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\mode<presentation>

\title[Building Reputation]{Building Reputation: State-Sponsored Rebellions and Transnational Identities}
%\subtitle{}
\author[Mercier, Silve \& Tremblay-Auger]{Marion Mercier\inst{1} \and Arthur Silve\inst{2} \and Benjamin Tremblay-Auger\inst{3}}
\institute[]{\inst{1}LEDa-DIAL, Paris-Dauphine PSL, IZA \and \inst{2} Universit\'e Laval, IAST \and \inst{3} IRES, Chapman University}
\date{2025}}

\begin{document}

\begin{frame}
\titlepage
\end{frame}

\section{Introduction}

\begin{frame}
\frametitle{Motivation}
\begin{center}
\begin{figure}
\includegraphics[width=9cm]{conflict_types_ucdp_updated.jpg}
\caption{Number of wars by type, 1946-2021.}
\end{figure}
\end{center}
\end{frame}

%\begin{frame}
%\frametitle{Motivation}
%
%Less inter-state wars, more ``internationalized'' civil wars, more ``proxy wars'' (Mumford, 2013; San-Akca, 2016)
%\vspace{10}
%    \begin{itemize}
%    \item<1-> Rwanda (and others)'s support to Kabila's AFDL in the first Congo war in the DRC to oust Mobutu from power
%    \vspace{10}
%    \item<2-> India's support to the LTTE in the Sri Lanka civil war
%    \vspace{10}
%    \item<3-> Russia's support for Russian-speaking separatist in Eastern Ukraine. %Inconsistent use of ``Compatriots" narrative in the near abroad. 
%    \end{itemize}
%
%
%    
%\end{frame}


\begin{frame}
\frametitle{Contribution}
%\item Fewer inter-state wars, more ``internationalized'' civil wars, more ``proxy wars'' (Mumford, 2013; San-Akca, 2016).
    %\begin{itemize}
    %\item[-] Rwanda (and others)'s support to Kabila's AFDL in the first Congo war in the DRC to oust Mobutu from power.
    %\item[-] India's support to the LTTE in the Sri Lanka civil war.
    %\end{itemize}
 Why support a rebellion abroad?
 \vspace{8pt}
    \begin{enumerate}
    \item Ideational attachment: for instance, co-ethnicity. \\  (San-Akca 2016)
    \vspace{8pt}
    \item Delegation of foreign policy: ``instrumental'' or ``state-centric'' motivation. \\ (Salehyan 2010; Padro-i-Miquel \& Yared 2012)
    \end{enumerate}
    \medskip
\visible{$\rightarrow$ We argue that the two motives are intertwined: states may build their reputation for (1) so as to achieve (2).}
\end{frame}



\begin{frame}
\frametitle{Contribution}
\begin{itemize}
\item Studies of states' reputation-building (Walter, 2006; Clare \& Danilovic, 2010; Dafoe et al. 2014)
    %\begin{itemize}
    %\vspace{8}
    %\item[-] Central state and separatist groups (Walter, 2006) 
    %\vspace{8}
    %\item[-] Interstate disputes (Clare \& Danilovic, 2010)
    %\item[-] Difficult to pinpoint empirically (Dafoe et al. 2014).
%        \begin{itemize}
%        \item[x] unobservability of the true motives for interventions.
%        \item[x] data limitation.
%        \end{itemize}
%    \end{itemize}
\medskip
\item What we do:
    \begin{enumerate}
    \item Study reputation-building in the context of sponsorship of rebellions
    \vspace{8pt}
        \item Game theoretic model of reputation-building (Kreps \& Wilson, 1982)
    \vspace{8pt}
    \item Empirical test of two implied theoretical predictions
    \end{enumerate}
\end{itemize}
\end{frame}


\section{Theory}

\begin{frame}
\frametitle{Setting}
\vspace{-0.65cm}
\begin{itemize}
\item Players:
    \begin{itemize}
    \item[-] $S$ wishes to extract policy concessions from its neighbors
    \item[-] $n$ neighbors (= potential target states) $j\in\{1,\ldots,n\}$
    \item[-] in each $j$: state $T_j$ and a group that may rebel
    \end{itemize}
\medskip
\item Utilities:
    \begin{itemize}
    \item[-] Rebel group: political inclusion $x_j\in\{0,1\}$
    \item[-] Target state $T_j$: $1-x_j$
    \item[-] Sponsor state $S$: $\sum_j\beta x_j$
%        \begin{itemize}
%        \item[] $\beta>0$: strength of the connection with the rebel groups:
\vspace{-0.2cm}
    $$
     \left.
    \begin{array}{ll}
        \beta_L\mbox{ : }& \mbox{ ``state-centric'' motivation} \\
        \beta_H\mbox{ : }& \mbox{ ``ideational'' motivation}
    \end{array}
\right \} \mbox{ with }0<\beta_L<\beta_H
$$
%        \end{itemize}
    \end{itemize}
\item Beliefs: All actors other than $S$ share the prior that $S$ is H-type with probability $\theta$ $\rightarrow$ update in function of $S$'s behaviour.
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Setting}
\begin{figure}[ht!]
\centering
\resizebox{\textwidth}{!}{
\scalebox{1}{
\begin{tikzpicture}
\draw (0,0) node[left]{$T_j$} -- (.5,.5) -- node[above]{concession} (7,.5);
\draw (0,0) -- (.5,-.5) -- node[below]{no concession} (4,-.5) node[above]{$S$} -- (4.5,-.2) -- node[above]{stays out} (7,-.2);
\draw (4,-.5) -- (4.5,-.8) -- node[below]{sponsors} (7,-.8);
\draw (8,1.5) node{$T_j$'s payoffs};
\draw (8,.5) node{0};
\draw (8,-.2) node{1};
\draw (8,-.8) node{$1-\pi-C_T$};
\draw (10.5,1.5) node{$S_E$'s payoffs};
\draw (10.5,.5) node{$\beta_L$};
\draw (10.5,-.2) node{0};
\draw (10.5,-.8) node{$\pi\beta_L-C_S$};
\draw (13,1.5) node{$S_I$'s payoffs};
\draw (13,.5) node{$\beta_H$};
\draw (13,-.2) node{0};
\draw (13,-.8) node{$\pi\beta_H-C_S$};
\end{tikzpicture}}
}
\end{figure}

\hypertarget{setting}{}     \hyperlink{assum}{\beamergotobutton{Main assumptions}}
\end{frame}
\begin{frame}
\frametitle{Equilibrium}
\begin{itemize}
\item If $S$ is H-type, it always intervenes.
\item If at one point $T_i$ refused a concession and $S$ did not sponsor rebellion, common belief that $S$ is H-type $p_i=0$.
\item If $S$ retaliated against every refusal, $p_i>0$.
\medskip
\item If $S$ is L-type and there is no policy concession, $S$ intervenes with certainty if $p_i$ is relatively large (common belief that $S$ is H-type), and with a probability if $p_i$ is relatively small (common belief that $S$ is L-type).
%     \begin{itemize}
%     \item $S$ does not intervene when $i=1$
%     \item when $i>1$, $S$ intervenes with certainty if $p_i$ is relatively large (common belief that $S$ is H-type), and with a certain probability if $p_i$ is relatively small (common belief that $S$ is L-type)
%    \end{itemize}
\medskip
\item If $p_i$ is sufficiently large, $T_i$ makes a concession. If $p_i$ is sufficiently small, it refuses to do so.
\end{itemize}
\hypertarget{seqeq}{}     \hyperlink{fullseqeq}{\beamergotobutton{Full results}}
\end{frame}

%\begin{frame}
%\frametitle{Equilibrium: main intuitions}
%\vspace{-0.3cm}
%\begin{itemize}
%\item \small Common belief on the probability that $S$ is H-type
%    \begin{itemize}
%    \item[-] \footnotesize $0$ if $S$ did not intervene when $T_j$ refused a concession
%    %\item[-] \footnotesize $>0$ and growing with the number of interactions if $S$ systematically retaliates in case of refusal.
%    \item[-] \footnotesize increases when $S$ retaliates in case of refusal
%    \end{itemize}
%\medskip
%\item \small $T_j$'s makes a concession if the belief that S is H-type is strong enough
%%    \begin{itemize}
%%    \item[-] \footnotesize concession if strong enough belief that S is H-type.
%%    \item[-] \footnotesize may adopt a mixed strategy.
%%    \item[-] \footnotesize No concession if common belief that $S$ is H-type with a relatively low probability.
%%    \end{itemize}
%\medskip
%\item \small $S$'s behaviour
%    \begin{itemize}
%    \item[-] \footnotesize an H-type always intervenes; an L-type intervenes if the belief that it is H-type is strong enough
%%        \begin{itemize}
%%        \item[x] \footnotesize intervenes if strong enough belief that it is H-type.
%%        \item[x] \footnotesize mixed strategy otherwise.
%%        \end{itemize}
%    \end{itemize}
%\end{itemize}
%\hypertarget{seqeq}{}     \hyperlink{fullseqeq}{\beamergotobutton{Full results}}
%\end{frame}

\begin{frame}
\frametitle{Equilibrium step-by-step}
Possible situations:
\begin{itemize}
\item[a)] If $n$ is large enough, $S$ always intervenes $\rightarrow$ $T$ concedes.
\item[b)] If $n$ is large, the probability that $S$ intervenes is very high $\rightarrow$ $T$ concedes.
\item[c)] If $n$ is of intermediate size, $T$ concedes with a certain probability, and an L-type $S$ intervenes with a certain probability in the opposite case.
\item[d)] If $n$ is small, $T$ denies concession, and an L-type $S$ intervenes with a certain probability.
\end{itemize}
\hypertarget{seqeq2}{}     \hyperlink{fullseqeq}{\beamergotobutton{Full results}}
\end{frame}

\begin{frame}
\frametitle{Two interconnected theoretical predictions}
\begin{enumerate}
\item In any target country, the probability of a sponsor state supporting a rebellion increases in the number of other target countries of that sponsor state, until the number is large enough that the target country would rather concede than face a sponsored rebellion.
\begin{itemize}
    \item[$\rightarrow$] States seek to build reputation.
\end{itemize}
\bigskip
\item The political integration of an ethnic group in any target country increases in the number of other targets of a potential sponsor.
\begin{itemize}
    \item[$\rightarrow$] The mechanism is effective.
\end{itemize}
\end{enumerate}
\end{frame}




\section{Empirical approach}
% \hypertarget{Data}{}
\begin{frame}
\frametitle{Empirical approach}
\begin{itemize}
\item Data on transnational co-ethnic ties
    \begin{itemize}
    \item Identify ethnic links between sponsor states and ethnic groups in target countries\medskip
    \end{itemize}
\item Two dep. var. %[possible attenuation bias in both cases]:
    \begin{itemize}
    \item Active support from a sponsor to an ethnic rebel group in a target state
%    \item[] [we rely on cases where the rebellion does happen -- if support exists but rebellion does not happen: not observed]
    \item Political inclusion of an ethnic group in a target state
    \end{itemize}
%\item Remark: relatively conservative setting
%    \begin{itemize}
%    \item[-] Only support to active rebel groups
%    \item[-] Only political inclusion as concession
%    \end{itemize}
\end{itemize}
 \hypertarget{Data}{}
 \hyperlink{Datasource}{\beamergotobutton{Data sources}}
\end{frame}

\begin{frame}
\frametitle{Unit of observation}
\begin{itemize}
\item Triad: ethnic group (politically relevant; EPR) $\times$ target state $\times$ potential sponsor state (macro-regions)\medskip
\item[$\rightarrow$] unbalanced panel of 1,287,813  triad-year obs, 1946 -- 2010. \\ 36,386 triads, 833 ethnic groups in 148 target states, 180 potential sponsors.
\end{itemize}
\hypertarget{stats}{}     \hyperlink{fullstats}{\beamergotobutton{Descriptive Stats}}
\end{frame}

\begin{frame}
\frametitle{Some descriptive stats}
\begin{table}[!htbp] \centering
\resizebox{0.9\textheight}{!}{
\begin{threeparttable}
\begin{small}
%\scalebox{0.017}{
\begin{tabular}{@{\extracolsep{5pt}}lcc}
\hline \hline
 & (1) & (2) \\
    & All & Link = 1 \\
\hline \\[-1.8ex]
\multicolumn{3}{l}{\textbf{Triad $\times$ year-lev\-el}}  \\[-1.8ex]\\
Link            & 1.29 \%          &           \\
Active support  & 0.06 \%          & 1.27\%   \\
Number of countries with a link with the sponsor state  &  2.01        & 5.85  \\
\# obs. &  1,287,813  & 16,572  \\
\\[-1.8ex] \hline \\[-1.8ex]
\multicolumn{3}{l}{\textbf{Sponsor $\times$ year-lev\-el}}  \\[-1.8ex]\\
At least one link            & 46.35\%          & \\
At least one active support  & 6.90\%          &  12.57\%\\
\# obs.  &   8,837 & 4,096  \\
\\[-1.8ex] \hline \\[-1.8ex]
\multicolumn{3}{l}{\textbf{Group in the target state $\times$ year-level}}  \\[-1.8ex]\\
At least one link            & 24.44\%   & \\
At least one active support  & 1.60\%    &  2.27\%\\
\# obs. &   35,546  & 8,686 \\
\hline\hline
\end{tabular}%}
\end{small}
\end{threeparttable}
}
\end{table}
\hypertarget{stats}{}     \hyperlink{fullstats}{\beamergotobutton{More}}
\end{frame}

\begin{frame}
\frametitle{Specification}
\begin{equation*}\label{eq:bench1}
S_{ijkt} = \alpha \onslide<1,2,3>{+ \delta N_{kt}} + \eta L_{ijkt}\times N_{kt} \only<1,2,3,4>{+\lambda_{ijk}} \only<5>{+\Lambda_{ijk}} + \mu_{{\onslide<4,5>{jk}}t} + \phi z_{ijt} + \chi x_{ikt} + \epsilon_{ijkt}
%\only<1,2,3>{\mu_t}\only<4,5>{\mu_{jkt}}
\end{equation*}

\vspace{-10pt}

\begin{overlayarea}{\textwidth}{6cm}
\only<1>{
\begin{footnotesize}
\begin{itemize}
\item $S_{ijkt} = 1$ if ethnic group $i$ in country $j$ receives active support from sponsor state $k$ at time $t$
\item $L_{ijkt} = 1$ if ethnic group $i$ is in power in sponsor state $k$ at time $t$
\item $N_{kt}$: number of neighbors with whom $k$ shares an ethnic tie
\item $\eta$: coefficient of interest.
\end{itemize}
\end{footnotesize}}
\only<2>{
\begin{footnotesize}
\begin{itemize}
\item $S_{ijkt} = 1$ if ethnic group $i$ in country $j$ receives active support from sponsor state $k$ at time $t$
\item $L_{ijkt} = 1$ if ethnic group $i$ is in power in sponsor state $k$ at time $t$
\item $N_{kt}$: number of neighbors with whom $k$ shares an ethnic tie
\item $\eta$: coefficient of interest
\item Triad ($\lambda_{ijk}$) and year ($\mu_{t}$) FE
\item Controls:
\begin{itemize}
    %\item[-] political status of group $i$ in target $j$ (6 dummies)
    \item[-] political status of group $i$ in sponsor $k$ (8 dummies)
    \item[-] group $i$ size in both countries (+ interac. w. $L_{ijkt}$)
\end{itemize}
\end{itemize}
\end{footnotesize}}

\only<3>{
\textbf{Specification 1: year FE, triad FE}
\begin{itemize}
\item \st{Source of variation of $L_{ijkt}$: $i$ gets power in $k$} \textcolor{red}{neutralized}
\item Sources of variation of $N_{kt}$
     \begin{itemize}
     \item[-] $i$ gets/loses representation in $k$
     \item[-] $i'$ gets/loses representation in $k$ %other new coalition members in $k$
     \item[-] structure of the neighbor(s) of country $k$ changes 
     \end{itemize}
\item Sources of variation of $L_{ijkt}\times N_{kt}$
     \begin{itemize}
     \item[-] $i$ gets/loses representation in $k$
     \item[-] $i'$ gets/loses representation in $k$ %other new coalition members in $k$
     \item[-] structure of the neighbor(s) of country $k$ changes 
%     \item[-] triads that get representation in $k$
%     \item[-] other new coalition members in $k$
%     \item[-] changes in the structure of country $k$'s neighbors
     \end{itemize}
\end{itemize}
}

\only<4>{
\textbf{Specif. 2: country-pair $\times$ year FE, triad FE}
\begin{itemize}
\item \st{Source of variation of $L_{ijkt}$: $i$ gets power in $k$} \textcolor{red}{neutralized}
\item \st{Sources of variation of $N_{kt}$} \textcolor{red}{neutralized}
     \begin{itemize}
     \item[-] \st{$i$ gets/looses representation in $k$} \textcolor{red}{neutralized}
     \item[-] \st{$i'$ gets/looses representation in $k$} \textcolor{red}{neutralized}
     \item[-] \st{structure of the neighbor(s) of country $k$ changes} \textcolor{red}{neutralized}
     \end{itemize}
\item Sources of variation of $L_{ijkt}\times N_{kt}$
     \begin{itemize}
     \item[-] $i$ gets/looses representation in $k$
     \item[-] $i'$ gets/looses representation in $k$ %other new coalition members in $k$
     \item[-] structure of the neighbor(s) of country $k$ changes 
     \end{itemize}
\end{itemize}
}

\only<5>{
\textbf{Specif. 3: country-pair $\times$ year FE, triad $\times$ power-in-$k$ FE}
\begin{itemize}
\item \st{Source of variation of $L_{ijkt}$: $i$ gets power in $k$} \textcolor{red}{neutralized}
\item \st{Sources of variation of $N_{kt}$} \textcolor{red}{neutralized}
     \begin{itemize}
     \item[-] \st{$i$ gets/looses representation in $k$} \textcolor{red}{neutralized}
     \item[-] \st{$i'$ gets/looses representation in $k$} \textcolor{red}{neutralized}
     \item[-] \st{structure of the neighbor(s) of country $k$ changes} \textcolor{red}{neutralized}
     \end{itemize}
\item Sources of variation of $L_{ijkt}\times N_{kt}$
     \begin{itemize}
     \item[-] \st{$i$ gets/looses representation in $k$} \textcolor{red}{neutralized}
     \item[-] $i'$ gets/looses representation in $k$
     \item[-] structure of the neighbor(s) of country $k$ changes \hypertarget{specs}{}     \hyperlink{cases}{\beamergotobutton{Examples}}
     \end{itemize}
\end{itemize}
}
\end{overlayarea}

\end{frame}


\section{Results}

\begin{frame}{Benchmark results}
\vspace{-0.8cm}
\begin{center}
\begin{table} \centering \small
\begin{threeparttable}
\resizebox{0.94\textwidth}{!}{
\begin{tabular}{@{\extracolsep{5pt}}l*{6}{c}}
\hline \hline
\\[-1.8ex] & (1) & (2) & (3) &(4) &(5) &(6)  \\
    & \multicolumn{3}{c}{\emph{Active support}} & \multicolumn{3}{c}{\emph{Political inclusion}} \\
\\[-1.8ex] \cline{2-4} \cline{5-7}\\[-1.8ex]
Nb of countries with a link&     -0.0000&            &            &     -0.0038&            &            \\
                    &     (0.000)&            &            &     (0.004)&            &            \\
                    &     [0.824]&            &            &     [0.307]&            &            \\
Link $\times$ Nb of countries with a link&      0.0025&      0.0041&      0.0075&      0.0364&      0.0652&      0.0731\\
                    &     (0.002)&     (0.002)&     (0.003)&     (0.018)&     (0.024)&     (0.040)\\
                    &     [0.249]&     [0.089]&     [0.027]&     [0.041]&     [0.007]&     [0.070]\\
 & & & & & & \\
Controls in Target$_{ijt}$&         Yes&         Yes&         Yes&         Yes&         Yes&         Yes\\
Controls in Sponsor$_{ikt}$&         Yes&         Yes&         Yes&         Yes&         Yes&         Yes\\
Triad$_{ijk}$ FE   &         Yes&         Yes&         &         Yes&         Yes&         \\
Year$_{t}$ FE       &   Yes         &            &            &     Yes       &            &            \\
Target$_{j}$*Sponsor$_{k}$*Year$_{t}$ FE&            &    Yes        &     Yes       &            &     Yes       &       Yes     \\
Triad$_{ijk}$*Power in sponsor$_{ik}$ FE&            &            &       Yes     &            &            &       Yes     \\
R$^2$               &      0.4453&      0.5816&      0.5876&      0.8855&      0.9126&      0.9128\\
Adjusted R$^2$      &      0.4291&      0.4630&      0.4706&      0.8821&      0.8878&      0.8880\\
%Observations        &     1,287,813&     1287813&     1287813&     1287813&     1287813&     1287813\\
\hline\hline
\end{tabular}
}
\begin{tablenotes}
\item \parbox{0.94\textwidth}{\tiny  OLS estimations. Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses. 1,287,813 obs. Controls target: group share (quartile dummies) + interactions w. Link. Controls sponsor: group share (quartile dummies) + interactions w. Link, 8 political status dummies in Columns (1)--(3) (\textit{Monopoly}, \textit{Dominant}, \textit{Senior partner}, \textit{Junior Partner}, \textit{Powerless}, \textit{Self-excluded}; \textit{Discriminated}; \textit{Irrelevant}: ref.=\textit{Absent}).} 
\end{tablenotes}
\end{threeparttable}
\end{table}

\end{center}
\end{frame}

\begin{frame}
\frametitle{(Non-)Monotonicity?}
\vspace{-1.2cm}
\small
%\begin{multline*}
%Y_{ijkt} = \alpha + \eta_1 L_{ijkt}\times d(N=2,3)_{kt} + \eta_2 L_{ijkt}\times d(N=4,5)_{kt} \\
%+ \eta_3 L_{ijkt}\times d(N=6,7)_{kt} + \eta_4 L_{ijkt}\times d(N=8,9)_{kt} \\
%+ \Lambda_{ijk} + \mu_{jkt} + \phi z_{ijt} + \chi x_{ikt}  + \epsilon_{ijkt}
%\end{multline*}
%Although the confidence intervals overlap, we see that we have a non-monotonic relationship for the first result and a monotonic relationship for the second result.

%\begin{figure}[!ht]
%    \centering
%    \scalebox{0.8}{
%    \begin{minipage}{.5\textwidth}
%        \centering
%        \includegraphics[width=0.99\linewidth,]{nl-support-ci95-both.pdf}
%        \caption{Dependent variable: Active support}
%    \end{minipage}%
%    \begin{minipage}{0.5\textwidth}
%        \centering
%        \includegraphics[width=0.99\linewidth]{nl-incl-ci95-both.pdf}
%        \caption{Dependent variable: Political inclusion}
%    \end{minipage}}
%\end{figure}
%\end{frame}
%\hypertarget{nonmonotone}{}
\begin{tabular}{cc}
\includegraphics[width=0.45\linewidth,]{nl-support-ci95-both(2).pdf} &  \includegraphics[width=0.45\linewidth]{nl-incl-ci95-both(2).pdf} \\
Dependent variable: Active support & Dependent variable: Political inclusion \\
\end{tabular}
\hyperlink{fullyflex}{\beamergotobutton{All dummies}}

\hyperlink{quadratic}{\beamergotobutton{Quadratic specification}}
%\hyperlink{rob}{\beamerbutton{Back}}
\end{frame}


\begin{frame}
\frametitle{Additional tests}
\hypertarget{rob}{}
\vspace{-0.5cm}
\begin{itemize}
%\item Non-monotonicity of active support \hyperlink{nonmonotone}{\beamergotobutton{Non-monotone}}
\item $i'$ reaching/exiting the coalition in $k$ %New coalition members in $k$: control for the size and composition of the coalition in $k$

\item Control for Nb potential/realized sponsors of group $i$\\ \hyperlink{changesruling}{\beamergotobutton{Potential confounders}} 

\item Data geometry
\begin{itemize}

\item[-] Weight 1 for each sponsor state %\hyperlink{weight}{\beamerbutton{Weighted results}} 
\item[-] \color{gray} Collapsed data at the ethnic group $\times$ target country level (ij) + dyad level (jk) %\hyperlink{polinclij}{\beamerbutton{Pol. incl.: dyadic $ij$ level}} 
\end{itemize}
%\item Alternative measures
%\begin{itemize}
%\item[-] Rebel groups with more than one ethnic background %\hyperlink{multiple}{\beamerbutton{Mult. ethn.}} 
%\item[-] Number of countries with link $i$-type ethnic link %\hyperlink{altn}{\beamerbutton{Alternative $N_{kt}$}} 
%\end{itemize}
\item Alternative datasets:
\begin{itemize}
\item[-] Ethnic group-balanced panel.
\item[-] Contiguous neighbors as potential targets: \hyperlink{alttar}{\beamergotobutton{Robustness}} 
\end{itemize}

\item Passive support as a placebo \hyperlink{placebo}{\beamergotobutton{Placebo}} 
\item Qualitative nature of the dep. var. \hyperlink{quali}{\beamergotobutton{Qual. dep. var.}}
\end{itemize}

\end{frame}

\begin{frame}{The scope of reputation-building}
\vspace{-0.8cm}
\begin{center}
\begin{table} \centering \footnotesize
\begin{threeparttable}
\resizebox{0.94\textwidth}{!}{
\begin{tabular}{@{\extracolsep{5pt}}l*{5}{c}}
%\hline \hline
%\\[-1.8ex] & (1) & (2) & (3) & (4) &(5) \\
    & Multiple ethnic & \multicolumn{2}{c}{\multirow{2}{*}{$i$-type links}} & \multicolumn{2}{c}{\multirow{2}{*}{Status in $k$}} \\
    & background \\
\\[-1.8ex] \cline{2-2} \cline{3-4} \cline{5-6}\\[-1.8ex]
    & \emph{Active sup.} & \emph{Active sup.} & \emph{Political incl.} & \emph{Active sup.} & \emph{Political incl.} \\
\\[-1.8ex] \cline{2-2} \cline{3-4} \cline{5-6}\\
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of countries with a link}}&      0.0082&      0.0041   &0.0907      \\
                    &     (0.004)&      (0.002)  &(0.045)    \\
                    &     [0.021]&      [0.054]   & [0.043]   \\
\multirow{2}{*}{\parbox{4cm}{Nb of countries with a link $\times$ $i$ in monopoly in $k$}}    &&&     &      0.0064&      0.0948\\
                    && &&    (0.003)&     (0.048)\\
                    && &&    [0.038]&     [0.049]\\
\multirow{2}{*}{\parbox{4cm}{Nb of countries with a link $\times$ $i$ dominant in $k$}}&&          & &      0.0081&      0.0402\\
                    &&&&     (0.004)&     (0.028)\\
                    &&&&     [0.031]&     [0.150]\\
\multirow{2}{*}{\parbox{4cm}{Nb of countries with a link $\times$ $i$ senior partner in $k$}}        &&&   &      0.0082&      0.0758\\
                    &&&&     (0.005)&     (0.042)\\
                    &&&&     [0.084]&     [0.070]\\
\multirow{2}{*}{\parbox{4cm}{Nb of countries with a link $\times$ $i$ junior partner in $k$}}        && &   &     -0.0010&     -0.0076\\
                    & &&&    (0.001)&     (0.018)\\
                    & &&&    [0.325]&     [0.672]\\
&&\\
Controls and FE&         Yes&         Yes&         Yes&         Yes&         Yes\\
R$^2$               &     0.5954&      0.5873& 0.9128  &      0.5876&      0.9128\\
Adjusted R$^2$      &      0.4806&      0.4702& 0.8880 &      0.4706&      0.8880\\
\hline\hline
\end{tabular}
}
\begin{tablenotes}
\item \parbox{0.94\textwidth}{\tiny  OLS estimations. Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses. 1,287,813 obs.} 
\end{tablenotes}
\end{threeparttable}
\end{table}

\end{center}
\end{frame}


\section{Conclusion}
\begin{frame}
\frametitle{Conclusion}
\vspace{-0.4cm}
\begin{itemize}
\item \small Reputation-building mechanism $\rightarrow$ Two predictions, hard to explain by other stories. A larger audience implies:
    \begin{enumerate}
    \item \footnotesize $\uparrow$ likelihood of sponsorship [non-monotonicity]
    \item[$\Rightarrow$] \footnotesize States seek to build their reputation.
    \item \footnotesize $\uparrow$ political representation
    \item[$\Rightarrow$] \footnotesize This reputation-building strategy is effective.
    \end{enumerate}
\medskip
\item \small Unique triad-year data structure
    \begin{itemize}
    \item[-] \footnotesize Support both predictions, with identification based on the most plausibly exogenous sources of variations.
     \end{itemize}
    \medskip
\item \small Policy implication: trying to discredit a transnational identity narrative (Compatriots doctrine) can backfire.

\end{itemize}
\end{frame}


\appendix





\begin{frame}\medskip
\frametitle{Assumptions}
\hypertarget{assum}{}
\begin{itemize}
\item Expected payoff in case of sponsored rebellion is positive for an I-type $S$: $\pi\beta_I-C_S>0$, \medskip
\item Expected payoff in case of sponsored rebellion is negative for an E-type $S$: $\pi\beta_E-C_S<0$... \medskip
\item[...] but the surplus of utility of the policy concession is large enough to compensate: $(1+\pi)\beta_E-C_S>0$. \medskip
\item Expected payoff in case of sponsored rebellion is negative for $T_j$ (preference for no rebellion) : $1-\pi-C_T<0$.
\end{itemize}
\hyperlink{setting}{\beamergotobutton{Back}}
\end{frame}

\begin{frame}\medskip
\hypertarget{fullseqeq}{}
\frametitle{Equilibrium}
\begin{footnotesize}
\begin{itemize}
\item If $S$ is I-type, it always intervenes.
\item If $S$ is E-type and there is no policy concession:
     \begin{itemize}
     \begin{tiny}
     \item $S$ does not intervene when $i=1$
     \item when $i>1$, $S$ intervenes with certainty if $p_i\ge(\pi+C_T)^{1-i}$, and with probability $((\pi+C_T)^{i-1}-1)p_i/(1-p_i)$ if $p_i<(\pi+C_T)^{1-i}$
     \end{tiny}
     \end{itemize}
\item If the history of the play up to stage $i<n$ includes any instance that a state $T_j$ ($j>i$) refused a concession yet state $S$ did not retaliate by supporting a rebellion there $\rightarrow$ commonly shared belief that state $S$ is I-type $p_i=0$.
\item If $S$ retaliated against every refusal so far, and the last refusal occurred in stage $k>i$, then $p_i=\max\{(\pi+C_T)^{1-k},\theta\}$.
\item If $p_i > (\pi+C_T)^{-i}$, $T_i$ makes a concession. If $p_i < (\pi+C_T)^{-i}$, it refuses to do so. If $p_i = (\pi+C_T)^{-i}$, it randomizes, making a concession with probability $\beta_E/(C_S-\pi\beta_E)$.
\end{itemize}
\end{footnotesize}
\hyperlink{setting}{\beamergotobutton{Back}}
\end{frame}

\begin{frame}\medskip
\frametitle{Equilibrium} \tiny
The game starts at $i=n$ and $p_i=\theta$ in one of four situations:
\begin{itemize}
\item[a)]  $n \ge 1-\ln p_i/\ln(\pi+C_T)$: $S$ always intervenes; $T_n$ concedes.
\item[b)] $1-\ln p_i/\ln(\pi+C_T) > n > -\ln p_i/\ln(\pi+C_T)$: the probability that $S$ intervenes is too high; $T_n$ concedes.
\item[c)] $n = -\ln p_i/\ln(\pi+C_T)$: $T_n$ concedes with probability $\beta_E/(C_S-\pi\beta_E)$.
\item[d)] $-\ln p_i/\ln(\pi+C_T) > n$: $T_n$ denies the concession. In both situations c) and d), an extrinsically motivated $S_E$ would intervene with probability $((\pi+C_T)^{i-1}-1) p_i/(1-p_i)$% (an intrinsically motivated $S_I$ would of course intervene).
\end{itemize}
\begin{figure}[ht!]
\centering
\begin{tikzpicture}
    \node[main node] (1) {a};
    \node[main node] (2) [right = 2cm of 1] {b};
    \node[main node] (3) [right = 2cm of 2] {d};
    \node[main node] (4) [right = 2cm of 3] {c};
    \node[end node] (5) [below right = .5cm and .5cm of 3] {end};
    \node[end node] (6) [below right = .5cm and .5cm of 4] {end};
    
    \draw[thick,->,shorten >=1pt] (1) to (2);
    \draw[thick,->,shorten >=1pt] (2) to (3);
    \draw[thick,->,shorten >=1pt] (3) to (4);
    \draw[thick,->] (3) to (5);
    \draw[thick,->] (4) to (6);
    \draw[thick,->,shorten >=1pt, dashed] (1) to [out = 30, in = 150] (4);
    \draw[thick,->,shorten >=1pt] (1) to [out=60,in=120,loop,looseness=4.8] (1);
    \draw[thick,->,shorten >=1pt] (4) to [out=60,in=120,loop,looseness=4.8] (4);

\end{tikzpicture}
\hyperlink{setting}{\beamergotobutton{Back}}

\end{figure}
\end{frame}

\begin{frame}
\hypertarget{Datasource}{}
\frametitle{Main data sources}
\begin{itemize}[<+->]
\item EPR 2019 (Vogt et al. 2019)\medskip 
\begin{itemize}
\item[-] EPR Core: politically relevant ethnic groups and their level of political representation in target and sponsor states\medskip 
\item[-] Transborder Ethnic Kin \medskip
\item[-] ACD2EPR: links ethnic groups with rebel groups \medskip
\end{itemize}
\item San Akca (2016): international support of rebel groups.% (1925--2010).% and provides a wealth of information on the nature of that support that exceeds our needs in this paper.
\end{itemize}
\hyperlink{Data}{\beamergotobutton{Back}}
\end{frame}

\begin{frame}
\frametitle{Descriptive stats}
\hypertarget{fullstats}{}
\begin{table}[!htbp] \centering
\resizebox{0.6\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lcc}
\hline \hline
\\[-1.8ex] & (1) & (2) \\ \textbf{Triad $\times$ year-lev\-el}   & All & Link = 1 \\
\\[-1.8ex] \hline \\[-1.8ex]
%\multicolumn{3}{l}{\textbf{Triad $\times$ year-lev\-el}}  \\[-1.8ex]\\
Link            & 1.29 \%          &           \\
Active support  & 0.06 \%          & 1.27\%   \\
Passive support  & 0.09 \%          & 1.06\%   \\
Number of countries with a link with the sponsor state  &   2.01        & 5.85  \\
Group size in target state                              &   17.47\%     & 26.51\%  \\
Group size in sponsor state                             &   1.21\%     & 51.97\%  \\
Status in target: Monopoly                   &    4.73\%     & 10.18\%  \\
Status in target: Dominant                   &    6.13\%     & 8.83\%  \\
Status in target: Senior Partner              &   9.88\%     & 13.74\%  \\
Status in target: Junior Partner              &   20.28\%     & 18.89\%  \\
Status in target: Powerless            &   41.58\%     & 30.20\%  \\
Status in target: Self-excluded            &   1.61\%     & 1.00\%  \\
Status in target: Discriminated                         &   15.80\%     & 17.17\%  \\
Status in sponsor: Monopoly         &  0.38\%     & 29.73\% \\
Status in sponsor: Dominant         &  0.31\%     & 24.45\%  \\
Status in sponsor: Senior Partner   &  0.59\%     & 45.82\% \\
Status in sponsor: Junior Partner   &  0.60\% \\
Status in sponsor: Powerless   &   1.39\% \\
Status in sponsor: Self-excluded   &   0.06\% \\
Status in sponsor: Discriminated   &   1.06\% \\
Status in sponsor: Irrelevant   &   0.55\% \\
Status in sponsor: Absent            &   95.06\%   \\
\# obs. &  1,287,813  & 16,572  \\
\\[-1.8ex] \hline \\[-1.8ex]
\end{tabular}
\end{small}
\end{threeparttable}
}
\end{table}
 \hyperlink{stats}{\beamergotobutton{Back}}
\end{frame}


\begin{frame}
\frametitle{Descriptive stats}
\begin{table}[!htbp] \centering
\resizebox{0.6\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lcc}
\hline \hline
\\[-1.8ex] & (1) & (2) \\ \textbf{Sponsor $\times$ year-lev\-el}   & All & Link = 1 \\
\\[-1.8ex] \hline \\[-1.8ex]
%\multicolumn{3}{l}{\textbf{Triad $\times$ year-lev\-el}}  \\[-1.8ex]\\
At least one link            & 46.35\%          & \\
Number of links              & 1.88          & \\
At least one active support  & 6.90\%          &  12.57\%\\
Number of active supports    & 0.09          & 0.17 \\
At least one passive support  & 10.34\%          &  16.38\%\\
Number of passive supports    & 0.13          & 0.22 \\
Number of countries with a link with the sponsor state  &   1.65        & 3.55 \\
Group size in sponsor state                             &   1.47\%     & 56.39\% \\
Status in sponsor: Monopoly         &  0.34\%     & 22.95\% \\
Status in sponsor: Dominant         &  0.61\%     & 32.96\%  \\
Status in sponsor: Senior Partner   &  0.57\%     & 44.09\% \\
Status in sponsor: Absent            &   94.65\%   \\
Status in sponsor: Other   &   3.83\% \\
\# obs.  &  8,837 & 4,096 \\
\\[-1.8ex] \hline \\[-1.8ex]
\end{tabular}
\end{small}
\end{threeparttable}
}
\end{table}
 \hyperlink{stats}{\beamergotobutton{Back}}
\end{frame}

\begin{frame}
\frametitle{Descriptive stats}
\begin{table}[!htbp] \centering
\resizebox{0.6\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lcc}
\hline \hline
\\[-1.8ex] & (1) & (2) \\ \textbf{Group in the target state $\times$ year-level}   & All & Link = 1 \\  \\[-1.8ex] \hline \\[-1.8ex]
At least one link            & 24.44\%    & \\
Number of links              & 0.47        & \\
At least one active support  & 1.60\%    &  2.27\% \\
%Number of active supports    & 0.023       & 0.042 \\
At least one passive support  & 2.08\%    &  1.83\% \\
%Number of passive supports    & 0.033       & 0.040 \\
Group size in target state                   &   18.05\%     & 25.02\% \\
Status in target: Monopoly                   &   5.34\%     & 7.74\% \\
Status in target: Dominant                   &   6.56\%     & 8.07\% \\
Status in target: Senior Partner              &   9.26\%     & 13.26\% \\
Status in target: Junior Partner              &   18.26\%     & 19.61\% \\
Status in target: Powerless                &   42.42\%     & 32.73\% \\
Status in target: Self-excluded            &   1.60\%     & 1.31\% \\
Status in target: Discriminated                         &   16.57\%     & 17.28\% \\
\# obs. &  35,546  & 8,686 \\
\\[-1.8ex] \hline \\[-1.8ex]
\end{tabular}
\end{small}
\end{threeparttable}
}
\end{table}
 \hyperlink{stats}{\beamergotobutton{Back}}
\end{frame}

\begin{frame}
\frametitle{Illustration: Afghanistan 2005--2006}
    \includegraphics[width=0.85\textwidth,trim={0 0 6.9cm 0}]{map_afg2005_NEW2024.pdf}
    \hypertarget{cases}{}
\end{frame}

\begin{frame}
    \frametitle{Illustration: Afghanistan 2005--2006}
    \includegraphics[width=.9\textwidth,trim={0 0 5cm 0}]{map_afg2006_NEW2024.pdf}
\end{frame}
%    \frametitle{Illustration: Afghanistan 2005--2006}
%    \includegraphics[width=\textwidth,trim={6cm 0 5cm 0}]{map_afg2005(1).pdf}
%\end{frame}
%
%\begin{frame}
%    \frametitle{Illustration: Afghanistan 2005--2006}
%    \includegraphics[width=.9\textwidth,trim={0 0 5cm 0}]{map_afg2006_new.pdf}
%\end{frame}

\begin{frame}
    \frametitle{Illustration: Thailand 1979--1980}
\includegraphics[width=.8\textwidth,trim={6cm 0 9cm 1.5cm}]{map_tha1979.pdf}
\end{frame}

\begin{frame}
    \frametitle{Illustration: Thailand 1979--1980}
\includegraphics[width=.8\textwidth,trim={6cm 0 9cm 1.5cm}]{map_tha1980.pdf}

 \hyperlink{specs}{\beamergotobutton{Back}}
\end{frame}

\begin{frame}\frametitle{Fully flexible specification}
\hypertarget{fullyflex}{}
\begin{figure}
    \centering
    \begin{minipage}{.5\textwidth}
        \centering
        \includegraphics[width=0.95\linewidth,]{nl-support-ci95-both_9bins.pdf}
        Dep. variable: Active support
        %\caption*{Dependent variable: Active support}
    \end{minipage}%
    \begin{minipage}{0.5\textwidth}
        \centering
        \includegraphics[width=0.95\linewidth]{nl-incl-ci95-both_9bins.pdf}
        Dep. variable: Pol. inclusion
        %\caption*{Dependent variable: Political inclusion}
    \end{minipage}
\end{figure}
\end{frame}

\begin{frame}\frametitle{Quadratic specification}
\hypertarget{quadratic}{}
\vspace{-20pt}
\begin{table} \centering
\resizebox{0.8\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{l*{4}{c}}
%\hline\hline
                    &\multicolumn{1}{c}{(1)}&\multicolumn{1}{c}{(2)}&\multicolumn{1}{c}{(3)}&\multicolumn{1}{c}{(4)} \\
                    &\multicolumn{2}{c}{\emph{Active support}}&\multicolumn{2}{c}{\emph{Political inclusion}} \\
\\[-1.8ex] \cline{2-5}
\\[-1.8ex]
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of countries with a link}}&      0.0075&      0.0334&    0.0731&      0.0998 \\
                    &     (0.003)&     (0.012)&    (0.040)&     (0.100) \\
                    &     [0.027]&     [0.007]&  [0.070]&     [0.318] \\
&&\\
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of countries with a link squared}} &            &     -0.0021&    &     -0.0022 \\
                    &            &     (0.001)&   &     (0.011) \\
                    &            &     [0.007]&   &     [0.842] \\
\\
Joint significance test, p-val &  & 0.0252 & & 0.2096 \\
\\
%Threshold & & 7.95 & & 22.7 \\
Controls and FE&         Yes&         Yes&         Yes&         Yes \\
%Mean dep. var.      &      0.0006&      0.0006&    1.5993&      1.5993 \\
R$^2$               &      0.5876&      0.5881 & 0.9128&      0.9128 \\
Adjusted R$^2$      &      0.4706&      0.4712&  0.8880&      0.8880 \\
%Obs                 &     1287813&     1287813&     1287813&     1287813 \\
\hline\hline
\end{tabular}
\end{small}
\begin{tablenotes}
\item \parbox{0.94\textwidth}{\tiny OLS estimations at the triad level. 1,287,813 obs. Target controls: group size (+ interac. w. $L_{ijkt}$). Sponsor controls: group size (+ interac. w. $L_{ijkt}$), 8 political status dummies. Robust standard errors clustered at the tar\-get-coun\-try and spon\-sor-coun\-try levels in parentheses. P-values in squared brackets.}
\end{tablenotes}
\end{threeparttable}
}
\end{table}
 \hyperlink{specs}{\beamergotobutton{Back}}
\end{frame}

\begin{frame} \frametitle{Potential confounders}
\hypertarget{changesruling}{}
\vspace{-1cm}
\begin{table}[!ht] \centering
\resizebox{0.8\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}l*{8}{c}}
\hline \hline
\\[-1.8ex] & (1) & (2) & (3) &(4) &(5) &(6) &(7) & (8)  \\
    & \multicolumn{4}{c}{\emph{Active support}} & \multicolumn{4}{c}{\emph{Political inclusion}} \\
\\[-1.8ex] \cline{2-5} \cline{6-9}\\[-1.8ex]
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of countries with a link}} &      0.0075&      0.0078&      0.0076&      0.0075&      0.0731&      0.0741&      0.0705&      0.0725\\
                    &     (0.003)&     (0.004)&     (0.003)&     (0.003)&     (0.040)&     (0.041)&     (0.038)&     (0.040)\\
                    &     [0.027]&     [0.040]&     [0.026]&     [0.027]&     [0.070]&     [0.070]&     [0.064]&     [0.067]\\
  & & & \\
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of groups in power ($G_{kt}$)}} &            &     -0.0069&            &            &            &     -0.0294&            &            \\
                    &            &     (0.027)&            &            &            &     (0.081)&            &            \\
                    &            &     [0.799]&            &            &            &     [0.715]&            &            \\
  & & & \\
\multirow{2}{*}{\parbox{3cm}{Link $\times$ Power switch ($PS_{kt}$)}}   &            &     -0.0162&            &            &            &     -0.0218&            &            \\
                    &            &     (0.012)&            &            &            &     (0.072)&            &            \\
                    &            &     [0.168]&            &            &            &     [0.762]&            &            \\
  & & & \\
\multirow{2}{*}{\parbox{4cm}{Nb of potential sponsors}}&            &            &     -0.0003&            &            &            &      0.0111&            \\
                    &            &            &     (0.000)&            &            &            &     (0.067)&            \\
                    &            &            &     [0.347]&            &            &            &     [0.869]&            \\
  & & & \\
\multirow{2}{*}{\parbox{4cm}{Nb of other ongoing supports}}&            &            &            &      0.0044&            &            &            &     -0.2207\\
                    &            &            &            &     (0.001)&            &            &            &     (0.099)\\
                    &            &            &            &     [0.000]&            &            &            &     [0.025]\\
 & & \\
Controls and FE&         Yes&         Yes&         Yes&         Yes&         Yes&         Yes&         Yes&         Yes\\
%Mean dep. var.      &      0.0006&      0.0006&      0.0006&      0.0006&      1.5993&      1.5993&      1.5993&      1.5993\\
R$^2$               &      0.5876&      0.5877&      0.5876&      0.5880&      0.9128&      0.9128&      0.9128&      0.9131\\
Adjusted R$^2$      &      0.4706&      0.4706&      0.4706&      0.4711&      0.8880&      0.8880&      0.8880&      0.8885\\
\hline\hline
\end{tabular}
\end{small}
\begin{tablenotes}
\begin{footnotesize}
\item OLS estimations at the triad level. Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses.
\end{footnotesize}
\end{tablenotes}
\end{threeparttable}
}
\end{table}
\vspace{-1.2cm}
\hyperlink{rob}{\beamerbutton{Back}}
\end{frame}



%\begin{frame}
%\frametitle{Alternative measures of the number of links}
%\hypertarget{altn}{}
%\begin{center}
%\begin{small}
%\resizebox{0.9\textwidth}{!}{
%\begin{tabular}{@{\extracolsep{5pt}}lc}
%\hline \hline
%Number of countries with a link with the sponsor state & 1.45 \\
%Total number of links of the sponsor state & 1.70 \\
%Number of countries with a link of the same nature with the sponsor state & 0.13 \\
%\hline \hline
%\end{tabular}
%}
%\end{small}
%\end{center}
%\end{frame}




\begin{frame}
\frametitle{Additional Tests}
\hypertarget{alttar}{}
\vspace{-1.2cm}
\begin{table}[!h] \centering
\resizebox{0.8\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}l*{6}{c}}
\hline \hline
\\[-1.8ex] & (1) & (2) & (3) &(4) \\
    & \multirow{2}{*}{Benchmark} & \multirow{2}{*}{Weighted data} & Group-balanced & Contiguous \\
    & & & panel & countries \\
\\[-1.8ex] \cline{2-5} \\[-1.8ex]
\emph{Panel A: Active support} \\
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of countries with a link}}&      0.0075&      0.0054&            0.0103&      0.0113\\
                    &     (0.003)&     (0.002)&        (0.005)&     (0.006)\\
                    &     [0.027]&     [0.030]&          [0.022]&     [0.068]\\
%Mean dep. var.      &      0.0006&      0.0006&      0.0010&      0.0006&      0.0006&      0.0031\\
&&\\
R$^2$               &      0.5876&      0.6572&            0.5009&      0.6147\\
Adjusted R$^2$      &      0.4706&      0.5600&           0.3845&      0.5358\\
%Obs                 &     1287813&     1287813&     1287813&     1287813&     1550451&      276755\\
\\[-1.8ex] \cline{2-5} \\[-1.8ex]
\emph{Panel B: Political inclusion} \\
\multirow{2}{*}{\parbox{4cm}{Link $\times$ Nb of countries with a link}}&      0.0731&      0.0751&      0.0566&      0.0898\\
                    &     (0.040)&     (0.032)&     (0.033)&     (0.051)\\
                    &     [0.070]&     [0.019]&     [0.090]&     [0.079]\\
%Mean dep. var.      &      1.5993&      1.6317&     & 1.5993&      1.4978&      1.4094\\
&&\\
R$^2$               &      0.9128&      0.9343&      0.8733&      0.9357\\
Adjusted R$^2$      &      0.8880&      0.9157&      0.8438&      0.9225\\
& \\
Controls and FE&         Yes&         Yes&         Yes&         Yes\\
Observations                        & 1,287,813&     1,287,813&     1,550,451&      276,755\\
\hline\hline
\end{tabular}
\end{small}
\begin{tablenotes}
\begin{footnotesize}
\item OLS estimations at the triad level. Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses.
\end{footnotesize}
\end{tablenotes}
\end{threeparttable}
}
\end{table}
\vspace{-1.2cm}
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\end{frame}


\begin{frame}
\frametitle{Weighted estimations}
\hypertarget{weight}{}
\vspace{-0.5cm}
\begin{itemize}
    \item By construction, a sponsor with more neighbors is a member of more triads.

    \item $\rightarrow$ Each sponsor is allocated a weight of 1, all triads involving the same sponsor state (and all years involving the same triad) representing the same weight for the sponsor. 
\end{itemize}
\hyperlink{rob}{\beamerbutton{Back}}
\end{frame}


\begin{frame}\medskip
\frametitle{Pol. inclusion, group-level estimations}
\hypertarget{polinclij}{}
\begin{equation*}\label{eq:gplevincl}
I_{ijt} = \alpha + \kappa K_{ijt} + \nu NK_{ijt} + \phi' z_{ijt} + \lambda_{ij} + \mu_t + \epsilon_{ijt}
\end{equation*}
\medskip

\begin{itemize}
\item $K_{ijt}$: number of possible sponsor states with whom group $i$ in country $j$ shares an ethnic tie.
\medskip
\item $NK_{ijt}$: sum of the number of countries with whom each possible sponsor shares an ethnic tie.
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{Pol. inclusion, group-level estimations}
\vspace{-1.2cm}
\begin{table}[!ht] \centering
\resizebox{0.5\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lc}
\hline \hline
\\[-1.8ex] \emph{Dependent variable: Political inclusion}& (1) \\
\\[-1.8ex] \hline\\[-1.8ex]
Nb of possible sponsors with a link&    -0.1505\\
                    &       (0.088)\\
                    &       [0.090]\\
Number of links of possible sponsors&      0.0273\\
                    &      (0.013)\\
                    &      [0.038]\\
  &   \\
Group$_{ij}$ FE     &         Yes\\
Country$_{j}$*Year$_{t}$ FE&      Yes\\
Controls$_{ijt}$    &         Yes\\
%\\[-1.8ex] \hline \\[-1.8ex]
R$^2$               &           0.9189\\
Adjusted R$^2$      &         0.8959\\
Observations        &        35546\\
\hline
\hline \\[-1.8ex]
\end{tabular}
\end{small}
\begin{tablenotes}
\begin{footnotesize}
\item OLS estimation at the ethnic group---target state level. Robust standard errors clustered at the target-country level in parentheses. P-values in squared parentheses.
\end{footnotesize}
\end{tablenotes}
\end{threeparttable}}
\end{table}
\vspace{-1.2cm}
\hyperlink{rob}{\beamerbutton{Back}}
\end{frame}



\begin{frame}
\frametitle{Country-pair level results}
\hypertarget{jk}{}
\begin{equation*}
S_{jkt} = \alpha + \rho NL_{jkt} + \delta N_{kt} + \sigma NL_{jkt} \times N_{kt} + \tau_{jk} + \mu_t + \epsilon_{jkt}
\end{equation*}

\begin{itemize}
\item $S_{jkt}$: one if at least one ethnic group in country $j$ is actively supported by country $k$ at time $t$.
\medskip
\item $NL_{jkt}$: number of ethnic links (possibly greater than one) between countries $j$ and $k$ at time $t$.
\medskip
\item $N_{kt}$: (as before) number of countries with whom $k$ shares an ethnic tie at time $t$.
%\medskip
%\item dyad ($\tau_{jk}$) and year $\mu_t$ (fixed-effects).
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{Country-pair level results}
\vspace{-1.2cm}
\begin{table}[!ht] \centering
\resizebox{0.63\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lccc}
\hline \hline
\\[-1.8ex] \emph{Dependent variable: (At least one) Active support}& (1) & (2) & (3) \\
\\[-1.8ex] \hline\\[-1.8ex]
Nb of links in the dyad&      -0.045&      -0.045&      -0.047\\
                    &     (0.022)&     (0.022)&     (0.023)\\
                    &     [0.040]&     [0.040]&     [0.037]\\
   & & &\\
Nb of countries with a link with the sponsor&      -0.001&      -0.001&            \\
                    &     (0.001)&     (0.001)&            \\
                    &     [0.330]&     [0.330]&            \\
   & & &\\
Interaction         &       0.011&       0.011&       0.012\\
                    &     (0.006)&     (0.006)&     (0.006)\\
                    &     [0.080]&     [0.080]&     [0.065]\\
   & & &\\
Dyad$_{jk}$ FE      &         Yes&         Yes&         Yes\\
Year$_{t}$ FE       &         Yes&         Yes&            \\
Sponsor$_{k}$*Year$_{t}$ FE&            &            &         Yes\\
%\\[-1.8ex] \hline \\[-1.8ex]
R$^2$               &      0.4198&      0.4198&      0.4423\\
Adjusted R$^2$      &      0.4046&      0.4046&      0.4063\\
Observations        &      248,987&      248,939&      248,939\\
%Nb of target states  & XX & XX & XX \\
%Nb of sponsor states & XX & XX & XX \\
\hline
\hline \\[-1.8ex]
\end{tabular}
\end{small}
\begin{tablenotes}
\begin{footnotesize}
\item OLS estimations at the dyad level. Column (2): sample of sponsor countries observed in more than one dyad (for comparability with Column (3), which omits sponsor countries that belong to one dyad only as it introduces sponsor-specific year FE). Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses.
\end{footnotesize}
\end{tablenotes}
\end{threeparttable}}
\end{table}
\vspace{-1.2cm}
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\end{frame}




\begin{frame}
\frametitle{Placebo test}
\hypertarget{placebo}{}
\vspace{-0.75cm}
\footnotesize Passive support (San Akca 2016): 1 when a rebel group uses a foreign state for its activity without its consent (ex. groups from country $j$ hiding in state $k$).\\
\footnotesize $\rightarrow$ Prevalence similar to active support, both are correlated (34\%).
%\item Remark: passive support could activate a low-intensity reputation-building mechanism.
%\pause
\vspace{-0.1cm}
\begin{table}[!ht] \centering \large
\resizebox{0.5\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lccc}
\hline \hline
\\[-1.8ex] \emph{Dependent variable: Passive support}& (1) & (2) & (3) \\
\\[-1.8ex] \hline\\[-1.8ex]
Nb of countries with a link&      0.0001&            &            \\
                    &     (0.000)&            &            \\
                    &     [0.418]&            &            \\
  & & & \\
Link $\times$ Nb of countries with a link&      0.0013&      0.0009&      0.0027\\
                    &     (0.001)&     (0.001)&     (0.002)\\
                    &     [0.293]&     [0.518]&     [0.212]\\
  & & & \\
Controls and Triad$_{ijk}$ FE    &         Yes&         Yes&         Yes\\
Year$_{t}$ FE       &         Yes&            &            \\
Target$_{j}$*Sponsor$_{k}$*Year$_{t}$ FE&            &         Yes&         Yes\\
Triad$_{ijk}$*Power in sponsor$_{ik}$ FE&            &            &         Yes\\
%Mean dep. var.      &      0.0009&      0.0009&      0.0009\\
R$^2$               &      0.4704&      0.5747&      0.5758\\
Adjusted R$^2$      &      0.4550&      0.4541&      0.4554\\
\hline
\hline \\[-1.8ex]
\end{tabular}
\end{small}
\begin{tablenotes}
\begin{footnotesize}
\item OLS estimations at the triad level. 1,287,813 observations. Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses.
\end{footnotesize}
\end{tablenotes}
\end{threeparttable}}
\end{table}
\vspace{-1.2cm}
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\end{frame}


\begin{frame}
\frametitle{Number of observations with large predicted values}
\hypertarget{quali}{}
\begin{table}[!ht] \centering
\resizebox{0.8\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{10pt}}lcccccc}
\hline \hline
\\[-1.8ex] & (1) & (2) & (3) &(4) &(5) &(6)  \\
Cutoffs    & \multicolumn{3}{c}{\emph{Active support}} & \multicolumn{3}{c}{\emph{Political inclusion}} \\
\\[-1.8ex] \cline{2-4} \cline{5-7}\\[-1.8ex]
$<-0.1$; $>1.1$ & 0 & 426 & 419 &  &  &   \\
$<-0.2$; $>1.2$ & 0 & 57 & 77 &  &  &   \\
$<-0.5$; $>1.5$ & 0 & 0 & 0 &  &  &   \\
$<-0.1$; $>5.1$ &   &    &    & 1,424 & 16,588 & 16,596\\
$<-0.2$; $>5.2$ &   &    &    & 45 & 9,522 & 9,659\\
$<-0.5$; $>5.5$ &   &    &    & 0 & 654 & 658 \\
\hline
\hline \\[-1.8ex]
\end{tabular}
\end{small}
%\begin{tablenotes}
%\begin{footnotesize}
%\end{footnotesize}
%\end{tablenotes}
\end{threeparttable}}
\end{table}
\end{frame}

\begin{frame}
\frametitle{Excluding predicted values outside the expected range}
\vspace{-0.3cm}
\begin{table}[!ht] \centering \small
\resizebox{0.85\textwidth}{!}{
\begin{threeparttable}
\begin{small}
\begin{tabular}{@{\extracolsep{5pt}}lcccccccc}
\hline \hline
\\[-1.8ex] & (1) & (2) & (3) &(4) &(5) &(6) \\
    & \multicolumn{3}{c}{\emph{Active support}} & \multicolumn{3}{c}{\emph{Political inclusion}} \\
\\[-1.8ex] \cline{2-4} \cline{5-7}\\[-1.8ex]
\multirow{2}{*}{\parbox{3cm}{Nb of countries with a link}}&     -0.0004&            &            &     -0.0040&            &            \\
                    &    (0.0006)&            &            &    (0.0040)&            &            \\
                    &    [0.5553]&            &            &    [0.3106]&            &            \\
  & & & \\
\multirow{2}{*}{\parbox{3cm}{Link $\times$ Nb of countries with a link}}&      0.0304&      0.0347&      0.0289&      0.0438&      0.0723&      0.0756\\
                    &    (0.0125)&    (0.0064)&    (0.0054)&    (0.0192)&    (0.0293)&    (0.0515)\\
                    &    [0.0147]&    [0.0000]&    [0.0000]&    [0.0225]&    [0.0138]&    [0.1426]\\
  & & & \\
Controls and Triad$_{ijk}$ FE    &         Yes&         Yes&         Yes&         Yes&         Yes&         Yes\\
Year$_{t}$ FE       &         Yes&            &            &         Yes&            &            \\
Target$_{j}$*Sponsor$_{k}$*Year$_{t}$ FE&            &         Yes&         Yes&            &         Yes&         Yes\\
Triad$_{ijk}$*Power in sponsor$_{ik}$ FE&            &            &         Yes&            &            &         Yes\\
Mean dep. var.      &      0.0012&      0.0015&      0.0009&      1.6281&      1.6192&      1.6401\\
R$^2$               &      0.4375&      0.8596&      0.8612&      0.8656&      0.9031&      0.9023\\
Adjusted R$^2$      &      0.4058&      0.7967&      0.8078&      0.8614&      0.8748&      0.8734\\
Obs                 &      664817&      519507&      865448&     1215576&     1220430&     1208789\\
\hline
\hline \\[-1.8ex]
\end{tabular}
\end{small}
\begin{tablenotes}
\begin{footnotesize}
\item OLS estimations at the triad level. Columns (1)-(3) exclude observations with predicted values below 0 or above 1. Columns (4)-(6) exclude observations with predicted values below 0 or above 5. Robust standard errors clustered at the target-country and sponsor-country levels in parentheses. P-values in squared parentheses.
\end{footnotesize}
\end{tablenotes}
\end{threeparttable}}
\end{table}
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\end{frame}

\end{document}
