Expressions

This page collects the expression sub-language: the operators, functions, and literals that may appear on the right of an equation, in a parameter assignment, in an initval, in a steady-state assignment or in a shock path. The same grammar applies everywhere; the only context-dependent restrictions are noted below.

Literals

42, 3.14, 1.5e-3

Decimal literals (integer, fractional, optional exponent).

'hello' or "hello"

String literals. Only meaningful as equation tags and similar metadata; using one in a numeric position raises a CodegenError.

{key1: expr, key2: expr} or {}

Dict literals. Used only as the value of the e= keyword in initval(steady, e={…}) and steady_state(v, e={…}); using one in a numeric position raises a CodegenError.

Identifiers

Any declared name resolves to its value at the point of evaluation:

  • a parameter resolves to its assigned value;

  • a var (endogenous) resolves to its current state on the grid;

  • a varexo resolves to the value at the current time of the active shock path;

  • the reserved t resolves to the current time.

Arithmetic operators

Operator

Meaning

+

Addition

-

Subtraction / unary minus

*

Multiplication

/

Division

^

Power (right-associative)

Precedence (low → high): + -, * /, unary -, ^. Use parentheses for any clarification.

Comparison and logical operators

Comparisons return 0 or 1 (as in Dynare):

  • <, <= — less-than, less-or-equal;

  • >, >= — greater-than, greater-or-equal;

  • == — equal;

  • != — not equal.

Logical operators on these 0/1 values:

  • && — logical AND;

  • || — logical OR;

  • ! — logical NOT.

Comparisons are non-chainable (a < b < c is a syntax error; write a < b && b < c).

Mathematical functions

The functions below are available in every block that accepts expressions:

  • exponentials and logs: exp, ln (alias log), log10, sqrt;

  • trigonometric and hyperbolic: sin, cos, tan, asin, acos, atan, sinh, cosh, tanh;

  • error function: erf;

  • pointwise: abs, sign;

  • variadic: min(a, b, …), max(a, b, …) (at least two arguments).

The conditional if(condition, then, else) (with the 1-argument sugar if(cond, x) ≡ if(cond, x, 0)) is allowed everywhere.

Note

min and max are useful for occasionally-binding constraints such as the ZLB (i = max(0, …)). Newton may have trouble at the kink for some calibrations; if convergence fails, raise N or use a smooth approximation like 0.5*(z + sqrt(z*z + eps)) in place of max(0, z).

Context-specific extras

The shock-shape helpers (step, pulse, ramp, bump, expdecay, smoothstep) are available only inside ``shocks`` paths and are rejected in model equations. See The shocks block.

The time derivative diff(x) is allowed only inside the model block (and as a left-hand side in initval).

The steady-state callable steady_state(var) and steady_state(var, e={…}) is allowed only inside the initval block; see Initial conditions: initval and initial_guess.

Comments

// introduces a line comment, /* … */ a block comment. Comments are ignored by the parser.