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\title[ECB-BASE-MCE]{Model-consistent-expectations in the ECB-BASE: First results and Roadmap}
\author[Adjemian \and Bokan \and Darracq Pariès]{Stéphane Adjemian \and Nikola Bokan \and Matthieu Darracq Pariès}

\date{July, 2020}

\begin{document}
\maketitle

\section*{Context}

\begin{frame}
  \frametitle{Context}

  \textit{MCE activities within the ECB-MC project}

  \bigskip

  \begin{itemize}

  \item Starts from the ECB-BASE (backward) model with few changes\newline

    \begin{itemize}

    \item re-estimation of the model on more recent euro area data\newline

    \item appropriate convergence towards the balance growth path\newline

    \item other minor fixes\newline
    \end{itemize}

  \item Further work is still needed to fine tune the re-estimation of the ECB-BASE (backward) model\newline

  \item MCE activities will proceed in parallel to this process

  \end{itemize}


\end{frame}

\section{MCE specification}


\subsection{Price and wage setting blocks}


\begin{frame}
  \frametitle{MCE specification: wapro and wage blocks}

  \textit{MCE in the wage and price setting equations}

  \bigskip

  \begin{itemize}

  \item Replacing the VAR-based expectation by MCE expectation for the next period inflation term in the GDP-deflator equation\newline

  \item Replacing the VAR-based expectation by MCE expectation for the next period wage gap term in the wage gap equation\newline

  \item Long-term inflation expectations remain imperfectly anchored as in the backward model\newline

  \end{itemize}

\end{frame}


\subsection{Financial block}


\begin{frame}
  \frametitle{MCE specification: financial block}

  \textit{MCE in the term structure of interest rate}

  \bigskip

  \begin{itemize}

  \item Long-term interest rates\newline

    \begin{itemize}

    \item Expectation theory for the risk-free 10-year OIS rate: we introduce a consol bond serving geometrically decaying coupons, discounted by the short-term policy rate and a duration corresponding the one of a 10-year zero coupon.\newline

    \item The 10-year OIS rate accounting for a term premium: we introduce a similar consol with a discounting of coupons augmented by a term premium.\newline

    \item Similar treatment for corporate bond\newline

    \end{itemize}

  \end{itemize}

\end{frame}


\begin{frame}
  \frametitle{MCE specification: financial block}

  \textit{MCE in financial spreads}

  \bigskip

  \begin{itemize}

  \item Replacing the VAR-based expectation by MCE expectation for 10-year average of expected output gap\newline

  \item this variable then loads into the financial spreads (term premium, corporate spread, lending rate spreads and cost-of-equity)\newline

  \item Consistent reformulation of the revaluation effects on households net financial wealth\newline

  \end{itemize}

  \bigskip

  \begin{center}
    \textit{Follow-up: stock prices may be formally specified}
  \end{center}

\end{frame}


\subsection{Exchange rate determination}


\begin{frame}
  \frametitle{MCE specification: Exchange rate determination}

  \textit{MCE for the Uncovered Interest rate Parity equation (UIP)}

  \bigskip

  \begin{itemize}

  \item Replacing the "level" equation for the nominal exchange rate in the backward model by a UIP condition\newline

  \item The expected depreciation rate depends on the short-term interest rate differential...\newline

  \item ... augmented with a term premium effect to obtain a plausible "APP-like" transmission of term premium shocks\newline

  \item Given the consumption specification, adding a term on NFA in the UIP is not necessary to ensure stationary NFA dynamics\newline

  \end{itemize}

  \bigskip

  \begin{center}
    \textit{Empirical and theoretical challenges remain on the UIP specification}
  \end{center}

\end{frame}


\subsection{Consumption block}


\begin{frame}
  \frametitle{MCE specification: Consumption block}

  \bigskip

  \begin{itemize}

  \item Permanent incomes.\newline

    \begin{itemize}

    \item Infinite sums of discounted expected incomes can be rewritten recursively as forward AR(1) models\newline

    \end{itemize}

  \item PAC equation.\newline

    \begin{itemize}

    \item Depends on the expected path of the consumption target\dots

    \item Expressed as an infinite sum of expected growth rates

    \item Can be rewritten recursively as a forward AR(p) model\newline

    \end{itemize}

  \end{itemize}

\end{frame}


\section{Simulations}


\subsection{Benchmark backward model}


\begin{frame}[fragile]
  \frametitle{Old vs New infrastuctures}

  \begin{center}
    \includegraphics[page=1, scale=0.25]{../plots/new_vs_wp.pdf}\includegraphics[page=2, scale=0.25]{../plots/new_vs_wp.pdf}
  \end{center}
\end{frame}

\subsection{Backward versus full MCE}

\begin{frame}[fragile]
  \frametitle{Responses to a one point shock on the nominal interest rate}

  \begin{center}
    \includegraphics[scale=1.0]{../plots/backward-full-comparison-res_U2_STN.pdf}\\
    {\tiny{\color{blue}---} Backward model, {\color{red}---} Full MCE model}
  \end{center}

\end{frame}


\begin{frame}[fragile]
  \frametitle{Responses to a one point shock on the term premium}

  \begin{center}
    \includegraphics[scale=1.0]{../plots/backward-full-comparison-res_U2_TP_10Y.pdf}\\
    {\tiny{\color{blue}---} Backward model, {\color{red}---} Full MCE model}
  \end{center}

\end{frame}


\subsection{Standard shocks across MCE specifications}


\begin{frame}
  \frametitle{Simulations}

  \begin{itemize}

  \item[{\color{blue} ---}] Backward model,\newline

  \item[{\color{red} ---}] Full MCE,\newline

  \item[{\color{cyan} ---}] Same as {\color{red} ---} without MCE in PAC equations,\newline

  \item[{\color{green} ---}] Same as {\color{red} ---} without MCE in consumption block,\newline

  \item[{\color{yellow} ---}] Same as {\color{red} ---} without MCE in financial block,\newline

  \item[{\color{gray} ---}] Same as {\color{red} ---} without MCE in exchange rate / UIP block.\newline

  \end{itemize}

\end{frame}


\begin{frame}[fragile]
  \frametitle{Responses to a one point shock on the nominal interest rate}

  \begin{center}
    \includegraphics[scale=1.0]{../plots/irfs-res_U2_STN.pdf}\\

    \bigskip

    {\tiny {\color{blue}---} Backward model, {\color{red}---} Full MCE model, {\color{cyan}---} Hybrid model without MCE in PAC,
      {\color{green}---} Hybrid model without MCE in consumption,\\ {\color{yellow}---} Hybrid model without MCE in financial,
      {\color{gray}---} Hybrid model without MCE/UIP}
  \end{center}

\end{frame}


\begin{frame}[fragile]
  \frametitle{Responses to a one point shock on the term premium}

  \begin{center}
    \includegraphics[scale=1.0]{../plots/irfs-res_U2_TP_10Y.pdf}\\

    \bigskip

    {\tiny {\color{blue}---} Backward model, {\color{red}---} Full MCE model, {\color{cyan}---} Hybrid model without MCE in PAC,
      {\color{green}---} Hybrid model without MCE in consumption,\\ {\color{yellow}---} Hybrid model without MCE in financial,
      {\color{gray}---} Hybrid model without MCE/UIP}
  \end{center}

\end{frame}

\subsection{Forward guidance shocks}

\begin{frame}
  \frametitle{Forward guidance (full MCE)}

  \begin{center}
    \includegraphics[scale=0.35]{../plots/forward-guidance-full.pdf}\\
  \end{center}

\end{frame}


\begin{frame}
  \frametitle{Forward guidance (without mce in consumption)}

  \begin{center}
    \includegraphics[scale=0.35]{../plots/forward-guidance-without-mce-in-consumption.pdf}\\
  \end{center}

\end{frame}


\begin{frame}
  \frametitle{Forward guidance (without mce in financial)}

  \begin{center}
    \includegraphics[scale=0.35]{../plots/forward-guidance-without-mce-in-financial.pdf}\\
  \end{center}

\end{frame}


\begin{frame}
  \frametitle{Forward guidance (without mce in exchange rate)}

  \begin{center}
    \includegraphics[scale=0.35]{../plots/forward-guidance-without-mce-in-exchange-rate.pdf}\\
  \end{center}

\end{frame}


\subsection{Anticipated productivity shocks}

\begin{frame}[fragile]
  \frametitle{Expected TFP growth shock in 10 years for one year (4$\times$1\%)}

  \begin{center}

    \includegraphics[scale=1.0]{../plots/expected-tfp-growth-shock.pdf}\\

    \bigskip

  {\tiny
      {\color{red}---} Full hybrid model, {\color{cyan}---} Hybrid model without MCE in PAC,
      {\color{green}---} Hybrid model without MCE in consumption,\\ {\color{yellow}---} Hybrid model without MCE in financial,
      {\color{gray}---} Hybrid model without MCE/UIP
    }
  \end{center}

\end{frame}


\section{Roadmap for MCE activities}


\begin{frame}
  \frametitle{Next steps}

  \textit{Main deliverables for the end-August milestone}

  \bigskip

  \begin{itemize}
  \item Freeze the benchmark backward model\newline

  \item Systematic comparison of shock transmission between the backward model, the hybrid expectations model and the full MCE model\newline

  \item Further examples of anticipated shocks\newline

  \item Policy application\newline

  \end{itemize}

\end{frame}


\begin{frame}
  \frametitle{Follow-up activities}

  \textit{Possible workstreams}

  \bigskip

  \begin{itemize}

  \item Stationary version of the model and linear approximation\newline

    \begin{itemize}
    \item Tractability of stochastic simulations

    \item Filtering\newline

    \end{itemize}

  \item Empirical validation of the MCE model\newline

    \begin{itemize}

    \item Indirect inference on the Wapro/wage blocks

    \item System-wide inference using the linear model\newline

    \end{itemize}

  \item Policy analysis with the MCE model\newline

    \begin{itemize}

    \item Nesting a term-structure model into the ECB-BASE-MCE

    \item Optimal policy projections

    \end{itemize}

  \end{itemize}

\end{frame}


\end{document}




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