Extensions · robustness beyond the core battery
Every harder test the canonical reviewer would request.
Bottom line. The extensions battery applies the same identification framework as the core 18-cell battery but pushes the analysis through synthetic difference-in-differences, cohort-level DiD against the 20-firm SB-29-era-mover panel, BHAR with Romano-Wolf step-down, GARCH-corrected leakage-window inference, and pre-trend Granger F-tests. EquipmentShare.com's extensions battery is pending the per-firm event-study run.
Estimator table (pending per-firm run)
| Estimator | τ | Inference | Verdict |
|---|---|---|---|
| Naïve synthetic-control gap (no time weights) | [PENDING] | [PENDING] | [PENDING] |
| Arkhangelsky SDiD (250-day pre, canonical) | [PENDING] | placebo permutation p = [PENDING] | [PENDING] |
| Arkhangelsky SDiD (60-day pre, sensitivity) | [PENDING] | placebo permutation p = [PENDING] | [PENDING] |
| ADH classical (250-day pre, canonical) | [PENDING] | rank [PENDING] of 21 | [PENDING] |
| ADH classical (60-day pre, sensitivity) | [PENDING] | rank [PENDING] of 21 | [PENDING] |
| Cohort-level DiD on N=19 SB-29-era movers | [PENDING] | [PENDING] | [PENDING] |
| BHAR over [0, +21 trading days] | [PENDING] | Romano-Wolf min-p = [PENDING] | [PENDING] |
| GARCH(1,1)-corrected [T−10,+0] | [PENDING] | z = [PENDING] | [PENDING] |
Pre-trend / parallel-trends diagnostic
Granger F-test for pre-trend over [T−30, T−1]: [DATA PENDING: F-stat + p-value]. Parallel-trends visual inspection on /evidence Figure 5. The diagnostic checks whether EquipmentShare.com's pre-period return trajectory differed systematically from the synthetic-control donor pool's, which would compromise the synthetic-control identification.
Leakage-inclusive window
[T−10, +0] cumulative AR under FF6+BNO: [DATA PENDING]. The window tests for pre-announcement information leakage — i.e., whether information about the Texas redomiciliation moved EquipmentShare.com's stock before the [DATA PENDING] X-statement. For EquipmentShare.com specifically, the Tornetta v. Musk Chancery ruling on January 30, 2024 is a confounding within-window event; the analysis distinguishes Tornetta-driven price movement from redomiciliation-anticipation movement via the placebo-in-time test.
Robustness extensions documented elsewhere
- Stress tests: see /stress_tests for the eight adversarial-attack tests (estimation-window sensitivity, peer-firm sanity, rolling β, GARCH leakage, placebo-in-time, sector split, oil-instrument sensitivity, refiner-vs-E&P).
- Statutory analysis: see /statutes for the doctrinal context driving the redomiciliation.
- Coalition arithmetic: see /coalition for the private — founder-led dynamic and institutional-coalition pathways.
Primary sources
Extensions methodology references
- Arkhangelsky et al., Synthetic Difference-in-Differences, 111 Am. Econ. Rev. 4088 (2021)
- Callaway, Brantly & Pedro H.C. Sant'Anna, Difference-in-Differences with Multiple Time Periods, 225 J. Econometrics 200 (2021)
- Granger, C.W.J., Investigating Causal Relations by Econometric Models and Cross-spectral Methods, 37 Econometrica 424 (1969)
- Engle, Robert F., Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, 50 Econometrica 987 (1982)
Full Bluebook-format citations in SOURCES.md.