min

Define loss function for optimal policy

Syntax

min(Disc) Expr;

Syntax for exact non-linear simulations

min#(Disc) Expr;

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), and the expression Expr defines the loss fuction. The Disc expression must not contain a comma.

If you use the min#(Disc) syntax, all equations created by differentiating the lagrangian w.r.t. individual variables will be earmarked for exact nonlinear simulations provided the respective derivative is nonzero. This only makes sense if the loss function is other than quadratic, and hence its derivatives are nonlinear.

There are two types of optimal policy that can be calculated: time-consistent discretionary policy, and time-inconsistent optimal policy with commitment. Use the option 'optimal=' in the function model at the time of loading the model file to switch between these two types of policy; the option can be either 'discretion' (default) or 'commitment'.

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;