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b39be9875e Cleaned and updated slides 2022-11-02 21:24:08 -06:00
92aa0f85a0 Typos 2022-11-02 14:26:04 -06:00
158b87310b Small typos 2022-11-02 14:24:06 -06:00
488c80480b Spelling and orginziation 2022-11-02 13:45:44 -06:00
cac9613329 Lots of spelling and grammar fixes 2022-11-01 22:44:46 -06:00
20 changed files with 131 additions and 104 deletions

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%---------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------
% TITLE PAGE % TITLE PAGE
%---------------------------------------------------------------------------------------- %----------------------------------------------------------------------------------------
\title[Bitcoin Mining, a Coproduct of Oil Production]{Bitcoin Mining, a Coproduct of Oil Production} % The short title appears at the bottom of every slide, the full title is only on the title page %\title[Bitcoin Mining, a Coproduct of Oil Production]{Bitcoin Mining, a Coproduct of Oil Production} % The short title appears at the bottom of every slide, the full title is only on the title page
\title[Will Bitcoin Mining Create the Next Shale Boom?]{Will Bitcoin Mining Create the Next Shale Boom?} % The short title appears at the bottom of every slide, the full title is only on the title page
\subtitle{An Estimation of Long Run Regional Welfare Effects} \subtitle{An Estimation of Long Run Regional Welfare Effects}
\author[Alex Gebben] {Alexander Gebben} \author[Alex Gebben] {Alexander Gebben}
@ -42,19 +43,23 @@
\section{Introduction \& Overview} \section{Introduction \& Overview}
\input{./Sections/Intro.tex} \input{./Sections/Intro.tex}
\input{./Sections/About_me.tex} \input{./Sections/About_me.tex}
\input{./Sections/Other_Research.tex}
\section{Background} \section{Background}
\input{./Sections/Background.tex} \input{./Sections/Background.tex}
\input{./Sections/Key_Questions.tex} \input{./Sections/Key_Questions.tex}
\input{./Sections/Diagram.tex} \input{./Sections/Diagram.tex}
\input{./Sections/Mechanism.tex} \input{./Sections/Mechanism.tex}
\section{Bitcoin Mining} \section{Bitcoin Mining}
\input{./Sections/Bitcoin_Intro.tex}
\input{./Sections/Bitcoin_Incentives.tex} \input{./Sections/Bitcoin_Incentives.tex}
\input{./Sections/Mining_Structure.tex} \input{./Sections/Mining_Structure.tex}
\input{./Sections/Mining_Model.tex} \input{./Sections/Mining_Model.tex}
\input{./Sections/Mining_elast.tex} \input{./Sections/Mining_elast.tex}
\input{./Sections/Reg_elas.tex} %\input{./Sections/Reg_elas.tex}
\section{Oil Market} \section{Oil Market}
\input{./Sections/Oil_Intro.tex}
\input{./Sections/Oil_Structure.tex} \input{./Sections/Oil_Structure.tex}
\input{./Sections/Oil_Assumptions.tex}
\input{./Sections/Oil_Econometrics.tex} \input{./Sections/Oil_Econometrics.tex}
\input{./Sections/Data.tex} \input{./Sections/Data.tex}
\section{Results} \section{Results}
@ -63,6 +68,7 @@
\input{./Sections/Results.tex} \input{./Sections/Results.tex}
\section{Conclusion} \section{Conclusion}
\input{./Sections/Conclusion.tex} \input{./Sections/Conclusion.tex}
\input{./Sections/Questions.tex}
\section{Bibliography} \section{Bibliography}
\input{./Sections/bib.tex} \input{./Sections/bib.tex}

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\column{.45\textwidth} % Left column and width \column{.45\textwidth} % Left column and width
\textbf{Experience} \textbf{Experience}
\begin{itemize} \begin{itemize}
\item PhD candidate in Mineral and Energy Economics at CSM \item PhD candidate in Mineral and\newline Energy Economics % at Colorado School of Mines
\item Petroleum Engineering B.S \item Mineral and Energy Economics, M.S.
\item Petroleum Engineering, B.S.
\item Worked as a data analyst for oil companies \item Worked as a data analyst for oil companies
\end{itemize} \end{itemize}
\textbf{Personal} \textbf{Personal}
\begin{itemize} \begin{itemize}
\item{Coding and Linux} \item{Coding and Linux}
\item{Fly fishing} \item{Fly fishing}
\item{Foraging} \item{Camping}
\end{itemize} \end{itemize}
\column{.5\textwidth} % Right column and width \column{.5\textwidth} % Right column and width
\includegraphics[width=\columnwidth,height=\textheight,keepaspectratio]{./img/fish.jpg} \includegraphics[width=\columnwidth,height=\textheight,keepaspectratio]{./img/fish.jpg}
\tiny Greenback trout caught at Rocky Mountain National Park
Cutbow caught at Rocky Mountain National park
\end{columns} \end{columns}
\end{frame}
\begin{frame}{Other research}
\begin{columns}[c] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment
\column{.45\textwidth} % Left column and width
\textbf{Previous Topics of Research}
\begin{itemize}
\item{Ground water with USDA grant\footnote{(loos et al.,2022)}}
\item{Critical materials}
\item{Wind energy (economics and engineering)}
\item{CGE and electricty grids}
\item{Instituional economics in resource management}
\end{itemize}
\column{.5\textwidth} % Right column and width
\includegraphics[width=\columnwidth,height=\textheight,keepaspectratio]{./img/SLV_Map.png}
\end{columns}
\end{frame} \end{frame}

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@ -41,7 +41,7 @@
\begin{columns}[c] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment \begin{columns}[c] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment
\column{.45\textwidth} % Left column and width \column{.45\textwidth} % Left column and width
\textbf{Factors of the Wyoming market} \textbf{Factors of the Wyoming Market}
\begin{itemize} \begin{itemize}
\item Increasing flaring rates \item Increasing flaring rates
\item Regulatory concerns about emissions \item Regulatory concerns about emissions
@ -52,12 +52,8 @@
\end{itemize} \end{itemize}
\column{.5\textwidth} % Right column and width \column{.5\textwidth} % Right column and width
Percentage of US Flaring by State Percentage of U.S. Flaring by State
\includegraphics[width=\columnwidth,height=\textheight,keepaspectratio]{./img/flared.jpeg} \includegraphics[width=\columnwidth,height=0.85\textheight,keepaspectratio]{./img/flared.jpeg}
Filler: Include heat map of US flaring
\end{columns} \end{columns}
\end{frame} \end{frame}

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@ -1,9 +1,9 @@
%------------------------------------------------ %------------------------------------------------
\begin{frame}{Bitcoin Mining Rewards} \begin{frame}{Bitcoin Mining Rewards}
Two sources of income for Bitcoin Miners, a Block Reward and a User fee Two sources of income for Bitcoin Miners, a Block Reward and a User Fee.
\newline \newline
\begin{center} \begin{center}
Constant Miner Reward \textbf{Constant Miner Reward}
\begin{formal} \begin{formal}
``The steady addition of a constant amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.'' ``The steady addition of a constant amount of new coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.''
\begin{list}{$-$} \begin{list}{$-$}
@ -14,10 +14,10 @@
\end{center} \end{center}
%Current reward is 6.5 Bitcoin %Current reward is 6.5 Bitcoin
\begin{center} \begin{center}
Variable User Fees \textbf{Variable User Fees}
\begin{formal} \begin{formal}
%The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free. %The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free.
``The incentive can also be funded with transaction fees\ldots Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees'' ``The incentive can also be funded with transaction fees\ldots Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees.''
\begin{list}{$-$} \begin{list}{$-$}
\item{Satoshi Nakamoto} \item{Satoshi Nakamoto}
\end{list} \end{list}

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\begin{frame}[plain]{Understanding the Bitcoin Mining Market}
\begin{center}
\includegraphics[width=\textwidth,height=0.85\textheight,keepaspectratio]{./img/Bitcoin_miners.jpg}
\end{center}
\end{frame}

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%------------------------------------------------ %------------------------------------------------
\begin{frame}{Conclusion} \begin{frame}{Conclusion}
The market for Bitcoin can create a new co-product in oil production, acting like a subsidy. The revenue increase is senteive to the price of bitcoin but is likley to persist even if the price of bitcoin becomes drops. % The market for Bitcoin can create a new coproduct in oil production, acting like a subsidy. The revenue increase is sensitive to the price of bitcoin but is likely to persist even if the price of bitcoin drops.
\newline
There is spatial variation in the size of the subsidy to oil production. The effect is predicted to shift the location of wells genreally north, to lower population and higher GOR states. % There is spatial variation in the size of the subsidy to oil production. The effect is predicted to shift the location of wells generally north, to lower population and higher GOR states.
\newline % Bitcoin mining is starting to be used to increase the profits of oil wells in remote areas. States like Wyoming could see an increase in oil production of \(\approx 1.4\%\) Thethe U.S. has a lower average effect.
Bitcoin miners are starting to use flared natural gas as an afforable source of electricity. This will have long run impact on the oil market.
Prelminary results show that state like Wyoming could see an increase in oil production of \(\approx 1.4\%\) due to the subisdy effect, while the US has a lower average effect \begin{itemize}
% \item{Bitcoin mining can become a coproduct to oil production}
\item{The price of Bitcoin affects the price paid for the natural gas}
\item{A subisdy effect will persist even when Bitcoin prices are low}
\item{The profitability depends on geology}
\item{Bitcoin mining will disproportionately effect states like Wyoming, and North Dakota}
\end{itemize}
\end{frame} \end{frame}

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\begin{enumerate} \begin{enumerate}
\item{Enverus} \item{Enverus}
\begin{itemize} \begin{itemize}
\item{U.S. Well Data} \item{U.S. well data}
\item{Gas Hookup Company} \item{Gas hookup company}
\item{SPUD Date} \item{SPUD date}
\end{itemize} \end{itemize}
\item{Energy Information Administrations} \item{Energy Information Administrations}
\begin{itemize} \begin{itemize}
\item{Population weighted coooling degree days (CDD)} \item{Population weighted cooling degree days (CDD)}
\item{Population weighted heating degree days (HDD)} \item{Population weighted heating degree days (HDD)}
\item{Storage Levels} \item{Storage Levels}
\item{Price data} \item{Price data}
\end{itemize} \end{itemize}
\item{National Oceanic and Atmospheric Administration} \item{National Oceanic and Atmospheric Administration}
\begin{itemize} \begin{itemize}
\item{Disaster Events} \item{Disaster events}
\end{itemize} \end{itemize}
\end{enumerate} \end{enumerate}
\end{frame} \end{frame}

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%------------------------------------------------ %------------------------------------------------
\begin{frame}{Key Questions} \begin{frame}{Key Questions}
\textbf{What are the long run regional welfare changes that can be expected as Bitcoin mining becomes a coproduct of oil?} \textbf{What are the long term regional welfare changes that can be expected as Bitcoin mining becomes a coproduct of oil?}
\pause \begin{enumerate}
\item{How much extra revenue will oil producers receive?}
\item{How will levels of drilling change?}
\item{How will the location of of drilling change?}
\end{enumerate}
\end{frame}
\begin{frame}{Strategy}
\begin{itemize} \begin{itemize}
\item What type of incentives are created? \item{Identify the incentives}
\begin{itemize} \begin{itemize}
\item{Microeconomics model of Bitcoin mining \& oil production choices} \item{Microeconomics model of Bitcoin mining}
\item{Upstream oil production model}
\end{itemize} \end{itemize}
\pause \pause
\item What is the regional distribution of these incentives? \item{Find regional variation of the incentives}
\begin{itemize} \begin{itemize}
\item{Collection of well attribute data} \item{Collect well attribute data}
\item{Estimate of gas produced in oil wells}
\item{Identify wells that do not have a gas pipeline}
\end{itemize} \end{itemize}
\pause \pause
\item How might producers respond in each region? \item{Identify responses of oil producers in each region}
\begin{itemize} \begin{itemize}
\item{Econometric estimates state-basin level elasticity of supply} \item{Estimate response to oil and gas price changes}
\item{Econometric estimates at the state-basin level of elasticity of supply}
\item{Forecast new wells \& oil production}
\end{itemize} \end{itemize}
\pause \pause
\item How will consumer and producer welfare change? \item{\emph{Future Work:} Estimate other welfare changes }
\begin{itemize} \begin{itemize}
\item{Model revenue changes}
\item{Engineering based pollution estimates} \item{Engineering based pollution estimates}
\item{Local externality counterfactual} \item{Local externality counterfactual}
\end{itemize} \end{itemize}
\end{itemize} \end{itemize}
\pause %\textbf{Results in counterfactual oil production by geologic basin and state, in key metrics.}
\textbf{Results in counterfactual oil production by geologic basin and state, in key metrics.}
\end{frame} \end{frame}

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\begin{frame}{Mechanisms} \begin{frame}{Mechanisms}
Bitcoin miners that pay for flared gas subsidize oil produciton When Bitcoin miners pay for flared gas, the change in income is equivalent to a subsidy on oil production.
\newline \newline
\newline \newline
\textbf{Direct Effects} \textbf{Direct Effects}
\begin{enumerate} \begin{enumerate}
\item{More drilling} \item{More drilling}
\item{Diffrent location of wells} \item{Different location of wells}
\item{Bitcoin Miners clean the gas} \item{Bitcoin miners clean the gas}
\end{enumerate} \end{enumerate}
\end{frame} \end{frame}
\begin{frame}{Outcomes} \begin{frame}{Outcomes}
@ -14,19 +14,19 @@ Bitcoin miners that pay for flared gas subsidize oil produciton
\column{.5\textwidth} % Left column and width \column{.5\textwidth} % Left column and width
\textbf{Certain Outcomes} \textbf{Certain Outcomes}
\begin{itemize} \begin{itemize}
\item{Increase number of wells} \item{Increase in number of wells}
\item{Increase in profits} \item{Increase in profits}
\item{Decrease price of oil} \item{Decrease in price of oil}
\item{Non-decreasing price of gas} \item{Non-decreasing price of gas}
\end{itemize} \end{itemize}
\column{.5\textwidth} % Left column and width \column{.5\textwidth} % Left column and width
\textbf{Uncertain Outcomes} \textbf{Uncertain Outcomes}
\begin{itemize} \begin{itemize}
\item{More pollution: More wells drilled} \item{More pollution: More wells drilled}
\item{Less pollution: Gas is cleaned} \item{Less pollution: Gas is cleaned}
\item{Localized beneftis: New location of wells} \item{Localized benefits: New location of wells}
\item{Localized costs: New location of wells} \item{Localized costs: New location of wells}
\end{itemize} \end{itemize}
\end{columns} \end{columns}
\end{frame} \end{frame}

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@ -2,7 +2,7 @@
\begin{frame}{Bitcoin Mining} \begin{frame}{Bitcoin Mining}
\begin{columns}[t] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment \begin{columns}[t] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment
\column{.45\textwidth} % Left column and width \column{.45\textwidth} % Left column and width
\textbf{Rewards and fees} \textbf{Rewards and Fees}
\begin{enumerate} \begin{enumerate}
\item{Awarded by ``lottery''} \item{Awarded by ``lottery''}
\item{Lottery completes \(\approx \) every 10 minutes} \item{Lottery completes \(\approx \) every 10 minutes}
@ -19,7 +19,7 @@
\mbox{} \mbox{}
\newline \newline
\newline \newline
\textbf{Model of single period returns} \textbf{Model of Single Period Returns}
\newline \newline
\(Revenue=\text{Total Reward}\cdot \frac{\text{Tickets Owned}}{\text{All Tickets}}\) \(Revenue=\text{Total Reward}\cdot \frac{\text{Tickets Owned}}{\text{All Tickets}}\)
\newline \newline

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Where \(R_{i,t}\) is the revenue of miner \(i\in I\), at time t. \(q_{i}\) is the hash power of a miner i, and \(Q^{-i}_{t}\) is the hash of all other miners. The miner reward is \(\eta\) Where \(R_{i,t}\) is the revenue of miner \(i\in I\), at time t. \(q_{i}\) is the hash power of a miner i, and \(Q^{-i}_{t}\) is the hash of all other miners. The miner reward is \(\eta\)
\begin{block}{Revenue change from t to t+1} \begin{block}{Revenue change from t to t+1}
\begin{align*} \begin{align}
% R_{i,t+1}-R_{i,t}=\eta \cdot\frac{q_{i}}{Q^{-i}_{t+1}-Q^{-i}_{t}} % R_{i,t+1}-R_{i,t}=\eta \cdot\frac{q_{i}}{Q^{-i}_{t+1}-Q^{-i}_{t}}
% \\ % \\
\%\Delta R=\%\Delta P_{btc}(1-\epsilon) \%\Delta R=\%\Delta P_{btc}(1-\epsilon)
\end{align*} \end{align}
\end{block} \end{block}
If the Bitcoin price elasticity of hash \(\epsilon\) is greater than one (elastic), than a decrease in price will \alert{increase profits} for the low marginal cost producers, like the miners using flared gas. If the Bitcoin price elasticity of hash \(\epsilon\) is greater than one (elastic), than a decrease in price will \alert{increase profits} for the low marginal cost producers, like the miners using flared gas.
\end{frame} \end{frame}

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\begin{frame}{Oil and Gas Production: Assumptions }
\textbf{Assumptions}
\begin{enumerate}
\item{Engineer probabilistically knows the production path of each well }
\item{Marginal production choice is to drill a new well in a particular location}
\item{Future production is modeled by a best fit Arps model}
\item{Constant discount rate of 4.5\%}
\end{enumerate}
\end{frame}

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@ -1,12 +1,3 @@
\begin{frame}{Oil and Gas Production: Assumptions }
\textbf{Assumptions}
\begin{enumerate}
\item{Engineer probabilistically knows the production path of each well }
\item{Marginal production choice is to drill a new well in a particular location}
\item{Future production is modeled by a best fit Arps model}
\item{Constant discount rate of 4.5\%}
\end{enumerate}
\end{frame}
\begin{frame}{Oil and Gas Production: Econometric Model } \begin{frame}{Oil and Gas Production: Econometric Model }
\begin{block}{Estimated model} \begin{block}{Estimated model}
@ -14,14 +5,15 @@
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} 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{equation}
\end{block} \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.\newline 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 Square is used, with instruments of:} \textbf{Three-stage least squares is used with instruments of:}
\begin{enumerate} \begin{enumerate}
\item{VAR model residuals of oil refinery volumes, and gas storage} \item{Oil refinery shocks}
\item{Natural gas storage shocks}
\item{Regional population weighted cooling and heating degree days} \item{Regional population weighted cooling and heating degree days}
\item{Sum of the standard of each instrument over the last 12 months} \item{Sum of the standard deviation of each instrument over the preceding 12 months}
\end{enumerate} \end{enumerate}
\end{frame} \end{frame}

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\begin{frame}[plain]{Understanding Oil Production Decisions}
\begin{center}
\includegraphics[width=\textwidth,height=0.85\textheight,keepaspectratio]{./img/Well.jpg}
\end{center}
\end{frame}

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\begin{frame}{Other Research}
\begin{columns}[c] % The "c" option specifies centered vertical alignment while the "t" option is used for top vertical alignment
\column{.45\textwidth} % Left column and width
\textbf{Previous Topics of Research}
\begin{itemize}
\item Ground water with USDA grant \newline (loos et al.,2022) % \footnote{(loos et al.,2022)} %
\item Critical materials
\item Wind energy
\item CGE and electricity grids
\item Institutional economics in resource management
\end{itemize}
\column{.5\textwidth} % Right column and width
% \scalebox{.5}{\includegraphics{./img/SLV_Map.png} % scales both width and height by 0.5
\includegraphics[width=\columnwidth,height=\textheight,keepaspectratio]{./img/SLV_Map.png}
% \scalebox{.1}{\includegraphics{./img/SLV_Map.png}} % scales both width and height by 0.5
\end{columns}
\end{frame}

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\begin{frame}[plain]{Questions}
\huge
\begin{center}
Thank you for your time
\end{center}
\end{frame}

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\column{.5\textwidth} \column{.5\textwidth}
\tiny \tiny
\input{tables/reg.tex}\footnote{Year/Month fixed effects omited}\footnote{All reported values are logged}\footnote{Single stage preliminary results do not cite} \input{tables/reg.tex}\footnote{Year/Month fixed effects omitted}\footnote{All reported values are logged}
\column{.5\textwidth} % Left column and width \column{.5\textwidth} % Left column and width
\normalsize \normalsize
@ -17,7 +17,7 @@
\end{block} \end{block}
\normalsize \normalsize
\center \center
\(\beta_{1}=0.198\),\(\beta_{2}=0.143\) %\(\beta_{1}=0.198\),\(\beta_{2}=0.143\)
\begin{equation*} \begin{equation*}
\Delta Q_{O}= 0.18\cdot \Delta P_{WTI} \Delta Q_{O}= 0.18\cdot \Delta P_{WTI}
\end{equation*} \end{equation*}
@ -26,7 +26,7 @@
\end{columns} \end{columns}
\end{frame} \end{frame}
\begin{frame}{Intial Estimates} \begin{frame}{Initial Estimates}
\textbf{United States} \textbf{United States}
\begin{itemize} \begin{itemize}
@ -36,7 +36,7 @@
\textbf{Wyoming} \textbf{Wyoming}
\begin{itemize} \begin{itemize}
\item{Subsidy of 2.13\% to WTI } \item{Subsidy of 2.13\% to WTI }
\item{\(\Delta Q_{Wy}\approx 1.43\% \)\footnote{Elasticty of 0.67 (Mason et all,2017)}} \item{\(\Delta Q_{Wy}\approx 1.43\% \)\footnote{Elasticity of 0.67 (Mason et all,2017)}}
\end{itemize} \end{itemize}
\end{frame} \end{frame}

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% Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
% Date and time: Mon, Oct 31, 2022 - 04:40:50 PM % Date and time: Mon, Oct 31, 2022 - 04:40:50 PM
\begin{table}[!htbp] \centering \begin{table}[!htbp] \centering
\caption{US Elasticity of Oil Supply} \caption{U.S. Elasticity of Oil Supply}
\label{} \label{}
\begin{tabular}{@{\extracolsep{1pt}}lc} \begin{tabular}{@{\extracolsep{1pt}}lc}
\\[-1.8ex]\hline \\[-1.8ex]\hline
@ -28,6 +28,6 @@ Residual Std. Error & 0.173 (df = 255) \\
F Statistic & 26.828$^{***}$ (df = 39; 255) \\ F Statistic & 26.828$^{***}$ (df = 39; 255) \\
\hline \hline
\hline \\[-1.8ex] \hline \\[-1.8ex]
\textit{} & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ \textit{Note: Preliminary results} & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\
\end{tabular} \end{tabular}
\end{table} \end{table}