The model block

The model; block lists the equations of the dynamic system. Each equation is a continuous-time relation in the endogenous variables, the exogenous processes, the parameters, and the reserved time t.

model;
  diff(K) = Y - C - delta*K;                     // state equation
  diff(A) = theta*(1 - A) + e;                   // state equation
  diff(C) = C * (alpha*Y/K - delta - rho);       // jump equation (Euler)
  Y = A * K^alpha;                               // algebraic equation
end;

Equation forms

Two forms are accepted:

Explicit

LHS = RHS ; — interpreted as the residual LHS - RHS = 0.

Bare

expr ; — interpreted as expr = 0.

Both forms produce a residual; the assembled vector F(ẋ, x, e, θ, t) = 0 is what the solver discretises and stacks.

Time derivatives: diff

The time derivative of a variable is written diff(x). Higher-order derivatives may be written diff(x, k) (these are reduced to a chain of first-order auxiliary states by the IR). diff is only meaningful in the model block.

A var(state) or var(jump) must have its time derivative defined on the left-hand side of exactly one equation; an algebraic var must not.

Equation tags

Each equation may carry one or more comma-separated tags in square brackets immediately before it:

[name='Euler']
diff(C) = C * (alpha*Y/K - delta - rho);

Tags are stored on the equation in the IR; they have no numerical effect (yet), but are useful labels for diagnostics and post-solve inspection.

What model does not accept

• The shock-path shape helpers (step, pulse, ramp, bump, expdecay, smoothstep) are forbidden in model. They are only meaningful as time-shape sugars in shocks paths; using one in model raises a clear CodegenError.

• Strings and dict literals have no numeric meaning in a model expression and are rejected.

For the operators and functions allowed in equations see Expressions.