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H:exclusion-dominates — The lost-discipline channel dominates the protected-pool offset in the absolute price decomposition

The set-aside changes the price-forming pool on two margins: it removes non-SMEs from eligible auctions (the lost-discipline channel) and it changes the protected SME pool through additional participation and composition (the protected-pool offset). The decomposition compares \(|S_2 - S_1|\) (the lost-discipline magnitude, holding the pre-policy SME pool fixed) against \(|S_3 - S_2|\) (the protected-pool offset, replacing the fixed pool with the observed post-policy pool). The paper's headline claim is that the first magnitude dominates the second in standardized non-pharmaceutical procurement.

Intuition (plain-language)

The set-aside moves the price on two levers: it removes the non-SMEs who were setting the price, and it changes who is left in the SME pool. The decomposition asks which lever does more work. For ordinary (non-pharma) goods, simply removing the disciplining non-SMEs accounts for about 72% of the price change. The SME pool's response is real but secondary — exclusion, not composition, is the main story.

Evidence strength: Partial (strongly supported). AN-010 reports an absolute exclusion share of 72.0% (non-pharma) and 68.8% (pharma) — lost-discipline channel dominates protected-pool offset. AN-017 shows strict invariance (\(F_c^{\mathrm{SME,Post}} = F_c^{\mathrm{SME,Pre}}\)) reinforces dominance: share rises to 85% (NP) / 79% (PH) when SME composition is held fixed. AN-022 cluster bootstrap (B=500) reports 95% CI [64.5, 86.8] (NP) and [61.6, 85.2] (PH) on the absolute exclusion share — the lower endpoint exceeds 50% in every cell × winner-censoring regime, so the dominance ordering survives bootstrap inference. Pharma inherits additional model sensitivity (AN-016), hence the boundary-case treatment.

Theory

In an independent-private-values English auction with a type-mixed bidder pool, the expected payment under counterfactual bidder-pool \(V\) is \(E[c_{(2)}^V]\) where \(c_{(2)}\) is the second-order statistic. Comparing three counterfactuals isolates two margins: \(S_2 - S_1\) removes the non-SME draws while holding the SME-draw distribution fixed — a pure removal effect; \(S_3 - S_2\) replaces the SME draw distribution with the post-policy estimate — a pure protected-pool composition + entry effect. The decomposition follows the price-formation logic in (Vickrey 1961; Haile and Tamer 2003; Athey and Haile 2002).

Prediction

In standardized non-pharma, \(|S_2 - S_1| > |S_3 - S_2|\). Operationalized: the absolute exclusion share \(|S_2-S_1| / (|S_2-S_1| + |S_3-S_2|)\) should exceed 50%, and meaningfully so (paper headline: ~72%). The exclusion-to-net ratio \((S_2-S_1) / (S_3-S_1)\) should likewise exceed 1.

Competing prediction

Protected pool fully responds. If the post-policy SME pool entirely replaced the price-forming role of the excluded non-SMEs, the offset \(|S_3-S_2|\) would be at least as large as the exclusion magnitude. The direct evidence against this alternative is the post-policy SME bidder count: it rises sharply but does not reach the level required to recreate the lost discipline. See H:protected-pool-responds.

Setting evidence

São Paulo's BEC Pregão is an English-reverse auction that records drop-out prices for every losing bidder. The structural sample is built from these drop-outs, type-coded by SME status. The maintained IPV-clock interpretation (H:ipv-clock-admissible) is load-bearing for the decomposition.

Empirical test

  • Outcome variable: simulated \(E[c_{(2)}^V]\) normalized by the buyer reference price, for \(V \in \{S_1, S_2, S_3\}\).
  • Variation: counterfactual bidder pool — \(S_1\) open pre-policy, \(S_2\) SME-only pre-policy SME pool, \(S_3\) SME-only observed post-policy SME pool.
  • Specification: BNE simulation (v7-jpube-tight/scripts/45_bne_simulation.R) on recovered type-specific cost distributions, by class (non-pharma standardized, pharma).
  • Sample: BEC Pregão drop-outs, period spanning the March 2018 cutoff; class-level cells (medical/hospital non-pharma vs pharmaceuticals).

Data requirements and limitations

The decomposition inherits two structural restrictions: (1) the IPV-clock reading of drop-outs and (2) the Krasnokutskaya-style auction-level heterogeneity correction. Both are tested in robustness (AN-014, AN-015). The \(S_3 - S_2\) term should not be read as a pure entry parameter — it combines additional participation with changes in the active SME pool composition (see H:protected-pool-responds).

Evidence

Analysis Bearing Key takeaway
AN-010 Supports Absolute exclusion share ~72% in standardized non-pharma; exclusion-to-net ratio exceeds 1 in both non-pharma and pharma cells.
AN-017 Pending Strict-invariance specification holding the SME pool fixed in composition — should preserve the dominance ordering if compositional churn is not the main driver.
AN-016 Mixed Pharma magnitudes larger but more model-sensitive; not load-bearing for the headline.
AN-014 Supports UH-correction ICCs 0.36–0.59; Gaussian-copula ρ_c=0.3 share drift <5pp, total drift <10%. Decomposition not mechanically produced by scale shocks.
AN-022 Supports 95% CI on absolute exclusion share [64.5, 86.8] NP / [61.6, 85.2] PH — lower endpoint exceeds 50% dominance threshold in every cell × regime. Δ_total CI excludes zero.

Open tests

Cross-modality validation

Re-run the decomposition on Convite first-price bids using a GPV recovery; the converging direction would discipline the IPV-clock restriction. Lives in v7-jpube-tight/scripts/38_cross_modality.R.

Bootstrap dominance ordering

Done in AN-022: cluster bootstrap (B=500) at auction level. 95% CI on absolute exclusion share [64.5, 86.8] NP / [61.6, 85.2] PH — exceeds 50% threshold in every cell × regime. Open: BCa intervals and subsampling variants for skew-robust inference; stratification by adherence-rate for the fiscal-cost CI alignment.