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\chapter{Supporting Materials for Chapter \ref{rnns-causal}}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/basque-sim.png}
\caption{Placebo tests on Basque Country terrorism data:
{\protect\tikz \protect\draw[color={rgb:red,4;green,0;yellow,1}] (0,0) -- plot[mark=o, mark options={scale=2}] (0.25,0) -- (0.5,0);}, DID;
{\protect\tikz \protect\draw[color={rgb:red,244;green,226;blue,66}] (0,0) -- plot[mark=triangle*, mark options={scale=2,fill=white}] (0.25,0) -- (0.5,0);}, ED;
{\protect\tikz \protect\draw[color={rgb:red,0;green,5;blue,1}] (0,0) -- plot[mark=+, mark options={scale=2}] (0.25,0) -- (0.5,0);}, MC-NNM;
{\protect\tikz \protect\draw[color={rgb:red,66;green,200;blue,244}] (0,0) -- plot[mark=x, mark options={scale=2}] (0.25,0) -- (0.5,0);}, RVAE;
{\protect\tikz \protect\draw[color={rgb:red,66;green,107;blue,244}] (0,0) -- plot[mark=diamond, mark options={scale=2}] (0.25,0) -- (0.5,0);}, SCM;
{\protect\tikz \protect\draw[color={rgb:red,244;pink,66;blue,223}] (0,0) -- plot[mark=triangle, mark options={scale=2, rotate=180}] (0.25,0) -- (0.5,0);}, VT-EN.\label{basque-sim}}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/germany-sim.png}
\caption{Placebo tests on West German reunification data:
{\protect\tikz \protect\draw[color={rgb:red,4;green,0;yellow,1}] (0,0) -- plot[mark=o, mark options={scale=2}] (0.25,0) -- (0.5,0);}, DID;
{\protect\tikz \protect\draw[color={rgb:red,244;green,226;blue,66}] (0,0) -- plot[mark=triangle*, mark options={scale=2,fill=white}] (0.25,0) -- (0.5,0);}, ED;
{\protect\tikz \protect\draw[color={rgb:red,0;green,5;blue,1}] (0,0) -- plot[mark=+, mark options={scale=2}] (0.25,0) -- (0.5,0);}, MC-NNM;
{\protect\tikz \protect\draw[color={rgb:red,66;green,200;blue,244}] (0,0) -- plot[mark=x, mark options={scale=2}] (0.25,0) -- (0.5,0);}, RVAE;
{\protect\tikz \protect\draw[color={rgb:red,66;green,107;blue,244}] (0,0) -- plot[mark=diamond, mark options={scale=2}] (0.25,0) -- (0.5,0);}, SCM;
{\protect\tikz \protect\draw[color={rgb:red,244;pink,66;blue,223}] (0,0) -- plot[mark=triangle, mark options={scale=2, rotate=180}] (0.25,0) -- (0.5,0);}, VT-EN.\label{germany-sim}}
\end{figure}
\begin{figure*}[htbp]
\centering
\begin{subfigure}[t]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-dens.png}
\caption{Unweighted}
\end{subfigure}
~
\begin{subfigure}[t]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-dens-w.png}
\caption{Weighted by propensity score}
\end{subfigure}
\caption{Pre-period densities of log per-capita state government education spending by treatment status: {\protect\tikz \protect\draw[color=black] (0,0) -- plot[mark=square, mark options={scale=2, fill=white}] (0.25,0) -- (0.5,0);}, Control;
{\protect\tikz \protect\draw[color={rgb:red,104;green,122;blue,255}] (0,0) -- plot[mark=square*, mark options={scale=2,fill={rgb:red,104;green,122;blue,255}}] (0.25,0) -- (0.5,0);}, Treated \label{educ-dense}}
\end{figure*}
\begin{figure}[htbp]
\centering
\includegraphics[width=0.9\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-sim.png}
\caption{Placebo tests on education spending data: {\protect\tikz \protect\draw[color={rgb:red,4;green,0;yellow,1}] (0,0) -- plot[mark=o, mark options={scale=2}] (0.25,0) -- (0.5,0);}, DID;
{\protect\tikz \protect\draw[color={rgb:red,244;green,226;blue,66}] (0,0) -- plot[mark=triangle*, mark options={scale=2,fill=white}] (0.25,0) -- (0.5,0);}, ED;
{\protect\tikz \protect\draw[color={rgb:red,0;green,5;blue,1}] (0,0) -- plot[mark=+, mark options={scale=2}] (0.25,0) -- (0.5,0);}, MC-NNM;
{\protect\tikz \protect\draw[color={rgb:red,66;green,200;blue,244}] (0,0) -- plot[mark=x, mark options={scale=2}] (0.25,0) -- (0.5,0);}, RVAE;
{\protect\tikz \protect\draw[color={rgb:red,66;green,107;blue,244}] (0,0) -- plot[mark=diamond, mark options={scale=2}] (0.25,0) -- (0.5,0);}, SCM;
{\protect\tikz \protect\draw[color={rgb:red,244;pink,66;blue,223}] (0,0) -- plot[mark=triangle, mark options={scale=2, rotate=180}] (0.25,0) -- (0.5,0);}, VT-EN.
\label{educ-sim}}
\end{figure}
\begin{figure*}[htbp]
\centering
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-ed-linear.png}
\caption{Linear interpolation}
\end{subfigure}
~
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-ed-median.png}
\caption{Median replacement}
\end{subfigure}
~
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-ed-random.png}
\caption{Random replacement}
\end{subfigure}
\caption{Encoder-decoder estimates of the impact of the HSA on state government education spending, using differently imputed data: {\color{Darjeeling15}{\sampleline{}}}, observed treated;
{\color{Darjeeling11}{\sampleline{dashed}}}, observed control;
{\color{Darjeeling15}{\sampleline{dotted}}}, counterfactual treated;
{\color{Darjeeling15}{\sampleline{dash pattern=on .7em off .2em on .05em off .2em}}}, $\boldsymbol{\bar{\upphi}^{(t)}}$.\label{educ-ed-imp}}
\end{figure*}
\begin{figure*}[htbp]
\centering
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-rvae.png}
\caption{LOCF interpolation}
\end{subfigure}
~
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-rvae-linear.png}
\caption{Linear interpolation}
\end{subfigure}
~
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-rvae-median.png}
\caption{Median replacement}
\end{subfigure}
~
\begin{subfigure}[t]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{/media/jason/Dropbox/github/rnns-causal/paper/plots/educ-rvae-random.png}
\caption{Random replacement}
\end{subfigure}
\caption{RVAE estimates of the impact of the HSA on state government education spending, using differently imputed data: {\color{Darjeeling15}{\sampleline{}}}, observed treated;
{\color{Darjeeling11}{\sampleline{dashed}}}, observed control;
{\color{Darjeeling15}{\sampleline{dotted}}}, counterfactual treated;
{\color{Darjeeling15}{\sampleline{dash pattern=on .7em off .2em on .05em off .2em}}}, $\boldsymbol{\bar{\upphi}^{(t)}}$.\label{educ-rvae-imp}}
\end{figure*}