

    \filetitle{min}{Define the loss function in a time-consistent optimal policy model}{modellang/min}

	\paragraph{Syntax}

\begin{verbatim}
min(DISC) EXPRESSION;
\end{verbatim}

\paragraph{Syntax for exact non-linear
simulations}

\begin{verbatim}
min#(DISC) EXPRESSION;
\end{verbatim}

\paragraph{Description}

The loss function must be types as one of the transition equations. The
\texttt{DISC} is a parameter or an expression defining the discount
factor (applied to future dates), the \texttt{EXPRESSION} defines the
loss fuction proper.

If you use the \texttt{min\#(DISC)} syntax, all equations created by
differentiating the lagrangian w.r.t. individual variables will be
earmarked for exact non-linear simulations provided the respective
derivative is nonzero.

\paragraph{Example}

This is a simple model file with a Phillips curve and a quadratic loss
function.

\begin{verbatim}
!transition_variables
    x, pi

!transition_shocks
    u

!parameters
    alpha, beta, gamma

!transition_equations
    min(beta) pi^2 + lambda*x^2;
    pi = alpha*pi{-1} + (1-alpha)*pi{1} + gamma*y + u;
\end{verbatim}


