Equation Syntax Reference • koma

Overview

This vignette describes the syntax for specifying stochastic and identity equations, priors, and lags in the koma package.

1. Stochastic Equations

Stochastic (regression) equations model a dependent variable with an error term. An intercept is included by default.

# With default intercept:
consumption ~ gdp + consumption.L(1)

# Without intercept:
consumption ~ gdp + consumption.L(1) - 1

# Explicit intercept:
consumption ~ 1 + gdp + consumption.L(1)

2. Identity Equations

Identity equations enforce exact relationships.

# Identity equations with explicitly defined weights:
# To aggregate the component growth rates into a growth rate for GDP we need to define weights.
# This is done by specifying the weights in the equation. 
# You can, e.g. use the nominal level weights of the last observed period.
gdp == 0.7*consumption + 0.2*investment + 0.2*government - 0.1*net_exports

3. Injected Parameters & Constants

Known constants or parameters can be inserted via () in any equation.

# Injected parameter s:
gdp == (s) * cons

# Ratios computed from data:
gdp == (nom_cons/nom_gdp) * cons

4. Lag Notation

Lags are specified with L() or lag() notation. Ranges and combinations are supported.

# Single lag:
x.L(1)
lag(x, 1)

# Range of lags:
x.L(1:4)
lag(x, 1:4)

# Mix range and specific lags:
x.L(1:3, 5)

5. Priors

Specify priors before coefficients using curly braces {}.

# normal(1,0.1):
{1, 0.1} x3

6. Equation-specific Tau

You can override the default tau in your gibbs_settings for a single equation by appending [tau = value] after its equation. If the acceptance rate falls outside 30%-60 %, a warning is emitted.

"consumption ~ constant + gdp + consumption.L(1) + consumption.L(2) [tau = 1.2]"