Steady-state

The deterministic state of a model corresponds to steady-state values $\overline{m}$ of the exogenous process. States and controls satisfy:

$\overline{s} = g\left(\overline{m}, \overline{s}, \overline{x}, \overline{m} \right)$

$0 = \left[ f\left(\overline{m}, \overline{s}, \overline{x}, \overline{m}, \overline{s}, \overline{x} \right) \right]$

where $g$ is the state transition function, and $f$ is the arbitrage equation. Note that the shocks, $\epsilon$, are held at their deterministic mean.

The steady state function consists in solving the system of arbitrage equations for the steady state values of the controls, $\overline{x}$, which can then be used along with the transition function to find the steady state values of the state variables, $\overline{s}$.