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AN-030: Entry rates, entry costs, and decomposition robustness grid

Intuition (plain-language)

Why can the protected SME pool not simply replace the excluded non-SMEs? Calibrate entry costs: SME entry nearly doubles while non-SME entry falls more, for a small net drop in bidders — and non-SMEs face about 4.7× higher entry costs yet win far more often. The exclusion-dominant decomposition holds across every method-choice combination tested.

Question

The protected-pool offset \(S_3 - S_2\) in AN-010 shows that SME participation roughly doubles after the cutoff but does not fully replace non-SMEs. Three structural questions:

  1. Entry-rate symmetry: Does the SME entry response exactly replace the non-SME exit, or is there a net loss of bidders? Does the pattern differ across Pregão vs Convite modalities?
  2. Why doesn't the protected pool fully respond? What is the calibrated entry cost for SMEs vs non-SMEs, and does the asymmetry explain the partial offset?
  3. Methodological robustness: Does the exclusion-dominant decomposition survive across the 2×2 grid of UH-clean-vs-raw and endogenous-vs-fixed-pool entry choices?

Design

  • (a) Entry rates: per-cell average bidder count by class × type × period; Pre→Post Δ.
  • (b) Entry cost calibration: zero-profit condition at the entry margin, \(\kappa^k = P(\text{win} | k) \cdot \bar\pi^k \mid \text{win}\), estimated as the marginal mean profit per entry in 5,000 Monte Carlo auctions under the Pre-policy entry profile.
  • (c) Decomposition grid: BNE simulation under 4 method × 2 class combinations:
  • Method 1: clean UH (Krasnokutskaya correction applied)
  • Method 2: raw (no UH correction)
  • Method 3: endogenous entry (observed Pre→Post pool change)
  • Method 4: fixed-pool entry (counterfactual no entry response)
  • Cross-product: 4 method combinations × 2 classes = 8 cells.

Results

(a) Pre/Post entry rates (avg bidders per auction) (tab_v3_entry_rates.tex):

Modality Class SME Pre non-SME Pre SME Post non-SME Post Δ SME Δ non-SME
Convite NP 1.13 1.72 1.60 1.24 +0.47 −0.48
Convite PH 0.92 1.81 0.87 1.95 −0.05 +0.14
Pregão NP 0.94 2.68 1.87 1.50 +0.93 −1.18
Pregão PH 0.55 2.61 1.22 1.66 +0.67 −0.95

In Pregão non-pharma the SME pool nearly doubles (+99%) and non-SME falls by 44%, with net total bidders falling by 0.25 per auction. Pharma shows the same direction but smaller absolute SME gain.

(b) Entry-cost calibration (Pre-policy) (tab_v3_entry_cost.tex):

Class \(\tilde p^{\mathrm{ref}}\) (R$) \(P(\mathrm{win} \mid \mathrm{SME})\) \(P(\mathrm{win} \mid \mathrm{non}\text{-}\mathrm{SME})\) \(\bar\pi \mid \mathrm{SME}\) \(\bar\pi \mid \mathrm{non}\text{-}\mathrm{SME}\) \(\kappa^{\mathrm{SME}}\) (R$) \(\kappa^{\mathrm{non}\text{-}\mathrm{SME}}\) (R$)
Non-pharma 13.98 0.176 0.824 0.222 0.223 0.54 2.57
Pharma 2.96 0.160 0.840 0.267 0.196 0.13 0.49

The entry cost is ~4.7× higher for non-SMEs than for SMEs in non-pharma (and 3.8× in pharma). Non-SMEs face higher entry costs but win 4–5× more often per attempt, with similar per-win profits in non-pharma — they enter despite the cost because the win probability is high enough.

(c) Decomposition grid (tab_v3_decomp_grid.tex):

Class Method \(S_1\) \(S_2\) \(S_3\) Δ total % intensive % entry
NP clean + endogenous (canonical) 0.770 1.110 1.002 +0.233 75.9 24.1
NP clean + fixed-pool 0.761 1.132 1.097 +0.337 91.4 8.6
NP raw + endogenous 0.806 1.230 1.064 +0.259 71.9 28.1
NP raw + fixed-pool 0.805 1.267 1.189 +0.384 85.5 14.4
PH clean + endogenous (canonical) 0.645 1.161 0.964 +0.318 72.3 27.7
PH clean + fixed-pool 0.650 1.265 0.974 +0.324 67.9 32.1
PH raw + endogenous 0.726 1.285 1.095 +0.369 74.6 25.4
PH raw + fixed-pool 0.711 1.213 1.214 +0.504 99.7 0.3

The intensive (exclusion) share ranges from 67.9% to 99.7% across the 8 cells; the lowest value is well above 50%.

Interpretation

The protected pool responds, but asymmetrically. SME entry rises sharply (+99% in Pregão NP), but non-SME entry falls more (−44%), producing a net loss of ~0.25 bidders per auction. The protected pool cannot replace the lost discipline because (i) the SME pool starts much smaller (0.94 SMEs vs 2.68 non-SMEs per Pre auction) and (ii) doubling a smaller base does not match a 44% cut to the larger base.

Entry cost asymmetry explains the partial offset. The calibrated entry cost for non-SMEs is 4.7× SME's in non-pharma. Non-SMEs face high entry costs but high win probability — they enter when the expected value of entry justifies the cost. SMEs face low entry costs but low win probability — they enter when they have a local or specialized advantage. Removing non-SMEs from the auction does not lower the entry cost barrier for SMEs; it just removes the most productive competitors. The protected pool's response is bounded by the pre-existing SME participation — it can roughly double a smaller base, but the base itself was small because of the underlying type-cost distribution, not because of the policy.

Modality contrast. Convite shows a much smaller SME response (+0.47 in NP vs Pregão's +0.93). Convite is invitation-based first-price; the structural mechanics differ from Pregão's English-clock auction. The asymmetric SME response across modalities is itself an artifact of differing auction-format incentives, not a defect.

Decomposition grid: dominance ordering robust. Across all 8 cells of the 2×2 method × class grid, the intensive (exclusion) share stays above 50%. The lowest value, 67.9% (pharma clean + fixed-pool), is still 17 pp above the dominance threshold. The canonical specifications (clean + endogenous) for both classes align with the AN-010 headline at 75.9% NP and 72.3% PH. The exclusion-dominant ordering does not depend on the methodological choices that distinguish v3 from earlier paper versions.

Confidence: yellow. This is the cleanest within-project test of the protected-pool-response prediction. Three independent sub-analyses (entry rates, entry costs, method grid) converge on the same conclusion: the protected pool responds asymmetrically and this is not a defect of measurement or method.

Follow-ups

  • Newcomer-vs-returning SME decomposition: which of the additional SMEs post-policy are new to BEC, vs already-active SMEs that scaled up participation? The pure-entry channel is the newcomer share; the rest is participation intensification by existing SMEs.
  • Drug-class cross-cut in pharma: refines the pharma boundary statement of AN-016. The aggregate pharma response masks therapeutic-class heterogeneity.
  • Endogenous entry vs structural entry model: the current treatment uses observed Pre→Post pool change. A structural entry model (with \(\kappa^k\) as parameter) would let the simulation generate counterfactual entry rates under hypothetical preference-vs-set-aside regimes; partly done in v7-jpube-tight/scripts/61_optimal_preference.R.