%\documentclass[usenames,dvipsnames,11pt]{beamer}%

\documentclass[xcolor={usenames,dvipsnames,svgnames,table}, 11pt]{beamer}%
%\documentclass[xcolor={usenames,dvipsnames,svgnames,table},  11pt, trans]{beamer}%
 %,
\usetheme{Singapore}
\usepackage{adjustbox}
\usepackage{booktabs}
\usepackage[flushleft]{threeparttable}
\usepackage{bm}
\usepackage{tabu}
\usepackage{array}
\usepackage{multirow}
\usepackage{multicol}
\usepackage{setspace}
\usepackage{amssymb}
\usepackage[space]{grffile}
\usepackage{bbm}
\usepackage{verbatim}
\usepackage{xcolor}
\usepackage{xcolor}

%%%%%%%%

  
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{array}
\usepackage{tcolorbox}

\usepackage{booktabs}
\usepackage{bm}

\usepackage{caption}
\usepackage{csquotes}
\usepackage{centernot}
\usepackage{color}

\usepackage{dcolumn}

\usepackage{epstopdf}
\usepackage{eurosym}

\usepackage{etex}

\usepackage{float}


\usepackage{geometry}
\usepackage{graphicx}
\usepackage[space]{grffile}

%\usepackage[hidelinks]{hyperref}

\usepackage{ifplatform}
\usepackage{import} 

\usepackage{lscape}
\usepackage{longtable}

\usepackage{multirow}
\usepackage{multimedia}
\usepackage{multicol}
\usepackage{mathrsfs}
\usepackage{mathpazo}
\usepackage{makecell}

\usepackage{natbib}

\usepackage{pdfpages}
\usepackage{subcaption}

\usepackage{threeparttable}
\usepackage{tikz,forest}

\usepackage{xcolor}
\usepackage{xparse}
\usepackage{CJKutf8}

\usetheme{Singapore}%%%%%%%%%%%




\setbeamertemplate{frametitle}[default][center]
\usenavigationsymbolstemplate{}
\setbeamercovered{transparent}

\newcounter{tmp}
\newcommand\savecounter{\setcounter{tmp}{\value{enumi}}}
\newcommand\continuecounter{\setcounter{enumi}{\value{tmp}}}
\def\insertpresentationendframe{\inserttotalframenumber}

\newcolumntype{L}[1]{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}
\newcolumntype{R}[1]{>{\raggedleft\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}

\def\insertpresentationendframe{\inserttotalframenumber}
\makeatletter
\g@addto@macro{\appendix}{\immediate\write\@auxout{\string\@writefile{nav}{\noexpand\headcommand{\noexpand\def\noexpand\insertpresentationendframe{\the\c@framenumber}}}}}
\makeatother

\makeatletter
\newenvironment{customlist}[2]{
	\ifnum\@itemdepth >2\relax\@toodeep\else
	\advance\@itemdepth\@ne%
	\beamer@computepref\@itemdepth%
	\usebeamerfont{itemize/enumerate \beameritemnestingprefix body}%
	\usebeamercolor[fg]{itemize/enumerate \beameritemnestingprefix body}%
	\usebeamertemplate{itemize/enumerate \beameritemnestingprefix body begin}%
	\begin{list}
		{
			\usebeamertemplate{itemize \beameritemnestingprefix item}
		}
		{ \leftmargin=#1 \itemindent=#2
			\def\makelabel##1{%
				{%  
					\hss\llap{{%
							\usebeamerfont*{itemize \beameritemnestingprefix item}%
							\usebeamercolor[fg]{itemize \beameritemnestingprefix item}##1}}%
				}%  
			}%  
		}
		\fi
	}
	{
	\end{list}
	\usebeamertemplate{itemize/enumerate \beameritemnestingprefix body end}%
}
\makeatother

\newcommand{\modelA}{}
\newcommand{\modelB}{}
\newcommand{\modelC}{}

\graphicspath{{../Model/figures/}}

\makeatletter
\setbeamertemplate{footline}{%
	\leavevmode
	\vbox{\begin{beamercolorbox}[dp=1.25ex,ht=2.75ex]{fg=black}%	
		\end{beamercolorbox}%
	}%
	{\color{gray}\llap{\insertframenumber\,/\,\insertpresentationendframe\,}}
	
}
\makeatother

\setbeamersize{text margin left=2em,text margin right=2em}
\setbeamertemplate{itemize items}{\Large \textbullet}
\setbeamertemplate{itemize subitem}{\tiny$\blacksquare$}
\setbeamertemplate{itemize subsubitem}{$\star$}


	\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
%\makeatletter
%\def\thickhline{%
%  \noalign{\ifnum0=`}\fi\hrule \@height \thickarrayrulewidth \futurelet
%   \reserved@a\@xthickhline}
%\def\@xthickhline{\ifx\reserved@a\thickhline
%               \vskip\doublerulesep
%               \vskip-\thickarrayrulewidth
%             \fi
%      \ifnum0=`{\fi}}
%\makeatother
%\usebackgroundtemplate{\tikz\node[opacity=0.1] {\includegraphics[height=\paperheight,width=\paperwidth]{shipping.jpg}};}

\title{\textbf{The Pro-competitive Effects \\of Trade Agreements}}

\author
{%
	\texorpdfstring{
		\begin{tabular}{ccccc}
			Meredith Crowley & & Lu Han & & Thomas Prayer \\
			\scriptsize{Cambridge and CEPR} & &\scriptsize{Bank of Canada and CEPR} & & \scriptsize{Cambridge} 
	\end{tabular}}{}
}
\date{\small SEM, Milan \\   June 29, 2023}



\begin{document}
	{
	\setbeamertemplate{footline}{} 
	\begin{frame}[plain]
		\makebox[\linewidth][c]{%
			\begin{minipage}{\dimexpr\textwidth+1em\relax}
				\raggedright\titlepage
				\vspace{3em}
				 \scriptsize Disclaimer: The views expressed in this paper and presentation are those of the authors and do not necessarily reflect those of the Bank of Canada or its Governing Council. \vspace*{-5em}				
			\end{minipage}%
		}%
	\end{frame}
}

\setlength{\leftmarginii}{0.6cm}	
\setcounter{framenumber}{0}
\section{Introduction}
\begin{frame}
	\frametitle{Introduction}
	
	A WTO member belongs to 13 Preferential Trade Agreements (PTAs) on average.  
	
	\bigskip 
	%PTAs vary in scope and depth, with some making substantial commitments to domestic competition policy. 
	\begin{columns}
		\begin{column}{0.5\textwidth}	\includegraphics[width=\linewidth]{map-wto-rta.png} 
			\footnotesize	\begin{itemize}
				\item Darkest Red $\Rightarrow$ 40 PTAs
				\item Lightest Pink $\Rightarrow$1 PTA
			\end{itemize}
		\end{column}
		\begin{column}{0.5\textwidth}\textbf{Questions:} 
			\begin{itemize}
				\small 
				\item How do PTAs affect market competition, and exporters' market power and markups? 
				\medskip 
				\item How does the distribution of markups change under a PTA and what does this imply about global allocative efficiency?
			\end{itemize}
		\end{column}
	\end{columns}
\end{frame}



%------------------------------------------------------------------------------------------------------------------------------%

\begin{frame}
	\frametitle{Our approach}
	
	\textbf{Empirical: }  Using  product-level exports from 582k  firms located in 11 emerging and low-income countries to 165 destinations, 
	we examine 83 PTAs to estimate impacts on
	\smallskip
	
	
	\begin{itemize}
		\item number of firms participating in a market,
		\item market shares and markups.
		%\item  markups. 
	\end{itemize}
	\pause
	
	\bigskip
	
	\textbf{Theoretical:} We build a GE trade model featuring oligopolistic competition from multiple origins and variable markups. 
	
	\begin{itemize}
		%\item Match the model using Method of Simulated Moments and conduct counterfactual policy analysis.  
		\item Estimate model parameters using SMM and conduct counterfactual policy analysis
		\item How do markups from multiple exporting countries change under a preferential trade liberalization that only benefits a subset?
	\end{itemize}
	
	
	
	
	
\end{frame}

%------------------------------------------------------------------------------------------------------------------------------%

\begin{frame}
	\frametitle{Empirical findings}
	\bigskip
	
	
	\bigskip We document an \textcolor{red}{empirical puzzle} in light of the workhorse model of international pricing from Atkeson and Burstein (2008). 
	
	\bigskip
	
	In response to a 10\% cut in a tariff, we find:
	
	\begin{itemize} 
		\item an exporting \textcolor{red}{firm's import market share} in a destination \textcolor{red}{$\uparrow$ 8\%}
		\item an exporting \textcolor{red}{firm's markup $\downarrow$ 4\%}.
	\end{itemize}
	\pause
	\bigskip
	According to the AB (2008) model, firms face a variable demand elasticity in which: 
	
	\bigskip
	firm's market share $\uparrow$ $\Rightarrow$ more market power $\Rightarrow$ markup $\uparrow$ \pause
	
	\bigskip
	\textcolor{red}{Findings contradict markup predictions of AB (2008) model.}
\end{frame}

\begin{frame}
	\frametitle{Theoretical contribution}
	\bigskip
	To reconcile our empirical findings with economic theory, we extend Atkeson and Burstein (2008): \pause
	\medskip
	
	\begin{enumerate} 
		\item introduce multiple origins competing in multiple destinations \pause
		\smallskip
		\item  introduce an additional nest to CES consumption to allow for \textcolor{red}{more intense competition among firms from the same origin}
	\end{enumerate}
	\bigskip
	\pause
	$\Rightarrow$ Two different market shares - \textcolor{red}{\textbf{origin}} AND \textcolor{blue}{\textbf{firm within origin}} - enter demand elasticity\\
	\medskip
	%$\Rightarrow$ opposing forces affect markups
	
	$\Rightarrow$ Tariff cut \textbf{\textcolor{red}{raises}} the market power of the origin in the destination, but \textbf{\textcolor{blue}{reduces}} the market power of individual firms among compatriots. \\
	\medskip
	\pause
	
	$\Rightarrow$ Markups can (theoretically) rise or fall depending upon which force dominates.
	
\end{frame}

%------------------------------------------------------------------------------------------------------------------------------%

\begin{frame}		
	\frametitle{Literature }
	\footnotesize \textbf{Empirical: Price and Markup Responses to ...} 
	\begin{itemize}\item \scriptsize \textbf{Trade policy:} De Loecker, Goldberg, Khandelwal \& Pavcnik 2016; Fitzgerald \& Haller 2018; Amiti, Redding \& Weinstein 2019; Fajgelbaum, Goldberg, Kennedy \& Khandelwal 2019; Kikkawa, Mei, Santamarina 2019; Flaaen, Hortacsu \& Tintelnot 2020; Huang, Manova,  Perello \& Pisch 2022
		\item \scriptsize \textbf{Exchange rates:} Fitzgerald \& Haller 2014;  Amiti, Itskhoki, and Konings 2014, 2019; Corsetti, Crowley,  Han \& Song 2021; Corsetti, Crowley \& Han 2022
	\end{itemize}
	\smallskip  %\pause
	
	\footnotesize
	\textcolor{blue}{Our contribution $\Rightarrow$ }
	
	\textbf{Exporters cut markups} after a trade liberalization \\
	\begin{itemize}
		\item \textbf{crucial to examine multiple origins} to understand how and why 
	\end{itemize}	
%\pause
	
	\bigskip
	\textbf{Theoretical: Macro models of international pricing}
	\begin{itemize}
		\item \scriptsize Atkeson \& Burstein (2008); Edmond, Midrigan, and Xu (2015)
	\end{itemize} 
	\smallskip  %\pause
	
	\textcolor{blue}{	Our contribution $\Rightarrow$ }
	
	Extend to show \textbf{two market share reallocation effects} -- \textcolor{red}{ across origins} AND \textcolor{blue}{ across firms within an origin} -- impact a firm's elasticity of demand  and its markup.
	\bigskip 
	
	
\end{frame}



\begin{frame}
	\frametitle{Roadmap}
	
	\begin{itemize}
		\item Data and empirical findings
		\bigskip
		\item Theoretical model 
		\bigskip		
		\item Counterfactuals and aggregate implications 
	\end{itemize}
\end{frame}



\section{Empirics}
\begin{frame}
	\frametitle{Firms' product-level exports from 11 origin countries}
	\framesubtitle{25.2 million firm-product-origin-destination-year observations}
	
	\begin{figure}[H]
		\centering
		\includegraphics[width=0.7\linewidth]{mapof11countries.png}
	\end{figure}
	\vspace{-1em}	
	\begin{table}[h!]
		\centering
		\scriptsize	
		\begin{tabular}{lclclc} \hline
			Albania & 2004-2012 & 	Egypt & 2005-2013  &Senegal & 2000-2012\\
			
			Burkina Faso & 2005-2012&  Malawi & 2006-2012 &Uruguay & 2001-2012\\
			
			Bulgaria & 2001-2006 &  Mexico & 2000-2012  &Yemen & 2008-2012 \\ 
			
			China & 2000-2006 &  Peru & 2000-2013 \\
			\hline
		\end{tabular}
		
	\end{table}
	\footnotesize	HS06 product-level tariff data for 165 destinations from WTO \begin{itemize}
		\item MFN, pref. and/or unilateral tariff imposed on each origin by destinations
		\item Follow Feenstra and Romalis procedure to fill in missing data and phase-ins
	\end{itemize}
	% \begin{itemize} \item{\color{blue} (direct)  trade policy} against origin %and \item {\color{blue}(indirect, third-country)  trade policy} against origin's competitors. \end{itemize}
	
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{frame} \frametitle{Impact of  trade policy changes}
	
	\begin{equation*}
		\label{eq: key empirical spec}
		\text{Outcome}_{fiodt} =  \beta_{1} \cdot \text{PTA}_{odt}    + \beta_{2} \cdot \text{Tariff}_{iodt}    + \text{Fixed Effects} + \zeta_{fiodt}
	\end{equation*}
	\footnotesize	
	$\quad \quad$ with $f, i, o, d, t$ denoting firm, HS06 product, origin, destination, and year. 
	
	\bigskip
	
	\pause
	where $	\text{Outcome}_{fiodt}$  is: 
	\begin{itemize}
		\item\textcolor{blue}{export value,} used to estimate elast.  of \textcolor{blue}{ firm's mkt share in the destin.} $\omega_{fiodt}$ \pause
		\item \textcolor{red}{FOB unit value} used to estimate elasticity of the \textcolor{red}{markup $\mu_{fiodt}$}
	\end{itemize}\pause
	
	
	
	\bigskip 
	Fixed effects:
	\begin{itemize}
		\item $\delta_{fiot}$: firm-product-origin-year fixed effects (control for e.g. marginal cost)
		\item $\delta_{idt}$: product-destination-year fixed effects (e.g. changes in demand)
		\item $\delta_{od}$: origin-destination fixed effects (e.g. gravity variables)
	\end{itemize}
	
	
\end{frame}



{\setbeamercovered{} 
\begin{frame} \frametitle{Identifying market share  elasticities}
	
	\begin{equation*}
		\label{eq: key empirical spec}
		\text{Outcome}_{fiodt} =  \beta_{1} \cdot \text{PTA}_{odt}    + \beta_{2} \cdot \text{Tariff}_{iodt}    + \text{Fixed Effects} + \zeta_{fiodt}
	\end{equation*}

When ${Outcome}_{fiodt}$  is: 
\bigskip

	\begin{itemize}
		\item \textcolor{blue}{$\ln$(export value)} and $idt$ fixed effects are included $\Rightarrow$
\bigskip

 $\beta_2$ is  elast. of  a \textcolor{red}{ firm's mkt share in the destin.}	to  tariff. 

\bigskip

		\begin{equation*} \omega_{fiodt} = sales_{fiodt}/Consumption_{idt} \end{equation*}

		\begin{equation*}
	{\color{blue}\ln(v_{fiodt})} =		{\color{red}	\ln(\omega_{fiodt}) } + \underbrace{\ln(\sum_{f,o} {v_{fiodt}})}_\text{absorbed by $idt$ fixed effects}
		\end{equation*}
		%\item<3-> \textcolor{blue}{$\ln$(FOB unit value)}  to capture the variation of the \textcolor{red}{markup}
		%		\begin{equation*}
		%	{\color{blue}\ln(p_{fiodt})} = {\color{red} \ln(\mu_{fiodt})} + \underbrace{\ln({mc_{fiot}})}_\text{absorbed by $fiot$ fixed effects}
	%	\end{equation*}
	\end{itemize}
	
	

	
\end{frame}
}


{\setbeamercovered{} 
\begin{frame} \frametitle{Identifying markup  elasticities}
	
	\begin{equation*}
		\label{eq: key empirical spec}
		\text{Outcome}_{fiodt} =  \beta_{1} \cdot \text{PTA}_{odt}    + \beta_{2} \cdot \text{Tariff}_{iodt}    + \text{Fixed Effects} + \zeta_{fiodt}
	\end{equation*}

When ${Outcome}_{fiodt}$  is: 
\bigskip

	\begin{itemize}
	%	\item<2-> \textcolor{blue}{$\ln$(export value)} and $idt$ fixed effects are included $\Rightarrow$
%\bigskip

 %$\beta_2$ is  elast. of  a \textcolor{red}{ firm's mkt share in the destin.}	to  tariff. 

%\bigskip

	%	\begin{equation*} \omega_{fiodt} = sales_{fiodt}/Consumption_{idt} \end{equation*}

	%	\begin{equation*}
%	{\color{blue}\ln(v_{fiodt})} =		{\color{red}	\ln(\omega_{fiodt}) } + \underbrace{\ln(\sum_{f,o} {v_{fiodt}})}_\text{absorbed by $idt$ fixed effects}
%		\end{equation*}
		\item \textcolor{blue}{$\ln$(FOB unit value)}  and $fiot$ fixed effects are included $\Rightarrow$
\bigskip

 $\beta_2$ is the  elasticty of  a \textcolor{red}{firm's markup}	to the  tariff. 

\bigskip 
				\begin{equation*}
			{\color{blue}\ln(p_{fiodt})} = {\color{red} \ln(\mu_{fiodt})} + \underbrace{\ln({mc_{fiot}})}_\text{absorbed by $fiot$ fixed effects}
		\end{equation*}
	\end{itemize}
	
	

	
\end{frame}
}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
	\frametitle{Impacts of PTAs on Firm's Market Share in the Destination}
	\begin{columns}
		\begin{column}{.6\linewidth}	
			\vspace*{-1em}
			
			\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			
			\begin{table}[h!]
				\begin{adjustbox}{max width=1\textwidth}
					\centering
					\begin{threeparttable}
						%\scriptsize		
						\footnotesize
						\begin{tabular}{lccccc} \hline
							
							&\multicolumn{1}{c}{Firm's mkt} \\
							&\multicolumn{1}{c}{share in dest.}  \\ 
							&  $\omega_{fiodt}$ \\
							\midrule
							& & \\%& &    \\
							\hspace{0.25cm} PTA\(_{odt}\)&  0.02       \\
							&   (0.021)                        \\
							\hspace{0.25cm} Tariff\(_{iodt}\)&        {\cellcolor{blue!20}  -0.79***} \\
							&  (0.243)                           \\
							
							&                                           &                  \\
							\hspace{0.25cm} Observations&         15,793,386         \\
							\midrule
							\multicolumn{1}{l}{\textbf{Fixed Effects}	} &    \\
							\multicolumn{1}{l}{	Firm-prod-origin-year} &\checkmark  \\
							\multicolumn{1}{l}{Product-destin-year}& \checkmark  \\
							\multicolumn{1}{l}{Origin-destination}&  \checkmark \\
							\hline			
						\end{tabular}
					\end{threeparttable}
				\end{adjustbox}
			\end{table}
			
			
			
		\end{column}
		\begin{column}{.45\linewidth}
			PTA effects come via tariff cuts\\
			\bigskip 
			%\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			10\% cut in tariff  $\Rightarrow$
			
			\begin{itemize} 
				\smallskip	
				\item \textcolor{blue}{MS $\uparrow$ 8\%} 
			\end{itemize} 
		\end{column}	
	\end{columns}
	\begin{itemize}
		\item The preferential tariff cut increases the market access of firms from the preferred origin (at the expense of  firms from other origins and domestic firms). 
	\end{itemize}
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\begin{frame}
	\frametitle{How \textcolor{red}{\emph{should}} markups adjust?} 
	\framesubtitle{Predictions from Atkeson-Burstein (2008) Nested CES Model}
	
	The markup of firm $f$ selling product $i$ from origin $o$ in destination $d$ is:
	\begin{equation*}
		\mu_{fiodt}=\frac{\varepsilon(\omega_{fiodt})}{\varepsilon(\omega_{fiodt})-1} 
	\end{equation*}
	
	where the demand elasticity is a function of  the firm's market share in the destination $\omega_{fiodt}$, the elasticity of substitution within product $\rho$,  and across products $\eta$:  
	\begin{equation*}
		\varepsilon(\omega_{fiodt}) = \rho - (\rho-\eta) \omega_{fiodt}
	\end{equation*}
	when $\rho>>\eta$.
	
	\bigskip
	\pause
	
	Implication: %{\color{red}$\mu_{fiodt}$ and $\omega_{fiodt}$ move in the same direction} \\
	%\medskip 	
	If a bilateral tariff cut leads the firm's market share to increase, then it will face a \textcolor{red}{less elastic demand curve} and its \textcolor{red}{markup will increase}. 
	
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
	\frametitle{Impacts of PTAs on Markups}
	\begin{columns}
		\begin{column}{.6\linewidth}	
			
			\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			
			\begin{table}[h!]
				\begin{adjustbox}{max width=1\textwidth}
					\centering
					\begin{threeparttable}
						%\scriptsize		
						\footnotesize
						\begin{tabular}{lccccc} \hline
							
							&\multicolumn{1}{c}{Firm's mkt}&\multicolumn{1}{c}{Markups}\\
							&\multicolumn{1}{c}{share in dest.}  &  FOB\\
							&  $\omega_{fiodt}$ & $\mu_{fiodt}$ \\
							\midrule
							%	\multicolumn{2}{l}{\textbf{All Goods}}&&&&& \\
							& & \\%& &    \\
							\hspace{0.25cm} PTA\(_{odt}\)&  0.02        &     -0.02***\\
							&   (0.021)                       &  (0.008)         \\
							\hspace{0.25cm} Tariff\(_{iodt}\)&        {\cellcolor{blue!20}  -0.79***}&        {\cellcolor{red!20} \textbf{  0.41***}}\\
							&  (0.243)                    &    (0.073)         \\
							
							&                                           &                  \\
							\hspace{0.25cm} Observations&       15,793,386   & 15,793,386         \\
							\midrule
							\multicolumn{1}{l}{\textbf{Fixed Effects}	} &    & \\
							\multicolumn{1}{l}{	Firm-prod-origin-year} &\checkmark & \checkmark \\
							\multicolumn{1}{l}{Product-destin-year}& \checkmark & \checkmark \\
							\multicolumn{1}{l}{Origin-destination}&  \checkmark & \checkmark \\
							\hline			
						\end{tabular}
					\end{threeparttable}
				\end{adjustbox}
			\end{table}
			
			
			
		\end{column}
		\begin{column}{.3\linewidth}
			Signing a PTA  $\Rightarrow$ 
			\begin{itemize} 
				\smallskip	
				\item  Markups $\downarrow$ 2\%
			\end{itemize} 
			\bigskip
			
			%\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			10\% cut in tariff  $\Rightarrow$
			
			\begin{itemize} 
				\smallskip	
				\item \textcolor{blue}{Mkt shares $\uparrow$ 8\%} 
				\item  \textcolor{red}{Markups $\downarrow$ 4\%}
			\end{itemize} 
		\end{column}	
	\end{columns}
	\pause 
	\begin{customlist}{2em}{0em}
		\small 
		\item[Puzzle:]  Markups fall as market power (firm's mkt sh in the destin) increases!\\
		Findings  \textcolor{red}{ contradict the predictions of an  oligopolistic comp. model. }
		
	\end{customlist}
\end{frame}




\begin{frame} \frametitle{Decomposing market share changes}
	\framesubtitle{}
	
	\begin{equation*}
		\label{eq: key empirical spec}
		\text{Mkt share measures} =  \beta_{1} \cdot \text{PTA}_{odt}    + \beta_{2} \cdot \text{Tariff}_{iodt}    + \text{Fixed Effects} +  \zeta_{fiodt}
	\end{equation*}
	\begin{enumerate}
		\item 		Firm's within-origin mkt share 
		\begin{equation*}
			ms_{fiodt} = \frac{v_{fiodt}}{\sum_{f\in \mathcal{F}_{iodt}} v_{fiodt}} 
		\end{equation*}
		\item 	Origin's mkt share in destination-product market
		\begin{equation*}
			ms_{iodt} = \frac{v_{iodt}}{\sum_{o} v_{iodt}} 
		\end{equation*}
	\end{enumerate}
	\begin{itemize}
		\item A firm's market share in a destination is $ \omega_{fiodt} = ms_{fiodt}* ms_{iodt} $
	\end{itemize}
	\vspace*{2em}
	\vfill
	\footnotesize  $f,i, o,d, t$  = firm,  HS06 product,  origin, destination, and year 
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{frame}
	\frametitle{Understanding market share changes}
	
	\begin{columns}
		\begin{column}{.6\linewidth}	
			\vspace*{-1em}
			
			\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			\vspace*{-1em}
			
			\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			
			\begin{table}[h!]
				\begin{adjustbox}{max width=1\textwidth}
					\centering
					\begin{threeparttable}
						%\scriptsize		
						\footnotesize
						\begin{tabular}{lccccc} \hline
							
							&\multicolumn{1}{c}{Origin's}  &\multicolumn{1}{c}{  Firm's within-origin}\\
							& mkt share & mkt share & \\
							& $ms_{iodt}$ & $ms_{fiodt}$  \\% &\\	
							\midrule
							%	\multicolumn{2}{l}{\textbf{All Goods}}&&&&& \\
							& & \\%&    \\
							\hspace{0.25cm} PTA\(_{odt}\)      &         -0.04  &  0.06**          \\%   &       -0.02***\\
							&  (0.031)      &  (0.027)        \\%    &  (0.009)         \\
							\hspace{0.25cm} Tariff\(_{iodt}\)&       {\cellcolor{red!20} \textbf{ -3.67***}} &     {\cellcolor{blue!20} \textbf{ 2.87***}}& \\% 0.40***\\
							&  (0.428)   &  (0.322)       \\%  &    (0.073)         \\
							
							&                 &                           \\%   &                  \\
							\hspace{0.25cm} Observations              & 15,793,386   &15,793,386        \\%       &15,793,386         \\
							\midrule
							\multicolumn{1}{l}{\textbf{Fixed Effects}	}   & &  & \\
							\multicolumn{1}{l}{	Firm-prod-origin-year}  & \checkmark  &  \checkmark \\
							\multicolumn{1}{l}{Product-destin-year} & \checkmark &  \checkmark  \\%& \checkmark \\
							\multicolumn{1}{l}{Origin-destination} & \checkmark   & \checkmark  \\%& \checkmark \\
							\hline			
						\end{tabular}
					\end{threeparttable}
				\end{adjustbox}
			\end{table}			
		\end{column}
		\begin{column}{.45\linewidth}			
			
			\vspace*{-2em}			
			%\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			10\% cut in tariff $\Rightarrow$
			
			\begin{itemize} 
				\small 				
				\smallskip
				
				\item \textcolor{red}{ Origin's mkt share $\uparrow$ 37\%} 
				\smallskip
				\item \textcolor{blue}{Average within-origin mkt share $\downarrow$ 29\%} 
			\end{itemize} 
			
			\bigskip
			
			Firm's market share in destination is $ \omega_{fiodt} = ms_{fiodt} ms_{iodt} $
			
		\end{column}	
	\end{columns}
	\bigskip 
	\pause 
	Tariff cut \textbf{\textcolor{red}{raises}} the market power of the origin in the destination, but \textbf{\textcolor{blue}{reduces}} the within-origin market power of individual firms. 
\end{frame}



\begin{frame}
	\frametitle{Understanding market share changes}
	\vspace*{2em}
	\begin{columns}
		\begin{column}{0.7\linewidth}	
			\vspace*{-1em}
			
			\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			\vspace*{-1em}
			
			\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}
			
			\begin{table}[h!]
				\begin{adjustbox}{max width=1\textwidth}
					\centering
					\begin{threeparttable}
						%\scriptsize		
						\footnotesize
						\begin{tabular}{lccccc} \hline
							
							&\multicolumn{1}{c}{Origin's}  &\multicolumn{1}{c}{  Firm's within-origin}  & No. of \\
							& mkt share & mkt share & Firms \\
							& $ms_{iodt}$ & $ms_{fiodt}$ & (PPML)  \\% &\\	
							\midrule
							& & &  \\%&    \\
							\hspace{0.25cm} PTA\(_{odt}\)      &         -0.04   &  0.06**  & -0.05***         \\%   &       -0.02***\\
							&  (0.031)      &  (0.027)           &  (0.009)         \\
							\hspace{0.25cm} Tariff\(_{iodt}\)&   -3.67*** &     {\cellcolor{blue!20}   \textbf{ 2.87***}}&  {\cellcolor{blue!20} \textbf{-2.21***}} \\
							&  (0.428)   &  (0.322)       &  (0.162)            \\
							
							&                 &                             &                  \\
							\hspace{0.25cm} Observations               & 15,793,386    & 15,793,386      & 2,750,833    \\
							\midrule
							\multicolumn{1}{l}{\textbf{Fixed Effects}	}   & &  & \\
							\multicolumn{1}{l}{	Firm-prod-origin-year} & \checkmark & \checkmark  &  \\
							
							\multicolumn{1}{l}{Product-origin-year} &   & & \checkmark \\
							\multicolumn{1}{l}{Product-destin-year} & \checkmark &  \checkmark  & \checkmark \\
							\multicolumn{1}{l}{Origin-destination} & \checkmark   & \checkmark  & \checkmark \\
							\bottomrule			
						\end{tabular}
					\end{threeparttable}
				\end{adjustbox}
			\end{table}			
		\end{column}
	\end{columns}
	\begin{itemize} 
		
		\small 
		\item A 10\% tariff cut $\Rightarrow$ 22\% $\uparrow$ in number of exporters. 
		\item Entry from one's own origin  drives the decline in firms' within-origin market shares.
	\end{itemize} 
\end{frame}


	
	
	\section{Analytical Framework}
	\begin{frame}	
		\frametitle{Model outline}
		\flushleft
		\small
		Goal: Develop a model of oligopolistic  competition in which \textcolor{red}{markups $\Downarrow$} when  a  firm's \textcolor{red}{mkt share in the destination $\Uparrow$}\\[1em]
		
		$\Rightarrow$ Decompose the conventional mkt share channel into two opposing effects
		
		\bigskip 
		\vspace*{1em}
		\pause 
		Key elements:  
		\begin{itemize}
	\item[\textbullet] Multi-country GE with heterogeneous products and firms 
\smallskip
\item[\textbullet] Limited number of firms at product-origin-destination level
\smallskip
\item[\textbullet] Firms re-optimize exporting decisions after a trade policy shock
\smallskip			

\item[\textbullet] Variable markups which depend on market structure

\item[]$\Rightarrow$ allow for different degree of competition for firms from the same origin versus those from other origins
			%\smallskip
			%\smallskip
			%\begin{itemize}
			%	\footnotesize
			%\item Similar to Atkeson \& Burstein 2008; Edmond, Midrigan \& Xu 2015
			%\smallskip	
			
			%\item allow for different degree of competition for firms from the same origin versus those from different origins
			%\end{itemize}
		%	\item[\textbullet] Fixed cost of entering a market
			%\smallskip
		%	\item[\textbullet]  Allow for different degree of competition for firms from the same origin versus those from different origins
			
		\end{itemize}	
		
		
	\end{frame}



\begin{frame}
\frametitle{Market structure}
%\framesubtitle{}

A triple nested CES demand structure with {\color{blue}limited number of firms within each origin} to incorporate imperfect competition
\begin{equation*}
	\begin{array}{lcc}
		\text{Across products} & \quad  & Y_{dt}=\bigg(\int_{i} y_{idt}^{\frac{\eta-1}{\eta}} di \bigg)^{\frac{\eta}{\eta-1}}, \\[1em]
		\text{Within product, across origins} &	\quad  & y_{idt}=\bigg(\sum_{o} y_{iodt}^{\frac{\rho-1}{\rho}} \bigg)^{\frac{\rho}{\rho-1}}, \\[1em]
		\text{Across firms within an origin} & \quad & y_{iodt}=\bigg(\sum_{f \in \mathcal{F}_{iodt}} y_{fiodt}^{\frac{\sigma-1}{\sigma}} \bigg)^{\frac{\sigma}{\sigma-1}}, \\[1em]
	\end{array}
\end{equation*}
{\color{blue}allowing for $\sigma \neq \rho$}. \\[1em]

\vfill
\scriptsize
Notation: $f$ (firm), $i$ (product), $o$ (origin), $d$ (destination), $t$ (time)
\end{frame}

%------------------------------------------------------------------------------------------------------------------------------%

\begin{frame}
\frametitle{Markups and demand elasticities}
The triple nested market structure implies two distinct market shares that matter for demand elasticity $\varepsilon_{fiodt}$ and markup $\mu_{fiodt}$: 
\begin{align*}
	\varepsilon_{fiodt} \; = & \;\;  \sigma -\textcolor{blue}{ms_{fiodt}}[\sigma -\rho  + (\rho -\eta )\textcolor{red}{ms_{iodt}} ]  \\
	\mu_{fiodt} \;= & \;\;  \frac{\varepsilon_{fiodt}}{\varepsilon_{fiodt}-1}  		
\end{align*}
where 
\begin{itemize}
	\small
	\item \textcolor{blue}{$ms_{fiodt}$}: firm $f$'s market share \textbf{among all firms from origin $o$} selling product $i$ in destination $d$ at time $t$ 
	\smallskip
	\item \textcolor{red}{$ms_{iodt}$}: origin $o$'s market share of product $i$  in destination $d$ at time $t$
%	\smallskip
%	\item[Note:] A firm's market share in a destination is $ \omega_{fiodt} = ms_{fiodt}* ms_{iodt} $
\end{itemize}

\bigskip
\pause			
Implication: 
A bilateral tariff reduction leads to \textcolor{red}{$\Uparrow ms_{iodt}$}  and \textcolor{blue}{$\Downarrow ms_{fiodt}$} \\
\medskip 
\begin{itemize}
	\small
	\item[$\Rightarrow$] 
	Demand facing a firm could become more or less elastic, depending on which of the two forces dominates
	\item[$\Rightarrow$] Markups may rise or fall 
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Market structure and demand elasticities}

\vspace*{0.5em}
\footnotesize 

General case: oligopolistic competition within origin and industry
\begin{equation*}
	\varepsilon_{fiodt}  =  \sigma -\textcolor{blue}{ms_{fiodt}}[\sigma -\rho  + (\rho -\eta )\textcolor{red}{ms_{iodt}} ] 
\end{equation*}


Special cases:
\vskip 5pt
\begin{enumerate}
\footnotesize 
\item<2-> \textbf{Monopolistic competition} (e.g. Melitz 2003) \\when $N_{iodt}$ is large and/or $\sigma=\rho=\eta$: 
\begin{equation*}
\text{Constant markup:} \quad \frac{\varepsilon_{fiodt}}{\varepsilon_{fiodt}-1} = \frac{\sigma}{\sigma-1}
\end{equation*}
\item<3-> \textbf{Oligopolistic competition within industry} (e.g. Atkeson and Burstein 2008) \\when $\sum_{o} N_{iodt}$ is finite and $\sigma = \rho > \eta$:
\begin{equation*}
	\varepsilon_{fiodt} = \rho -(\rho -\eta )\textcolor{blue}{ms_{fiodt}}\textcolor{red}{ms_{iodt}} 
\end{equation*}
\item<4-> \textbf{Oligopolistic competition within origin} \\when  $N_{iodt}$ is finite but $\sum_{o} N_{iodt}$ is large: 
\begin{equation*}
\varepsilon_{fiodt} \rightarrow \sigma - \textcolor{blue}{ms_{fiodt}}(\sigma -\rho) \label{eq demand elasticity origin}
\end{equation*} 
\end{enumerate}
\scriptsize  
Note: Elasticity of substitution within origin ($\sigma$), across origins ($\rho$), across products ($\eta$) 
\end{frame}



\begin{frame}
\frametitle{Markup adjustments to a trade policy change}
\label{decomp}
Markup adjustments can be decomposed into two channels:		
\begin{equation*}
	\small
	\widehat{\mu}_{fiodt} =  \underbrace{ A(\sigma,\rho,\eta,ms_{fiodt},ms_{iodt}) \cdot \textcolor{blue}{\widehat{ms}_{fiodt}}}_{\text{Within-origin reallocation effect}}  + \underbrace{ B(\sigma,\rho,\eta,ms_{fiodt},ms_{iodt}) \cdot \textcolor{red}{\widehat{ms}_{iodt}}}_{\text{Cross-origin reallocation effect}} \label{eq: markup elasticity}
\end{equation*}
%\vspace*{-1em}
\small 
\begin{itemize}
	\item<2-> When $\sigma = \rho$,  $A(.) = B(.) > 0 $ $\Rightarrow$ Direction of markup adj. depends solely on the sign of  $\widehat{\omega}_{fiodt} = \textcolor{blue}{\widehat{ms}_{fiodt}} + \textcolor{red}{\widehat{ms}_{iodt}}$
	\begin{itemize}
		\item 	$ \widehat{\mu}_{fiodt} < 0 $ iff $\widehat{\omega}_{fiodt} < 0$
	\end{itemize}
\medskip 
	\item<3-> When $\sigma > \rho$,  $A(.) > B(.) > 0 $ $\Rightarrow$ Direction of markup adj. also depends on the magnitude of $A(.)$ and $B(.)$ 
	\begin{itemize}
	\item $ \widehat{\mu}_{fiodt} < 0 $ even if $\widehat{\omega}_{fiodt} \geq 0$ (what we observed empirically)
\end{itemize}

\end{itemize}
\bigskip
Recall empirically: after a bilateral tariff cut  
\begin{itemize}
	\item  $\textcolor{blue}{\widehat{ms}_{fiodt} < 0}$ and $\textcolor{red}{\widehat{ms}_{iodt} > 0}$ 
	\item $\widehat{\mu}_{fiodt} < 0$ and $\widehat{\omega}_{fiodt}  > 0$
\end{itemize}
\hfill \hyperlink{the entry effect}{\beamerbutton{The entry effect}}

\end{frame}


\section{Counterfactuals}


\begin{frame}
	\frametitle{Quantitative model}
	\small
	\begin{itemize}
		\item Simulate a model of 5 countries with 4000 products \\
		\vskip 5pt
		\item SMM: vary parameters to match empirical estimates
	\end{itemize}

	\begin{table}
		\centering
		\small
		\begin{tabular}{lccc}
			\toprule
			Tariff elasticity estimates 	& Data & Model \\
			\midrule 
			Markup  $(\mu_{fiodt})$ & 0.41  & 0.47  \\
			Firm's mkt share in dest.  $(\omega_{fiodt})$ & -0.79  & -0.85   \\
			Firm's within-origin mkt share  $(ms_{fiodt})$ & 2.87 & 2.60  \\
			Origin's mkt share in dest.  $(ms_{iodt})$	& -3.67  & -3.45  \\ 
			\bottomrule
		\end{tabular}
	\end{table}
	
	\begin{table}
		\centering
		\small
		\begin{tabular}{lccc}
			\toprule
			Key estimated parameters	& Value \\
			\midrule 
			Within-origin elasticity of substitution $\sigma$ & 3.30 \\
			Cross-origin elasticity of substitution $\rho$ & 2.33 \\ 
			Cross-product elasticity of substitution $\eta$ & 1.52 \\ 
			Productivity dispersion (inverse) & 11.83 \\
			\bottomrule
		\end{tabular}
	\end{table}
	
\end{frame}



\begin{frame}
\frametitle{Counterfactual analysis: Bilateral tariff reduction}
Simulate the model for two years:
\medskip
\begin{customlist}{4em}{0em}
  	\item[1st year:] Model reaches its competitive equilibrium where there is a 10\% tariff for all products among all trade partners
  	\medskip 
\item[2nd year:] Countries 1 \& 2 sign a trade agreement, which reduces the bilateral tariff to zero for all products
\end{customlist}

\bigskip 

$\Rightarrow$ Investigate changes in distributions of market shares and markups 
\end{frame}


\begin{frame}
	\frametitle{Summary of results}
	\framesubtitle{10\% bilateral tariff cut between 1 \& 2}
	
	
	
	\medskip
	Focus on mkt shares and markups in country 2:\\ (symmetric responses in country 1)
	\medskip 
	\begin{itemize} 
		\item<2-> Origin 1's mkt share $\Uparrow$ \\(positive cross-origin realloc. effect for origin 1 firms) 		
		\medskip 
		\item<3-> Within-origin mkt share of origin 1 firms $\Downarrow$ 
		\\(negative within-origin realloc. effect {\color{red}due to new firm entry})
		\medskip 
		\item<4-> Markups of origin 1 firms $\Downarrow$ 
		\\(within-origin realloc. effect dominates) 
		\medskip 
		\item<5-> Mean markup of firms from non-PTA countries $\Uparrow$ 
		\\(due to exits of small and less competitive firms)
		\medskip
	\end{itemize}	

Aggregate productivity $\Uparrow$ globally; bigger gains in PTA countries
\end{frame}

\renewcommand{\modelA}{N10_M4_flexiableE_C5_shocktype2_FWfalse_SYM0_GE}
\renewcommand{\modelB}{N10_M4_fixedE_C5_shocktype2_FWfalse_SYM0_GE}
\renewcommand{\modelC}{N10_M4_flexiableE_C5_shocktype3_FWfalse_SYM0_GE}




\section{Conclusion}
\begin{frame}
	\frametitle{Conclusion}
	
	We examine the impacts of PTAs and preferential tariffs on market competition: 
	\bigskip

	\begin{itemize}		
		\item PTAs and tariff reductions are in general pro-competitive 	
		\item[] {\footnotesize$\Rightarrow$ Encourage entry and reduce markups}
		\bigskip
		
		\item  Two opposing forces on competition after a bilateral tariff cut:

		\item[] {\footnotesize$\Rightarrow$ Within-origin reallocation reduces  markups}
		\item[] {\footnotesize$\Rightarrow$ Cross-origin reallocation increases markups}
		\item[] {\footnotesize$\Rightarrow$ Within-origin reallocation dominates when $\sigma > \rho$ }
		\bigskip
		
		\item Efficiency gains from a bilateral trade agreement for all countries 
	%	\item[] {\footnotesize$\Rightarrow$ Work-in-progress: decomposing the gains into different margins}
	\end{itemize}
	
\end{frame}

\appendix 
\section{Appendix}
\begin{frame}
	\centering
	\Huge Appendix
\end{frame}


{\setbeamercovered{} 
	\begin{frame}
		\frametitle{\large Distribution of firms' within-origin market shares over 4000 products}
		\framesubtitle{Before and after a 10\% bilateral tariff cut between 1 \& 2} 
		
		\bigskip 
		\hspace*{-1.5em}\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			Within-origin market share $ms_{fiodt}$\\
			(for origin 1 firms selling to country 2)  \\[1em]
			\includegraphics[width=\linewidth]{IODT_OMShare_\modelA.pdf}
		\end{minipage}\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			\onslide<2->	Counterfactual within-origin market share without entry/exit\\
			(for origin 1 firms selling to country 2) 	\includegraphics<2->[width=\linewidth]{IODT_OMShare_\modelB.pdf}
		\end{minipage}
		\onslide<1->
		\begin{itemize}
			\small
			\item Within-origin market share of origin 1 firms $\Downarrow$ (left)
			\item[] $\Rightarrow$ Mainly driven by entry: no. of firms increases from 8,921 to 10,061
			\smallskip 
			\item<2-> Virtually no within-origin reallocation if no entry \& exits (right)
		\end{itemize}	
	\end{frame}
}


{\setbeamercovered{} 
	\begin{frame}
		\frametitle{Markups of country 1 firms selling in country 2}
		\framesubtitle{Before and after a 10\% bilateral tariff cut between 1 \& 2} 
		
		
		
		\bigskip 
		\hspace*{-1.5em}	\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			Markups
			\includegraphics[width=\linewidth]{IODT_Markups_\modelA.pdf}\\
			\scriptsize Mean markup: Before = 54.4\%; After = 52.3\%
		\end{minipage}\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			\onslide<2->	Counterfactual markups without entry/exit
			\includegraphics<2->[width=\linewidth]{IODT_Markups_\modelB.pdf}\\
			\scriptsize Mean markup: Before = 54.4\%; After = 54.5\%
		\end{minipage}
		\onslide<1->
		\smallskip 
		\begin{center}
			\scalebox{0.95}{%
				Recall:	$\quad \widehat{\mu}_{fiodt} =  \underbrace{ A(.) \cdot \textcolor{black}{\widehat{ms}_{fiodt}\Downarrow}}_{\text{Within-origin reallocation effect}}  + \underbrace{ B(.) \cdot \textcolor{black}{\widehat{ms}_{iodt}\Uparrow}}_{\text{Cross-origin reallocation effect}}$
			}
		\end{center}
		\begin{itemize}
			\setlength{\itemindent}{-1em}
			\footnotesize
			\item Within-origin reallocation effect dominates and markup drops
			\item<2->Without entry/exit, much weaker within-origin reallocation and no markup adj.
			%\item[]<2->$\Rightarrow$ no markup adj.
		\end{itemize}	
	\end{frame}
}



\begin{frame}
	\frametitle{Changes in aggregate productivity}
	\framesubtitle{After a 10\% bilateral tariff cut between 1 \& 2} 
	
	\footnotesize 
	%	\begin{center}
		%		\scalebox{1.0}{%
			%			Measure:	$	A_{ot} = \left[\sum_i\sum_{d}   \sum_f  \left(\frac{1}{A_{fiot}}\right)\frac{  y_{fiodt}}{\sum_i\sum_{d}   \sum_f  y_{fiodt}}  \right]^{-1} 	$
			%		}
		%	\end{center}
	\begin{center}
		\begin{minipage}{0.75\linewidth}
			\centering
			\scriptsize
			\includegraphics[width=\linewidth]{AggProdChgs_\modelA.pdf}
			\vspace{-0.9cm}
			\begin{equation*}	
				\quad \quad \quad  \underbrace{\quad \quad \quad \quad \quad \quad \quad \quad}_{\text{\scriptsize PTA partner countries}}  \quad \underbrace{\quad \quad \quad \quad\quad \quad \quad \quad \quad\quad\quad }_{\text{ \scriptsize Non-PTA partner countries}} 
			\end{equation*}
		\end{minipage}
	\end{center}	
	
	\begin{itemize}
		\footnotesize
		\item The signing countries gain efficiency from a bilateral trade agreement, while other countries also benefit due to the increase in competitive pressure.
		%	\item Significant efficiency gains in all countries for the multilateral trade agreement 
	\end{itemize}	
	
	
\end{frame}

{\setbeamercovered{} 
	\begin{frame}
		\frametitle{\large Distribution of firms' within-origin market shares over 4000 products}
		\framesubtitle{Before and after a 10\% bilateral tariff cut between 1 \& 2} 
		
		\bigskip 
		\hspace*{-1.5em}\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			Within-origin market share $ms_{fiodt}$\\
			(for origin 1 firms selling to country 2)  \\[1em]
			\includegraphics[width=\linewidth]{IODT_OMShare_\modelA.pdf}
		\end{minipage}\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			\onslide<2->	Counterfactual within-origin market share without entry/exit\\
			(for origin 1 firms selling to country 2) 	\includegraphics<2->[width=\linewidth]{IODT_OMShare_\modelB.pdf}
		\end{minipage}
		\onslide<1->
		\begin{itemize}
			\small
			\item Within-origin market share of origin 1 firms $\Downarrow$ (left)
			\item[] $\Rightarrow$ Mainly driven by entry: no. of firms increases from 8,921 to 10,061
			\smallskip 
			\item<2-> Virtually no within-origin reallocation if no entry \& exits (right)
		\end{itemize}	
	\end{frame}
}


{\setbeamercovered{} 
	\begin{frame}
		\frametitle{Markups of country 1 firms selling in country 2}
		\framesubtitle{Before and after a 10\% bilateral tariff cut between 1 \& 2} 
		
		
		
		\bigskip 
		\hspace*{-1.5em}	\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			Markups
			\includegraphics[width=\linewidth]{IODT_Markups_\modelA.pdf}\\
			\scriptsize Mean markup: Before = 54.4\%; After = 52.3\%
		\end{minipage}\begin{minipage}{0.55\linewidth}
			\centering
			\scriptsize
			\onslide<2->	Counterfactual markups without entry/exit
			\includegraphics<2->[width=\linewidth]{IODT_Markups_\modelB.pdf}\\
			\scriptsize Mean markup: Before = 54.4\%; After = 54.5\%
		\end{minipage}
		\onslide<1->
		\smallskip 
		\begin{center}
			\scalebox{0.95}{%
				Recall:	$\quad \widehat{\mu}_{fiodt} =  \underbrace{ A(.) \cdot \textcolor{black}{\widehat{ms}_{fiodt}\Downarrow}}_{\text{Within-origin reallocation effect}}  + \underbrace{ B(.) \cdot \textcolor{black}{\widehat{ms}_{iodt}\Uparrow}}_{\text{Cross-origin reallocation effect}}$
			}
		\end{center}
		\begin{itemize}
			\setlength{\itemindent}{-1em}
			\footnotesize
			\item Within-origin reallocation effect dominates and markup drops
			\item<2->Without entry/exit, much weaker within-origin reallocation and no markup adj.
			%\item[]<2->$\Rightarrow$ no markup adj.
		\end{itemize}	
	\end{frame}
}



\begin{frame}
	\frametitle{Changes in aggregate productivity}
	\framesubtitle{After a 10\% bilateral tariff cut between 1 \& 2} 
	
	\footnotesize 
	%	\begin{center}
		%		\scalebox{1.0}{%
			%			Measure:	$	A_{ot} = \left[\sum_i\sum_{d}   \sum_f  \left(\frac{1}{A_{fiot}}\right)\frac{  y_{fiodt}}{\sum_i\sum_{d}   \sum_f  y_{fiodt}}  \right]^{-1} 	$
			%		}
		%	\end{center}
	\begin{center}
		\begin{minipage}{0.75\linewidth}
			\centering
			\scriptsize
			\includegraphics[width=\linewidth]{AggProdChgs_\modelA.pdf}
			\vspace{-0.9cm}
			\begin{equation*}	
				\quad \quad \quad  \underbrace{\quad \quad \quad \quad \quad \quad \quad \quad}_{\text{\scriptsize PTA partner countries}}  \quad \underbrace{\quad \quad \quad \quad\quad \quad \quad \quad \quad\quad\quad }_{\text{ \scriptsize Non-PTA partner countries}} 
			\end{equation*}
		\end{minipage}
	\end{center}	
	
	\begin{itemize}
		\footnotesize
		\item The signing countries gain efficiency from a bilateral trade agreement, while other countries also benefit due to the increase in competitive pressure.
		%	\item Significant efficiency gains in all countries for the multilateral trade agreement 
	\end{itemize}	
	
	
\end{frame}


\begin{frame}
	\frametitle{The effect of entry on incumbent exporters' markups}
	\label{the entry effect}
	Under a 1\% preferential tariff reduction,  the markup adjustment (in percentage) of firms from the preferred origin (up to a first order approximation) is given by:	
	\begin{equation*}
		\widehat{\mu}_{fiodt}	\approx   {\color{red}\Upsilon_{fiodt}} - \underbrace{\left(1- {\color{red}\Upsilon_{fiodt}} \right){\color{blue}\Phi_{iodt}}\widetilde{ms}_{jiodt}}_{\textbf{Entry effect}}  \label{eq: prop2}
	\end{equation*}
	where
	
	\begin{enumerate}
		\item  $0\leq {\color{red}\Upsilon_{fiodt}}<1$ is the markup adjustment in absence of entry;
		\item  ${\color{blue}\Phi_{iodt}}$ captures the strength of the entry effect; 
		\item $\widetilde{ms}_{jiodt} $ is the sum of within-origin market shares of new entrants from origin $o$ in product-market $id$ (due to the preferential tariff reduction).
		\tiny
	\end{enumerate}

	\end{frame}
	
	\begin{frame}\frametitle{The strength of the entry effect, $\Phi_{iodt}$}
		%\framesubtitle{is increasing in the difference between the within and across elasticities, $\sigma-\rho$}
		\begin{center}
			\includegraphics[width=.6\linewidth]{figure_entry1_alt.pdf}
		\end{center}
		\scriptsize Notes: The figure plots the  $\Phi_{iodt}$ function for different values of $\sigma$ and the number of incumbent firms $N$ in the market before the tariff cut hits with $ ms_{fiodt}=1/N$, $ms_{iodt}=0.1$, $\rho=3$ and $\eta=1.2$.\\
		\normalsize
		\hfill \hyperlink{decomp}{\beamerbutton{Back}}
		
	\end{frame}


\begin{frame}		
	\frametitle{Data Sources}
	
	\begin{columns}[T]
		\begin{column}{.5\linewidth}	
			\textbf{Firm-Product-Level Exports}
			\begin{itemize}
				\item World Bank Exporter Dynamics Database
				\item Chinese and Egyptian Customs Authorities
			\end{itemize}		
			\medskip		
			\textbf{Industry-Level Imports}
			\begin{itemize}
				\item UN Comtrade
			\end{itemize}	
		\end{column}
		
		\begin{column}{.5\linewidth}	
			\textbf{Trade Agreements}
			\begin{itemize}
				\item World Bank Deep Trade Agreements Database
			\end{itemize}
			\medskip		
			\textbf{Tariffs}
			\begin{itemize}
				\item WTO
				\item Feenstra \& Romalis 2014
			\end{itemize}
		\end{column}
	\end{columns}	
	
	\vspace{0.75cm}
	Variation to identify  trade policy impacts: 
	\begin{table}[h!]
		\centering
		\footnotesize	
		\begin{tabular}{lccc}
			
			Country & Observations (firm-product-origin-destination-year) &  ... with PTA
 \\
			\hline
			China & 20,043,162 & 1,168,391  \\
			Mexico  & 3,608,510 & 2,353,379  \\ 
			\hline			
		\end{tabular}
	\end{table}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Variation in Markup Impact by Type of Good}
\begin{columns}
\begin{column}{.6\linewidth}	
	\vspace*{-1em}

	\definecolor{darkviolet}{rgb}{0.58, 0.0, 0.83}

	\begin{table}[h!]
		\begin{adjustbox}{max width=1\textwidth}
		\centering
		\begin{threeparttable}
\scriptsize		
		\begin{tabular}{lccccc} \hline
			
		&\multicolumn{1}{c}{Markups}  &\multicolumn{1}{c}{Markups} &\multicolumn{1}{c}{Markups} \\
 &all  &high diff  &HD cons.\\
 &goods   &goods &goods\\	
			\midrule
		%	\multicolumn{2}{l}{\textbf{All Goods}}&&&&& \\
PTA\(_{odt}\)       &        -0.02**&   -0.02  &    -0.03* \\
                            &          (0.008)      &     (0.014)       &       (0.015)            \\
\textcolor{red}{ Tariff\(_{iodt}\)}&               0.41***  & {\cellcolor{red!20} \textbf{  0.88*** }}  &    {\cellcolor{red!20} \textbf{    1.01***}}\\
 &     (0.073)    &     (0.106)      &     (0.129)       \\
 Observations                           & 15,793,386  &   5,792,021        &   4,074,107   \\
\midrule
			\multicolumn{1}{l}{\textbf{Fixed Effects}	} &   \\
			\multicolumn{1}{l}{	Firm-prod-origin-year} &  \checkmark  &  \checkmark  &  \checkmark  \\

		%	\multicolumn{1}{l}{Product-origin-year}&  \\
			\multicolumn{1}{l}{Product-destin-year}&   \checkmark  &  \checkmark  &  \checkmark \\
			\multicolumn{1}{l}{Origin-destination} & \checkmark  &  \checkmark  &  \checkmark \\
			\hline			
		\end{tabular}
		\end{threeparttable}
		\end{adjustbox}
\end{table}


\end{column}
\begin{column}{.45\linewidth}
\footnotesize
For more differentiated goods: 
\smallskip
\begin{itemize} 
\item  highly differentiated goods \\

%\textcolor{blue}{PTA $\Rightarrow$ markup $\downarrow$ 3\%}\\
\textcolor{red}{10\% tariff $\downarrow$ $\Rightarrow$ markup $\downarrow$ 8.8\% }\\



	\item highly diff'd consumer goods \\
	
%\textcolor{blue}{	PTA$\Rightarrow$ markup $\downarrow$ 5\% } \\
\textcolor{red}{	10\% tariff $\downarrow$ $\Rightarrow$ markup $\downarrow$ 10\%} \\
	\end{itemize}
\bigskip 


	
%Indirect: all competitors join \\
%\hspace{0.25cm} PTA$\Rightarrow$


\end{column}	
\end{columns}
\footnotesize
Markup changes are consistent with changes in firms' within-origin market shares:
\begin{itemize}
\footnotesize
\item For highly differentiated goods, a 10\% cut in tariffs $\Rightarrow$ 

average within-origin market share $\downarrow$ 44\% 
\medskip

\item For highly differentiated consumption goods, a 10\% cut in tariffs $\Rightarrow$ 

average within-origin market share $\downarrow$ 51\%
\end{itemize}
\end{frame}


\begin{frame}
	\frametitle{Aggregate market share in country 2}
	\framesubtitle{Before and after a 10\% bilateral tariff cut between 1 \& 2} 
	\begin{figure}
		\centering
		\includegraphics[width=0.8\linewidth]{AggMS2_\modelA.pdf}
	\end{figure}
	\begin{itemize}
		\small
		\item Firms from origin 1 gain market share
		\item Firms from other origins lose market share
	\end{itemize}
\end{frame}


\end{document}

