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H:parallel-trends-hold — Pre-treatment placebos null, HonestDiD survives M̄ violations, Lee bounds tight

The DiDiR design identifies the open-vs-SME-only effect by comparing the switched group 65 to the always-treated control groups. Identification requires that, absent the policy reversal, group 65 prices would have moved in parallel with the control groups. Three complementary checks test this: pre-treatment placebos (which apply the DiDiR to a fake pre- treatment date and should yield null), HonestDiD (which constructs robust CIs under controlled M̄ violations and should keep the effect significant), and Lee bounds (which tighten the price coefficient against differential completion).

Intuition (plain-language)

The design assumes that, absent the policy reversal, Group 65 prices would have tracked the control groups. You cannot observe that counterfactual, but you can stress it: fake-date placebos should find nothing, the effect should survive controlled violations of parallel trends, and selection on which auctions complete should not move the estimate. All three checks hold, so the comparison is credible.

Evidence strength: Partial (strongly supported). Six convergent identification checks now back the design. Sun-Abraham (item-level) ATT 0.108 reproduces DDR 0.113 within 0.005 on log prices, with similar tight convergence on firms and distance (AN-018). Callaway-Sant'Anna at group×month gives 0.237* — same direction, wider SE due to aggregation level. Goodman-Bacon decomposition reports 100% weight on the clean Treated-vs-Untreated 2×2 — the heterogeneous-timing-bias concern does not apply to this single-cohort design (AN-020). Synthetic control with Ridge augmentation matches group 65's pre-treatment trajectory exactly (L2 imbalance 0.0000); post-period ATT 0.171 in the same direction; placebo \(p = 0.103\) borderline (AN-021). Plus placebo nulls on prices (AN-004), tight Lee bounds (AN-005), and HonestDiD survives M̄ (AN-006). Three of four estimators (DDR, SA, GB) earn green or near-green; synth's placebo \(p = 0.103\) is the one open piece of the gauntlet.

Theory

DiDiR identification of the pre-switch-period effect requires parallel trends in the absence of the policy reversal. The standard battery (Roth, Sant'Anna, Bilinski and Poe 2023): - Pre-treatment placebos: applying the DiDiR specification to a fake pre-treatment date should yield null if parallel trends hold. - HonestDiD: Rambachan and Roth (2023) construct robust CIs allowing the post-treatment trend to deviate by at most M̄ in some sense from the pre-treatment path. - Lee bounds: Lee (2009) bounds correct the price coefficient against differential completion (the price equation conditions on completed items).

Prediction

(i) Pre-treatment placebos on the price outcome should be small in magnitude and statistically insignificant. (ii) HonestDiD CIs should exclude zero for M̄ up to at least the empirical pre-trend magnitude. (iii) Lee bounds on the price coefficient should be tight (lower-upper gap small) and both endpoints significant.

Competing prediction

Differential pre-trends. If group 65 prices were already on a differential downward path before March 2018, the DiDiR coefficient captures the trend extrapolation rather than the policy effect. The placebo test directly addresses this: a significant pre-treatment coefficient would reveal the differential trend. The price-margin placebo is null; firm-count and bid-count placebos are significant but reflect the control groups' gradual SME restriction rollout, not a group-65-specific shock — see H:entry-thickens-pool.

Setting evidence

The pre-treatment period is long enough to test trend stability. The placebo design uses Sep 2017, Mar 2017, and Jun 2017 as fake treatment dates, splitting the pre-period into nominal "pre" and "post" halves while applying the same DiDiR specification.

Empirical test

  • Pre-treatment placebos: DiDiR with fake treatment dates Sep 2017, Mar 2017, and Jun 2017; price coefficient should be small relative to the real cutoff.
  • HonestDiD: Rambachan-Roth bounds on the post-treatment trend deviation; the price effect should remain significant for moderate M̄.
  • Lee bounds: Lee (2009) selection-bound formula applied to the conditional price coefficient under differential completion rates.
  • Staggered-DiD estimators: Callaway-Sant'Anna (2021) and Sun-Abraham (2021) reproductions to address heterogeneous-timing bias.

Data requirements and limitations

The placebo test uses pre-treatment data only; the post-treatment period is excluded from the test by construction. HonestDiD requires the event-study specification (already in docs/results.md). Lee bounds require the completion indicator (already in BEC). Callaway-Sant'Anna requires defining treatment cohorts; since group 65 is a single switching event, the staggered application is to the control groups' rollout history, not to group 65 itself.

Evidence

Analysis Bearing Key takeaway
AN-004 Supports Pre-reform price placebos small and negative: β = −0.013 / −0.030 / −0.034 at Sep / Mar / Jun 2017, all far below the real-cutoff −0.108 to −0.142 range — not driving the main result.
AN-005 Supports Bounds −0.131 to −0.123, both highly significant; differential completion has negligible impact.
AN-006 Supports Price effect remains significant under substantial M̄ violations.
AN-018 Supports Sun-Abraham item-level ATT 0.108 vs DDR 0.113 (Δ<0.005 on log prices); CS2021 group-month 0.237* same direction; convergence across three estimators on direction, on magnitude for SA.
AN-020 Supports (green) Weight = 1.000 on clean Treated-vs-Untreated 2×2; zero forbidden comparisons. Heterogeneous-timing-bias mathematically absent in this single-cohort design.
AN-021 Mixed Pre-treatment gap 0.0000 (parallel trends enforced); post ATT 0.171 directionally consistent; placebo p=0.103 borderline (not significant at 5%).
AN-023 Supports Dropping the 8-month BEC enablement window reduces β from −0.109 to −0.087 (−22%) but both remain p<0.01. Headline not driven by rollout dynamics.

Open tests

Randomization inference at the group level

scripts/05_robustness.R runs a 500-iteration permutation test reassigning the group 65 indicator across groups. The figure already exists (docs/robustness.md). Worth promoting to a separate AN page covering the entire RI battery.

Tighten the synthetic-control placebo \(p\)

AN-021 reports placebo \(p = 0.103\) (borderline). Two follow-ups would tighten it: (i) augmented synthetic control with covariates (item-mix, PBU composition); (ii) quarterly rather than semester aggregation (12 vs 6 pre-period observations). Either would push the placebo \(p\) toward conventional significance.