AN-025: Annualized welfare cost — adherence-rate sensitivity¶
Intuition (plain-language)
The per-auction welfare cost is fixed by the structure; what scales the annual bill is how often buyers actually comply with SME-only tendering. Across the 30–70% adherence range reported in the paper the Group-65 cost spans R\(38–89M/yr; at the observed 43% adherence it is about R\)55M/yr. Adherence is the dial on the realized fiscal cost.
Question¶
The structural welfare loss in AN-011 and AN-024 is per affected auction. To translate into an annualized public-finance magnitude on Group 65 alone, we need to multiply by (i) the annual Group-65 outlay and (ii) the adherence rate — the share of the Group-65 outlay that actually procured under the SME-only rule. Adherence is below 100% in practice because some Group-65 items exceed the R$80K SME-eligibility ceiling, some Group-65 procurement remains under emergency / specialized exemptions, and buyer compliance with the SME-only mandate is imperfect.
Design¶
- Sample: Group 65 BEC outlays, Post-policy run-rate annualized from the 18-month Post window \(m \in [698, 715]\).
- Variation: adherence rate \(\in \{30, 43, 55, 70, 85, 100\}\)%.
- Specification: annualized welfare cost = per-auction structural welfare cost (\(\lambda = 0.30\) from AN-011) × annual Group-65 outlay × adherence rate. Pharma and non-pharma additive.
- Annual reference outlays: pharma R\(363M/yr; non-pharma R\)345M/yr (own tabulation; 18-month Post window annualized to 12 months).
- Per-auction welfare cost (λ=0.30, fixed across adherence grid): the canonical structural loss — 28.9% of the open-regime price in non-pharma, 44.8% in pharma (AN-011). Carried into the annual scaling, this anchors full (100%) adherence at R\(55M/yr (non-pharma) and R\)73M/yr (pharma) — an effective welfare cost of ≈0.16 and ≈0.20 of annual reference outlay, respectively.
- Empirical baseline: 43% — the state-level Post-period Group-65 SME-only adherence rate (paper §2 institutional).
Results¶
| Adherence rate | 30% | 43% | 55% | 70% | 85% | 100% |
|---|---|---|---|---|---|---|
| Pharma (R$ M/yr) | 22 | 31 | 40 | 51 | 62 | 73 |
| Non-pharma (R$ M/yr) | 16 | 24 | 30 | 38 | 47 | 55 |
| Total Group 65 (R$ M/yr) | 38 | 55 | 70 | 89 | 109 | 128 |
| US$ M/yr (R$3.50 end-2018) | 11 | 16 | 20 | 25 | 31 | 37 |
Reported range vs. extrapolation
The paper reports the 30–70% adherence range → R\(38–89M/yr (US\)11–25M/yr), matching AN-011 and the Welfare cost panel in docs/extensions.md. The 85% and 100% columns are arithmetic extrapolations beyond the reported range (full SME-eligible adherence is not observed) and are shown only to illustrate the adherence lever. The bold 43% column is the empirical post-cutoff adherence cited in paper §2 and implies ~R$55M/yr.
Output: output/tables/tab_welfare_adherence_sensitivity.tex and
tab_welfare_adherence_sensitivity.csv.
Interpretation¶
**The R\(38–89M range is an adherence-grid sensitivity, not a structural uncertainty band.** The per-auction welfare cost is *fixed* at the canonical λ=0.30 structural point estimate (28.9% of the open-regime price in non-pharma, 44.8% in pharma); the range spans the paper's reported 30–70% adherence band. The empirically observed adherence of 43% implies **~R\)55M/yr (US\(16M/yr)**; the upper bound of the reported range, at 70% adherence, is **R\)89M/yr (US\(25M/yr)**. (A hypothetical 100% adherence would reach ~R\)128M/yr, but that is an extrapolation beyond the range the paper reports.)
The structural CI is a separate uncertainty band. The bootstrap CI in AN-024 is on the per-auction welfare cost; multiplying it through the adherence grid produces a joint structural × adherence range. At the baseline 43% adherence, the joint range is roughly R$40–70M/yr (combining the welfare CI lower endpoint with the central adherence).
Context. Group 65 is one product group of São Paulo's ~R\(13B/yr procurement platform. The annual cost of R\)55M sits at ~0.4% of total state procurement volume. The same per-auction logic applied to the broader SME-restricted procurement (which spans many other product groups already SME-only pre-2018, and other state jurisdictions nationally) would yield substantially larger aggregate fiscal costs. That broader extrapolation is out of scope for this paper.
Adherence as a policy lever. The grid implies that partial enforcement (adherence well below 100%) is welfare-favorable relative to full enforcement, under the assumption that the non-adhering Group-65 procurements default to open competition. This is consistent with the paper's recasting of the policy frontier: not "support SMEs vs not", but "exclusionary redistribution vs support-with-preserved-pool". Higher adherence raises the welfare loss monotonically; relative to the 70% upper bound of the paper's reported range (R\(89M/yr), the empirical 43% adherence leaves about R\)34M/yr of welfare loss unrealized.
Confidence: yellow. The arithmetic is deterministic given the per-auction structural cost and the reference outlays. The yellow caveat is inherited from H:static-welfare-loss-large on the per-auction cost. The reference-outlay tabulation is a simple sum over the 18-month Post window and is robust to specification choice within the window.
Follow-ups¶
- Joint structural × adherence CI: combine the welfare CI from AN-024 with the adherence grid to produce a joint range at the baseline 43%.
- Per-PBU adherence heterogeneity: not all PBUs adhere at the same rate. A PBU-level decomposition would identify which buyer types contribute most to the realized fiscal cost.
- Other product groups: replicate this exercise on product groups that were SME-only throughout the sample (the always-treated controls). Their welfare cost is the baseline of the comparison — currently unmodeled but bears on the broader policy reading.
- National-aggregate extrapolation: scale to ComprasNet or other state platforms; bears on whether the headline finding generalizes beyond São Paulo. Cross-jurisdictional replication path.