Figure 7 · In-time placebo · 100 pseudo-events

The announcement-day gap was ordinary, not an outlier

If we pretend each of 100 random pre-announcement days was the real announcement day, what would the synthetic-control gap look like? The histogram shows the distribution. The real announcement-day gap (red) sits squarely in the center — 95 of 100 pretend days had a larger absolute gap.

Actual announcement day: −0.03% 0 10 20 30 Pseudo-events −3.5% −2% −1% 0 +1% +2% +3.5% Pseudo-event-day synthetic-control gap (percentage points) Pseudo-event gaps (100) Actual announcement day
95 / 100
Pseudo-events with a larger absolute gap than the real announcement day
−0.03%
Actual announcement-day gap (essentially zero)
0.95
Empirical p-value — the real day looks ordinary
Sources & methodology notes
In-time placebo: distribution of pseudo-event-day gapsp̂placebo,time = (1/Tp) Στ=1Tp 𝒲[|gapτ| ≥ |gap0|]
Tp = 100 pseudo-event dates drawn from the 220 pre-period trading days. Observed Day-0 gap +0.15 pp/day sits inside placebo IQR; one-sided p = 0.50. Post/pre RMSPE ratio = 0.88 (ADH threshold 2.0).

This figure runs the synthetic-control estimator at 100 randomly-drawn pre-event dates and compares the resulting distribution of pseudo-event-day gaps to the observed Day-0 gap. The procedure is the “in-time placebo” recommended by Abadie (2021) §6.3 as a complement to the cross-firm placebo permutation. The seed was fixed at 42 for reproducibility; the 100 pseudo-dates are uniformly drawn from the 220-day pre-event period without replacement.

  1. Alberto Abadie, Alexis Diamond & Jens Hainmueller, Synthetic Control Methods for Comparative Case Studies, 105 J. Am. Stat. Ass’n 493 (2010). Introduces in-time placebo at §5; formal inference instrument complementing the cross-firm placebo permutation. doi.org/10.1198/jasa.2009.ap08746.
  2. Alberto Abadie, Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects, 59 J. Econ. Literature 391, 407–09 (2021). §6.3 expands the in-time-placebo procedure with practical recommendations on date-selection and the post/pre RMSPE ratio threshold (2.0; observed 0.88 here, well below).
  3. R. A. Fisher, The Design of Experiments 17–21 (Oliver & Boyd 1935). Foundational permutation-inference framework that the placebo permutation operationalizes for non-experimental settings.
  4. Shane Goodwin, Read the Fine Print: What ExxonMobil’s Proxy Actually Says About Texas Redomiciliation, Columbia Law School Blue Sky Blog (May 2026). Companion paper. Article fn. 28 reports the published in-time placebo p = 0.92 (yfinance-based with nested-ADH); this chart’s CIQ-replicated value is p = 0.95 (frozen-weights, same 220-day pre-period, seed 42). Both are unambiguously null.

Data attribution. 100 pseudo-event dates drawn from the 220-day pre-event period (2025-05-19 to 2026-02-26). Synthetic-control gap computed at each pseudo-date using the 10-firm pre-registered frozen donor weights against the S&P Capital IQ panel. Seed = 42; reproducible from wave2_data.json on file with the SMU Corporate Governance Initiative.

Source: Author’s calculations from S&P Capital IQ daily adjusted closing prices; in-time placebo procedure from Abadie (2021) §6.3; methodology in Goodwin (May 2026) fn. 28.