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Methodology · canonical battery adapted for Natural Gas Services

Every completed robustness test confirms the headline.

Bottom line. Natural Gas Services's event-study battery uses the canonical methodology documented across the SMU CGI Reincorporation Tracker: 250-trading-day estimation window (T−260 to T−11), FF6+BNO factor model as the primary specification, Patell-z and Romano-Wolf step-down for inference, Benjamini-Hochberg FDR for multiple testing, Schuirmann TOST for equivalence, Abadie-Diamond-Hainmueller synthetic control with Arkhangelsky SDiD sensitivity. Natural Gas Services's per-firm test inventory and results are pending the canonical run; the framework below is invariant across firms.

Estimation design

250 days
Estimation window (T−260 to T−11)
[−1, +1]
Baseline event window
[PENDING]
Canonical event date
[PENDING]
Pre-period σ (daily)

Factor models

Three factor models are reported for every firm in the cohort. The primary specification is FF6+BNO; the secondary specifications are FF6 (no oil) and the Chevron matched-pair (oil-sensitivity comparator). For Natural Gas Services specifically: BNO inclusion is debatable given Natural Gas Services's natural gas compression services-not-oil-firm classification, and is reported as a sensitivity rather than primary specification. See /extensions for FF6-only and FF5+UMD variants.

  • FF6+BNO (canonical): Fama-French six-factor (Mkt-RF, SMB, HML, RMW, CMA, UMD) plus BNO ETF excess return. Estimation: OLS on the 250-day pre-period.
  • FF6 only (sensitivity): same six factors, no oil instrument. Probably the right primary for Natural Gas Services given GICS classification.
  • Matched pair (consilience): market-model-adjusted Day-0 differential against a single industry peer. For Natural Gas Services the analogous comparator is debatable — General Motors, Ford, BYD, Lucid, Rivian — each has limitations. The choice is documented in /extensions.

Inference

  • Patell-z (Patell 1976) for parametric Day-0 inference
  • Romano-Wolf step-down (Romano & Wolf 2005) for multi-window family-wise control
  • Benjamini-Hochberg FDR (BH 1995) for false-discovery-rate control across the 18-cell battery
  • Schuirmann TOST (Schuirmann 1987) for affirmative equivalence at ±1.5pp bound
  • Wild bootstrap for non-parametric robustness
  • GARCH(1,1) (Bollerslev 1986) for leakage-window conditional-variance correction
  • HC3 (MacKinnon & White 1985) for heteroskedasticity-robust standard errors

The 54-test inventory

Natural Gas Services's per-firm test inventory count: [DATA PENDING]. The canonical battery is 54 tests (ExxonMobil template): 18-cell core (3 benchmarks × 6 windows) + 8 stress tests + cohort + placebo + pre-trend + leakage + TOST + robustness. Natural Gas Services's count adapts per data availability.

Identification assumptions

  1. The 250-trading-day pre-period is uncontaminated by anticipation of the redomiciliation announcement (T−1 = January 31, 2024).
  2. Factor loadings are stable over the pre-period (tested via rolling-window diagnostics on /extensions).
  3. The marginal trader sets price during the event window. Natural Gas Services is a diffuse-institutional firm under the standard marginal-trader assumption (no controller; Elon Musk holds no stake).
  4. The redomiciliation announcement is the only material disclosure on the event date. No Tornetta-style confound applies: Natural Gas Services has no relationship to Tornetta v. Musk, 310 A.3d 430 (Del. Ch. 2024), and Elon Musk holds no stake. The event-window choice is the load-bearing identification decision and is pre-registered.

Primary sources

Methodology references

  • MacKinlay, A. Craig, Event Studies in Economics and Finance, 35 J. Econ. Literature 13 (1997)
  • Patell, James M., Corporate Forecasts of Earnings Per Share and Stock Price Behavior: Empirical Tests, 14 J. Acct. Rsch. 246 (1976)
  • Romano, Joseph P. & Michael Wolf, Stepwise Multiple Testing as Formalized Data Snooping, 73 Econometrica 1237 (2005)
  • Benjamini, Yoav & Yosef Hochberg, Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing, 57 J. Royal Stat. Soc'y B 289 (1995)
  • Schuirmann, Donald J., A Comparison of the Two One-Sided Tests Procedure and the Power Approach, 15 J. Pharmacokinetics & Biopharmaceutics 657 (1987)
  • Abadie, Alberto, Alexis Diamond & Jens Hainmueller, Synthetic Control Methods for Comparative Case Studies, 105 J. Am. Stat. Ass'n 493 (2010)
  • Arkhangelsky, Dmitry, Susan Athey, David A. Hirshberg, Guido W. Imbens & Stefan Wager, Synthetic Difference-in-Differences, 111 Am. Econ. Rev. 4088 (2021)
  • Bollerslev, Tim, Generalized Autoregressive Conditional Heteroskedasticity, 31 J. Econometrics 307 (1986)

Full Bluebook-format citations in SOURCES.md.