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 applies, not how much the cartel overcharges.
Headline reversal (AN-019):
| Specification | FL price coefficient |
|---|---|
| Baseline FE (FL14 on price) | +6.36% |
| Overlap-cell ATT (matched within same cell) | −9.72% |
| PS ATT (trimmed) | −30.67% |
The sign flips when the comparison stratum is disciplined to within- cell. 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. 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 loser-side adjacency 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:
\valMatchBaselineCoef(+6.36%),\valMatchOverlapCoef(−9.72%),\valMatchPSCoef(−30.67%),\valFalBinPregCoef(+9.59%),\valFalBinConvCoef(+3.92%),\valFalBinRatio(2.45×),\valMcCraryRatio(0.94),\valRDDtight/Mid/Wide. - 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.