
\begin{frame}{Oil and Gas Production: Econometric Model }
	\begin{block}{Estimated model}
		\begin{equation}
			Q_{O,b,t}=\beta_{1} Q_{O,b,t-1}+\beta_{2} P_{WTI,t-1}+\beta_{3} P_{HH,t-1}+\beta_{4}\theta_{t}+\gamma_{t,b}+\epsilon_{b,t}  
	\end{equation}
\end{block}
Where \(Q_{O,b,t}\) is the net present oil produced in a basin state pair b, at time t, \(P_{WTI}\) is the West Texas Intermediate futures price, \(P_{HH}\) is the futures price of the Henry Hub spot market, \(\theta_{t}\) is a month dummy, and \(\gamma_{b,t}\) is a variable that represents the amount of monetary damage from natural disasters.\footnote{(Gilbert and Gavin, 2020)}\newline 


\textbf{Three-stage least squares is used with instruments of:}
	\begin{enumerate}
		\item{Oil refinery shocks}
		\item{Natural gas storage shocks}
		\item{Regional population weighted cooling and heating degree days}
		\item{Sum of the standard deviation of each instrument over the preceding 12 months}
	\end{enumerate}

\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Oil and Gas Production: Model Sequence of Events}
	\begin{center}
\begin{tikzpicture}
	\draw [thick,->] (1.5,0) -- (14,0);
	\node[align=center] at (2.5,0.25) {\(Y_{t-1}\)};
	%%%%%%%%%
	%%%left
	\node[align=center] at (6,2.25) {\(Q_{energy}\)};
	\draw [thick,-] (6,1.75) -- (6,2);
	%%%right
	\node[align=center] at (4,2.25) {\(\theta_{oil}\)};
	\draw [thick,-] (4,1.75) -- (4,2);
	%%Middle line
	\draw [thick,->] (5,1.75) -- (5,0.15);
	%%Down line
	\draw [thick,-] (4,1.75) -- (6,1.75);
	%%%%%%%%%%%%%%%%%%%%%%%

	\tikzset{font=\footnotesize}
	\node[align=center] at (5,-.25) {\(t\)};
	\node[align=center] at (10,-.25) {\(t+1\)};
	\node[align=left] at (5,3.25) {Shocks to oil supply \\Shocks to shared supply};

	\tikzset{font=\normalsize}
	\draw [thick,decorate,decoration={brace,amplitude=6pt,raise=0pt}] (4,2.5) -- (6,2.5);
	%%%%%%%%%%%%%%%%%%%%%%
	%%Mid brace
	\draw [thick,decorate,decoration={brace,amplitude=6pt,raise=0pt,mirror}] (5,-0.5) -- (10,-0.5);
	\tikzset{font=\footnotesize}
	\node[align=left] at (7.75,-1.5) {Shocks to oil demand \\ Shocks to gas demand\\Shocks to general demand};
	\tikzset{font=\normalsize}
	\node[align=center] at (7.5,0.25) {\(Y_{t}\)};
	\node[align=center] at (12.5,0.25) {\(Y_{t+1}\)};
	%%%left
	\node[align=center] at (6.5,1.25) {\(P_{oil}\)};
	\draw [thick,-] (6.5,0.75) -- (6.5,1);
	%%%mid
	\node[align=center] at (7.5,1.25) {\(P_{gas}\)};
	\draw [thick,-] (7.5,0.75) -- (7.5,1);
	%%%right
	\node[align=center] at (8.5,1.25) {\(D_{i}\)};
	\draw [thick,-] (8.5,0.75) -- (8.5,1);

	%%Down line
	\draw [thick,-] (7.5,0.75) -- (7.5,0.45);
	%%Middle line
	\draw [thick,-] (6.5,0.75) -- (8.5,0.75);
	%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%Mid brace
	%%%left
	\node[align=center] at (11,2.25) {\(Q_{energy}\)};
	\draw [thick,-] (11,1.75) -- (11,2);
	%%%right
	\node[align=center] at (9,2.25) {\(\theta_{oil}\)};
	\draw [thick,-] (9,1.75) -- (9,2);
	%%Middle line
	\draw [thick,->] (10,1.75) -- (10,0.15);
	%%Down line
	\draw [thick,-] (9,1.75) -- (11,1.75);
	%%%%%%%%%%%%%%%%%%%%%%%

\end{tikzpicture}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Oil and Gas Production: Econometric Model }
	\begin{block}{Supply Choices}
		\begin{equation}
			q_{t}=\rho_{11}Y_{t-1}+\cdots+\rho_{1\ell}Y_{t-\ell}+f_{w}(t)+\epsilon_{q_{t}}
		\end{equation}
		\begin{equation}
			\theta_{t}=\rho_{21}Y_{t-1}+\cdots+\rho_{2\ell}Y_{t-\ell}+f_{\theta}(t)+\epsilon_{\theta_{t}}
		\end{equation}

\end{block}
	\begin{block}{Demand Shifters}
		\begin{equation}
			I_{t}=\rho_{31}Y_{t-1}+\cdots+\rho_{3\ell}Y_{t-\ell}+f_{I}(t)+\epsilon_{I}
		\end{equation}
		\begin{equation}
			p_{g}=\beta_{43}I_{t}+\rho_{41}Y_{t-1}+\cdots+\rho_{4\ell}Y_{t-\ell}+f_{p_{g}}(t)+\epsilon_{p_{g}}
		\end{equation}
		\begin{equation}
			p_{o}=\beta_{53}I_{t}+\beta_{54}P_{g}+\rho_{51}Y_{t-1}+\cdots+\rho_{5\ell}Y_{t-\ell}+f_{p_{o}}(t)+\epsilon_{p_{o}}
		\end{equation}

\end{block}




\end{frame}
\begin{frame}{Oil and Gas Production: Econometric Model }
	\[
\begin{pmatrix}
	e_{t}^{\Delta Btu}\\
	e_{t}^{\Delta \theta}\\
	e_{t}^{\Delta I}\\
	e_{t}^{\Delta p_{g}}\\
	e_{t}^{\Delta p_{o}}
  \end{pmatrix}
=
  \begin{bmatrix}
    a_{11} & 0 & 0 & 0  & 0\\
    0 & a_{22} & 0 & 0 & 0   \\
    0 & 0 & a_{33} & 0 & 0 \\
    a_{41} & a_{42} & a_{43}& a_{44} & 0 \\
    a_{51} & a_{52} & a_{53} & a_{54}& a_{55}
\end{bmatrix}
\begin{pmatrix}
	\epsilon_{q}\\
	\epsilon_{\theta}\\
	\epsilon_{I}\\
	\epsilon_{g}\\
	\epsilon_{o}
  \end{pmatrix}
\begin{matrix}
	\textrm{Drilling supply shock} \\
	\textrm{Composition supply shock} \\
	\textrm{Aggregate demand shock} \\
	\textrm{Gas specfic demand shock} \\
	\textrm{Oil specfic demand shock}
  \end{matrix}
\]

\end{frame}


