<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath}
\usepackage[copyright]{ccicons}

\usetheme{Boadilla}

\title{The Dynare Macro Processor}
\subtitle{Dynare Summer School 2018}
\author{Sébastien Villemot}
%\pgfdeclareimage[height=0.6cm]{logo}{logo-ofce}
\institute{CEPREMAP}
\date{June 6, 2018}

\AtBeginSection[]
{
  \begin{frame}
    \frametitle{Outline}
    \tableofcontents[currentsection]
  \end{frame}
}

\begin{document}

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

\begin{frame}
  \frametitle{Outline}
  \tableofcontents
\end{frame}

\section{Overview}

\begin{frame}
  \frametitle{Motivation}
  \begin{itemize}
  \item The \textbf{Dynare language} (used in MOD files) is well suited for many economic models
  \item But it lacks some useful features such as:
    \begin{itemize}
    \item a loop mechanism for automatically repeating similar blocks of equations (e.g. multi-country models)
    \item an operator for indexed sums or products inside equations
    \item a mechanism for splitting up large MOD files into smaller, modular files
    \item the possibility of conditionally including some equations or some runtime commands
  \end{itemize}
  \item The \textbf{Dynare Macro-language} was specifically designed to address these issues
  \item Being flexible and fairly general, it can also be helpful in other situations
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Design of the macro-language}
  \begin{itemize}
  \item The Dynare Macro-language provides a new set of \textbf{macro-commands} which can be used in MOD files
  \item Language features include:
    \begin{itemize}
    \item file inclusion
    \item loops (\textit{for} structure)
    \item conditional inclusion (\textit{if/else} structures)
    \item expression substitution
    \end{itemize}
  \item The macro processor transforms a MOD file with macro-commands into a MOD file without macro-commands (doing text expansions/inclusions) and then feeds it to the Dynare parser
  \item The key point to understand is that the macro processor only does \textbf{text substitution} (like the C preprocessor or the PHP language)
  \end{itemize}
\end{frame}

\begin{frame}
  \frametitle{Design of Dynare}
  \includegraphics[width=0.95\linewidth]{new-design.pdf}
\end{frame}

\section{Syntax}

\begin{frame}[fragile=singleslide]
  \frametitle{Macro Directives}
  \begin{itemize}
  \item Directives begin with an at sign followed by a pound sign: \verb+@#+
  \item A directive produces no output but gives instructions to the macro processor
  \item Main directives are:
    \begin{itemize}
    \item file inclusion: \verb+@#include+
    \item definition of a macro processor variable: \verb+@#define+
    \item conditional statements: \verb+@#if/@#ifdef/@#ifndef/@#else/@#endif+
    \item loop statements: \verb+@#for/@#endfor+
    \end{itemize}
  \item Most directives fit on one line. If needed however, two backslashes (i.e. \verb+\\+) at the end of a line indicate that the directive is continued on the next line.
  \end{itemize}
\end{frame}


\begin{frame}
\frametitle{Variables}
\begin{itemize}
\item The macro processor has its own list of variables which are different than model variables and MATLAB/Octave variables
\item There are 4 types of macro-variables:
  \begin{itemize}
  \item integer
  \item string (declared between \textit{double} quotes)
  \item integer array
  \item string array
  \end{itemize}
\item No boolean type:
  \begin{itemize}
  \item false is represented by integer zero
  \item true is any non-zero integer
  \end{itemize}
\end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Macro-expressions (1/2)}
  It is possible to construct macro-expressions using standard operators.
  \begin{block}{Operators on integers}
    \begin{itemize}
    \item arithmetic operators: \texttt{+ - * /}
    \item comparison operators: \texttt{&lt; &gt; &lt;= &gt;= == !=}
    \item logical operators: \verb+&amp;&amp; || !+
    \item integer ranges: \texttt{1:4} is equivalent to integer array \texttt{[1,2,3,4]}
    \end{itemize}
  \end{block}

  \begin{block}{Operators on character strings}
    \begin{itemize}
    \item comparison operators: \texttt{== !=}
    \item concatenation: \texttt{+}
    \item extraction of substrings: if \texttt{s} is a string, then one can write \texttt{s[3]} or \texttt{s[4:6]}
    \end{itemize}
  \end{block}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Macro-expressions (2/2)}
  \begin{block}{Operators on arrays}
    \begin{itemize}
    \item dereferencing: if \texttt{v} is an array, then \texttt{v[2]} is its $2^{\textrm{nd}}$ element
    \item concatenation: \texttt{+}
    \item difference \texttt{-}: returns the first operand from which the elements of the second operand have been removed
    \item extraction of sub-arrays: \textit{e.g.} \texttt{v[4:6]}
    \item testing membership of an array: \texttt{in} operator \\ (example:
      \texttt{"b" in ["a", "b", "c"]} returns \texttt{1})
    \end{itemize}
  \end{block}

  Macro-expressions can be used in two places:
  \begin{itemize}
  \item inside macro directives; no special markup is required
  \item in the body of the MOD file, between an at sign and curly braces (like \verb+@{expr}+); the macro processor will substitute the expression with its value
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Define directive}

  The value of a macro-variable can be defined with the \verb+@#define+ directive.

  \begin{block}{Syntax}
    \verb+@#define +\textit{variable\_name}\verb+ = +\textit{expression}
  \end{block}

  \begin{block}{Examples}
\begin{verbatim}
@#define x = 5              // Integer
@#define y = "US"           // String
@#define v = [ 1, 2, 4 ]    // Integer array
@#define w = [ "US", "EA" ] // String array
@#define z = 3 + v[2]       // Equals 5
@#define t = ("US" in w)    // Equals 1 (true)
\end{verbatim}
  \end{block}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Expression substitution}
  \framesubtitle{Dummy example}
  \begin{block}{Before macro-processing}
\begin{verbatim}
@#define x = [ "B", "C" ]
@#define i = 2

model;
  A = @{x[i]};
end;
\end{verbatim}
  \end{block}
  \begin{block}{After macro-processing}
\begin{verbatim}
model;
  A = C;
end;
\end{verbatim}
  \end{block}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Inclusion directive (1/2)}
  \begin{itemize}
  \item This directive simply inserts the text of another file in its place
    \begin{block}{Syntax}
      \verb+@#include "+\textit{filename}\verb+"+
    \end{block}
    \begin{block}{Example}
\begin{verbatim}
@#include "modelcomponent.mod"
\end{verbatim}
    \end{block}
  \item Equivalent to a copy/paste of the content of the included file
  \item Note that it is possible to nest includes (\textit{i.e.} to include a
    file with an included file)
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Inclusion directive (2/2)}
  \begin{itemize}
\item The filename can be given by a macro-variable (useful in loops):
    \begin{block}{Example with variable}
\begin{verbatim}
@#define fname = "modelcomponent.mod"
@#include fname
\end{verbatim}
    \end{block}
  \item Files to include are searched for in current directory. Other directories can
    be added with
    \texttt{@includepath} directive, \texttt{-I} command line option or
    \texttt{[paths]} section in config file.
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Loop directive}
  \begin{block}{Syntax}
\verb+@#for +\textit{variable\_name}\verb+ in +\textit{array\_expr} \\
\verb+   +\textit{loop\_body} \\
\verb+@#endfor+
  \end{block}
  \begin{block}{Example: before macro-processing}
    \small
\begin{verbatim}
model;
@#for country in [ "home", "foreign" ]
  GDP_@{country} = A * K_@{country}^a * L_@{country}^(1-a);
@#endfor
end;
\end{verbatim}
    \normalsize
  \end{block}

  \begin{block}{Example: after macro-processing}
    \small
\begin{verbatim}
model;
  GDP_home = A * K_home^a * L_home^(1-a);
  GDP_foreign = A * K_foreign^a * L_foreign^(1-a);
end;
\end{verbatim}
    \normalsize
  \end{block}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Conditional inclusion directives (1/2)}

  \begin{columns}[T]
    \column{0.47\linewidth}
    \begin{block}{Syntax 1}
\verb+@#if +\textit{integer\_expr} \\
\verb+   +\textit{body included if expr != 0} \\
\verb+@#endif+
    \end{block}

    \column{0.47\linewidth}
    \begin{block}{Syntax 2}
\verb+@#if +\textit{integer\_expr} \\
\verb+   +\textit{body included if expr != 0} \\
\verb+@#else+ \\
\verb+   +\textit{body included if expr == 0} \\
\verb+@#endif+
    \end{block}
  \end{columns}

  \begin{block}{Example: alternative monetary policy rules}
    \scriptsize
\begin{verbatim}
@#define linear_mon_pol = 0 // or 1
...
model;
@#if linear_mon_pol
  i = w*i(-1) + (1-w)*i_ss + w2*(pie-piestar);
@#else
  i = i(-1)^w * i_ss^(1-w) * (pie/piestar)^w2;
@#endif
...
end;
\end{verbatim}
    \scriptsize
  \end{block}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Conditional inclusion directives (2/2)}

  \begin{columns}[T]
    \column{0.47\linewidth}
    \begin{block}{Syntax 1}
\verb+@#ifdef +\textit{variable\_name} \\
\verb+   +\textit{body included if variable defined} \\
\verb+@#endif+
    \end{block}

    \column{0.47\linewidth}
    \begin{block}{Syntax 2}
\verb+@#ifdef +\textit{variable\_name} \\
\verb+   +\textit{body included if variable defined} \\
\verb+@#else+ \\
\verb+   +\textit{body included if variable not defined} \\
\verb+@#endif+
    \end{block}
  \end{columns}

\bigskip

There is also \verb+@#ifndef+, which is the opposite of \verb+@#ifdef+
(\textit{i.e.} it tests whether a variable is \emph{not} defined).
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Echo and error directives}

  \begin{itemize}
  \item The echo directive will simply display a message on standard output
  \item The error directive will display the message and make Dynare stop (only makes sense inside a conditional inclusion directive)
  \end{itemize}

  \begin{block}{Syntax}
\verb+@#echo +\textit{string\_expr} \\
\verb+@#error +\textit{string\_expr}
  \end{block}

  \begin{block}{Examples}
\begin{verbatim}
@#echo "Information message."
@#error "Error message!"
\end{verbatim}
  \end{block}
\end{frame}

\begin{frame}
  \frametitle{Saving the macro-expanded MOD file}
  \begin{itemize}
  \item For \textbf{debugging or learning} purposes, it is possible to save the output of the macro processor
  \item This output is a valid MOD file, obtained after processing the macro-commands of the original MOD file
  \item Just add the \texttt{savemacro} option on the Dynare command line (after the name of your MOD file)
  \item If MOD file is \texttt{filename.mod}, then the macro-expanded version will be saved in \texttt{filename-macroexp.mod}
  \item You can specify the filename for the macro-expanded version with the syntax \texttt{savemacro=mymacroexp.mod}
  \item To end processing when macro processing is finished, add the option \texttt{onlymacro} to the Dynare command line
  \end{itemize}
\end{frame}

\section{Common uses}

\begin{frame}[fragile=singleslide]
  \frametitle{Modularization}
  \begin{itemize}
  \item The \verb+@#include+ directive can be used to split MOD files into several modular components
  \item Example setup:
    \begin{description}
    \item[\texttt{modeldesc.mod}:] contains variable declarations, model equations and shocks declarations
    \item[\texttt{simulate.mod}:] includes \texttt{modeldesc.mod}, calibrates parameters and runs stochastic simulations
    \item[\texttt{estim.mod}:] includes \texttt{modeldesc.mod}, declares priors on parameters and runs bayesian estimation
    \end{description}
  \item Dynare can be called on \texttt{simulate.mod} and \texttt{estim.mod}
  \item But it makes no sense to run it on \texttt{modeldesc.mod}
  \item Advantage: no need to manually copy/paste the whole model (at the beginning) or changes to the model (during development)
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Indexed sums or products}
  \framesubtitle{Example: moving average}
  \begin{columns}[T]
    \column{0.47\linewidth}
    \begin{block}{Before macro-processing}
\begin{verbatim}
@#define window = 2

var x MA_x;
...
model;
...
MA_x = 1/@{2*window+1}*(
@#for i in -window:window
        +x(@{i})
@#endfor
       );
...
end;
\end{verbatim}
    \end{block}
    \column{0.47\linewidth}
    \begin{block}{After macro-processing}
\begin{verbatim}
var x MA_x;
...
model;
...
MA_x = 1/5*(
        +x(-2)
        +x(-1)
        +x(0)
        +x(1)
        +x(2)
       );
...
end;
\end{verbatim}
    \end{block}
  \end{columns}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Multi-country models}
  \framesubtitle{MOD file skeleton example}
  \scriptsize
\begin{verbatim}
@#define countries = [ "US", "EA", "AS", "JP", "RC" ]
@#define nth_co = "US"

@#for co in countries
var Y_@{co} K_@{co} L_@{co} i_@{co} E_@{co} ...;
parameters a_@{co} ...;
varexo ...;
@#endfor

model;
@#for co in countries
 Y_@{co} = K_@{co}^a_@{co} * L_@{co}^(1-a_@{co});
...
@# if co != nth_co
 (1+i_@{co}) = (1+i_@{nth_co}) * E_@{co}(+1) / E_@{co}; // UIP relation
@# else
 E_@{co} = 1;
@# endif
@#endfor
end;
\end{verbatim}
  \normalsize
\end{frame}

\begin{frame}
  \frametitle{Endogeneizing parameters (1/4)}
  \begin{itemize}
  \item When doing the steady-state calibration of the model, it may be useful to consider a parameter as an endogenous (and vice-versa)
  \item Example:
    \begin{gather*}
      y = \left(\alpha^{\frac{1}{\xi}} \ell^{1-\frac{1}{\xi}} + (1-\alpha)^{\frac{1}{\xi}}k^{1-\frac{1}{\xi}}\right)^{\frac{\xi}{\xi - 1}} \\
      lab\_rat = \frac{w \ell}{p y}
    \end{gather*}
  \item In the model, $\alpha$ is a (share) parameter, and $lab\_rat$ is an endogenous variable
  \item We observe that:
    \begin{itemize}
    \item calibrating $\alpha$ is not straigthforward!
    \item on the contrary, we have real world data for $lab\_rat$
    \item it is clear that these two variables are economically linked
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Endogeneizing parameters (2/4)}
  \begin{itemize}
  \item Therefore, when computing the steady state:
    \begin{itemize}
    \item we make $\alpha$ an endogenous variable and $lab\_rat$ a parameter
    \item we impose an economically relevant value for $lab\_rat$
    \item the solution algorithm deduces the implied value for $\alpha$
    \end{itemize}
  \item We call this method ``variable flipping''
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Endogeneizing parameters (3/4)}
  \framesubtitle{Example implementation}
  \begin{itemize}
  \item File \texttt{modeqs.mod}:
    \begin{itemize}
    \item contains variable declarations and model equations
    \item For declaration of \texttt{alpha} and \texttt{lab\_rat}:
    \footnotesize
\begin{verbatim}
@#if steady
 var alpha;
 parameter lab_rat;
@#else
 parameter alpha;
 var lab_rat;
@#endif
\end{verbatim}
    \normalsize
    \end{itemize}

  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{Endogeneizing parameters (4/4)}
  \framesubtitle{Example implementation}
  \begin{itemize}
  \item File \texttt{steadystate.mod}:
    \begin{itemize}
    \item begins with \verb+@#define steady = 1+
    \item then with \verb+@#include "modeqs.mod"+
    \item initializes parameters (including \texttt{lab\_rat}, excluding \texttt{alpha})
    \item computes steady state (using guess values for endogenous, including \texttt{alpha})
    \item saves values of parameters and endogenous at steady-state in a file, using the \texttt{save\_params\_and\_steady\_state} command
    \end{itemize}
  \item File \texttt{simulate.mod}:
    \begin{itemize}
    \item begins with \verb+@#define steady = 0+
    \item then with \verb+@#include "modeqs.mod"+
    \item loads values of parameters and endogenous at steady-state from file, using the \texttt{load\_params\_and\_steady\_state} command
    \item computes simulations
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{MATLAB/Octave loops vs macro processor loops (1/3)}
  Suppose you have a model with a parameter $\rho$, and you want to make
  simulations for three values: $\rho = 0.8, 0.9, 1$. There are
  several ways of doing this:
  \begin{block}{With a MATLAB/Octave loop}
\begin{verbatim}
rhos = [ 0.8, 0.9, 1];
for i = 1:length(rhos)
  rho = rhos(i);
  stoch_simul(order=1);
end
\end{verbatim}
  \end{block}
  \begin{itemize}
  \item The loop is not unrolled
  \item MATLAB/Octave manages the iterations
  \item Interesting when there are a lot of iterations
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{MATLAB/Octave loops vs macro processor loops (2/3)}
  \begin{block}{With a macro processor loop (case 1)}
\begin{verbatim}
rhos = [ 0.8, 0.9, 1];
@#for i in 1:3
  rho = rhos(@{i});
  stoch_simul(order=1);
@#endfor
\end{verbatim}
  \end{block}
  \begin{itemize}
  \item Very similar to previous example
  \item Loop is unrolled
  \item Dynare macro processor manages the loop index but not the data array (\texttt{rhos})
  \end{itemize}
\end{frame}

\begin{frame}[fragile=singleslide]
  \frametitle{MATLAB/Octave loops vs macro processor loops (3/3)}
  \begin{block}{With a macro processor loop (case 2)}
\begin{verbatim}
@#for rho_val in [ "0.8", "0.9", "1"]
  rho = @{rho_val};
  stoch_simul(order=1);
@#endfor
\end{verbatim}
  \end{block}
  \begin{itemize}
  \item Advantage: shorter syntax, since list of values directly given in the loop construct
  \item Note that values are given as character strings (the macro processor does not
    know floating point values)
  \item Inconvenient: can not reuse an array stored in a MATLAB/Octave variable
  \end{itemize}
\end{frame}

% \begin{frame}[fragile=singleslide]
%   \frametitle{Possible future developments}
%   \begin{itemize}
%   \item Find a nicer syntax for indexed sums/products
%   \item Implement other control structures: \texttt{elsif}, \texttt{switch/case}, \texttt{while/until} loops
%   \item Implement macro-functions (or templates), with a syntax like:
%     \small
%     \verb+@#define QUADRATIC_COST(x, x_ss, phi) = phi/2*(x/x_ss-1)^2+
%     \normalsize
%   \end{itemize}
% \end{frame}

\begin{frame}
  \begin{center}
    \vfill {\LARGE Thanks for your attention!} \vfill
    {\LARGE Questions?}
    \vfill
  \end{center}
  \vfill
  \begin{columns}[T]
    \column{0.2\textwidth}
    \column{0.09\textwidth}

    \ccbysa
    \column{0.71\textwidth}
    \tiny
    Copyright © 2008--2017 Dynare Team \\
    Licence: \href{http://creativecommons.org/licenses/by-sa/4.0/}{Creative
      Commons Attribution-ShareAlike 4.0}
    \end{columns}
  \end{frame}


\end{document}
</pre></body></html>