IRIS Toolbox Reference Manual

min

Define the loss function in a time-consistent optimal policy model

Syntax

min(DISC) EXPRESSION;

Syntax for exact non-linear simulations

min#(DISC) EXPRESSION;

Description

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

If you use the 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.

Example

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

!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;