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;

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