AN-016: Pharma boundary case — same direction, fragile magnitude¶
Intuition (plain-language)
Pharma's reduced-form effects are even bigger than non-pharma's — but the structural story is fragile there: most post-policy SME pharma firms are brand-new entrants, the cost primitives do not stay invariant, and the welfare ranking flips between specifications. So pharma is reported as a same-direction confirmation, not a second headline you can lean on.
Question¶
Across the structural decomposition (AN-010), welfare arithmetic (AN-011), bootstrap CI (AN-022), λ sensitivity (AN-024), strict invariance (AN-017), and entry-rate analysis (AN-030), pharmaceutical procurement appears consistently. The point estimates are larger in pharma than in non-pharma — welfare loss 44.8% vs 28.9%; exclusion share 68.8% versus 72.0%. But the paper treats pharma as a boundary case rather than a second headline. Why?
Design¶
This AN consolidates pharma-specific evidence across five diagnostic margins, comparing each to non-pharma:
- Within-Group-65 falsification — medications (CADMAT 6531) vs other
medical supplies (online appendix OA-B;
tab_within_g65.tex). - Sample composition — how many SME firms are new entrants post-policy, in pharma vs non-pharma.
- Primitive-invariance KS test on the drop-out distribution pre vs post.
- Strict-invariance welfare ranking — does the welfare conclusion survive holding the SME cost distribution fixed at the pre-policy level?
- Implied SME welfare weight under main vs strict-invariance specifications.
Results¶
1. Reduced-form effects (within-Group-65 falsification)¶
The canonical reduced-form pharma evidence is the within-Group-65 falsification reported in the online appendix (OA-B) and AN-027: the CMED-regulated medications subclass (CADMAT 6531) versus other Group-65 medical supplies, 18-month window, both compared to non-Group-65 controls.
| Outcome | Medications (6531), base / PBU FE | Other medical supplies, base / PBU FE |
|---|---|---|
| Log prices | −0.166 / −0.174** | −0.099 / −0.097 |
| Log firms | +0.152 / +0.161** | +0.044 / +0.050 |
The regulated-medications cell is larger in magnitude (price −0.166 vs −0.099; firms +0.152 vs +0.044) but the effect is present and significant in both subclasses — a confounder operating only through CMED-regulated medicines would not move the non-medication cell. CMED ceilings cap prices, so contamination would attenuate the medications coefficient, not amplify it. The larger medications magnitude is consistent with deeper non-SME pharmaceutical bidder pools, not pharma inflation.
2. Structural decomposition (pharma cell)¶
Recovered from values.tex:
| Object | Pharma | Non-pharma |
|---|---|---|
| \(S_1\) (open pre) | 0.654 | 0.774 |
| \(S_2\) (SME-only, pre-pool fixed) | 1.219 | 1.144 |
| \(S_3\) (SME-only, post-pool) | 0.963 | 1.000 |
| Lost-discipline (S₂−S₁) | +0.565 | +0.371 |
| Protected-pool offset (S₃−S₂) | −0.256 | −0.144 |
| Net effect (S₃−S₁) | +0.309 | +0.227 |
| Absolute exclusion share | 68.8% | 72.0% |
| Bootstrap 95% CI on share | [61.6, 85.2] | [64.5, 86.8] |
3. Welfare arithmetic (pharma cell, λ=0.30)¶
| Pharma | Non-pharma | |
|---|---|---|
| \(\Delta_{\mathrm{gov}}\) | 0.298 | 0.247 |
| DWL\(_{\mathrm{alloc}}\) | 0.207 | 0.148 |
| Loss / \(p^{S_1}\) (λ=0.30) | 44.8% | 28.9% |
| Bootstrap 95% CI (λ=0.30) | [34.9, 55.9] | [20.5, 34.8] |
| Implied SME weight (main) | 2.61 | 2.42 |
| Implied SME weight (strict-inv) | 0.7 | (stable; ranking unchanged) |
The implied weight under strict invariance in pharma drops to 0.7 — below unity. Under that specification, even a utilitarian planner with no SME-specific weighting would not prefer the set-aside.
4. Sample composition — turnover¶
From values.tex:
| Statistic | Pharma | Non-pharma |
|---|---|---|
| % of post-policy SME firms that are new entrants | 61.9% | (n.r.) |
| % of post-policy SME bids from new firms | 37.8% | 23.0% |
| Pregão Pre SME (auctions) | 13,022 | (smaller base) |
| Pregão Post SME (auctions) | 19,994 |
Nearly two-thirds of post-policy pharma SME firms are new entrants to BEC — versus less than a quarter in non-pharma. The pharma protected-pool composition turns over substantially under the policy.
5. Primitive-invariance KS distance¶
| Test | Pharma | Non-pharma |
|---|---|---|
| KS distance, Pregão pre-UH | 0.072 | (passes) |
| KS distance, Pregão post-UH correction | 0.141 | (passes) |
The pharma Pregão primitive-invariance diagnostic FAILS after UH correction. The drop-out distribution shifts between pre and post periods in pharma in ways the heterogeneity correction does not absorb — meaning the recovered cost primitives are not stable across the policy break in pharma. They are stable in non-pharma.
6. Strict-invariance welfare ranking¶
From AN-017:
| Specification | Pharma ranking | Non-pharma ranking |
|---|---|---|
| Main (endogenous post-policy SME pool) | \(V_3 \succ V_0\) | \(V_3 \succ V_0\) |
| Strict invariance (\(F_c^{\mathrm{SME,Post}} = F_c^{\mathrm{SME,Pre}}\)) | \(V_0 \succ V_3\) (flip) | \(V_3 \succ V_0\) |
Pharma ranking flips between main and strict-invariance specifications; non-pharma is stable. From AN-024, this flip is not driven by λ — the pharma flip is constant across the entire λ ∈ [0.15, 0.45] grid within each spec.
Output: within-Group-65 falsification tab_within_g65.tex (OA-B);
v7-jpube-tight/output/tables/tab_v3_pharma_counts.tex (counts); welfare
macros in v8-jpube/output/values.tex.
Interpretation¶
Pharma is structurally different on four dimensions that collectively justify the boundary-case treatment:
-
Thinner pre-policy SME pool. Pre SME Pregão count = 0.55 bidders per auction in pharma vs 0.94 in non-pharma. The base from which the protected-pool response operates is half as deep in pharma.
-
Heavier turnover post-policy. 61.9% of post SME firms are new entrants in pharma — the active SME pool is not mostly the same firms with more entries; it is new firms. The composition change is large.
-
Primitive-invariance failure. UH-corrected Pregão drop-outs shift between periods (KS 0.141), meaning the cost-distribution recovery is more fragile across the break. In non-pharma the same diagnostic passes.
-
Welfare ranking sensitivity. When the SME pool composition is held fixed at the pre-policy level, the pharma welfare ranking flips (implied weight drops to 0.7, below unity); non-pharma's ranking is stable across the same specification choice.
What the boundary-case treatment does and does not say.
It says: the direction of the pharma decomposition is the same as non-pharma — exclusion dominates, prices rise — and that direction survives every diagnostic in AN-013 through AN-022. Pharma is a qualitative confirmation of the non-pharma headline.
It does not say: the pharma magnitudes are headline-citable. The 44.8% welfare loss in pharma should be read with the boundary flag: it depends on how the post-policy SME pool is modeled, and under the strict-invariance benchmark the welfare ranking reverses. Anyone citing 44.8% should also cite the strict-invariance reversal.
Why pharma is fragile (mechanism reading). Pharma is where products are most heterogeneous (thousands of distinct drug-SKU combinations), regulation is tightest (CMED price caps interact with procurement), and the SME pool is most likely to be entering the market for the first time in response to the policy (specialized small distributors that did not exist in BEC pre-2018). All four conditions interact: heterogeneity makes IPV-clock weaker; regulation distorts cost recovery; new firms have different cost distributions that the model treats as the same as incumbents.
Confidence: yellow. The boundary-case documentation is honest and load-bearing — it is the reason the paper does not promote pharma to a headline. Yellow because the diagnostics that fail in pharma all bear on the structural recovery, and the strict-invariance flip is the cleanest test of that fragility. Green would require either an independent pharma replication (out of jurisdiction) or a structural model that explicitly handles the new-firm entry channel — neither in scope for this paper.
Follow-ups¶
- Drug-class cross-cut: split pharma into therapeutic categories (antibiotics, oncology, generics, etc.). Some sub-classes may pass the primitive-invariance diagnostic where others fail.
- CMED-cap interaction: directly model the CMED price ceiling as a binding constraint on bid recovery. The 44.8% loss may attenuate if the price ceiling limits the structural cost distribution.
- New-firm cost distribution: estimate the post-policy SME cost distribution separately for new entrants vs incumbents. If new entrants have systematically different costs, the strict-invariance benchmark is misspecified — the right comparison is not "pre-policy SMEs" but "incumbent SMEs only".
- Cross-jurisdictional pharma: replicate the decomposition on pharmaceutical procurement in another state or in ComprasNet. If the boundary-case pattern persists, pharma is structurally different everywhere; if it disappears, the São Paulo BEC pharma setting has idiosyncratic features.