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.
Why this matters
The placebo Tuesdays
The example
Anna (Figure 3) takes the diabetes pill on Tuesday at noon. Her blood sugar drops 12 mg/dL below her synthetic-twin’s. Is that real, or just noise? To find out, you go back and pretend the pill was administered on 100 different randomly-chosen Tuesdays from the year before the real Tuesday — days when no pill was actually given. You compute Anna’s gap-vs-synthetic on each of those 100 fake-pill days. Then you ask: of those 100 random-Tuesday gaps, how many were as big as the real one? If the real Tuesday’s gap is bigger than 95 of the 100 fake Tuesdays, the pill worked. If it’s smaller than most of them, the “effect” was just normal noise.
What this means for the chart
Each gray bar in the histogram is one of 100 random fake-announcement days drawn from the 220 trading days before March 10. The horizontal axis is the Day-0 gap each fake day produced. The red vertical line is the real announcement day. If the real announcement moved the stock, the red line should sit far in the right tail of the histogram (a big, rare gap). Instead it sits near the center — 95 of 100 random Tuesdays produced a bigger gap than the real one.
Connection to ExxonMobil
A real governance shock from the NJ→TX redomiciliation would put the red line in the rightmost tail — bigger than 95+ of the random pre-announcement days. Instead the placebo p-value is 0.95: the actual announcement day looked like an unusually quiet day, not a shock. The market did not respond to the redomiciliation as a meaningful governance event.
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.
- 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.
- 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).
- 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.
- 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.