normalize.svar: Likelihood normalization of SVAR models

Description

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

Usage

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

Arguments

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.

Value

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

Details

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.

References

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