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AN-014: Auction-level heterogeneity correction + dependence relaxation

Intuition (plain-language)

Some auctions are simply expensive across the board (a common cost shock). The Krasnokutskaya-style correction strips out that shared component so the decomposition reflects firm-level cost differences, not common shocks — and it checks the result survives letting bidders' costs be correlated within an auction. The exclusion-dominant story holds.

Question

Two diagnostic concerns about the structural recovery:

  1. Common auction-level scale shocks: Bids in a single auction can move together because of volume, delivery burden, regulatory documentation, or item-specific complexity. Normalization by the buyer reference price absorbs cross-item scale differences but not these auction-level co-movements. Does a Krasnokutskaya (2011)-style heterogeneity correction mechanically produce the exclusion-dominant decomposition by removing too much variance, or does the decomposition survive?
  2. Within-auction cost independence: The IPV-clock interpretation assumes types draw independent costs within each auction. If moderate within-auction cost correlation exists (sourcing shocks, common input prices), does it overturn the decomposition?

Design

  • Sample: Pregão drop-outs from AN-013, by class and bidder type.
  • Variation: within-auction vs between-auction variance in \(y_{it} = \log(b_{it} / p_t^{\mathrm{ref}})\).
  • Specification (UH correction): method-of-moments variance decomposition; estimate \(\hat{a}_t\) as auction-level scale component; remove via best-linear-predictor shrinkage; use cleaned \(\exp(\hat{e}_{it})\) for downstream BNE simulation.
  • Specification (dependence relaxation): re-run BNE simulation under a Gaussian-copula joint distribution with within-auction cost correlation \(\rho_c \in \{0, 0.1, 0.2, 0.3\}\).
  • Outcomes: per-cell intraclass correlation (ICC); cleaned bid distribution; exclusion share + net effect across \(\rho_c\) grid.

Results

Intraclass correlations (paper §3): Pregão ICCs in the main cells range from 0.36 (non-pharma SMEs) to 0.59 (pharma non-SMEs) — comparable to procurement settings where the Krasnokutskaya correction is standard (e.g., Krasnokutskaya 2011's Florida road auctions).

Gaussian-copula dependence relaxation (paper §6.2):

  • Within-auction cost correlation tested up to \(\rho_c = 0.3\).
  • Across the \(\rho_c\) grid:
  • Exclusion share moves by less than 5 percentage points.
  • Total effect moves by less than 10 percent.

Filter sensitivity at \(c_\epsilon \leq 3\) and 6/12/18-month windows also leave the exclusion component as the larger component in both classes.

Output: v7-jpube-tight/output/uh_decomposition.parquet; documented in paper_v8.tex §6.2 (Willingness-to-supply recovery and auction primitives).

Interpretation

Common scale shocks do not produce the exclusion result. After the UH correction removes auction-level scale, the cleaned per-cell cost distributions still generate the exclusion-dominant decomposition. The correction narrows the simulation's noise but does not change the qualitative ordering.

Moderate within-auction cost correlation does not overturn the decomposition. Allowing within-auction \(\rho_c\) up to 0.3 — a substantial deviation from the IPV-clock independence assumption — moves the exclusion share by less than 5 pp and the total effect by less than 10%. This is not a test that IPV-clock holds; it is a test that moderate deviations from IPV-clock are not the reason the decomposition reads as it does.

What the correction does not purge. Two channels remain in the cleaned distribution: (i) bidder-type selection (SMEs vs non-SMEs genuinely have different cost distributions, which is the substantive finding the paper builds on); (ii) post-policy SME pool composition changes (selection into the protected market, sourcing or product-mix changes). The strict-invariance check (AN-017) is the test for whether the second channel matters for the dominance ordering.

Confidence: yellow. The UH correction is methodologically standard; the ICC magnitudes are comparable to other procurement settings; the dependence-relaxation grid is informative. The reading remains yellow rather than green because the correction is a necessary discipline on the structural recovery, not a proof that the recovered objects are literal costs.

Follow-ups

  • ICC stability across the policy break: re-estimate ICCs separately in pre and post periods. A discontinuous shift would indicate the auction-level scale structure changed under the policy.
  • Iterative refinement (v7-jpube-tight/scripts/43_uh_invariance_update.R): the decomposition should be stable across iterative updates of the correction.
  • Cross-modality consistency: per paper_v8.tex §6.2, the Convite first-price GPV recovery and Pregão drop-out recovery line up in the key pharma non-SME pre-period cell after UH correction — a cross-modality discipline that deserves its own AN page.