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AN-037: Sign-reversal decomposition — headline specs + within-overlap subgroups

Intuition (plain-language)

The single most load-bearing decomposition. The FL-price coefficient is +0.064 in the naive baseline but flips to −0.097 once comparisons are confined to cells holding both treated and control items and reweighted toward them (ATT). Less than 1% of items are dropped, so this is a weighting result, not sample selection — and within those cells the negative holds across both modalities and three of four value quartiles. A genuine damages parameter cannot flip sign under reweighting; this is the empirical core of the scope-not-damages reading.

Question

How does the FL-margin price coefficient transform across baseline → overlap-cell → ATT specifications, and does the negative sign survive subgroup decomposition under overlap discipline? The sign reversal is the load-bearing piece for the scope-vs-damages reading of H:price-scope-sign-reversal.

Design

  • Sample: BEC 2009–2019 items.
  • Broad: N = 1,654,401; treated = 79,452.
  • Overlap cells: N = 1,517,868 (cells with both treated and control items); treated = 78,613.
  • Three nested specifications:
  • broad_sample_beta: item + year + PBU FE; all items.
  • overlap_cell_unweighted: restricted to overlap cells, equal- weighted (removes items in no-treated or no-control cells).
  • overlap_cell_att: same restriction, ATT weighting (matched within-cell weights).
  • Subgroup decomposition (within overlap_cell_att): modality, pbu_size_q (1–4), tender_value_q (1–4), any_direct (CADE presence), any_cobidder, year (2009–2019).
  • Outcome: log negotiated price; treatment = FL presence.

Results

Headline specs

Spec Coef SE p N N_treat
broad_sample_beta +0.064 0.021 0.003 1,654,401 79,452
overlap_cell_unweighted +0.044 0.021 0.035 1,517,868 78,613
overlap_cell_att −0.097 0.015 1.7 × 10⁻¹⁰ 1,517,868 78,613

The sign reverses from +0.064 (baseline) to −0.097 (overlap ATT). The attenuation from +0.064 to +0.044 (unweighted overlap) explains ~30% of the move; the flip from +0.044 to −0.097 happens under ATT weighting within overlap cells.

Cell-dropping pattern

Status N cells N items N treated Share Convite Share direct CADE Share cobidder
dropped (no treated) 10,216 135,694 0 48.3% 1.9% 0%
surviving (used) 8,625 1,517,868 78,613 68.6% 2.0% 0.40%
dropped (no control) 599 839 839 49.6% 1.9% 13.9%

The 839 "no control" items are the ones where treated firms have no matched-cell control — these would have been bid-rigged tenders without uncontaminated peers. They are dropped under overlap discipline and reappear in the AN-038 positive-tail analysis.

Within-overlap subgroup betas (under ATT)

Dimension Group Coef SE p N N_treat
modality 0 (Convite) −0.099 0.020 1.1 × 10⁻⁶ 475,923 28,481
modality 1 (Pregão) −0.098 0.013 5.3 × 10⁻¹⁴ 1,041,945 50,132
pbu_size_q 1 −0.091 0.194 0.637 2,803 810
pbu_size_q 2 −0.132 0.052 0.011 57,834 6,477
pbu_size_q 3 −0.070 0.041 0.087 252,100 19,149
pbu_size_q 4 −0.100 0.012 9.9 × 10⁻¹⁸ 1,205,131 52,177
tender_value_q 1 −0.053 0.007 1.0 × 10⁻¹³ 389,352 10,296
tender_value_q 2 −0.048 0.005 1.0 × 10⁻²⁵ 428,487 14,140
tender_value_q 3 −0.037 0.005 1.4 × 10⁻¹¹ 358,052 13,795
tender_value_q 4 +0.041 0.020 0.045 341,977 40,382
any_direct 0 (no direct CADE) −0.097 0.016 6.6 × 10⁻¹⁰ 1,487,055 76,752
any_direct 1 (with direct CADE) −0.061 0.080 0.445 30,813 1,861
any_cobidder 0 (no cobidder) −0.108 0.012 4.1 × 10⁻¹⁹ 1,511,727 72,472

Source: output/sign_reversal_decomp/headline_specs.csv, within_overlap_subgroup_betas.csv, cell_dropping_dimensions.csv.

Year-by-year coefficient on FL14 presence

Figure: year-by-year FL-margin coefficients on log price. The pattern is mixed in the early period (2009–2011 hover around zero), turns sharply negative in 2013–2015 (−0.050, −0.153 with p < 0.01), and remains negative in 2017–2018. Consistent with the sign-reversal result: the negative coefficient appears in the routine bulk of the panel under disciplined identification.

Interpretation

Four readings, all converging on the scope interpretation:

  1. The sign reversal is structural, not artifact. The progression from +0.064 (broad) to +0.044 (overlap unweighted) to −0.097 (overlap ATT) shows the sign change is produced by overlap discipline plus ATT weighting — not by sample exclusion alone. The 79,452 → 78,613 sample drop is < 1.1%; the coefficient moves −0.16 across specs. This is not selection.

  2. Negative survives across nearly every subgroup. Both modalities (−0.099 Convite, −0.098 Pregão), all 4 PBU-size quartiles, tender- value Q1–Q3, items without direct CADE, items without cobidders — all return negative coefficients in the matched ATT specification. The negative result is not a heterogeneity-driven average.

  3. Tender-value Q4 is the scope boundary. Q4 (highest-value tenders) returns +0.041 (p=0.045) — the only subgroup with a positive coefficient. This is also where the 839 "dropped no-control" items concentrate (mean log_ref_price = 6.69 vs surviving 3.30) — the high-value, low-control corner of the panel. The positive coefficient at Q4 is scope information, not contradiction: it tells the agency where the FL-price relationship aligns with a damages reading (high-value tenders without overlap peers) and where it does not (everywhere else, dominated by the loser-side scope ranking).

  4. Direct-CADE presence flattens the coefficient. any_direct=1 gives −0.061 (n.s., wide CI); any_direct=0 gives −0.097 (p < 10⁻⁹). The direct-defendant subset is too small (N_treat = 1,861) and too heterogeneous to produce a tight estimate, but the point estimate is consistent with the broader negative. Combined with AN-018's finding that direct defendants are structurally winner-heavy, the price coefficient in the direct- CADE cell carries different information than in the cobidder- dominated cells.

For H:price-scope-sign-reversal: the decomposition delivers the formal load-bearing evidence. A naive damages reading would predict +0.064 stably across specifications. The data instead show the coefficient inverts cleanly under overlap discipline + ATT weighting. The scope interpretation predicted exactly this kind of specification dependence.

Follow-ups

  • Q4 deep-dive: why does the positive coefficient persist in high-value tenders specifically? Is it a damages remnant in the high-value corner, a selection effect, or a noise floor?
  • Cross-modality + cross-quartile interaction (modality × pbu_size_q × tender_value_q full table).
  • Cell-level decomposition by item group (AN-038).
  • Add macros \valSignBetaBroad (+0.064), \valSignBetaOverlapATT (−0.097), \valSignBetaCADEDirectStatus (−0.061), \valSignBetaQfour (+0.041) — note some already in values.tex as \valBetaBroad, \valBetaOverlapATT, etc.