The steady_state_model block

The steady_state_model; block gives an analytical steady state for the model — one assignment per endogenous variable, expressing it as a function of the parameters and the exogenous values:

steady_state_model;
  A = 1 + e/theta;
  K = (alpha*A/(rho+delta))^(1/(1-alpha));
  Y = A * K^alpha;
  C = Y - delta*K;
end;

The left-hand side of each assignment must be the name of a declared endogenous variable (state, jump, or algebraic). The right-hand side may reference parameters, exogenous variables, and any endogenous variable already assigned above it in the block.

The block must cover every endogenous variable; a missing assignment raises an IR error. An initial_guess block (see Initial conditions: initval and initial_guess) may be added as a Newton seed when the steady state has multiple solutions, but it does not replace the analytical block.

Numerical fallback

When no steady_state_model block is present, the steady state is computed numerically (Newton on the residual with all time derivatives set to zero). For most non-trivial models the analytical block is both faster and more robust, and is what the shipped examples use.

How the steady state is used

The computed steady state serves three purposes:

1. As the terminal anchor of every jump variable in each segment: the solver enforces jump(t_end) = SS(jump) so that the continuous-time saddle path is selected.

2. As the initial guess for Newton (tiled across the grid).

3. As the value of the steady_state(var) callable inside initval (see Initial conditions: initval and initial_guess).

The steady state used at each of those places is computed at the exogenous values active for that segment / time, except where overridden explicitly with e={…} (see Initial conditions: initval and initial_guess).