AN-029: Price effect at fixed bidder count — composition, not headcount¶
Intuition (plain-language)
Does open competition lower prices only by adding bidders? Fix the bidder count at exactly 2, 3, or 5+ and the price effect persists — so it is not pure headcount. The reason, in the paper's order-statistic reading, is who is in the pool: with the count held fixed, removing low-cost non-SMEs and leaving higher-cost SMEs raises the price-forming (second-lowest) draw. It also lifts the share of tenders that actually complete by about 11 percentage points. This is a composition/admissibility effect, not firms choosing to "bid harder."
Framing: order statistic, not behavioral aggressiveness
The v8 manuscript reads Pregão drop-outs as willingness-to-supply under the IPV clock, so the mechanism is which order statistic forms the price — not that protected firms "bid less aggressively" (§3, §2 explicitly: "an admissibility effect rather than evidence of less aggressive SME bidding"). The fixed-N evidence on this page is therefore evidence for the composition / order-statistic channel inside lost-discipline, not for a behavioral per-bidder-aggressiveness channel. The page is worded accordingly.
Question¶
AN-002 shows open competition raises the number of bidder firms by 10–22%. The natural reading is that more firms → lower prices via the auction-thicker-pool channel. But two complementary questions are open:
- Extensive margin: does open competition affect the probability that an auction successfully procures (completion rate)?
- Composition vs headcount: does the price effect persist when the bidder count is held fixed? If it does, the effect is not purely the mechanical addition of bidders — it reflects which bidders are in the pool (composition), which in the order-statistic reading shifts the price-forming draw.
The first asks whether open competition expands the set of successful auctions; the second asks whether the price effect is headcount alone or also the composition of the eligible pool at a given count.
Design¶
- Sample:
- (a) BEC all items, 6/12/18-month windows.
- (b) BEC completed items 18m, conditioned subsamples with fixed number of firms (\(N \in \{2, 3, \geq 5\}\)).
- (c) BEC completed items 18m, runner-up bid observed.
- Specifications:
- (a) Extensive margin: DiDiR with outcome \(1\{\text{item completed}\}\); group FE; PBU FE in second column; item-clustered SE.
- (b) Conditional-on-N price effect: re-estimate the DiDiR price coefficient on subsamples with fixed bidder counts. If the price effect were purely from headcount, conditioning on fixed \(N\) should kill it.
- (c) Runner-up gap: outcome = normalized gap \((p^{(2)} - p^{(1)}) / p^{\mathrm{ref}}\) — a smaller gap signals the second-lowest (price-forming) draw sits closer to the lowest, which in the order-statistic reading reflects a lower-cost eligible pool.
- Identification threats: completion margin may interact with selection of which items get bids; runner-up gap analysis requires the runner-up to be observed (N ≥ 2).
Results¶
(a) Extensive margin (completion rate) (tab_extensive.tex):
| Window | Base β | PBU-FE β | N |
|---|---|---|---|
| 6m | +0.117*** (0.004) | +0.118*** (0.004) | 304,392 |
| 12m | +0.124*** (0.004) | +0.127*** (0.004) | 609,299 |
| 18m | +0.107 (0.003)* | +0.113 (0.003)* | 901,506 |
Open competition raises the tender completion rate by +10.7 pp (18m baseline). Highly significant in all windows.
(b) Price effect conditional on fixed bidder count N
(tab_bid_aggressiveness.tex):
| Subsample | β on \(g65 \times \text{Pre}\) | SE | N |
|---|---|---|---|
| Baseline (all firms) | −0.1087*** | (0.012) | 649,714 |
| N = 2 firms (fixed) | −0.0926*** | (0.017) | 105,957 |
| N = 3 firms (fixed) | −0.1076*** | (0.018) | 102,831 |
| N ≥ 5 firms (fixed) | −0.1073*** | (0.021) | 260,530 |
The price effect is essentially unchanged when we fix the bidder count. Even when restricted to auctions with exactly 2 firms (the minimum competitive count), the DiDiR price effect is −0.09*** — about 85% of the unconditional baseline.
(c) Runner-up bid gap (tab_runnerup_gap.tex):
| Subsample | Normalized gap β | Log-gap β | N |
|---|---|---|---|
| Full sample | −0.0271 (0.005)* | −0.0188 (0.003)* | 471,344 |
| N = 2 firms | +0.0071 (n.s.) | +0.0035 (n.s.) | 69,634 |
| N = 3 firms | −0.0121 (n.s.) | −0.0092 (n.s.) | 81,249 |
| N ≥ 5 firms | −0.0104* (0.005) | −0.0082** (0.004) | 245,002 |
Under open competition the normalized winner-to-runner-up gap shrinks by 2.7 percentage points (full-sample, p<0.01). In the order-statistic reading, the second-lowest (price-forming) willingness to supply sits closer to the lowest because the eligible pool includes lower-cost non-SMEs — a composition effect on the gap, not a behavioral change in how aggressively any one firm bids.
Output: output/tables/tab_extensive.tex,
tab_bid_aggressiveness.tex, tab_runnerup_gap.tex.
Interpretation¶
Pure-headcount explanation rejected. If open competition lowered prices only because more firms bid, then fixing the number of firms should kill the price effect. It does not. At N = 2 (minimum competitive), the price effect is β = −0.093 — 85% of baseline. At N ≥ 5, it is −0.107 (essentially the same as the unconditional −0.109* baseline). The composition channel is therefore real: at a given bidder count, which firms are eligible moves the price-forming order statistic.
The price-forming gap narrows in larger auctions. The gap-shrinking at N ≥ 5 (β = −0.010*) but not at N = 2 or N = 3 is consistent with the order-statistic reading: in thicker pools the second-lowest willingness-to-supply draw sits closer to the lowest. Under the maintained IPV clock this is a property of the draw distribution and pool composition, not a strategic change in how any one firm bids.
Extensive margin is real. A 10.7 pp rise in completion rate is economically large — open competition not only lowers prices on completed items but increases the share of items that successfully procure. The two effects multiply: more auctions reach successful completion, AND those completed auctions deliver lower prices.
Reading for H2. The "open auctions thicken the bidder pool" prediction holds on three fronts: - More firms participate (AN-002: +10–22%) - The auctions successfully complete more often (this AN: +10.7 pp) - The price effect is composition-driven, not headcount-only: it survives fixing \(N\), and the price-forming gap narrows in thicker pools (this AN)
The unconditional reduced-form price effect (~−0.11, 18m) therefore combines more entrants, more completions, and a composition shift in the eligible pool at any given count. The structural model in AN-010 refines this into the exclusion-vs-protected-pool split; the fixed-N composition result is direct evidence for the order-statistic channel inside lost-discipline — not for a behavioral per-bidder-aggressiveness channel, which the v8 manuscript explicitly disavows.
Confidence: yellow. Three separate channels are documented with independent tests. The reading is yellow because: - The N-conditioned subsamples are not random samples — items with exactly 2 firms differ from items with 5+ firms in observables (value, complexity). The price-effect persistence under fixed N is informative but not a clean test of aggressiveness alone. - The runner-up gap narrowing is consistent with the order-statistic / composition reading, but the design cannot fully separate it from any residual within-firm behavioral response; the IPV-clock interpretation (H:ipv-clock-admissible) is maintained, not proven.
Follow-ups¶
- Within-firm bid behavior across the policy break: for firms that bid in both pre and post periods, compare bid moments. A within-firm shift in mean bid (relative to reference) would isolate the per-bidder composition channel from any residual within-firm behavioral response. Not yet authored as a standalone AN.
- Newcomer firms: which firms participating post are new entrants to BEC vs returning bidders? If many SMEs are newcomers, the entry response is real expansion not rotation.
- Item-complexity heterogeneity: the conditional-N analysis would benefit from a within-PADRAOdesc cross-cut.