AN-017: Strict-invariance specification¶
Intuition (plain-language)
Maybe the result is an artifact of how the SME pool's composition changes after the policy. Strict invariance freezes the SME cost distribution at its pre-policy shape while keeping observed entry counts. The price effect not only survives — the exclusion share rises to 85% — so composition change is not what drives dominance.
Question¶
The protected-pool offset \(S_3 - S_2\) combines additional SME participation with changes in the active SME pool composition observed post-policy. The strict-invariance specification fixes the SME cost distribution at the pre-policy distribution but keeps observed post-policy SME bidder counts — testing whether the dominance ordering of H:exclusion-dominates is driven by compositional churn in the active SME pool or by the underlying type-cost gradient.
Design¶
- Sample: structural cells from AN-010.
- Variation: BNE decomposition with the constraint \(F_c^{\mathrm{SME,Post}} = F_c^{\mathrm{SME,Pre}}\) while observed post-policy SME entry counts are retained.
- Specification: re-run the BNE simulation under the strict constraint; report the resulting total effect and within-auction (exclusion) share.
- Outcomes: strict-invariance net \(S_3 - S_1\); corresponding exclusion share; comparison to the main specification.
Results¶
From v7-jpube-tight/output/strict_invariance.parquet (paper §6.3):
| Class | Main \(S_3-S_1\) | Strict-inv \(S_3-S_1\) | Main share | Strict-inv share |
|---|---|---|---|---|
| Non-pharma | 0.227 | 0.29 | 72.0% | 85% |
| Pharma | 0.309 | 0.47 | 68.8% | 79% |
Under strict invariance, both the total price effect and the exclusion share are larger than in the main specification.
Interpretation¶
Composition is not what makes the exclusion component dominate. Holding the SME cost distribution fixed at the pre-policy level increases both the total effect and the exclusion share. If compositional churn in the active SME pool had been responsible for the exclusion-dominant ordering, freezing composition would have made the offset disappear and the net effect would have grown larger through that offset reduction; instead, the same direction (lost discipline > offset) holds, more sharply.
What composition does affect. The non-strict-invariance specification reduces the net effect because the post-policy SME pool has a cleaner (lower-cost) cost distribution than the pre-policy SME pool — a positive selection effect into the protected market that partially offsets the lost competitive discipline. Under strict invariance that offset is shut off by construction, leaving the full lost-discipline channel exposed.
Composition matters more for the pharma welfare ranking. Pharma's strict-invariance share rises 10.2 pp (68.8 → 79); non-pharma's rises 13 pp (72.0 → 85). Both are large, but composition explains a larger fraction of the pharma protected-pool offset, consistent with the boundary-case treatment of pharma in AN-016.
Confidence: yellow. The strict-invariance comparison is a clean "composition-off" / "composition-on" cross-check. It is yellow rather than green because it inherits the structural recovery's restrictions (IPV-clock, UH correction) — same caveat ladder as the rest of the Cluster B/C structural pieces.
Follow-ups¶
- Mechanism decomposition of \(S_3 - S_2\) into pure entry (count change with composition fixed) vs pure composition (composition change with count fixed). Currently the strict-invariance fixes composition and lets count vary, isolating one direction. The complementary cut would expose the residual entry channel.
- Drug-class cross-cut in pharma: identify which therapeutic sub-classes drive the active-pool composition shift; this would refine the pharma boundary-case statement.