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\begin{document}

\title[Managing Relational Contracts]{Managing Relational Contracts}
\author[Troya-Martinez \& Wren-Lewis]{Marta Troya-Martinez (New Economic
School and CEPR) \and \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Liam Wren-Lewis
(Paris School of Economics)}
\date{}
\maketitle
\institute{}

\section{Introduction}

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\QTR{frametitle}{Teaching note}

{\large This paper can be taught when talking about the following topics:}

{\large - \textbf{Incentives in hierarchies}: how effort is incentivized in
hierarchical organizations that operate in informal environments}

{\large - \textbf{Management}: how to reward managers who may be susceptible
to corruption}

{\large - \textbf{Corruption}: how to set governance policies in
organizations that use informal incentives in corrupt environments}

{\large - \textbf{Development}: how reliance on relational contracts can
limit firm growth and facilitate corruption}

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\QTR{frametitle}{Introduction}

\begin{itemize}
\item {\large Informal relationships play a crucial role within and between
firms }

\item {\large These relationships are often delegated to managers who may
want to use the informal relationships to collude against the firm's
interests}

\item {\large A\'{e}ropostale provides an example of the situation we are
capturing in our model}
\end{itemize}

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\QTR{frametitle}{A\'{e}ropostale}

\begin{columns}
	\begin{column}{0.5\textwidth}
		\includegraphics[width=\textwidth]{aeropostale.png}
	\end{column}
	\begin{column}{0.5\textwidth}  %%<--- here
	\begin{itemize}
		\item {\large A\'{e}ropostale is a retailer of teen apparel}
		
		\item {\large In 2006, the firm accused its chief merchandising manager
			Christopher Finazzo of:}
		
		\begin{itemize}
			\item {\large inflating prices to its main supplier, South Bay}
			
			\item {\large receiving more than \$25 million in kickbacks from that
				supplier }
		\end{itemize}
	\end{itemize}
	\end{column}
\end{columns}


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\QTR{frametitle}{A\'{e}ropostale}

{\large Finazzo argued that:}

\begin{itemize}
\item {\large South Bay's products were of higher quality}

\item {\large South Bay was willing to hold and store inventory, which
allowed A\'{e}ropostale to "\textit{quickly start printing new styles}" }$%
\Longrightarrow ${\large \ very valuable to adapt to its \textquotedblleft 
\textit{fickle}\textquotedblright\ teenage customer base}

\item {\large A\'{e}ropostale is \textquotedblleft \textit{loyal}%
\textquotedblright\ and \textquotedblleft \textit{committed}%
\textquotedblright\ to long--time vendors even when those vendors
\textquotedblleft \textit{encountered production difficulties}%
\textquotedblright\ and even if that meant \textquotedblleft \textit{paying
higher prices}\textquotedblright\ Case No. 14-3213-cr(L)\ }
\end{itemize}

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\QTR{frametitle}{A\'{e}ropostale}

\begin{itemize}
\item {\large Finazzo and South Bay were found guilty of fraud in 2013}

\begin{itemize}
\item {\large restitution }$\rightarrow ${\large \ \textit{\textquotedblleft
the value of the kickbacks\textquotedblright }\ was used as \textit{%
\textquotedblleft a reasonable measure of the pecuniary loss
suffered\textquotedblright }\ }
\end{itemize}

\item {\large They appealed the restitution amount and in 2017 the Court of
Appeals for the Second Circuit demanded a recalculation}

\item {\large Judge Droney argued that:}

\begin{itemize}
\item {\large it was possible \textquotedblleft \textit{that A\'{e}ropostale
did not lose money as a result of this corrupt arrangement}%
\textquotedblright\ }

\item {\large Finazzo's \textit{\textquotedblleft conduct may have reduced
transactions costs for South Bay\textquotedblright }\ and the relationship
may have made it profitable for South Bay to pay kickbacks even at
non-inflated prices}
\end{itemize}
\end{itemize}

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\QTR{frametitle}{Procurement relationships and trust}{\large \ }

\begin{itemize}
\item {\large Relational contracts between organizations are ubiquitous and
are crucial for enforcing promises}

\item {\large Indeed, \textit{\textquotedblleft lack of trust and
commitment\textquotedblright }\ is behind most supplier collaboration
failures Webb (2017)}
\end{itemize}

\begin{center}
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\QTR{frametitle}{Procurement relationships and trust}{\large \ }

\begin{itemize}
\item {\large The task of maintaining these relationships is often delegated
to a manager like Finazzo}

\item {\large As ilustrated by A\'{e}ropostale's case, the firm can never
guarantee that the manager will exclusively act in the firm's best interest}

\item {\large What happens if this trust is used by managers to collude with
suppliers? }
\end{itemize}

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
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\QTR{frametitle}{This paper}

{\large We build a principal-manager-agent model:}%
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\begin{itemize}
\item {\large A "good" relational contract is needed to induce agent's effort%
}%
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\item {\large The principal delegates the implementation of the incentive
relational contract to a manager}

\begin{itemize}
\item Same technology: everything the manager does, the principal can do it
herself if she does not delegate

\item In particular, the manager is self-interested, strategic and carries
out payments without commitment just as the principal would

\item Key difference: she receives a share of the principal's payoff%
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\end{itemize}

\item {\large Manager can engage in taking (relational) bribes from agent}
\end{itemize}

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\QTR{frametitle}{Questions and answers}

{\large If collusion is possible, how do relational contracts behave?}%
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\bigskip

\begin{itemize}
\item {\large Is it still the case that a more valuable relationship
sustains more effort?}%
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\item[$\Longrightarrow $] {\large No, a more valuable relationship can lead
to less effort }%
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\end{itemize}

\bigskip

\begin{itemize}
\item {\large Should a principal delegate relational contracts?}%
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\item[$\Longrightarrow $] {\large Yes, when relational contracts are
difficult}
\end{itemize}

\bigskip

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\QTR{frametitle}{Literature}%Don't spend time on this slide.
%
%Fill gap between two large literatures. 
%In relational contracts we introduce a non-strategic supervisor. 
%In collusion in hierachies we consider the good side of the ongoing relationship to interact with collusion.
%
%Say that they know it better than I do

{\large \textbf{Relational contracts}}

\begin{itemize}
\item {\large Extend Levin (2003) by adding a manager}

\item {\large Literature focuses on delegation to agent (Goldlucke \& Kranz
2012; Li et.al., 2014)}

\item {\large Exception: in Fong and Li (2016) a non-strategic manager can
garble agent's evaluations intertemporally}
\end{itemize}

{\large \textbf{Collusion in hierarchies}}

\begin{itemize}
\item {\large Many models assume enforcement of collusion (e.g. Tirole,
1986; Banerjee, 2012). Few exceptions (Martimort 1999, Buccirossi and
Spagnolo 2001). None considers good side of repeated interaction (new role
for bribes).}

\item {\large Supervisor has the same "technology" as principal, but a
different payoff as in the \textbf{delegation} literature (e.g. Vickers,
1985; Katz 1991). First to consider corruption as a tool to influence the
manager's payoff}
\end{itemize}

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\section{Model}

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\begin{center}
{\Huge Model}
\end{center}

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\QTR{frametitle}{No delegation}

{\large Principal and agent interact repeatedly as in Levin (AER,2003)}
\begin{center}
\includegraphics[scale=0.24, trim = 0mm 0mm 0mm 0mm, clip]{PAtimeline_w_0_jeea_1.png} 
\end{center}

\begin{itemize}
\item {\large Agent pays upfront transfer }$%
{\large T}_{0}$

\item {\large Agent exerts private effort }${\large e}_{t}$ {\large at
a cost} ${\large c(e_{t})}$

\item {\large Everyone observes a non-verifiable quality }${\large y%
} ${\large \ with probability }${\large e}_{t}$ {\large (and no performance
otherwise)}

\item {\large Principal makes discretionary payments }${\large p}%
_{t}$
\end{itemize}


\end{frame}%

\begin{frame}[label=Many agents]%
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\QTR{frametitle}{Delegation: initial period} 


{\large Principal hires a manager to incentivize the agent}

\underline{{\large At time }${\large t=0}${\large :}}

\begin{itemize}
\item {\large Principal chooses some parameters of the contract:}

\begin{itemize}
\item {\large Share of her profits that the manager receives }${\large %
\alpha }$

\item {\large Limits the manager discretion by setting a maximum price }$%
\overline{{\large p}}$
\end{itemize}

\item {\large All these are assumed to be stationary and can be enforced by
the court}

\item {\large Principal takes no further action}

\item {\large In the model, we can have }${\large N}${\large \ agents 

\hyperlink{Nagents}{\beamergotobutton{More}}%

}
\end{itemize}


\end{frame}%

\begin{frame}%


\QTR{frametitle}{Delegation: managed relational contract}

\begin{center}

\includegraphics[scale=0.24, trim = 0mm
0mm 0mm 0mm, clip]{timeline_w_0_jeea_0.png} 
\end{center}

\begin{itemize}
\item {\large Manager/agent makes upfront side
payment }${\large S}_{0}$

\item {\large Manager and agent interact
repeatedly}

\item {\large Agent exerts private effort }$%
{\large e}_{t}$ {\large at a cost} ${\large c(e_{t})}$
\end{itemize}


\end{frame}%

\begin{frame}%


\QTR{frametitle}{Delegation: managed relational contract}

\begin{center}

\includegraphics[scale=0.24, trim = 0mm
0mm 0mm 0mm, clip]{timeline_w_0_jeea_0.png}
\end{center}

\begin{itemize}
\item {\large Manager and agent observe a non-verifiable quality }$%
{\large y}${\large \ with probability }${\large e_{t}}$ {\large (and no
performance otherwise)}

\item {\large Agent receives discretionary payments }${\large p}_{t}
\leq \overline{p}$ {\large chosen by the manager}

\item {\large Manager/agent make discretionary side payments }${\large s%
}_{t}$
\end{itemize}


\end{frame}%

\begin{frame}%
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\QTR{frametitle}{Payoffs with delegation} %show dynamically

{\large Principal's payoff:}%
\begin{equation*}
{\large \pi }_{t}{\large =E}\left[ (1-\delta )(1-\alpha
)(y_{t}-p_{t})+\delta \pi _{t+1}\right]
\end{equation*}%
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{\large Manager's payoff:}%
\begin{equation*}
{\large v}_{t}{\large =E}\left[ (1-\delta ){\left[ \alpha (y_{t}-p_{t})+%
{\large s}_{t}\right] +}\delta v_{t+1}\right] 
\end{equation*}%
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{\large Agent's payoff:}%
\begin{equation*}
{\large u}_{t}{\large =E}\left[ (1-\delta ){\left[ p_{t}-{\large s}%
_{t}-c(e_{t})\right] +}\delta u_{t+1}\right] 
\end{equation*}%
{\large where the outside options are normalized to }$0${\large \ and }$%
\delta $ {\large is the discount factor }

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\section{Results}

\medskip 
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\begin{center}
{\Huge Results}
\end{center}

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\QTR{frametitle}{No delegation (Levin, 2003)}

$\rhd $ {\large Optimal contract is stationary: }${\large p_{l}=0}$ and $%
{\large p_{h}}$ {\large limited by }$-{\large p}_{h}+\frac{{\large \delta
		\pi }}{{\large 1}-{\large \delta }}\geq {\large 0}$ {\large \ }%


\begin{figure}
\begin{minipage}[b]{0.45\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{bonusPA.png}
	\caption{Price premium} 
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[b]{0.45\linewidth}
	\centering
\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{ePA.png}  
	\caption{Effort}      
\end{minipage}
\end{figure}
\end{frame}%


\begin{frame}%


{\huge \ }

\begin{center}
{\huge 
\textcolor{blue} {What is the optimal relational contract between the manager and
the agent?}}
\end{center}

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\QTR{frametitle}{Managed relational contract}

$\rhd $ {\large Manager can motivate agent with price premium, }$p_{h} \geq
p_{l}$, {\large AND side payments }$s_{l} \geq s_{h}$

$\rhd $ {\large Manager has a comparative advantage enforcing} $p_{h}$

{\large 
\begin{equation}
-\alpha p_{h}+s_{h}+\frac{\delta v}{1-\delta}\geq0  \tag{$DE_{price}$}
\end{equation}
}

\only <2->{\ 
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\node[
rectangle,
draw=red,
fill=yellow,
text width=0.35\textwidth,
align=center,
anchor=center
] at (3.9,1) {\large No delegation case: \\ $-p_{h}+\frac{\delta \pi}{1-\delta }\geq 0 $
};
\end{tikzpicture}}

\vspace{-30pt}

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\pause

$\rhd $ {\large Cole and Tran (2011) document how side payments are used as
an enforcing mechanism}

\begin{quote}
{\large When \textbf{quality is not contractible}, the client holds "back
roughly 20 percent of the contract value (...), until the client is
satisfied that the product meets the specified quality". However, the 
\textbf{"kickback is paid only after all contract payments have been made"}}
\end{quote}

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\QTR{frametitle}{The problem}

\begin{itemize}
\item[$\vartriangleright $] {\large We show that the manager and agent
maximize their joint surplus:}%
\begin{equation*}
g=\alpha ey+(1-\alpha )(ep_{h}+(1-e)p_{l})-c(e)
\end{equation*}

\item[$\vartriangleright $] {\large For a given }$e$:

$\Longrightarrow ${\large \ Side payments do not affect surplus}

$\Longrightarrow $ {\large Price premiums increase surplus: }$\downarrow 
{\large p}_{l}$ {\large helps incentive provision but directly lowers surplus%
}

$\Longrightarrow $ {\large Side payments first, price premiums last! 
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\QTR{frametitle}{Delegation}

\begin{figure}
\begin{minipage}[b]{0.315\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec4bonus.png}
	\caption{Price premium} 
\end{minipage}
\hspace{0.05cm}\
\begin{minipage}[b]{0.315\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec4bribes.png}
	\caption{Side Payments} 
\end{minipage}
\hspace{0.05cm}
\begin{minipage}[b]{0.315\linewidth}
	\centering
\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec4effort.png}  
	\caption{Effort}      
\end{minipage}
\end{figure}



\end{frame}%

\begin{frame}[label=Example1]%


\QTR{frametitle}{Encouraging relationships and effort}
\noindent
\begin{columns}
\begin{column}{.6\textwidth}
\begin{figure}
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\end{column}
\hfill
\begin{column}{.4\textwidth}
 \emph{Guanxi} is a system of trust-based  informal relationships used to enforce contracts  in China
\end{column}
\end{columns}

\begin{quote}
{\textquotedblleft it would be naive to think---as many Western
executives do---that the more guanxi you have on the front lines in China,
the better\textquotedblright . It can \textquotedblleft divide the loyalties
of the sales and procurement people\textquotedblright\ Vanhonacker (2004)}
\end{quote}


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\QTR{frametitle}{Back to A\'{e}ropostale}

\begin{itemize}
\item In 2005 and 2006, South Bay had delivery delays "\textit{that cost A%
\'{e}ropostale approximately \$1.8 million in lost sales}"

\item A product manager suggested discounts "\textit{to compensate for the
delays}" but Finazzo refused it
\end{itemize}

\begin{columns}
	\begin{column}{.4\textwidth}
		Our model suggest that ... \\ 
		Finazzo had very \\ 
		high surplus%
		
			
			\centering

	\end{column}
	\hfill
	\begin{column}{.6\textwidth}
			\includegraphics[width=.7\textwidth]{sec4bonus.png}
			\end{column}
\end{columns}


\begin{equation*}
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$\FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec4bonus.png}{\special{language
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"1";cropright "1";cropbottom "0";filename 'sec4bonus.png';file-properties
"XNPEU";}}$ & 
\end{tabular}%
\end{equation*}

\end{frame}%
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\begin{center}
{\huge \textcolor{blue} {What is the optimal delegation arrangement?}}
\end{center}

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\QTR{frametitle}{Governing managed relational contracts}

\begin{itemize}
\item {\large How should the principal set }${\large \alpha }${\large \ and }%
$\overline{{\large p}}${\large ?}%
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\item {\large To\ prevent the manager colluding with the agent to pay a
premium price for low quality} {\large \ }${\large p_{l}>0}$

\item {\large When the "collusive" motive appears, the principal limits }$%
\overline{{\large p}}\rightarrow ${\large \ in the limit, the agent will
have no discretion}

\item {\large At this point, incentives are provided exclusively via side
payments }$\rightarrow ${\large \ Ledeneva (2013) finds evidence that, in
Russian procurement, kickbacks were "\textit{linked to performance and
facilitated the quality of service}"}

\item {\large Collusion is still costly for the principal because it forces
her to decrease the discretion available to the manager}
\end{itemize}

{\large 
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\begin{center}
{\huge \textcolor{blue} {When should the principal employ a manager?}}
\end{center}

\end{frame}%

\begin{frame}%


\QTR{frametitle}{When should the principal employ a manager?}

\begin{itemize}
\item {\large Sometimes the principal must entrust the relationship to the
manager...}

...{\large \ but sometimes she can choose to manage it herself}

\item {\large Potential collusion is a concern: Indian firm-owners
\textquotedblleft \textit{were concerned if they let their plant managers
procure yarn they may do so at inflated rates from friends and receive
kickbacks}" Bloom et al. (2013) }
\end{itemize}


\end{frame}%

\begin{frame}%


\QTR{frametitle}{When should the principal employ a manager?}{\large \ }

{\large The principal benefits from delegating if relational contracting is
difficult: }${\large \delta }$ or ${\large y}${\large \ is low or }$%
\underline{{\large u}}$ {\large is high }%

\begin{figure}
\begin{minipage}[b]{0.45\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec5profits.png}
	
\end{minipage}
\hspace{0.5cm}
\begin{minipage}[b]{0.45\linewidth}
	\centering
\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec5effortdeleg.png}  

\end{minipage}
\end{figure}

\begin{equation*}
\FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec5profits.png}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 2.4742in;height 2.4742in;depth
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"1";cropright "1";cropbottom "0";filename 'sec5profits.png';file-properties
"XNPEU";}}\FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec5effortdeleg.png}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 2.4742in;height 2.4742in;depth
0in;original-width 3.333in;original-height 3.333in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename
'sec5effortdeleg.png';file-properties "XNPEU";}}
\end{equation*}


\end{frame}%

\begin{frame}%

\QTR{frametitle}{\ }

\QTR{frametitle}{Costly corruption}

\begin{itemize}
\item {\large Suppose that when the agent pays }${\large S}${\large , the
manager only receives }${\large \kappa S}$ {\large for} ${\large 0}<{\large %
\kappa }\leq {\large 1}$

\item {\large Manager has bargaining power}

\item {\large When side-payments are more costly (}${\large \kappa
\downarrow }${\large ), principal shares less profit with the manager,
delegation is more attractive, and it involves greater effort}

\begin{itemize}
\item {\large If risk of corruption }$\downarrow ${\large \ }${\large %
\Longrightarrow }${\large \ principal can set a lower }${\Large \alpha }$%
{\large \ and still avoid }$p_{l}>0$

\item {\large Since }${\large \alpha }${\large \ is lower, manager-agent
relational contracting is easier }${\large \Longrightarrow }${\large \
principal can transfer less surplus to the manager}
\end{itemize}

\item {\large Bloom, Sadun and Van Reenen (2012): firms delegate more when
there is stronger rule of law or better monitoring practice}
\end{itemize}

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\section{Conclusions}

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\QTR{frametitle}{\ }

\QTR{frametitle}{Take-away messages}

\begin{itemize}
\item {\large First to study the impact of collusion on relational contracts}

\item {\large Collusion can crowd out productive effort when the
relationship between manager and agent is too strong}

\item {\large When trust is a scarce resource, managed relational contracts
are more credible and can incentivize more quality than direct relational
contracts}

\item {\large A principal delegating optimally will constrain the manager's
discretion so as to prevent overpayment }$\rightarrow ${\large \ delegation
may or may not benefit the principal}

\item {\large The model backs Judge Droney's argument that the \textit{%
\textquotedblleft negative correlation\textquotedblright }\ between
kickbacks and loss may not exist}
\end{itemize}

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\QTR{frametitle}{\ }

\QTR{frametitle}{Multi-tasking}

\begin{itemize}
\item {\large Suppose the agent can undertake two tasks:}

\begin{itemize}
\item ${\large e}_{1}${\large \ that benefits the principal by generating }$%
y $ {\large with probability }${\large e}_{1}$

\item ${\large e}_{2}${\large \ that benefits the manager by an amount }$%
{\large f(e}_{2}{\large )}${\large \ }
\end{itemize}

\item {\large The tasks are substitutes }${\large c(e}_{1},{\large e}_{2})$

\item {\large For simplicity, the manager observes so }${\large p=c(e}_{1},%
{\large e}_{2})$

\item {\large The manager's payoff: }${\large \alpha }({\large ye}_{1}-%
{\large b})+{\large f(e}_{2}{\large )}${\large \ }

\item {\large We show that if relational contracts are difficult, }$%
\downarrow {\large \alpha }${\large \ is beneficial for the principal
because it facilitates }${\large e}_{1}$

\item {\large Mechanism: }$\uparrow ${\large \ the value placed on collusion
as compared to the principal, enhances the manager credibility}
\end{itemize}

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\QTR{frametitle}{Many agents}

\begin{itemize}
\item {\large Principal, manager and }$N${\large \ technologically
independent agents}

\item {\large Bilateral relational contracting with each agent by Levin
(2002)}
\end{itemize}

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\QTR{frametitle}{\ }

\QTR{frametitle}{Many agents}

\begin{itemize}
\item {\large $e_{it}$ only observed by agent }$i$

\item {\large $y_{it}$ observed by agent }$i$ {\large and %
\textcolor{blue}{manager} but non-verifiable}

\item $Y_{t}=${\large \ }$\sum_{i=1}^{i=N}y_{it}+\epsilon _{t},\epsilon _{t}$
iid with $E(\epsilon _{t})=0$ {\large observable \& verifiable}
\end{itemize}

$\Longrightarrow $ {\large The results are unaffected in this new model}

$\Longrightarrow $ {\large Output-sharing with the agents:}

\begin{itemize}
\item {\large (}$+${\large ) Agents are also motivated with the output share 
}$\rightarrow ${\large \ relational contracts are relaxed }$\rightarrow $%
{\large \ }${\large -}${\large \ effective as }$\uparrow N$ {\large because
moral hazard in teams}

\item {\large (}$-${\large ) Each manager-agent relation has now less joint
surplus }$\rightarrow ${\large \ relational contracts are tightened }$%
\rightarrow ${\large \ }${\large +}${\large \ important as }$\uparrow N$
\end{itemize}

$\Longrightarrow $ {\large If }$N${\large \ is large enough, it is optimal
to share output only with the manager 
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\QTR{frametitle}{\ }

\QTR{frametitle}{Complete problem}

\begin{itemize}
\item Consider a manager-agent contract that in its first period calls for
payments $p(y)$, $s(y)$ and effort $e$

\item If the offer is made and accepted and the discretionary payments made,
the continuation contract gives payoffs $u(y)$, $v(y)$ as a function of the
observed outcome $y$

\item Let $u$, $v$ be the expected payoffs under this contract: 
\begin{align*}
u& \equiv (1-\delta )E\left[ p(y)-s(y)-c(e)|e\right] +\delta E\left[ u(y)|e%
\right]  \\
v& \equiv (1-\delta )E\left[ \alpha (y-p(y))+s(y)|e\right] +\delta E\left[
v(y)|e\right] 
\end{align*}

\item We follow Levin (2003) in defining this contract as \textit{%
self-enforcing} if and only if the following conditions hold
\end{itemize}

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\QTR{frametitle}{\ }

\QTR{frametitle}{A self-enforcing contract satisfies:}

\begin{enumerate}
\item[i] Parties willing to initiate the contract: $u\geq \underline{u}$ and 
$v\geq 0$

\item[ii] The agent is willing to choose $e$: 
\begin{equation*}
e\in \arg \max_{e}E\left[ p(y)-s(y)+\frac{\delta }{1-\delta }u(y)|e\right]
-c(e)
\end{equation*}

\item[iii] For all $y$, both parties willing to pay $p$: 
\begin{align}
(1-\delta )\left( -\alpha p(y)+s(y)\right) +\delta v(y)& \geq 0 
\tag{$DE_{price}$} \\
(1-\delta )\left( p(y)-s(y)\right) +\delta u(y)& \geq \delta \underline{u} 
\tag{$X$}
\end{align}

\item[iv] For all $y$, both parties willing to pay $s$: 
\begin{align}
(1-\delta )s(y)+\delta v(y)& \geq 0  \tag{$X$} \\
-(1-\delta )s(y)+\delta u(y)& \geq \delta \underline{u}  \tag{$DE_{bribe}$}
\end{align}

\item[v] Each continuation contract is self-enforcing: $u(y)$, $v(y)$
correspond to a self-enforcing contract that will be initiated in the next
period {\large 
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\end{enumerate}

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\QTR{frametitle}{Types of contracts}

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\begin{proposition}%
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{\large For a given }${\large \alpha }${\large \ and }$\overline{{\large p}}$%
{\large , }$\exists ${\large \ }$\left( {\large \delta }^{L},{\large \delta }%
^{H}\right) ${\large \ s.t. optimal manager-agent relational contract is
characterized as follows:}

\begin{itemize}
\item {\large If }${\large \delta }\geq {\large \delta }^{H}${\large :
Prices are not used to induce effort and effort is weakly increasing in }$%
\delta $

\item {\large If }${\large \delta }^{H}>{\large \delta }>{\large \delta }%
^{L} ${\large : Both side payments and prices are used to induce effort. If }%
$p_{l}>0${\large , then effort is decreasing in }${\large \delta }${\large ,
and otherwise it is increasing in }$\delta $

\item {\large If }${\large \delta }\leq {\large \delta }^{L}${\large : Side
payments are not used to induce effort and effort is weakly increasing in }$%
\delta $
\end{itemize}

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\QTR{frametitle}{Sketch proof of Proposition 1}

\underline{\textbf{Finding} $\mathbf{\delta }^{\mathbf{L}}$}

\begin{itemize}
\item Effort and surplus are increasing ${\large p}_{h}$

\item $\uparrow p_{h}$ and $\uparrow {\large s}_{h}$ by the same amount
without violating $(DE_{bonus})$

$\Longrightarrow $ Hence, $\uparrow p_{h}$ up to $\overline{p}$, unless $%
\uparrow {\large s}_{h}$ is not possible (i.e. ${\large s}_{h}={\large s}%
_{l} $). Then $p_{h}$ is bounded by $(IC-DE)$:%
\begin{equation*}
p_{h}=\min \{\overline{p},\frac{1}{\alpha }\frac{\delta g}{1-\delta }\}
\end{equation*}

\item Since $g$ is increasing in $\delta $, $\delta ^{L}$ uniquely defined
by: $\overline{p}=\frac{1}{\alpha }\frac{\delta ^{L}g}{1-\delta ^{L}}$
\end{itemize}

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\QTR{frametitle}{Sketch proof of Proposition 1}

\underline{\textbf{Finding} $\mathbf{\delta }^{\mathbf{H}}$}

\begin{itemize}
\item If $\delta ^{L}\leq \delta $, manager solves:%
\begin{gather*}
\max_{e}g(e,\overline{p},p_{l})\text{ subject to \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\
p_{l}=\frac{\delta g(e,\overline{p},p_{l})}{1-\delta }+(1-\alpha )\overline{p%
}-c^{\prime }(e)\text{ by }(IC-DE) \\
0\leq p_{l}\leq \overline{p}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }
\end{gather*}

\item We show that:

\begin{itemize}
\item if $p_{l}=0$ at $\delta $, then $p_{l}=0$ for all $\delta $ below

\item if $p_{l}=\overline{b}$\ at $\delta $, then $p_{l}=\overline{p}$ for
all higher $\delta $
\end{itemize}

\item $\delta ^{H}$ is the smallest $\delta $ such that the optimal solution
is $p_{l}=\overline{p}$
\end{itemize}

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\QTR{frametitle}{Sketch proof of Proposition 1}

\underline{\textbf{Relationship between }$\mathbf{e}$\textbf{\ and }$\mathbf{%
\delta }$}

\begin{itemize}
\item If $\delta \geq \delta ^{H}$, then $e$ is given by $(IC-DE)$: $\frac{%
c^{\prime }(e)+\alpha \overline{p}}{g(e,\overline{p},\overline{p})}=\frac{%
\delta }{1-\delta }$ $\Longrightarrow $ LHS is increasing in $e$ so $%
\uparrow \delta $ $\Longrightarrow \uparrow e$

\item If $\delta \leq \delta ^{L}$ and $p_{l}=0$, then $e$ maximizes $g(e,%
\frac{1}{\alpha }\frac{\delta g}{1-\delta },0)$ $\Longrightarrow $ $\uparrow
\delta $ $\Longrightarrow \uparrow $credible $p_{h}$ and hence $\uparrow e$

\item If $\delta ^{L}<\delta <\delta ^{H}$, then $p_{l}$ and $e$\ given by:%
\begin{gather*}
p_{l}=\frac{1-\alpha }{\alpha }\left( 1-e\right) c^{\prime \prime }(e)-y+%
\frac{1}{\alpha }\frac{\delta g(e,p_{h},p_{l})}{1-\delta }\text{ or }p_{l}=0
\\
c^{\prime }(e)=\overline{p}-p_{l}+\frac{\delta g(e,\overline{p},p_{l})}{%
1-\delta }-\alpha \overline{p}\text{ \ }(IC-DE)
\end{gather*}%
$\Longrightarrow $ When $p_{l}=0$, from $(IC-DE)$ we see that $\uparrow
\delta $ $\Longrightarrow $ $\uparrow e$

$\Longrightarrow $ When $p_{l}>0$, $c^{\prime }(e)+\frac{1-\alpha }{\alpha }%
\left( 1-e\right) c^{\prime \prime }(e)=\left( 1-\alpha \right) \overline{p}%
+y-\frac{1-\alpha }{\alpha }\frac{\delta g(e,\overline{p},p_{l})}{1-\delta }$
and $c^{\prime }(e)+\frac{1-\alpha }{\alpha }\left( 1-e\right) c^{\prime
\prime }(e)\uparrow $ if $p_{l}$ interior, hence $\uparrow \delta $ $%
\Longrightarrow $ $\downarrow e$ {\large 
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\end{itemize}

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\QTR{frametitle}{Governing supervised relational contracts}


\begin{proposition}%


{\large The principal sets }${\large \alpha }${\large \ and }$\overline{%
{\large p}}${\large \ such that }${\large p}_{l}{\large =0}${\large . }$%
\exists ${\large \ }$\left( {\large \delta }_{L},{\large \delta }_{H}\right) 
${\large \ s.t. optimal manager-agent relational contract is characterized
as follows:}

\begin{itemize}
\item {\large If }${\large \delta }\geq {\large \delta }_{H}${\large : only
side payments are used to induce effort and }$\overline{{\large p}}=0$

\item {\large If }${\large \delta }_{H}>{\large \delta }>{\large \delta }%
_{L} ${\large : side payments and bonuses are used to induce effort}

\item {\large If }${\large \delta }\leq {\large \delta }_{L}${\large : only
bonuses are used to induce effort}
\end{itemize}


\end{proposition}%

\end{frame}%

\begin{frame}[label=Example1]%

\begin{figure}
\begin{minipage}[b]{0.33\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec5bonus.png}
	\caption{Price premium} 
\end{minipage}
\hspace{0.05cm}\
\begin{minipage}[b]{0.33\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec5bribes.png}
	\caption{Side Payments} 
\end{minipage}
\hspace{0.05cm}
\begin{minipage}[b]{0.33\linewidth}
	\centering
	\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec5alpha.png}
	\caption{Alpha} 
\end{minipage}
\hspace{0.05cm}
\begin{minipage}[b]{0.33\linewidth}
	\centering
\includegraphics[trim={0mm 0mm 0mm 0mm},width=\textwidth]{sec5effort.png}  
	\caption{Effort}      
\end{minipage}
\end{figure}



\begin{equation*}
\begin{tabular}{ll}
\FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec5bonus.png}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"USEDEF";valid_file "F";width 2.4742in;height 2.4742in;depth
0in;original-width 3.333in;original-height 3.333in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'sec5bonus.png';file-properties
"XNPEU";}} & \FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec5bribes.png}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 2.4742in;height 2.4742in;depth
0in;original-width 3.333in;original-height 3.333in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'sec5bribes.png';file-properties
"XNPEU";}} \\ 
\FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec5alpha.png}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"USEDEF";valid_file "F";width 2.4742in;height 2.4742in;depth
0in;original-width 3.333in;original-height 3.333in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'sec5alpha.png';file-properties
"XNPEU";}} & \FRAME{itbpF}{2.4742in}{2.4742in}{0in}{}{}{sec5effort.png}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 2.4742in;height 2.4742in;depth
0in;original-width 3.333in;original-height 3.333in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'sec5effort.png';file-properties
"XNPEU";}}%
\end{tabular}%
\end{equation*}


\end{frame}%

\begin{frame}[label=Example1]%
%EndExpansion

\QTR{frametitle}{Credit Suisse First Boston}

\begin{itemize}
\item {\large The management of First Boston (FB), the manager, had been
very successful at maintaining long-term relationships with its bankers}%
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\item {\large \textbf{But also}, there was hierarchical collusion to
oversell:}
\end{itemize}

\begin{quotation}
{\large \textquotedblleft So much of communication wasn't captured in
e-mails or directly mentioned in meetings. It was implicit---understood
without words. If your chairman asked you to take a look at a stock, (...)
you didn't need to be told explicitly what to say or write. It was
understood, (...) that you were to comply by lavishing the stock or the deal
with positive comments\textquotedblright\ Prins (2006) }
\end{quotation}

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\QTR{frametitle}{Credit Suisse First Boston}

\begin{itemize}
\item {\large CS introduced measures to change the:\ \emph{\textquotedblleft
freewheeling atmosphere (...) notable for an absence of the layers of
controls... [and] for huge salaries and bonuses.\textquotedblright\ }Stewart
(1993) }%
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\item {\large It imposed a tighter bonus cap, and as a result, FB top
management could not longer pay bonuses they felt were sufficient to reward
their employees }$\Longrightarrow ${\large \ \emph{one manager
\textquotedblleft was so upset over the bonuses for his people that he
dipped into his own pocket to pay them more\textquotedblright\ }Stewart
(1993) }
\end{itemize}

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\QTR{frametitle}{Proof:}

\begin{itemize}
\item {\large If }${\large p}_{l}={\large p}_{h}${\large , then }$(IC-DE)$%
{\large \ is }$c^{\prime }(e)=\frac{\delta g}{1-\delta }-\alpha {\large p}%
_{h}${\large \ }$\Longrightarrow $ {\large principal can do better by
setting }$\overline{p}{\large =0}$ {\large and increasing }${\large \alpha }$%
{\large \ to keep }${\large g}${\large \ constant}

\item {\large If }$0<{\large p}_{l}<{\large p}_{h}${\large , the principal
chooses parameters so that the contract has }${\large p}_{{\large l}}{\large %
=0}$

\begin{itemize}
\item[$\hookrightarrow $] Suppose ${\large p}_{l}>{\large 0}$, then she can $%
\downarrow \overline{p}$ and $\uparrow \alpha $ so the manager is forced to
use the same price variation with ${\large p}_{l}={\large 0}$
\end{itemize}
\end{itemize}

{\large 
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