Main Results¶
The results organize around three findings. First, the simulated set-aside price effect is mostly within-auction: the within-auction share is 74.5% in non-pharma and 73.3% in pharma, and stays in the 73--85% range across cost-distribution estimators. Second, endogenous SME entry is a partial offset, not the source of the markup: without it the realized price and welfare cost would be 50--60% larger. Third, the policy comparison between bidder exclusion and a 10% price preference is conditional on goods characteristics — robust in thick standardized non-pharma markets, model-sensitive in thin heterogeneous pharma markets.
1. Entry response¶
| Pregao | SMEs Pre | SMEs Post | Non-SMEs Pre | Non-SMEs Post |
|---|---|---|---|---|
| Non-pharma | 0.94 | 1.87 | 2.68 | 1.50 |
| Pharma | 0.55 | 1.22 | 2.61 | 1.66 |
SMEs roughly double in both classes; non-SMEs fall sharply. The set-aside changes both the admissible pool and the equilibrium participation response.
2. Structural decomposition of the set-aside¶
Define pS1 as the simulated winning price under the pre-policy open regime, pS2 as the SME-only counterfactual at the pre-policy SME pool, and pS3 as the SME-only counterfactual at the observed post-policy SME pool. All numbers are normalized by the item reference price pref.
| pS1 (open) | pS2 (SME-only, fixed pool) | pS3 (SME-only, post pool) | Within-auction (S2−S1) | Entry offset (S3−S2) | Total (S3−S1) | |
|---|---|---|---|---|---|---|
| Non-pharma | 0.759 | 1.152 | 1.018 | +0.393 | −0.135 | +0.259 |
| Pharma | 0.656 | 1.141 | 0.964 | +0.485 | −0.177 | +0.308 |
The within-auction share — defined as |S2−S1| / (|S2−S1| + |S3−S2|) — is 74.5% in non-pharma and 73.3% in pharma under the main specification. The set-aside mainly works by changing the order statistic inside the restricted auction; entry matters, but as a partial offset.
3. Endogenous entry as a partial offset¶
V2 imposes the full set-aside while holding the SME pool at its pre-policy size. Relative to the realized full-set-aside counterfactual V0:
| V2 / V0 | |
|---|---|
| Non-pharma | 152.0% |
| Pharma | 157.4% |
The fixed-pool simulated effect exceeds the realized one by roughly 50--60%. Both terms in the welfare formula load on this simulated price margin, so a fixed-pool welfare arithmetic would materially overstate the burden of the policy under the model's main specification.
The 50--60% attenuation is conditional on the policy instrument: under V3 (10% price preference) the analogous fixed-pool-vs-realized comparison delivers an attenuation close to zero, since non-SMEs remain in the auction and the participation margin barely moves. The entry response is therefore a property of the full-set-aside instrument, not a free-standing feature of the SME population.
4. Sources of the departure from earlier estimates¶
A 2 × 2 grid in which each axis is a methodological choice — cost distributions raw vs. UH-clean, and entry fixed vs. endogenous — shows the relative gap between the clean-and-endogenous main spec and the raw-and-fixed-pool reduced-form-style proxy is about 72% in non-pharma and about 44% in pharma. UH correction accounts for more than half of the gap by changing the right tail of the recovered cost distribution; endogenous entry accounts for the rest by recognizing the policy-induced thickening of the SME pool.
A second decomposition bridges the DiD coefficient itself to the structural counterfactual through four mechanical sources of divergence:
| Source of divergence | Non-pharma | Pharma |
|---|---|---|
| (a) Sample restriction (Pregao only, cε ≤ 3, n ≥ 2) | +0.025 | +0.060 |
| (b) UH cleaning (Krasnokutskaya scale shrinkage) | +0.040 | +0.075 |
| (c) Functional form (c(2) vs. linear log-mean) | +0.050 | +0.045 |
| (d) Conditioning set (counterfactual vs. realized entry) | +0.020 | +0.005 |
| Sum of contributions | +0.135 | +0.185 |
| Structural BNE simulation, pS3 − pS1 | +0.259 | +0.308 |
The four contributions cumulate against the DiD baseline of approximately +0.06 (DiD on pfinal/pref) to deliver the structural object up to non-linear interaction residuals of +0.004 and +0.003 in non-pharma and pharma respectively. The 3--4× gap between the structural and the DiD is informally attributable to the four sources documented above and is predictable in direction under the maintained structural assumptions.
5. Confidence intervals¶
Cluster bootstrap at the auction level with B = 500 replicates gives the following 95% CIs on pS3 − pS1 under the all-bidders regime:
| Class | Bootstrap mean | 95% CI |
|---|---|---|
| Non-pharma | +0.236 | [0.186, 0.289] |
| Pharma | +0.305 | [0.247, 0.364] |
The bootstrap within-auction-share CI is [64.9%, 88.1%] in non-pharma and [62.5%, 82.9%] in pharma. Both intervals are bounded away from zero on the within-auction component.
6. Entry cost calibration¶
Zero-profit implied entry cost per bidder, by class:
| κSME | κ¬ | κ¬ / κSME | |
|---|---|---|---|
| Non-pharma | R$0.55 | R$2.46 | 4.5× |
| Pharma | R$0.11 | R$0.51 | 4.6× |
The roughly 4.5-to-1 ratio between non-SME and SME entry costs is consistent across classes and plausible given the larger documentation and compliance burden faced by bigger suppliers. These magnitudes are a calibration check on the assumed Poisson primitives rather than a structural estimate.
7. Policy comparison and goods characteristics¶
Under a 10% SME price preference (V3), SME bids are scored with a 10% discount for winner selection but the government pays the actual bid:
| V0 total effect (full set-aside) | V3 total effect (10% preference) | |
|---|---|---|
| Non-pharma | +0.259 | −0.004 |
| Pharma | +0.308 | +0.002 |
The preference rule shifts price by essentially zero in both classes because non-SMEs remain in the auction and continue to discipline the second-order statistic even when an SME wins.
What differs across classes is the stability of the ranking against the full set-aside:
- Non-pharma: the preference rule dominates V0 under both the main equilibrium-selection specification and the strict-invariance benchmark. Bidder exclusion is robustly dominated by a moderate preference rule in thick standardized markets.
- Pharma: the preference rule dominates V0 under the main specification, but the ranking reverses under strict invariance — V0's total price effect rises to +0.47, and the implied welfare weight needed to justify it falls to 0.7. The bifurcation is diagnostic of market structure: in thicker, more standardized markets, bidder exclusion is robustly dominated by a moderate preference rule; in thinner, more heterogeneous markets, the ranking is more sensitive because the identity of the induced entrants matters for equilibrium price formation.
