From b90813ce5c8f27b0cca913d4e1c5c28d7de96f06 Mon Sep 17 00:00:00 2001 From: alex Date: Mon, 5 Dec 2022 17:31:40 -0700 Subject: [PATCH] Writing slides --- .../Sections/Oil_Econometrics.tex | 143 +++++++++++++++--- 1 file changed, 121 insertions(+), 22 deletions(-) diff --git a/Defense_proposal/Sections/Oil_Econometrics.tex b/Defense_proposal/Sections/Oil_Econometrics.tex index 2ea3101..5699f5e 100644 --- a/Defense_proposal/Sections/Oil_Econometrics.tex +++ b/Defense_proposal/Sections/Oil_Econometrics.tex @@ -24,29 +24,128 @@ Where \(Q_{O,b,t}\) is the net present oil produced in a basin state pair b, at \begin{frame}{Oil and Gas Production: Model Sequence of Events} \begin{center} \begin{tikzpicture} - \draw [thick,decorate,decoration={brace,amplitude=6pt,raise=0pt}] (0.25,0.15) -- (3.25,0.15); - 1.25 - \node[align=center] at (2.4,0.55) {t}; - \node[align=center] at (0,0.95) {\(Y_{t-1}\)}; - \draw [thick,->] (0,.75) -- (0,0.15); - \node[align=center] at (2.25,.95) {\(Q_{energy}\)}; - \draw [thick,->] (2.25,.75) -- (2.25,0.15); - \draw [thick,->] (2.25,-0.75) -- (2.25,-0.15); - \node[align=center] at (2.25,-0.95) {\(\theta_{oil}\)}; + \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); + %%%%%%%%%%%%%%%%%%%%%%% - \node[align=center] at (3.15,0.55) {t+1}; - \draw [thick,decorate,decoration={brace,amplitude=6pt,raise=0pt}] (2.5,0.15) -- (3.75,0.15); - \draw [thick,->] (4,0.85) -- (4,0.15); - \node[align=center] at (6.25,0.6) {Infectious period}; - \draw [thick,->] (8.25,0.85) -- (8.25,0.15); - \node[align=center] at (9.15,0.5) {Immune\\stage}; - \draw [thick,decorate,decoration={brace,amplitude=6pt,raise=0pt}] (4.25,0.15) -- (8,0.15); - \draw [thick,->] (0,0) -- (10,0); - \draw [thick,->] (4.6,-0.85) -- (4.6,-0.15); - \draw [thick,->] (7.65,-0.4) -- (7.65,-0.15); - \draw [thick,decorate,decoration={brace,amplitude=6pt,raise=0pt,mirror}] (4.75,-0.15) -- (7.5,-0.15); - \node[align=center] at (6.25,-0.85) {Symptomatic\\period}; - \node[align=center] at (4.6,-1.3) {Onset of\\symptoms}; \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} + +