normalize.svar: Likelihood normalization of SVAR models
In MSBVAR: Markov-Switching, Bayesian, Vector Autoregression Models

Description Usage Arguments Details Value Note Author(s) References See Also

Computes various sign normalizations of Bayesian structural VAR (B-SVAR) models.

normalize.svar(A0unnormalized, A0mode,
               method = c("DistanceMLA", "DistanceMLAhat",
                          "Euclidean", "PositiveDiagA",
                          "PositiveDiagAinv", "Unnormalized"),
               switch.count = 0)

`A0unnormalized`	m x m unnormalized matrix value of A(0) in an B-SVAR
`A0mode`	m x m matrix of the A(0) to normalize around
`method`	string that selects the normalization method
`switch.count`	counter that counts the number of sign switches. Can be non-zero if you want to track the sign switches iteratively.

The likelihood of VAR models are invariant to sign changes of the structural equation coefficients across equations. Thus a VAR with m equations has a likelihood with 2^m identical peaks, each a different set of signs (but with the same posterior peak). Normalization is used to choose among these peaks. The most common choice is to select the peak where the diagonal elements of A(0) are all positive, but will not be possible in all cases since no such normalization may exist. Thus, one should select a single peak and map all of the draws back to that peak.

The available normalization methods are 1) "DistanceMLA" : normalize around the ML peak of A0mode, 2) "DistanceMLAhat" : normalize around the ML peak of inv(A0mode) 3) "Euclidean" : normalize by minimizing the distance between the two matrices. 4) "PositiveDiagA" : normalize by making the diagonal positive 5) "PositiveDiagAinv" : normalize by making the diagonal of inv(A0) positive. 6) "Unnormalized" : no normalization is performed and the function returns A0 unnormalized.

A list with two elements

`A0normalized`	m x m matrix, the normalized value of A(0) according to the selected normalization rule.
`switch.count`	Number of signs changed in the normalization

This function is called in gibbs.A0.BSVAR, the Gibbs sampling of szbsvar models. In those functions, the A(0) produced by szbsvar is unnormalized. The Gibbs sampled draws are then normalized using the "DistanceMLA" method, which is consistent with the positive system shocks typically seen in the literature, if such a normalization exists. Note that Waggoner and Zha prefer the "DistanceMLA" method.

Patrick T. Brandt

Waggoner, Daniel F. and Tao A. Zha. 2003a. "A Gibbs sampler for structural vector autoregressions" Journal of Economic Dynamics \& Control. 28:349–366.

Waggoner, Daniel F. and Tao A. Zha. 2003b. "Likelihood preserving normalization in multiple equation models". Journal of Econometrics. 114: 329–347.

szbsvar, gibbs.A0

MSBVAR documentation built on May 30, 2017, 1:23 a.m.