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%***********************************************************************************************

\title[Sticky Consumption Growth]{International Evidence on\\ Sticky Consumption Growth}

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

\author[Carroll, Slacalek and Sommer]{Christopher Carroll\inst{1} \and Jirka Slacalek\inst{2} \and Martin Sommer\inst{3}
}
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% - Keep it simple, no one is interested in your street address.
\institute{
  \inst{1} Johns Hopkins 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{January 2008}

%\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}



\bfr
\frametitle{Consumption Habits Are Pervasive}

\bi
\item Equity premium puzzle %(\cite{con90}, \cite{cc99})
%\item Granger causality from growth rates to saving rates %(\cite{cow00})
\item Hump-shaped response of consumption to income shocks %(\cite{fuh00})
\item Dynamic effects of fiscal policy %(\cite{lu00})
\item Persistence in current account balances %(\cite{gru04})
%\item Home-bias puzzle %(\cite{sw06})
\item \dots
\ei
\remph{\textbf{BUT}}
\bi
\item No consensus on whether the \cite{hal78} random walk model is in line with data
\item Few estimates of how sluggish C growth is (in particular in international data)
\item Estimates of habits often smaller than required by theory
\ei
\end{frame}

\bfr
\frametitle{The Hall Model and The Data}
\begin{block}{The \cite{hal78} Random Walk Model}
\small Consumption Growth Is Unpredictable and Thus Serially Uncorrelated
$$
\ex_t\Delta C_{t+1}=0 \Rightarrow \ex_t\big(\Delta C_{t}\times\Delta C_{t+1}\big)=0
$$
\end{block}
\begin{block}{Existing Empirical Work Reveals Predictability\dots}
with stock prices, income, consumer sentiment\dots
\bi
\item \cite{fla81}, \cite{cm89} and many others
\ei
\end{block}

\begin{block}{\dots But Not as much as in Most Calibrated Models with Habits}
\bi
\item First autocorrelation of C growth in aggregate US data $\approx0.35$
%\item Eg, \citet{cc99}: \remph{\textbf{Fill out habits numbers}}
\ei
\end{block}
\end{frame}

\bfr
\frametitle{Explanations of the ``Excess Sensitivity'' of Consumption}
\bi
\item Time Aggregation\\
\jemph{Cannot Explain Strong AC in C Growth}
\item Precautionary Savings\\
\jemph{Aggregate Uncertainty Is Small $\Rightarrow$ Limited Relevance in Macro Data}
\item Data Construction Methods [e.g., interpolation and imputation]\\
\jemph{We Argue This Is Important}
\item Rule-of-Thumb Consumers\\
\jemph{We Argue This Is Less Important Than Typically Believed}
\ei
\end{frame}

\bfr
\frametitle{Our Contribution}
\bi
\item \jemph{Estimate the role ``stickiness in aggregate C growth''} (which can be interpreted as habits or sticky expectations) correcting for the presence of \jemph{measurement error and transitory consumption} (IV and the Kalman filter)
\item Data from 13 countries
\ei

\begin{block}{Our Findings}
\bi
\item Strong Evidence of C Growth \remph{\textbf{``Stickiness''}}
\item The Weight of Habits/Sticky Expectations Is about 70 Percent
\item Typically Reject Rule-of-Thumb Consumers in Favor of Stickiness
\ei
\end{block}
\end{frame}


\bfr
\frametitle{Theories of Stickiness I.: Habit Formation}
\bi
\item \citet{muellbauerAES88}:
\begin{align*}
&\max\ex_s\sum_{t=s}^\infty\beta^{t-s}\mathbf{u}(C_t-\chi C_{t-1})\\
&\mbox{s.t. } B_{t+1}=(B_t-C_t)R+Y_{t+1}
\end{align*}
\item $\chi:$ Weight of Habits (Represented with $C_{t-1}$)
\item Both Level of C and Growth Matter: $$\mathbf{u}(C_t-\chi C_{t-1})=\mathbf{u}\big((1-\chi)C_t-\chi \Delta C_{t-1}\big)$$
\item Linearized FOC for CRRA Utility:
\begin{align*}
\Delta\log C_t&=\chi\Delta\log C_{t-1}+\varepsilon_t
\end{align*}
\ei
\end{frame}


\bfr
\frametitle{Theories of Stickiness II.: Sticky Expectations}
\bi
\item \citet{cs06}, \citet{rei06}: \jemph{Consumers  are inattentive}: know accurately their personal circumstances but follow macroeconomic developments only once in a while.
\item Consumers update their info about permanent income with probability $\Pi$ each period
\item \jemph{Individual consumption growth} is dominated by idiosyncratic shocks and \jemph{is white noise.}
\item \jemph{Aggregate consumption growth is AR(1)} with autocorrelation $1-\Pi$
\begin{align*}
\Delta\log C_t&=(1-\Pi)\Delta\log C_{t-1}+\varepsilon_t
\end{align*}
\item Both habits and sticky expectations have identical implications in aggregate data (but not in micro data)
\ei
\end{frame}


\bfr
\frametitle{Estimation Methods \`a la Sommer (2007)}
\begin{block}{Instrumental Variables}
\small
\begin{align*}
\Delta \log C_t = \varsigma+\chi \ex_{t-2}[\Delta \log C_{t-1}]+\eta \ex_{t-2}[\Delta \log Y_{t}]+\alpha \ex_{t-2}[A_{t-1}]+\varepsilon_t
\end{align*}
\end{block}
\begin{block}{Kalman filter}
\small
\begin{align*}
\Delta\log C_t&=\Delta\log C_t^*+u_t+(\theta-1)u_{t-1}-\theta u_{t-2},\\
\Delta\log C_t^*&=c_0+\chi\Delta\log C_{t-1}^*+v_t+\lambda_1(\chi)v_{t-1}+\lambda_2(\chi)v_{t-2},
\end{align*}
where $C^*$ is unobserved ``true'' consumption
\end{block}
\begin{block}{OLS Is Biased }
\bi
\item Measurement error
\item Transitory consumption (eg, hurricane Katrina)
\item Time aggregation
\ei
\end{block}
\end{frame}

\bfr
\frametitle{Instrumental Variables}
\small
\begin{align*}
\Delta \log C_t = \varsigma+\chi \ex_{t-2}[\Delta \log C_{t-1}]+\eta \ex_{t-2}[\Delta \log Y_{t}]+\alpha \ex_{t-2}[A_{t-1}]+\varepsilon_t
\end{align*}
\bi
\item Nests three alternatives:
\bi
\item $\chi=0$ and $\eta=0$: Random walk
\item $\chi=0$: Rule-of-thumb consumers (with $C_t=Y_t$)
\item $\eta=0$: C Stickiness (Habits/Sticky Expectations)
\ei
\item Financial assets ($A_{t-1}$) included to account for precautionary savings and/or time-variation in interest rates

\item With appropriate (ie, uncorrelated with measurement error and correlated with endogenous variables) instruments no need to specify the stochastic structure of measurement error.
\ei
\end{frame}


\bfr
\frametitle{Kalman Filter}
Two-stage procedure
\begin{enumerate}
\item Kalman filter---MA(1) measurement error in log-level of C
\begin{align*}
\Delta\log C_t&=\Delta\log C_t^*+u_t+(\theta-1)u_{t-1}-\theta u_{t-2},\\
\Delta\log C_t^*&=c_0+\chi\Delta\log C_{t-1}^*+v_t+\lambda_1(\chi)v_{t-1}+\lambda_2(\chi)v_{t-2},
\end{align*}
where $C^*$ is unobserved ``true'' consumption

\bi
\item $\lambda$s are nonlinear functions of $\chi$
\item MA(2) coefficient $\lambda_2$ is close to zero for reasonable $\chi\in(0, 1)$,
so that $\Delta\log C^*_t$ is approximately ARMA(1,1).
\ei

\item Instrumental variables on
\small
\begin{align*}
\Delta \log C_t^* = \varsigma+\chi \ex_{t-2}[\Delta \log C_{t-1}^*]+\eta \ex_{t-2}[\Delta \log Y_{t}]+\alpha \ex_{t-2}[A_{t-1}]+\varepsilon_t
\end{align*}
\end{enumerate}
\end{frame}


\bfr
\frametitle{Data}
\bi
\item 13 advanced economies
\item Quarterly data roughly over past 40 years
\item \jemph{Consumption:} Ideally, sum of nondurables and services (available only for Can, Fra, Ger, Ita, UK, US), else total personal consumption expenditures
\item \jemph{Income:} Disposable income
\item \jemph{Assets ($A$):} Ratio of financial assets to disposable income
\item \jemph{Instruments:} Various sets; baseline: unemployment rate, long-term interest
rate, index of price volatility and consumer sentiment
\ei
\end{frame}


\bfr
\frametitle{Baseline IV Results}
\input../tables/tAllCountriesFinBaseSlides.tex
\end{frame}

\bfr
\frametitle{Baseline IV Summary}
\begin{block}{Univariate Regressions}
\bi
\item Clear rejection of random walk
\item C Stickyness $\chi$ significant and around 0.7
\item Income share of rule-of-thumb consumers $\eta\approx0.4$, less significant
\item Coefficient on wealth $\alpha$ typically insignificant
\item First-stage $\bar{R}^2$ for C typically ranges between 0.1 and 0.2
\ei
\end{block}
\begin{block}{Horse-race Regressions}
\bi
\item Past C beats other regressors
\item $\chi$ drops only slightly (from 0.7 to 0.6) and remains significant in 10 countries
\item $\eta$ insignificant (except for Germany)
\item OID test does not reject instrument exogeneity
\ei
\end{block}
\end{frame}

\bfr
\frametitle{IV Results for Country Groups (Averages)}
\input../tables/tAllCgroupsBaseSlides.tex
\end{frame}

\bfr
\frametitle{Alternative Instrument Set [Un, Inc, IR Spread, Sent]}
\input../tables/tAllCountriesFinAltSlides.tex
\end{frame}

\bfr
\frametitle{Kalman Filter---First-Stage Results}
\input../tables/t1stStageSlides.tex
\end{frame}

\bfr
\frametitle{``True'' Consumption  Growth {\footnotesize(Kalman smoother, G7, demeaned, per cap)}}
\begin{figure}
\includegraphics[height=3in,width=4in]{../figures/fG7.eps}
\end{figure}
\end{frame}

\bfr
\frametitle{``True'' Consumption  Growth {\footnotesize(Kalman smoother, other countries)}}
\begin{figure}
\includegraphics[height=3in,width=4in]{../figures/fOther.eps}
\end{figure}
\end{frame}


\bfr
\frametitle{Kalman Filter---Second-Stage Results}
\input../tables/tAllCountriesFinMLEslides.tex
\end{frame}

\bfr
\frametitle{Kalman Filter Summary}
\bi
\item Clear rejection of random walk
\item C Stickiness $\chi$ highly significant and around 0.8 (in both panels)
\item $\chi$ generally close to IV estimates
\item Large fraction of transitory components in C growth (around 50 percent in US)
\item Little correlation between C and instrumented Y in univariate regressions, none in horse-race
\ei
\end{frame}

\bfr
\frametitle{Structural Interpretation}
The Kalman filter model fits into the structural DSGE framework of \citet{ire04}:
$
\mathbf{f}_t=\mathbf{Cs}_t+\mathbf{u}_t
$\\
$\mathbf{f}_t$: control variables,  $\mathbf{s}_t$: state variables,  $\mathbf{u}_t$: residuals\\[2mm]
{\small\jemph{Ireland:} ``the residuals [$\mathbf{u}_t$] may \dots\ soak up  both measurement errors, but they can be interpreted more liberally as capturing all of the movements and co-movements in the data that the real business cycle model, because of its elegance and simplicity, cannot explain.''}
\bi
\item For our model: $\mathbf{f}_t=\Delta\log C_t$, $\mathbf{s}_t=\Delta\log C^*_{t-1}$,  $\mathbf{C}=\chi$, $\mathbf{u}_t=u_t+(\theta-1) u_{t-1}-\theta u_{t-2}+v_t+\lambda_1(\chi)v_{t-1}+\lambda_2(\chi)v_{t-2}$
    \item Our model is simple and can be estimated with classical techniques. $\Rightarrow$ \\ Data have complete control over the estimates of $\chi$.
    \item Our estimates can be use to calibrate priors in larger-scale Bayesian DSGE models.
\ei
\end{frame}

\bfr
\frametitle{Conclusion}
Aggregate Consumption Growth Is Sticky.
\end{frame}
\appendix
\tiny
\bibliographystyle{econometricaFullnames}
\bibliography{economics}

\end{document}
