Waggoner & Zha (2003) row signs normalisation of the posterior draws for the structural matrix \(B\)

Normalises the sign of rows of matrix \(B\) MCMC draws, relative to matrix B_benchmark, provided as the second argument. The implemented procedure proposed by Waggoner, Zha (2003) normalises the MCMC output in an optimal way leading to the unimodal posterior. Only normalised MCMC output is suitable for the computations of the posterior characteristics of the \(B\) matrix elements and their functions such as the impulse response functions and other economically interpretable values.

Usage

normalise(posterior, B_benchmark = NULL)

Arguments

posterior: posterior estimation outcome obtained using function estimate() containing, amongst other draws, the S draws from the posterior distribution of the NxN structural matrix of contemporaneous relationships \(B\). These draws are to be normalised with respect to the matrix B_benchmark.
B_benchmark: the benchmark NxN structural matrix specified by the user to have the desired row signs

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

References

Waggoner, D.F., and Zha, T., (2003) Likelihood Preserving Normalization in Multiple Equation Models. Journal of Econometrics, 114(2), 329–47, doi:10.1016/S0304-4076(03)00087-3 .

Author

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)        # specify the model
#> The identification is set to the default option of lower-triangular structural matrix.
burn_in        = estimate(specification, 5)               # run the burn-in
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR model                 |
#> **************************************************|
#>  Progress of the MCMC simulation for 5 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
posterior      = estimate(burn_in, 5)                     # estimate the model
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR model                 |
#> **************************************************|
#>  Progress of the MCMC simulation for 5 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|

# normalise the posterior
BB             = posterior$last_draw$starting_values$B    # get the last draw of B
B_benchmark          = diag((-1) * sign(diag(BB))) %*% BB       # set negative diagonal elements
posterior      = normalise(posterior, B_benchmark)              # draws in posterior are normalised