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Welfare and Extensions

The welfare consequences of the set-aside are class-heterogeneous from the start. Under the main equilibrium-selection specification, the welfare cost is 28.7% of pS1 in non-pharma and 47.0% in pharma at λ = 0.30. The price effect is therefore only the beginning of the welfare account.

1. Welfare arithmetic

Per-auction welfare loss of the SME-only set-aside relative to the open regime:

\[\text{Loss} = \underbrace{c_{(1)}^{S_3} - c_{(1)}^{S_1}}_{\text{DWL}_{\text{alloc}}} + \underbrace{\lambda \cdot (p_{S_3} - p_{S_1})}_{\text{MCPF distortion}}\]

The first term is the allocative wedge: by how much the winner's production cost is higher in the restricted regime than in the open regime. The second term is the tax-distortion loss on the government's extra outlay Δgov, scaled by the marginal cost of public funds λ. The transfer from government to SMEs (Δgov minus the allocative wedge) is zero-sum in a social-planner ledger and is not destruction.

Point estimates at λ = 0.30 (Ballard, Shoven, and Whalley 1985 benchmark)

Δgov DWLalloc Implicit transfer MCPF distortion Total Loss / pS1
Non-pharma 0.242 0.150 0.092 0.073 28.7%
Pharma 0.328 0.210 0.118 0.098 47.0%

The allocative component dominates in both classes, but especially in pharma, where a thin SME pool and higher goods heterogeneity make bidder exclusion more likely to route the contract to a high-cost protected winner.

Welfare loss intervals
Figure 1. Welfare loss as % of pS1, by class and MCPF λ. Circles and horizontal whiskers report cluster-bootstrap mean and 95% CI under the main specification; triangles report the strict-invariance benchmark. The dotted vertical line marks the 11.8% benchmark implied by the DiD coefficient of −0.11 in absolute log-prices.

2. Endogenous entry as a partial offset in welfare units

The fixed-pool counterfactual exceeds the realized post-policy counterfactual by 52% in non-pharma and 57% in pharma. Both terms in the welfare formula load on the simulated price margin, so a fixed-pool welfare calculation would be roughly 50--60% larger than the realized one in normalized units. Endogenous entry does not change the ranking against the preference rule in non-pharma; it does materially reduce the welfare burden of bidder exclusion under the model's main specification.

3. Confidence intervals

Cluster bootstrap with B = 500 replicates delivers 95% CIs on Loss / pS1 at λ = 0.30:

Class Bootstrap mean 95% CI
Non-pharma 28.1% [21.3%, 35.3%]
Pharma 45.6% [35.1%, 56.2%]

The intervals leave no doubt about the ordering. Even the lower bound in pharma is above the non-pharma point estimate. The class heterogeneity is not sampling noise around a common welfare effect; it is a structural feature of the protected pool and the good being procured.

4. Sensitivity to λ (MCPF)

For λ ∈ {0.20, 0.30, 0.40} (point estimates):

Class λ = 0.20 λ = 0.30 λ = 0.40
Non-pharma 25.6% 28.7% 31.8%
Pharma 42.0% 47.0% 52.0%

Each 0.10 increment in λ adds about 3 percentage points in non-pharma and about 5 points in pharma. The level moves, but the class ranking does not. The non-pharma V3 > V0 ranking holds across λ ∈ [0.15, 0.45] under both specifications; the pharma V3 > V0 ranking holds across the same range under the main specification but reverses to V0 > V3 under strict invariance.

5. Welfare-weight implicit in the current regime

Following the generalized social-marginal-welfare-weight framework of Saez and Stantcheva (2016), a planner aggregating producer and consumer surplus with weight wSME on SME producer surplus is indifferent between the full set-aside (V0) and the 10% price preference (V3) when

\[w^{\text{SME}}_\star = \frac{\text{Loss}(V_0) - \text{Loss}(V_3)}{\text{SMESurplus}(V_0) - \text{SMESurplus}(V_3)}.\]
Loss differential SME-surplus differential wSME★
Non-pharma 0.223 0.092 2.42
Pharma 0.308 0.118 2.61

A planner willing to pay the non-pharma fiscal cost of bidder exclusion would have to value one real of SME surplus at more than twice a real of general welfare, even in a thick market where a preference rule achieves nearly the same allocative objective. Under strict invariance, the non-pharma preference ranking is unchanged; the pharmaceutical indifference weight falls to 0.7, below the utilitarian benchmark.

Implicit welfare weight
Figure 2. Implicit welfare weight wSME★ required to prefer the full set-aside over a 10% price preference, by class and specification. The grey band marks the 1.2--1.5 range typical of Brazilian cash-transfer programs; the dashed vertical line marks the utilitarian benchmark w = 1.

6. Scaling to the furosemida vignette

A pair of furosemida 40 mg purchases by the same Sao Paulo public buyer in February 2018 (open regime, ten firms bidding, clearing price ~12% below reference) and October 2018 (post-cutoff, three SMEs, clearing price just above reference) anchors the magnitudes.

Applying the pharmaceutical-class point estimates to that single purchase:

Value (units of pref)
Government's extra outlay Δgov +0.328
of which: allocative DWL 0.210
of which: implicit transfer to SME winner 0.118
Tax-distortion welfare cost (λ = 0.30) 0.098
Total welfare loss / pS1 47.0%

The per-auction number scales; the group-level fiscal consequence is substantial, and the welfare consequence is larger still.

7. Why the structural welfare loss exceeds the DiD benchmark

Two mechanical features drive the departure from the DiD benchmark of 11.8%:

  • Different functionals on different conditioning sets. The DiD recovers the average log-price difference between regimes conditional on item and month fixed effects, on completed transactions only. The structural object is the simulated mean of c(2) under each counterfactual entry profile, on UH-clean cost residuals, expressed as a ratio of the reference price. The two functionals differ both in transformation (log-price difference vs. level of c(2)/pref) and in conditioning set.
  • Tax distortion was not priced in the DiD benchmark. The MCPF term λ · Δgov adds about nine percentage points of pS1 in non-pharma and fifteen in pharma at λ = 0.30.

The 3--4× gap between the structural and the DiD is informally attributable to these differences and is predictable in direction under the maintained assumptions: the second-order statistic of an SME-only draw, expressed as a level relative to the open-regime baseline, is necessarily larger than the average log-price change averaged over the realized distribution conditional on item fixed effects. A misspecified model would not be guaranteed to deliver a gap of either consistent sign or consistent magnitude.

8. Extensions the paper does not attempt

Three extensions represent natural follow-on work:

  • Quantity response. The buyer's adjustment to higher prices is treated as inelastic at observed values. At a typical demand elasticity for essential medical supplies ε ∈ [0.1, 0.3], the quantity adjustment to the simulated 11% log-price increase would shave the fiscal cost by roughly 1--3 percentage points of pS1.
  • Dynamic capacity accumulation. SME firms protected by the rule may build production capacity that persists beyond the policy window — an externally validated mechanism in Ferraz et al. (2016) and Szerman (2023).
  • General-equilibrium SME surplus. The partial-equilibrium SMESurplus measure used in the welfare-weight identity could be extended to a GE framework with option value, capacity persistence, and private-sector spillovers.

Each is a margin a fully dynamic-general-equilibrium model would price; each would tend to enlarge the SME-side benefit and could shift the welfare-weight comparison. None changes the organizing lesson: the welfare ranking of bidder-exclusion rules is conditional on market structure.