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%% Supplementary Materials
%% Why the G7 Oil Price Cap Failed
%% For Review of World Economics (Springer)
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\begin{document}

\title[Supplementary Materials]{Supplementary Materials for: Why the G7 Oil Price Cap Failed: Shadow Fleets, War Premium Decay, and Lessons for Sanctions Design}

\author*[1]{\fnm{Tu\u{g}ba Ortay} \sur{Baykal}}\email{tugbaortaygokce@gmail.com}

\affil*[1]{\orgdiv{Department of Economics}, \orgname{Istanbul Ticaret University}, \orgaddress{\city{Istanbul}, \country{Turkey}}}

\abstract{This document reports additional robustness checks referenced in the main text.}

\maketitle

This document reports additional robustness checks referenced in the main text. All specifications use Newey-West HAC standard errors with 10 lags unless otherwise noted.

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\section{Alternative Spread Measures}
\label{sec:altspread}

Table~\ref{tab:altspread} reports Model~2 using Novorossiysk and average spread measures. Signs, significance, and magnitudes are consistent across specifications.

\begin{table}[htbp]
\centering
\caption{Alternative Spread Measures}
\label{tab:altspread}
\begin{tabular}{@{}lccc@{}}
\toprule
Variable & Baltic & Novorossiysk & Average \\
\midrule
Post War Outbreak & 26.59*** & 22.95*** & 24.77*** \\
Post Price Cap & $-$9.22*** & $-$7.52*** & $-$8.37*** \\
Post Biden Sanctions & $-$6.11*** & $-$8.08*** & $-$7.09*** \\
Shadow Fleet Share & $-$0.022*** & $-$0.027*** & $-$0.024*** \\
$R^2$ & 0.852 & 0.798 & 0.830 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\small
\item \textit{Notes:} $N=1{,}582$. Controls: DXY, VIX, BDTI, COVID (all standardized).
\end{tablenotes}
\end{table}

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\section{Lagged Shadow Fleet Share}
\label{sec:lagged}

The shadow fleet coefficient remains stable across lags of 1, 5, 7, and 14 days (Table~\ref{tab:lagged}), with virtually no attenuation.

\begin{table}[htbp]
\centering
\caption{Lagged Shadow Fleet Share}
\label{tab:lagged}
\begin{tabular}{@{}lcccc@{}}
\toprule
 & Lag 1 & Lag 5 & Lag 7 & Lag 14 \\
\midrule
Shadow Fleet Share & $-$0.018*** & $-$0.023*** & $-$0.021*** & $-$0.022*** \\
 & (0.006) & (0.006) & (0.006) & (0.007) \\
$R^2$ & 0.852 & 0.852 & 0.852 & 0.852 \\
\bottomrule
\end{tabular}
\begin{tablenotes}\small
\item \textit{Notes:} Model~2 specification with lagged shadow share replacing contemporaneous.
\end{tablenotes}
\end{table}

%% ============================================================
\section{Granger Causality Tests}
\label{sec:granger}

Bilateral Granger causality tests using first-differenced series yield no evidence of reverse causality (Table~\ref{tab:granger}).

\begin{table}[htbp]
\centering
\caption{Granger Causality Tests (First-Differenced)}
\label{tab:granger}
\begin{tabular}{@{}lcccc@{}}
\toprule
Direction & Lags & $F$-stat & $p$-value & Conclusion \\
\midrule
Shadow $\rightarrow$ Spread & 5 & 1.68 & 0.137 & Not significant \\
Shadow $\rightarrow$ Spread & 7 & 1.77 & 0.090 & Marginal \\
Shadow $\rightarrow$ Spread & 14 & 1.42 & 0.136 & Not significant \\
Shadow $\rightarrow$ Spread & 21 & 1.22 & 0.224 & Not significant \\
Spread $\rightarrow$ Shadow & 5 & 0.34 & 0.892 & Not significant \\
Spread $\rightarrow$ Shadow & 7 & 0.51 & 0.830 & Not significant \\
Spread $\rightarrow$ Shadow & 14 & 0.50 & 0.937 & Not significant \\
Spread $\rightarrow$ Shadow & 21 & 0.52 & 0.964 & Not significant \\
\bottomrule
\end{tabular}
\begin{tablenotes}\small
\item \textit{Notes:} Tests conducted on first-differenced series. Shadow $\rightarrow$ Spread tests whether lagged shadow share changes predict spread changes.
\end{tablenotes}
\end{table}

%% ============================================================
\section{VAR Model and Impulse Response Functions}
\label{sec:var}

A bivariate VAR(17) in first differences (lag length by AIC) confirms that shocks to shadow fleet share have small, oscillating effects on spread changes, while shocks to spread have near-zero effects on shadow fleet changes (Figure~\ref{fig:irf}).

\begin{figure}[htbp]
\centering
\includegraphics[width=0.85\textwidth]{fig_irf.png}
\caption{Impulse Response Functions from VAR(17) in First Differences.}
\label{fig:irf}
\end{figure}

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\section{Counterfactual Analysis}
\label{sec:counterfactual}

Using Model~2 coefficients, we simulate counterfactual spreads holding shadow fleet share at its pre-war mean (40.6\%). Without shadow fleet expansion, the post-cap spread would have been approximately \$0.49/bbl wider: the contribution is $(63.1 - 40.6) \times (-0.022) \approx -\$0.50$/bbl (Figure~\ref{fig:counterfactual}).

\begin{figure}[htbp]
\centering
\includegraphics[width=0.85\textwidth]{fig_counterfactual.png}
\caption{Counterfactual Analysis: Spread With vs.\ Without Shadow Fleet Expansion.}
\label{fig:counterfactual}
\end{figure}

%% ============================================================
\section{Specification and Diagnostic Tests}
\label{sec:diagnostics}

\begin{table}[htbp]
\centering
\caption{Diagnostic Tests (Model 2)}
\label{tab:diagnostics}
\begin{tabular}{@{}lcc@{}}
\toprule
Test & Statistic & $p$-value \\
\midrule
Ramsey RESET & $F = 0.01$ & 0.916 \\
Breusch-Pagan & $\chi^2 = 332.1$ & $<$0.001 \\
Durbin-Watson & 0.095 & --- \\
Jarque-Bera & 355.0 & $<$0.001 \\
Condition Number & 456.1 & --- \\
Max VIF & 8.63 & --- \\
\bottomrule
\end{tabular}
\end{table}

Ramsey RESET confirms no functional form misspecification ($p=0.92$). Breusch-Pagan and Durbin-Watson detect heteroskedasticity and autocorrelation, both addressed by Newey-West HAC standard errors. Maximum VIF is 8.63, below the conventional threshold of 10.

%% ============================================================
\section{Subsample Robustness}
\label{sec:subsample}

Results are robust to excluding the COVID period and restricting to post-2022 observations. The shadow fleet coefficient is larger in the post-2022 subsample ($-0.036$), consistent with the fleet's growing importance after sanctions intensified.

\end{document}
