- vs post-policy bid distributions.
• Censoring sensitivity: Turnbull NPMLE treating the winner's final price as left-censored, compared to the baseline upper-bound treatment.

Data requirements and limitations

The full battery requires (i) the BEC Pregão event log (v7-jpube-tight/scripts/35_pregao_dropouts.R extraction), (ii) Convite first-price data for the cross-modality check, and (iii) firm-pair historical co-bidding for the pair-classification screen. All three are in hand; the ANs are scaffolded but not yet authored.

Evidence

Analysis	Bearing	Key takeaway
AN-013	Supports	Three winner-censoring regimes (losers-only / all-bidders / Turnbull) give net \(S_3-S_1\) in [0.246, 0.275] (NP) and [0.308, 0.357] (PH); all positive, all large. Turnbull exclusion share 74% (NP) / 82% (PH).
AN-014	Supports	UH correction with ICCs 0.36 (NP-SME) to 0.59 (PH non-SME). Gaussian-copula ρ_c ≤ 0.3: exclusion share drift <5 pp; total drift <10%.
AN-015	Supports	Conley close-pair shares stable in NP (16.9→16.8) / fall in PH (27.6→24.4); Bajari-Ye T1 ratios fall in both classes (NP 2.63→1.83; PH 1.29→1.11). Differential-coordination story rejected.
AN-019	Supports (partial)	Cross-modality GPV from Convite first-price aligns with Pregão drop-outs in the load-bearing pharma non-SME pre cell (c₀.₅₀ = 0.712 vs 0.704); other 7 cells show a persistent ~0.2 wedge consistent with first-price bid shading. UH-corrected version broadens alignment (§6.2).
Exit-at-cost relaxation (§6.2, OA-C)	Supports	Exits treated as Haile–Tamer bounds, not costs. A common markup cancels in the decomposition differences; only a type-differential markup binds. Worst case (SME costs below exits, non-SMEs at face value, entry fixed): exclusion-dominant ordering survives a differential markup up to 0.29 of the exit price (non-pharma) and the entire [0, 0.30] grid (pharma). Reversal requires SMEs to under-bid ~30% more surplus than non-SMEs at every auction.

Open tests

Exit-at-cost departure bound (Lever A)

Done (paper §6.2, Online Appendix OA-C, Table OA-2; scripts/64_ipv_slack_bounds.R). The sharpest version of the threat — that drop-outs sit strictly above cost because firms quit the clock while still profitable — is bounded directly rather than assumed away. Following Haile–Tamer (2003), exits bound costs. Two channels: the mechanical Haile–Tamer increment bound is tight because BEC's electronic Pregão runs a near-continuous price clock; the behavioral channel (quitting while profitable) is what is bounded here. Because the decomposition compares order statistics across pools, a markup common to all bidders cancels in \(S_2-S_1\) and \(S_3-S_2\), so the binding departure is a type-differential markup \(c = \text{exit}\times(1-m_k)\). Sweeping the worst case for the conclusion (\(m_{\neg\mathrm{SME}}=0\), raising \(m_{\mathrm{SME}}\), entry held at observed rates), the exclusion-dominant ordering (net effect positive and absolute exclusion share above one half) survives a differential markup up to 0.29 of the exit price in non-pharma and through the entire [0, 0.30] grid in pharma. The conclusion reverses only if SMEs systematically leave nearly thirty percent more of their surplus unbid than non-SMEs at every auction — a behavioral asymmetry larger than the data suggest, and in the direction already biasing against finding exclusion to dominate.

Cross-modality convergence test

Done in AN-019: Convite first-price GPV vs Pregão drop-outs. Load-bearing pharma non-SME pre cell aligns (0.712 vs 0.704); other 7 cells show ~0.2 first-price wedge consistent with strategic bid shading. UH- corrected version broadens alignment per paper §6.2. Open: emit the UH-corrected table as macro-bound numbers (currently figure-only), and run a KS / quantile-equality test by cell for formal \(p\)-values.

Turnbull NPMLE on winner censoring

v7-jpube-tight/scripts/48_turnbull_fc.R treats the winner's final price as left-censored rather than as an upper-bound observation. The decomposition should survive both treatments. Documented in paper §6 robustness but not yet as a standalone AN.

Within-firm cost-distribution stability

If individual firms' drop-out behavior reflects strategic considerations rather than truthful cost revelation, within-firm cost distributions should shift discontinuously across the policy break. Not yet specified.