shock_decomposition: Historical Shock Decomposition

In dsge: Dynamic Stochastic General Equilibrium Models

Historical Shock Decomposition

Description

Decomposes the observed variables into the contributions of each structural shock. At each time t, the observed deviation from steady state is written as a sum of contributions from current and past shocks plus the initial condition contribution.

Usage

## S3 method for class 'dsge_solution'
shock_decomposition(x, data, ...)

shock_decomposition(x, ...)

## S3 method for class 'dsge_fit'
shock_decomposition(x, ...)

## S3 method for class 'dsge_bayes'
shock_decomposition(x, ...)

Arguments

x	A dsge_fit or dsge_bayes object.
data	Matrix or data frame of observed data with columns matching the model's observable names. Required when x is a dsge_solution.
...	Additional arguments (currently unused).

Details

The state-space solution gives:

x_t = H^t x_0 + \sum_{j=1}^{t} H^{t-j} M \varepsilon_j

The historical decomposition partitions the observed variables y_t = Z x_t into the contribution of each structural shock \varepsilon_j^{(k)} accumulated through the propagation mechanism. The sum of all contributions (including the initial condition term) reproduces the smoothed observables exactly.

Value

An object of class "dsge_decomposition" containing:

decomposition

A 3D array with dimensions [T, n_obs, n_shocks + 1]. The last slice contains the initial condition contribution.

obs_names

Character vector of observed variable names.

shock_names

Character vector of shock names (plus "initial").

observed

T x n_obs matrix of observed data (deviations).

Examples

m <- dsge_model(
  obs(y ~ z),
  state(z ~ rho * z),
  start = list(rho = 0.5)
)
set.seed(1)
e <- rnorm(100)
z <- numeric(100); for (i in 2:100) z[i] <- 0.8*z[i-1]+e[i]
fit <- estimate(m, data = data.frame(y = z))
hd <- shock_decomposition(fit)
plot(hd)

dsge documentation built on Sept. 25, 2026, 5:08 p.m.