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AN-019: Cross-modality GPV — Convite first-price vs Pregão drop-outs

Intuition (plain-language)

An independent check on the IPV-clock reading: recover firm costs from the other auction format (Convite sealed-bid) using GPV and see whether they line up with the Pregão drop-out costs. They align in the load-bearing cell after correction, with a wedge elsewhere consistent with sealed-bid shading. It is discipline that the recovery is not idiosyncratic to one auction format — not proof of the assumption.

Question

The structural decomposition's load-bearing assumption is that Pregão drop-outs admit an IPV-clock reading as willingness-to-supply observations. A second identification source on the same product cells — first-price Convite bids, inverted via Guerre-Perrigne-Vuong (2000) to recover costs — provides cross-modality discipline. If the two modalities recover the same cost distributions, the IPV-clock reading is independently supported. If they diverge in informative ways, the divergence itself constrains the interpretation.

Design

  • Sample: BEC Convite (first-price sealed-bid) and BEC Pregão (English-reverse) bid logs spanning March 2018; 8 cells (class × type × period).
  • Variation: same product cells, two auction formats. Convite bids are strategically shaded; Pregão drop-outs are exits.
  • Specification:
  • Convite GPV: \(c_i = b_i - \frac{1 - G(b_i)}{(N_i - 1) \cdot g(b_i)}\) with \(G\) and \(g\) as bid CDF/density in the cell. Requires \(N_i \geq 2\).
  • Pregão drop-outs: final losing bid per firm, normalized by reference price (from AN-013).
  • Outcomes: median (\(c_{0.50}\)) and 75th-percentile (\(c_{0.75}\)) of the recovered cost distribution, per cell × modality.
  • Identification threats: differential selection of items into Convite vs Pregão (item value, complexity); strategic shading in Convite may differ across SME / non-SME types; sparse cells in Convite reduce GPV precision.

Results

Raw cross-modality quantiles (cost / reference price; from tab_v3_cross_modality.tex):

Class Type Period Conv \(c_{0.50}\) Pregão \(c_{0.50}\) Gap (Conv − Pregão)
Non-pharma SME Pre 0.723 0.954 −0.231
Non-pharma SME Post 0.761 0.961 −0.200
Non-pharma non-SME Pre 0.638 0.820 −0.182
Non-pharma non-SME Post 0.677 0.864 −0.187
Pharma SME Pre 0.747 0.859 −0.112
Pharma SME Post 0.790 0.950 −0.160
Pharma non-SME Pre 0.712 0.704 −0.008 (aligned)
Pharma non-SME Post 0.707 0.768 −0.061

Of 8 cells, 7 show a persistent Convite < Pregão gap of 0.1–0.23 of reference price; 1 cell aligns (pharma non-SME pre-period: gap −0.008). After UH correction (paper §6.2, fig_v3_cross_modality_uh.pdf), alignment broadens — the qualitative text reports the modalities "line up" in the key pharmaceutical non-SME pre-period cell after auction-level scale shocks are removed.

Output: v7-jpube-tight/output/tables/tab_v3_cross_modality.tex; v7-jpube-tight/output/figures/fig_v3_cross_modality.pdf (raw) and fig_v3_cross_modality_uh.pdf (UH-corrected).

Interpretation

The cross-modality test is a discipline, not a proof. The 7-of-8 cells where Convite GPV quantiles sit ~0.2 below Pregão drop-out quantiles are consistent with the standard wedge between strategically shaded first-price bids and truthful English-clock exits in common-cost settings — but they are not literally identical. Reading: GPV and drop-out recoveries identify different underlying objects, with Convite naturally producing lower point estimates because the GPV inversion explicitly nets out the bid-shading wedge.

The key cell aligns. The pharma non-SME pre-period cell — which is the load-bearing population for the pharma welfare statement (H:static-welfare-loss-large and AN-016) — shows median quantiles of 0.712 (Convite) vs 0.704 (Pregão), a gap of −0.008. The two modalities agree on the central object that the paper's headline depends on most.

What the test does and does not say. It does not show that the Pregão drop-out reading is literally a cost recovery. It does show that the Pregão-based decomposition is not an idiosyncratic artifact of the English-clock format: a different auction format on the same product cells, recovered through a different point-identification strategy (GPV bid inversion), produces convergent estimates in the load-bearing cell and a known wedge (consistent with bid shading) in the rest. Combined with the UH-corrected figure that broadens the alignment, the cross-modality test is the strongest second identification source on the structural primitives.

Confidence: yellow. Cross-modality is the most informative diagnostic available within-project for H7. It rules out the threat that Pregão drop-outs are uniquely IPV-clock-incompatible across BEC. But it remains within-project (both modalities are BEC), it produces a partial rather than uniform alignment, and the UH-corrected version exists as a figure with qualitative paper text rather than as a macro-tabulated set of numbers. Promotion to green would require an out-of-jurisdiction replication, not just a within-project second modality.

Follow-ups

  • UH-corrected table: emit tab_v3_cross_modality_uh.tex to make the post-UH cell-by-cell comparison macro-citable, not figure-only. Currently only the raw table is macro-bound.
  • KS / quantile-equality formal test: a Kolmogorov-Smirnov or quantile-by-quantile equality test by cell would give a \(p\)-value on the alignment claim. Currently we eyeball the gap.
  • Cell-size and precision: the pharma non-SME pre cell may have small Convite \(N\). Reporting per-cell sample sizes and bootstrap CI on each quantile would temper or strengthen the "aligned cell" read.
  • Cross-jurisdictional: same exercise on ComprasNet or another state's procurement platform would be the path to 🟢. Out of scope for the current paper; flagged for future work.