svars: id.garch – R documentation

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id.garch

Identification of SVAR models through patterns of GARCH

Description

Given an estimated VAR model, this function uses GARCH-type variances 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', where Λ_t is the estimated conditional heteroskedasticity matrix.

Usage

id.garch(x, max.iter = 5, crit = 0.001, restriction_matrix = NULL)

Arguments

`x`	An object of class 'vars', 'vec2var', 'nlVar'. Estimated VAR object
`max.iter`	Integer. Number of maximum likelihood optimizations
`crit`	Numeric. Critical value for the precision of the iterative procedure
`restriction_matrix`	Matrix. A matrix containing presupposed entries for matrix B, NA if no restriction is imposed (entries to be estimated). Alternatively, a K^2*K^2 matrix can be passed, where ones on the diagonal designate unrestricted and zeros restricted coefficients. (as suggested in Luetkepohl, 2017, section 5.2.1).

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
`B_SE`	Standard errors of matrix B
`GARCH_parameter`	Estimated GARCH parameters of univariate GARCH models
`GARCH_SE`	Standard errors of GARCH parameters
`n`	Number of observations
`Fish`	Observed Fisher information matrix
`Lik`	Function value of likelihood
`iteration`	Number of likelihood optimizations
`method`	Method applied for identification
`A_hat`	Estimated VAR parameter via GLS
`type`	Type of the VAR model, e.g. 'const'
`restrictions`	Number of specified restrictions
`restriction_matrix`	Specified restriction matrix
`y`	Data matrix
`p`	Number of lags
`K`	Dimension of the VAR
`VAR`	Estimated input VAR object

References

Normadin, M. & Phaneuf, L., 2004. Monetary Policy Shocks: Testing Identification Conditions under Time-Varying Conditional Volatility. Journal of Monetary Economics, 51(6), 1217-1243.
Lanne, M. & Saikkonen, P., 2007. A Multivariate Generalized Orthogonal Factor GARCH Model. Journal of Business & Economic Statistics, 25(1), 61-75.

Examples

# data contains quartlery observations from 1965Q1 to 2008Q2
# assumed structural break in 1979Q3
# x = output gap
# pi = inflation
# i = interest rates
set.seed(23211)
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.garch(v1)
summary(x1)

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

# Restrictions
# Assuming that the interest rate doesn't influence the output gap on impact
restMat <- matrix(rep(NA, 9), ncol = 3)
restMat[1,3] <- 0
x2 <- id.garch(v1, restriction_matrix = restMat)
summary(x2)

svars

Data-Driven Identification of SVAR Models

v1.3.7

MIT + file LICENSE

Authors

Alexander Lange [aut, cre], Bernhard Dalheimer [aut], Helmut Herwartz [aut], Simone Maxand [aut], Hannes Riebl [ctb]

Initial release

2021-03-17