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\title[Dissecting Saving Dynamics]{\textbf{Dissecting Saving Dynamics\\ \large{Measuring Credit, Wealth and Precautionary Effects}}}

%\subtitle
%{Presentation Subtitle} % (optional)

\author[Carroll, Slacalek and Sommer]{Christopher Carroll\inst{1} \and Jiri Slacalek\inst{2} \and Martin Sommer\inst{3}}


% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.
\institute{
  \inst{1} Johns Hopkins University and NBER\\   \texttt{ccarroll@jhu.edu} \and
  \inst{2} European Central Bank\\   \texttt{jiri.slacalek@ecb.int} \and
  \inst{3} International Monetary Fund\\   \texttt{msommer@imf.org}
    }
\date{Presentation at Goethe-Universit\"at Frankfurt, May 2012}

%\subject{Talks}
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\begin{document}

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

%\begin{frame}
 % \frametitle{Outline}
  %\tableofcontents
  % You might wish to add the option [pausesections]
%\end{frame}


\begin{frame}
\frametitle{\textbf{US Personal Saving Rate ($\sRat$), 1966--2011}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/fPSR_slides.pdf}
%\end{center}
\end{figure}
\end{frame}

\begin{frame}\frametitle{\bf Literature}

\bi
\item \jemph{``Wealth Effects''}
\bi
\item Modigliani, Klein, MPS model, ...
\bi \item $\sRat_{t} = -0.05 \mRat_{t}$ + other stuff \ei
\ei
\item \jemph{``Precautionary''}
\bi
\item \cite{carroll:brookings}
\bi
\item Saving rate rises in recessions
\item $\Delta \log C_{t+1}$ strongly related to $\Ex_{t}(u_{t+1}-u_{t})$
\ei
\ei
\item \jemph{``Credit Availability''}
\bi
\item Secular Trend: \bi \item \cite{parker_nberma_spendthrift}, \cite{dynanKohn07_indebtedness}, Muellbauer (many papers) \ei
\item Cyclical Dynamics: \bi
\item \cite{glLiq}, \cite{gkLiq}, \cite{hall:slump} \ei
\ei
\ei


\end{frame}

\begin{frame}\frametitle{\textbf{Great Recession 2007--2009}}


\bi
\item $\sRat$ rises by $\sim$4--5 pp
\item \jemph{Bigger \&\ more persistent increase} than any postwar recession
\item But all three indicators also move a lot:
\bi
\item Credit conditions tighten
\item Unemployment Expectations rise
\item Wealth falls
\ei
\ei

\end{frame}



\begin{frame}
\frametitle{\textbf{Personal Saving Rate 2007-- $\boldsymbol{\uparrow}$ %by 5 pp
}}


\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/saving.pdf}
%\end{center}
\end{figure}
\end{frame}


\begin{frame}
\frametitle{\textbf{Household Wealth 2007--  $\boldsymbol{\downarrow}$ by 150\% of Income}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/fWealth.pdf}
%\end{center}
\end{figure}
\end{frame}



\begin{frame}
\frametitle{\textbf{Sustained Expectations of \underline{Rising} Unemp Risk}}
Thomson Reuters/University of Michigan $\Ex_{t}(u_{t+4}-u_{t})$

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=2.8in,width=4.5in]{../figures/fUExp.pdf}
%\end{center}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{\textbf{Tighter  HH Credit Supply (Based on Muellbauer)}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,4.5in]{../figures/fCredit.pdf}
%\end{center}
\end{figure}
\end{frame}

\begin{frame}\frametitle{\textbf{Our Contributions}}

\bi
\item \jemph{Theory}
\bi
\item Simple model with transparent role for all 3 channels
\item Qualitative implications of the model
\bi \item ``Overshooting'' $\Rightarrow$ possible role for fiscal policy
\ei
\ei
\item \jemph{Evidence}
\bi
\item Quantify importance of the 3 channels
\item Two estimated models of $\sRat$
\bi
\item \jemph{Reduced-form}---OLS
\item \jemph{Structural}---Nonlinear least squares
\ei
\ei
\ei

\end{frame}


\begin{frame}
\frametitle{\textbf{Why Do We Care?}}

\begin{itemize}
%\item Quantify impact of key determinants on \jemph{$\sRat$}
\item \jemph{\it Quantify} role of \jemph{credit, wealth and uncertainty}
\item Useful for in-sample and out-of-sample analysis
\item \jemph{Strength of recovery}/dynamics of GDP
%\item Time variation in \jemph{target wealth}
%\item Use larger-scale models (not univariate)
\end{itemize}

\end{frame}



\begin{frame}
\frametitle{\textbf{Theory \`a la \cite{ctDiscrete}}}

\begin{itemize}
\item CRRA utility, labor supply $\ell$, agg wage $\Wage$, emp status $\xi$:
\begin{eqnarray*}
\valfn(\mLev_{t})&=&\underset{\cLev_{t}}{\max } ~~
\util(\cLev_{t})+\Discount \Ex_{t}\big[ \valfn(\mLev_{t+1})
\big]  \label{eq:hetdecisionprobnashk}\\
\notag &\text{s.t.}&\\
  \mLev_{t+1} & = & (\mLev_{t}-\cLev_{t})\Rfree +\labor_{t+1}\Wage_{t+1}\empState_{t+1}  \label{eq:DBC}
\end{eqnarray*}
\item $\empState_{t+1} \in \{\empState^{u},\empState^{e}\}$ where $\empState^{u} < \empState^{e}$
\item $\labor$ and $\Wage$ grow at constant rate
%\bi
%\item CT model: $\{\empState^{u},\empState^{e}\}=\{0,1\}$
%\item Our model: wage-tax-financed UI system so $\empState^{u} > 0$
%\ei
\item Tractability: unemployment shocks are \jemph{permanent}
\bi
\item If $\empState_{t}=\empState^{u}$ then $\empState_{t+1}=\empState^{u}$
\ei
\item \jemph{Target wealth $\mTarg$} exists and is stable:
\bi
\item Consumption chosen so that $\mRat_t\rightarrow \mTarg$
\ei
\end{itemize}

\end{frame}


\begin{frame}
\frametitle{\textbf{Consumption Function}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/TractableBufferStockPhaseDiag.pdf}
%\end{center}
\end{figure}
\end{frame}


\begin{frame}
\frametitle{\textbf{Target Wealth} $\mTarg$}

Closed-form solution for target wealth depends on unemployment risk $\urate$ and generosity of unemployment insurance $\empState^{u}$:
$$
\jemph{\mTarg=f(\mathop{\urate}_{(+)},\mathop{\empState^{u}}_{(-)},\text{preferences}, \dots) \label{mTargetNonlin}}
$$
%where $\urate$ is unemployment risk.

%Why does target wealth decline in $\empState^{u}$?
%\bi
%\item $\empState^{u} \uparrow$ relaxes `Natural Borrowing Constraint' (NBC)
%\item NBC: `never end with $\aRat_{t}$ so low that $\cRat_{t+1} = 0$ is possible'
%\item PDV of unemployment benefits is $\empState^{u}/(\Rnorm-1)$
%\item So NBC says $a_{t} > -\empState^{u}/(\Rnorm-1)$
%\ei
%
%We {\it could} add a tighter, `artificial' borrowing constraint
%\bi
%\item But tightening natural borrowing constraint is just like tightening artificial one
%\item Adds complexity to the model without adding insight
%\ei
%
%$\Rightarrow$ we assume our measure of credit conditions identifies NBC
%\end{comment}

\end{frame}


\begin{frame}\frametitle{\textbf{Consumption After a Wealth Shock}}
\includegraphics[width=4in]{../figures/WealthShock.pdf}
\end{frame}

\begin{frame}\frametitle{\textbf{Permanent Rise in $\urate$}}

\includegraphics[width=4in]{../figures/cBeforeAndAfteruRise.pdf}

\end{frame}


\begin{frame}\frametitle{\textbf{Saving Rate After a Permanent Rise in $\urate$}}

\includegraphics[width=4in]{../figures/savRateAfterMhoRisePlot.pdf}

\end{frame}

\begin{frame}\frametitle{\bf Overshooting and Fiscal Policy}

DSGE models:
\bi
\item Frictions, frictions everywhere; but missing here
\item If $\Delta \cRat$ imposes `external' costs
\bi
\item Sticky prices/wages
\item Capital (or Investment) adjustment costs
\item Other reasons for `pecuniary externalities'
\ei
\item $\Rightarrow$ `stimulus' payments, fiscal policy may reduce cost of cycle
\item Justification for `automatic stabilizers'?
\ei


\end{frame}




\begin{frame}
\frametitle{\textbf{Credit Easing/Financial Innovation \& Deregulation}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[width=3.5in]{../figures/PhaseDiagramDebtLimRisePlot.pdf}
%\end{center}
\end{figure}

\jemph{$\mTarg$ is close to linear in credit conditions}

\end{frame}

\begin{frame}
\frametitle{\textbf{Data \& Sources}}

\bi
\item Quarterly 1966Q2--2011Q1
\item \jemph{Saving rate:} BEA NIPA
\item \jemph{Net worth:}  Flow of Funds Accounts, Fed
\begin{itemize}
\item (Model $m$ corresponds to 1 + ratio of Net worth to disposable income)
\end{itemize}
\item \jemph{Credit conditions:} ``Credit Easing Accumulated,'' CEA
\bi \item Senior Loan Officer Opinion Survey (SLOOS), Fed
\item {\footnotesize Banks' \jemph{willingness} to provide consumer installment loans}
\ei
\item \jemph{Unemployment risk:} using Thomson Reuters/UMichigan unemployment expectations
\ei

\end{frame}


\begin{frame}
\frametitle{\textbf{Net Worth (Ratio to Quarterly Disp Income)}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/fWyRat.pdf}
%\end{center}
\end{figure}

\end{frame}

\begin{frame}
\frametitle{\textbf{Credit Easing Accumulated (CEA) (\`a la Muellbauer)}}
Accumulated responses, weighted with debt--income ratio, to: \\
\footnotesize{``Please indicate your \jemph{bank's willingness to make consumer installment loans} now as opposed to three months ago.''}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=2.5in,width=4.5in]{../figures/fCredit.pdf}
%\end{center}
\end{figure}

\end{frame}

\begin{frame}
\frametitle{\textbf{$\urate_t$ Implied by Michigan U Expectations}}
\bi \footnotesize
\item Regress: $\Delta_4 u_{t+4}=\alpha_0+\alpha_1 UExp_t$
\item \jemph{U risk: $\urate_t=u_t+\Delta_4 \hat{u}_{t+4}$}
\item $\Delta_4 u_{t+4}\equiv u_{t+4}-u_t,\qquad \Delta_4 \hat{u}_{t+4}\equiv{} \text{fitted values}$
\item $\mho_t$ tracks \jemph{but precedes} actual U
\ei
{\scriptsize $UExp$: ``How about people out of work during the coming 12 months---do you think that there will be more unemployment than now, about the same, or less?''}
\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=2.35in,width=3.5in]{../figures/mhoUnem.pdf}
%\end{center}
\end{figure}

\end{frame}


\begin{frame}
\frametitle{\textbf{Reduced-Form Regressions}}

{\small\jemph{$s_t=\gamma_0+\gamma_m m_t +\gamma_{\CEA} \CEA_t+\gamma_{Eu}\Ex_t u_{t+4}+\gamma_t\,t+\gamma_{uC} (\Ex_t u_{t+4}\times\CEA_t)+\varepsilon_t $}}

\input ../tables/tOLS_prelim_time_slides.tex

\end{frame}


\begin{frame}
\frametitle{\textbf{Fit: Baseline vs Time Trend}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/fOLS_fit_time_compare_slides.pdf}
%\end{center}
\end{figure}
\end{frame}


\begin{frame}
%{\small $s_t=\gamma_1+\gamma_m m_t +\gamma_{\CEA}\CEA_t+\gamma_{Eu}\Ex_t u_{t+4}+\gamma'X_t+\varepsilon_t $}
\input ../tables/tOLS02_slides.tex

\end{frame}


\begin{frame}
\frametitle{\textbf{Fit: Baseline vs Post-1980}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/fPost80_slides.pdf}
%\end{center}
\end{figure}
\end{frame}


\begin{frame}
\frametitle{\textbf{Fit: Baseline vs Full Controls}}

\begin{figure}
%\begin{center}
%\vspace*{-4mm}
%\hspace*{-1.0cm}
\includegraphics[height=3in,width=4.5in]{../figures/fFullControls_slides.pdf}
%\end{center}
\end{figure}
\end{frame}



\begin{frame}
\frametitle{\textbf{Reduced-Form Regressions---Summary}}
The three factors explain saving well:
\begin{enumerate}
\item Credit conditions
\item Wealth
\item Unemployment risk
\end{enumerate}

\end{frame}


\begin{frame}
\frametitle{\textbf{Structural Estimation---Nonlinear Least Squares }}
Minimize distance between model-implied \jemph{$s_t^{\text{theor}}$} and actual \jemph{$s_{t}^{\text{meas}}$}:

$$
\hat{\Theta}=\argmin
\sum_{t=1}^T\bigg(s_{t}^{\text{meas}}-s_t^{\text{theor}}\Big(\Theta;
\mRat_t-\check{\mRat}\big(\bar{m}(\CEA_t),\mho(\Ex_tu_{t+4})\big)\Big)\bigg)^2,
$$
where
\bi
\item $\Theta=\{\Discount,\bar{\theta}_m,\theta_\CEA,\bar{\theta}_\mho,\theta_u\}$
\item $\bar{\mRat}_t=\bar{\theta}_\mRat+\theta_\CEA \CEA_t$
\item $\mho_t=\bar{\theta}_\mho+\theta_u \Ex_tu_{t+4}$
\item $\Discount$: discount factor
\ei

\end{frame}


\begin{frame}
\frametitle{\textbf{Structural Estimation---Asymptotics }}

\begin{block}{Delta Method}
$$
T^{1/2}(\hat{\Theta}-\Theta)\rightarrow_d \mathcal{N}(0, D^{-1}ED'^{-1}),
$$
where
\bi
\item $D=\Ex\frac{\partial q_t(\Theta)}{\partial \Theta'}$
\item $E=\var\big(q_t(\Theta)\big)$
\item Scores $q_t(\Theta)=\big(s_{t}^{\text{meas}}-s_t^{\text{theor}}(\Theta)\big)\frac{\partial s_t^{\text{theor}}(\Theta)}{\partial \Theta'}$
\ei
\end{block}

\end{frame}


\begin{frame}
\frametitle{\textbf{Structural Estimates }}
\input ../tables/tStructEst_slides.tex
\end{frame}

\begin{frame}\frametitle{\large\textbf{Estimated Extent of Credit Constraints $\bar{m}_t$ (Frac of DI)}}
\includegraphics[width=4in]{../figures/fCEA_est.pdf}
\end{frame}

\begin{frame}\frametitle{\textbf{Estimated Permanent Unemployment Risk $\mho_t$}}
\includegraphics[width=4in]{../figures/fMho_est.pdf}
\end{frame}

%\begin{frame}\frametitle{\textbf{Estimated Consumption Function}}
%\includegraphics[width=4in]{../figures/fEstCfunction.pdf}
%\end{frame}

\begin{frame}\frametitle{\textbf{Fit of the Structural Model}}
\includegraphics[width=4in]{../figures/fPSR_StructFit_slides.pdf}
\end{frame}

\begin{frame}\frametitle{\textbf{Decomposition of Fitted PSR}}
Fix $\mho_t$ and $\CEA_t$ at their sample means, back out the implied $\sRat_t$\\
\includegraphics[width=4in]{../figures/fPSR_StructDecomp.pdf}
\end{frame}

\begin{frame}\frametitle{\textbf{Fit: Structural Model vs Reduced-Form}}
\includegraphics[width=4in]{../figures/fOLS_fit_redStruct_compare.pdf}
\end{frame}


\begin{frame}
\frametitle{\textbf{Reduced-Form Regressions on Model Data}}

{\small\jemph{$s_t^{\text{theor}}=\gamma_0+\gamma_m m_t +\gamma_{\CEA} \CEA_t+\gamma_{Eu}\Ex_t u_{t+4}+\gamma_t\,t+\gamma_{uC} (\Ex_t u_{t+4}\times\CEA_t)+\varepsilon_t $}}

\input ../tables/tOLS_prelim_time_model_slides.tex

\end{frame}


\begin{frame}
\frametitle{\textbf{Reduced-Form Regressions on Actual Data}}

{\small\jemph{$s_t^{\text{meas}}=\gamma_0+\gamma_m m_t +\gamma_{\CEA} \CEA_t+\gamma_{Eu}\Ex_t u_{t+4}+\gamma_t\,t+\gamma_{uC} (\Ex_t u_{t+4}\times\CEA_t)+\varepsilon_t $}}

\input ../tables/tOLS_prelim_time_slides.tex

\end{frame}

\begin{frame}
\frametitle{\textbf{Structural Estimation---Summary}}

\bi
\item Model fits well\dots
\item \dots almost as well as reduced form\\ (Mincer--Zarnowitz puts weight 0.45 on structural model)
\item Substantial role for \jemph{time-varying precautionary saving}
\item \CEA\ matters for low frequency,\\ wealth for business-cycle frequency
\ei

\end{frame}




\begin{frame}
\frametitle{\textbf{PSR Forecasts---In Sample}}

\begin{block}{Great Recession 2007--2010}
\input ../tables/tPred_structRF.tex
\end{block}



\end{frame}

\begin{frame}
\frametitle{\textbf{PSR Forecasts---Out of Sample}}
2012--2015

\includegraphics[width=4in]{../figures/fPSRforecast.pdf}

Scenarios based on SPF and our judgement

\end{frame}


\begin{frame}
\frametitle{\textbf{Conclusions}}

\bi
\item All three effects present
\item Easier borrowing largely explains secular decline $\sRat$
\item Order of importance in Great Recession:
\begin{enumerate}
\item Wealth shock
\item Labor income risk
\item Credit tightening
%\item Deleveraging/elevated saving rate likely to continue for a while
\end{enumerate}
\item PSR to remain elevated
\ei

\end{frame}


\begin{frame}
\frametitle{\textbf{References}}
\tiny
\input bibMake
\end{frame}


\begin{frame}
\Large\remph{Background Slides}
\end{frame}



\begin{frame}\frametitle{\textbf{Alternative Measures of Credit Availability}}
\includegraphics[width=4in]{../figures/fCreditAvailability_compare.pdf}
\end{frame}


\begin{frame}\frametitle{\textbf{Assumptions/Scenarios for Out-of-Sample Forecasts}}
\includegraphics[width=4in]{../figures/fPSRforecastScenarios_1.pdf}
\end{frame}


\begin{frame}\frametitle{\textbf{Assumptions/Scenarios for Out-of-Sample Forecasts}}
\includegraphics[width=4in]{../figures/fPSRforecastScenarios_2.pdf}
\end{frame}

\begin{frame}\frametitle{\textbf{Actual and Target Wealth}}
\includegraphics[width=4in]{../figures/fWealthTarget.pdf}
\end{frame}

\end{document}
