AN-011: Horse race — continuous vs binary FL¶
Intuition (plain-language)
The screen comes in two forms — a binary flag (bid count above the cutoff) and the continuous log of bid count. The continuous score carries strictly more information and statistically dominates the binary (0.939 vs 0.924; DeLong p ≈ 10⁻⁵). The reading: the empirical primitive is loss intensity, a continuous quantity; FL14 is just the auditable on/off rule a regulator can defend in the field. The binary is for deployment, the continuous is for the underlying truth.
Question¶
Does the continuous log(1 + tenders_count) dominate the binary FL14
on the cobidder target? The binary rule is auditable but the continuous
score carries the full information.
Design¶
- Sample: harmonized same-sample set in BEC 2009–2019; N = 1,653,658 item-firm observations.
- Specifications: AUC of
FL14(binary) vslog(1 + tenders_count)(continuous). - Statistical test: DeLong AUC-difference test on paired predictions.
- Auxiliary: price coefficients in three configurations (FL14 alone, continuous alone, joint).
Results¶
| Score | AUC | 95% CI |
|---|---|---|
| FL14 (binary) | 0.924 | [0.921, 0.926] |
| Continuous log(1+tenders_count) | 0.939 | [0.932, 0.946] |
DeLong test: continuous dominates the binary flag (Z = −4.38, p = 1.2 × 10⁻⁵); the gap is 0.015 under the corrected FL14 (≥ 14) definition. The D1 re-run (2026-05-25) confirmed the direction; the earlier Z = −4.30 / p = 2 × 10⁻⁵ were computed under the superseded (> 14, i.e. FL15) cut.
Auxiliary price coefficients (item × year × PBU FE):
| Specification | FL coef | SE | Continuous coef | SE |
|---|---|---|---|---|
| FL14 binary alone | +0.0653*** | 0.0216 | — | — |
| Continuous alone | — | — | +0.0188*** | 0.0055 |
| Joint | −0.0746* | 0.0383 | +0.0349*** | 0.0108 |
Macros: \valAUCFLfirm, \valAUClogtc, \valDeLongZ, \valDeLongP,
\valHorseFLOne, \valHorseFLOneSE, \valHorseContTwo,
\valHorseFLThree, \valHorseContThree.
Figure: AUC point estimates with 95% CIs for the FL14 binary flag and continuous log(1+tenders_count). Continuous dominates; FL14 is the deployable simplification. Point estimates from the D1 re-run (2026-05-25); see the table above.
Interpretation¶
The continuous score dominates the binary at p < 10⁻⁴. FL14 is the
auditable deployable rule; the true signal is the continuous loss
intensity. This is the result that motivated the locked rule of
engagement: "loser-side concentration" is the concept; "frequent
losers" is the operational implementation. The paper's FL14 cutoff is
not defended as ontologically special — it is the operational
auditable layer over the continuous primitive.
In the joint price regression, the FL14 coefficient flips negative once the continuous score is included — the binary picks up a truncation-induced residual that the continuous score absorbs. This sign reversal is part of the price-scope evidence (AN-019, H:price-scope-sign-reversal).