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AN-039: Selection Mechanism Test (Test 1 of the Sign-Reversal Rationalization)

Intuition (plain-language)

First half of the explanation for the sign flip: selection. If cartels with cover bidders deliberately operate where the underlying product is structurally expensive (richer rents to capture), the naive positive coefficient is just sorting, not a price effect. The test looks only at NON-treated items: their prices climb monotonically with a cell's FL-share, and after full controls FL-share still predicts higher non-treated prices (+3.55). Cartels fish where the fish are expensive — that alone produces a positive raw correlation with no overcharge.

Question

Test 1 of the rationalization for the FL-price sign-reversal. The overlap-cell ATT result (−0.097, p < 10⁻⁹, AN-037) is interpreted in the manuscript as scope information rather than damages. A stronger substantive reading is that the sign reversal decomposes into a selection effect (positive across cells) and a within-cell mechanism effect (negative). This page tests the selection component: do cartels with cover bidders systematically end up in cells with higher underlying price levels, independent of any FL margin effect?

Design

  • Cell definition: same as scripts 51 and 59 — interaction(item_group, year, convite, pbu_size_q, tender_value_q, drop = TRUE).
  • Overlap cells: cells containing both treated (losers == 1) and untreated (losers == 0) items. 8,625 cells, 1,517,868 items.
  • Outcome: lneg_price (log of negotiated unit price) among non-treated items only (losers == 0). Sample: 1,439,255 non-treated items in overlap cells.
  • Predictor: cell-level fl_share = mean(losers == 1) for each cell.
  • Test 1a: bin cells by FL-share quintile; report mean log_price (non-treated only), weighted by N items per cell.
  • Test 1b: item-level OLS lneg_price ~ fl_share with three FE configurations.
  • Test 1c: Q5 vs Q1 difference.

Results

Test 1a: Mean non-treated log_price by cell FL-share quintile

FL-share quintile N cells N items N non-treated Mean non-treated log_price Mean cell FL-share
Q1 (lowest) 1,737 633,644 625,315 1.35 1.4%
Q2 1,713 430,039 414,506 2.40 3.7%
Q3 1,753 278,121 257,889 4.02 7.4%
Q4 1,703 129,933 111,486 5.47 15.3%
Q5 (highest) 1,719 46,131 30,059 6.93 41.3%

Monotone increase across quintiles. The relationship is not subtle.

Test 1b: Item-level OLS — log_neg_price (non-treated only) ~ fl_share

Specification fl_share coef SE N
Raw OLS (no FE) +22.65 0.033 1,439,255
+ item_group + year FE +24.04 0.555 1,439,255
+ all 5 cell-dimension marginal FE +3.55 0.229 1,439,255

The coefficient drops substantially when all 5 cell dimensions are included as marginal fixed effects — most of the raw selection is absorbed by the dimension marginals (item_group, year, modality, PBU-size quartile, tender-value quartile). But a +3.55 log-point coefficient remains after partialling out each dimension separately. Cartels select into high-price cells beyond what is captured by any single dimension.

Test 1c: Q5 vs Q1 comparison

  • Q1 mean non-treated log_price: 1.35
  • Q5 mean non-treated log_price: 6.93
  • Δ (Q5 − Q1): +5.58 log-points (≈ 265× nominal price ratio)

This is not a "5% premium for high-FL cells"; it is a structural ordering of product-buyer-modality-period-value strata. Cells where cartels concentrate are cells where the products being procured are fundamentally higher-priced (different goods, different procurement volumes).

AN-039 Test 1: selection mechanism

Figure: Panel A — mean log_neg_price among non-treated items rises monotonically from Q1 (1.35) to Q5 (6.93) across cell FL-share quintiles; Δ Q5 − Q1 = 5.58 log-points ≈ 265× nominal price ratio. Panel B — same data plotted against the cell's continuous FL-share shows a clean slope. Panel C — item-level OLS coefficient of fl_share on log_neg_price (non-treated items only) across three FE specifications: raw +22.65, with item+year FE +24.04, with all 5 marginal cell-dimension FE +3.55. The selection effect remains positive and highly significant even after partialling out each cell-dimension marginal effect.

Verdict

Test 1 PASSES. Selection mechanism is empirically real and large. The criterion was: Δ(Q5 − Q1) > 0.05 AND fully-FE-controlled coefficient

  1. Observed: Δ = 5.58, full-FE coefficient = +3.55 (SE 0.23, p < 10⁻⁵⁵).

Sources: output/selection_mechanism/selection_test_results.csv, output/selection_mechanism/non_treated_price_by_fl_share.csv.

Interpretation

The selection mechanism is the first half of the sign-reversal rationalization. Cartels with cover bidders are not randomly distributed across procurement cells — they systematically concentrate in cells where the underlying product value (and rent potential) is higher. The naive positive FL-price coefficient (+0.064 in the broad specification) therefore reflects, at least in part, this selection into high-value markets rather than any causal effect of FL presence on prices.

The decomposition logic:

Component Specification Coef Reading
Total Broad OLS with item+year+PBU FE +0.064 Joint effect of selection + mechanism + cross-cell
Selection (composition) Non-treated price ~ fl_share, full FE +3.55 Cartels in high-price cells
Mechanism (within-cell) Overlap-cell ATT −0.097 Cover-bidding theater depresses observed prices within cell

The two components have opposite signs and very different magnitudes. The selection effect (+3.55 on log-price per unit fl_share, where fl_share ranges 0–0.5) dominates the broad coefficient. The within-cell mechanism (−0.097) is what survives once selection is removed by ATT weighting.

For H:price-scope-sign-reversal: the sign-reversal is not merely a specification artifact. It is the empirical signature of a two-component decomposition: cartels with cover bidders select into high-rent cells (positive across cells) and depress observed prices within those cells via the cover-bidding theater (negative within cell). The overlap-ATT spec removes the selection and isolates the mechanism.

In the manuscript (§7) this is reported as descriptive scope evidence, not mechanism identification: the sign-reversal is consistent with the cover-bidding interpretation, but the paper explicitly states it does not identify a mechanism, a causal price effect, overcharges, or damages. The within-cell component is documented in Test 2 (AN-040): within overlap cells FL presence is associated with bidder-count inflation (+0.507 log-bidders) and a winner bid −0.048 closer to reference — a descriptive association consistent with economic non-neutrality, kept subordinate to the evidence-allocation claim.

Follow-ups

  • Test 2 (mechanism component): completed in AN-040 — within overlap cells FL presence moves the winner bid −0.048 closer to reference and the effect runs through bidder-count inflation (+0.507 log-bidders), completing the rationalization. (Done, 2026-05-22.)
  • Sub-period stability of the selection coefficient (does the monotone gradient hold in 2009–2013 vs 2014–2019?).
  • Cross-modality decomposition (does the Pregão vs Convite asymmetry in AN-016 reflect different selection patterns?).
  • Add macros \valSelTestQOne (= 1.35), \valSelTestQFive (= 6.93), \valSelTestDelta (= 5.58), \valSelTestCoefFullFE (= +3.55), \valSelTestSEFullFE (= 0.23) to the scripts/99_make_paper_values.R pipeline.