id.chol: Recursive identification of SVAR models via Cholesky decomposition

Description

Given an estimated VAR model, this function uses the Cholesky decomposition to identify the structural impact matrix B of the corresponding SVAR model $$y_t=c_t+A_1 y_{t-1}+...+A_p y_{t-p}+u_t =c_t+A_1 y_{t-1}+...+A_p y_{t-p}+B \epsilon_t.$$ Matrix B corresponds to the decomposition of the least squares covariance matrix $\Sigma_u=B\Lambda_t B'$.

Usage

id.chol(x, order_k = NULL)

Value

A list of class "svars" with elements

B: Estimated structural impact matrix B, i.e. unique decomposition of the covariance matrix of reduced form residuals
n: Number of observations
method: Method applied for identification
order_k: Ordering of the variables as assumed for recursive causality
A_hat: Estimated VAR parameter
type: Type of the VAR model, e.g. 'const'
y: Data matrix
p: Number of lags
K: Dimension of the VAR
VAR: Estimated input VAR object

Arguments

x: An object of class 'vars', 'vec2var', 'nlVar'. Estimated VAR object
order_k: Vector. Vector of characters or integers specifying the assumed structure of the recursive causality. Change the causal ordering in the instantaneous effects without permuting variables and re-estimating the VAR model.

References

Luetkepohl, H., 2005. New introduction to multiple time series analysis, Springer-Verlag, Berlin.

Examples

Run this code

# \donttest{

# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.chol(v1)
x2 <- id.chol(v1, order_k = c("pi", "x", "i")) ## order_k = c(2,1,3)
summary(x1)


# impulse response analysis
i1 <- irf(x1, n.ahead = 30)
i2 <- irf(x2, n.ahead = 30)
plot(i1, scales = 'free_y')
plot(i2, scales = 'free_y')


# }