Price coefficient sign reverses — scope, not damages¶
Intuition (plain-language)
It is tempting to read "frequent losers present → higher prices" as a damages number — proof the cartel overcharges. Resist it. Once you compare only genuinely similar tenders, the sign flips to negative. A correlation that changes sign depending on the comparison set cannot be a clean estimate of overcharge. What the price pattern can tell you is where the loser-side signal is economically live (it bites in the high-value segment the framework predicts), not how much anyone was overcharged. Scope, not damages.
🟡 The price coefficient associated with the FL margin reverses sign when overlap discipline is applied, in a pattern that defeats the naive damages reading and supports a scope interpretation: prices tell us where the loser-side ranking is economically live, not how much anyone was overcharged. Price is a scope instrument here, not a damages estimate.
Headline progression (AN-037):
| Specification | FL price coefficient |
|---|---|
| Broad (full-FE, FL14 on price) | +0.064 (selection into higher-price cells) |
| Overlap-cell ATT (matched within same cell) | −0.097 (p ≈ 1.7×10⁻¹⁰; blocks the markup reading) |
| High-value quadrant (Q4) | +0.041 (the only positive surviving cell) |
The broad positive coefficient is selection into higher-price cells, not a treatment effect; once the comparison is disciplined to within overlapping cells the sign flips negative (−0.097, negative in 14/15 cells), and the only segment where the association stays positive is the high-value Q4 quadrant (+0.041) — the segment the framework predicts the signal should bite. Against the 47 direct CADE defendants the price association is null, consistent with the scope (not damages) reading.
RDD coefficients across bandwidths are stable and small (+4.3%, +5.5%, +6.0%; AN-019); the McCrary density ratio at the cap is 0.94 (no bunching). The DiD around Decreto 9.412/2018 returns null on FL × cap interaction (AN-020).
Modal asymmetry (AN-016, AN-022):
| Modality | Binary FL coef | Continuous FL coef |
|---|---|---|
| Pregão | +9.59% (p < 10⁻³) | +2.62% |
| Convite | +3.92% (p = 0.037) | +1.24% |
Pregão/Convite ratio: 2.45× (binary), 2.11× (continuous).
Joint-specification sign reversal (AN-015, AN-022): when FL14 binary and continuous log_tc enter together, the FL14 coefficient flips negative (−0.075 in the full sample) while the continuous coefficient remains positive (+0.035). The binary picks up truncation noise that the continuous score absorbs.
Descriptive decomposition (AN-039, AN-040): the reversal decomposes into a positive across-cell selection component (non-treated price rises Δ = 5.58 log-points with cell FL-share; full-FE coefficient +3.55) and a negative within-cell association (winner-to-reference −0.048, accounted for by +0.507 log-bidders), exchanging sign at the tender-density margin. These are descriptive associations consistent with economic non-neutrality; they do not identify a mechanism, a causal price effect, overcharges, or damages. In particular, the cover-bidding "theater" mechanism is not identified — the price pattern is consistent with it but cannot establish that any firm staged deliberate losing bids. The manuscript (§7 / Appendix E) keeps the decomposition as scope evidence, subordinate to the evidence-allocation claim.
The sign reversal is, by itself, the load-bearing piece of legal disciplining: a screening tool that confused scope with damages would overreach in court, and the manuscript explicitly separates the two. The finding therefore enables the legal-economic claim of §7 rather than contradicting it.
Caveat. The sign reversal reading is consistent with the scope interpretation under the assumption that the adjudication-anchored exposure target is correctly identified. The price evidence is descriptive and supportive — not a counterfactual welfare exercise. The reading is 🟡 and explicitly not the headline of the paper; price evidence is framed as secondary to the triage and cobidder-concentration results.
Sources.
- Own analysis: AN-019 (RDD price + overlap ATT), AN-020 (DiD around decree), AN-016 (modal AUC asymmetry), AN-022 (modal falsification), AN-015 (joint-spec sign flip), AN-037 (headline three-spec progression +0.064 → −0.097, p = 1.7 × 10⁻¹⁰; within- overlap subgroup negative in 14/15 cells), AN-038 (item- group segment betas; group 37 −0.126 stays negative across specs), AN-039 (across-cell selection component, descriptive), AN-040 (within-cell association via bidder count, descriptive — not mechanism identification).
- Cross-refs: H:price-scope-sign-reversal; docs/extensions.md.
- Macros:
\valBetaBroad(+0.064 selection),\valBetaOverlapATT(−0.097),\valBetaQfour(+0.041 Q4-only positive),\valBetaCADENonDirect(−0.097; direct-CADE price null),\valFalBinPregCoef(+9.59%),\valFalBinConvCoef(+3.92%),\valFalBinRatio(2.45×),\valMcCraryRatio(0.94),\valMatchPSCoef(−30.67%). - Validation: backing scripts
scripts/13_rdd_cap.R,scripts/14_did_decreto_2018.R,scripts/37_gate_d2_modal_auc.R,scripts/46_falsification_pregao_only.R,scripts/51_item_level_scope_match.R,scripts/59_sign_reversal_decomp.R.