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

In svars: Data-Driven Identification of SVAR Models

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 ε_t.

Matrix B corresponds to the decomposition of the least squares covariance matrix Σ_u=BΛ_t B'.

Usage

id.chol(x, order_k = NULL)

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.

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

References

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

See Also

For alternative identification approaches see id.st, id.cvm, id.cv, id.dc or id.ngml

Examples

# 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')

svars documentation built on Feb. 16, 2023, 7:52 p.m.