id.ngml {svars}

Non-Gaussian maximum likelihood (NGML) identification of SVAR models

Description

Given an estimated VAR model, this function applies identification by means of a non-Gaussian likelihood for 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 unique decomposition of the least squares covariance matrix \Sigma_u=B B' if the vector of structural shocks \epsilon_t contains at most one Gaussian shock (Comon, 94). A likelihood function of independent t-distributed structural shocks \epsilon_t=B^{-1}u_t is maximized with respect to the entries of B and the degrees of freedom of the t-distribution (Lanne et al., 2017).

Usage

id.ngml(x, stage3 = FALSE, restriction_matrix = NULL)

Arguments

x

An object of class 'vars', 'vec2var', 'nlVar'. Estimated VAR object

stage3

Logical. If stage3="TRUE", the VAR parameters are estimated via non-gaussian maximum likelihood (computationally demanding)

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 errors

sigma

Estimated scale of the standardized matrix B_stand, i.e. B=B_stand*diag(\sigma_1,...,\sigma_K)

sigma_SE

Standard errors of the scale

df

Estimated degrees of freedom

df_SE

Standard errors of the degrees of freedom

Fish

Observed Fisher information matrix

A_hat

Estimated VAR parameter via ML

B_stand

Estimated standardized structural impact matrix

B_stand_SE

Standard errors of standardized matrix B_stand

Lik

Function value of likelihood

method

Method applied for identification

n

Number of observations

type

Type of the VAR model, e.g. 'const'

y

Data matrix

p

Number of lags

K

Dimension of the VAR

restrictions

Number of specified restrictions

restriction_matrix

Specified restriction matrix

stage3

Logical, whether Stage 3 is performed

VAR

Estimated input VAR object

References

Lanne, M., Meitz, M., Saikkonen, P., 2017. Identification and estimation of non-Gaussian structural vector autoregressions. J. Econometrics 196 (2), 288-304.
Comon, P., 1994. Independent component analysis, A new concept?, Signal Processing, 36, 287-314

See Also

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

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.ngml(v1)
summary(x1)

# switching columns according to sign pattern
x1$B <- x1$B[,c(3,2,1)]
x1$B[,3] <- x1$B[,3]*(-1)

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