H:sme-winner-share-falls — Open auctions reduce the probability that the winner is an SME¶
If non-SMEs are systematically lower-cost on the price-forming margin than SMEs are, allowing them into the auction should reduce the share of SMEs that win. The composition channel is a direct consequence of the same primitive that drives the price effect: type-specific willingness-to-supply distributions differ between SMEs and non-SMEs.
Intuition (plain-language)
If non-SMEs are genuinely cheaper on the margin that wins contracts, then opening the auction to them means SMEs win less often. That drop in the SME win share is not a separate phenomenon — it is the same cost-gap primitive that drives the price effect, read on the composition margin instead of the price margin.
Evidence strength: Partial (strongly supported). Three converging measures of the composition shift: Gelbach decomposition (AN-008) loads +185% on the SME-winner mediator; reduced-form SME-winner DiD (AN-009); RAIS-validated SME (≤49 employment) winner DiD (AN-028): −21 pp at 18m. The 21 pp shift on the administratively-recorded RAIS-validated indicator (orthogonal to BEC self-reported SME status) is the cleanest available test. The price effect itself survives restriction to RAIS-validated SMEs (β = −0.121* in SME-only subsample), so composition is one of several channels, not the entirety.
Theory¶
In an independent-private-values English auction, the winner is the lowest-cost active bidder. If non-SMEs draw from a stochastically lower type-conditional cost distribution than SMEs do, removing them flips the winner from a non-SME to an SME with positive probability. The composition shift is a direct mechanical consequence of the type-cost gradient — and only one component of the total price effect, since the remaining SMEs also reset their bids in the absence of the disciplining non-SMEs.
Prediction¶
The probability that the winning firm is an SME in switched group 65 should be lower in the pre-period (open) than in the post-period (SME-only), relative to always-treated controls. A Gelbach decomposition of the price effect should load a substantial share onto the SME-winner mediator.
Competing prediction¶
Sample-selection on completion. The probability of completion may differ between open and SME-only regimes, biasing the conditional SME-winner share. The Lee bounds in AN-005 speak to the price-margin selection but not directly to the composition margin. A composition-margin Lee bound is on the open-test list.
Setting evidence¶
BEC records the CNPJ of the winning firm. SME status is computed from the Receita Federal CNPJ-Raiz registration grain (where SME-eligibility is set under the federal SME law's revenue thresholds). The composition margin is well-defined for every completed item.
Empirical test¶
- Outcome variable: 1{winner is SME}, by item.
- Variation: DiDiR; Gelbach short-vs-full decomposition.
- Specification: linear probability model with item FE; Gelbach comparison adds (i) log firms, (ii) SME-winner as mediators to the short price equation.
- Sample: completed items.
Data requirements and limitations¶
The SME-winner indicator depends on the CNPJ-Raiz revenue classification, which is updated annually. Firms that cross the SME threshold mid-window are treated by their latest classification — a small share but worth flagging. The Gelbach decomposition does not separate the type-cost gradient from selection into the pool; that is the job of the structural decomposition (H:exclusion-dominates).
Evidence¶
| Analysis | Bearing | Key takeaway |
|---|---|---|
| AN-008 | Supports | Composition channel +185% of the Gelbach gap; competition channel −85% (partial offset). Large unexplained (~−0.123) component remains in the full regression. |
| AN-009 | Supports | Reduced-form extensions: open competition lowers SME winner probability; effect symmetric across direct/indirect administration PBUs. |
| AN-028 | Supports | RAIS-validated SME winner indicator falls −21 pp (18m DiDiR). Price β survives SME-restricted subsample (−0.121***); composition is one of several channels, not the entirety. |
Open tests¶
Composition-margin Lee bounds¶
The Lee (2009) selection-bound logic applied to the SME-winner indicator would tighten the composition reading against differential completion. Not yet specified.
Cross-cut by non-SME firm size¶
If the composition shift is driven by large non-SMEs winning under open, the result has different policy interpretation than if it is driven by marginal non-SMEs barely above the SME threshold. A RAIS-employment quartile cut on winners (planned, not run) would distinguish them.