Provides summary of verifying homoskedasticity

Provides summary of the Savage-Dickey density ratios for verification of structural shocks homoskedasticity. The outcomes can be used to make probabilistic statements about identification through heteroskedasticity following Lütkepohl, Shang, Uzeda & Woźniak (2024).

Usage

# S3 method for class 'SDDRidSV'
summary(object, ...)

Arguments

object: an object of class SDDRidSV obtained using the verify_identification.PosteriorBSVARSV function.
...: additional arguments affecting the summary produced.

Value

A table reporting the logarithm of Bayes factors of homoskedastic to heteroskedastic posterior odds "log(SDDR)" for each structural shock, their numerical standard errors "NSE", and the implied posterior probability of the homoskedasticity and heteroskedasticity hypothesis, "Pr[homoskedasticity|data]" and "Pr[heteroskedasticity|data]" respectively.

References

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2024) Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference. University of Melbourne Working Paper, 1–57, doi:10.48550/arXiv.2404.11057 .

Author

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
#> The identification is set to the default option of lower-triangular structural matrix.
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR-SV model              |
#>    Non-centred SV model is estimated              |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|

# verify heteroskedasticity
sddr           = verify_identification(posterior)
summary(sddr)
#>  **************************************************|
#>  bsvars: Bayesian Structural Vector Autoregressions|
#>  **************************************************|
#>    Summary of identification verification          |
#>      H0: omega_n = 0  [homoskedasticity]           |
#>      H1: omega_n != 0 [heteroskedasticity]         |
#>  **************************************************|
#>           log(SDDR) NSE  Pr[H0|data] Pr[H1|data]
#> shock 1  -1.9483887   0 1.247292e-01   0.8752708
#> shock 2 -18.9022616   0 6.178060e-09   1.0000000
#> shock 3   0.3139002   0 5.778370e-01   0.4221630

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 10) |> 
  verify_identification() |> 
  summary() -> sddr_summary
#> The identification is set to the default option of lower-triangular structural matrix.
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR-SV model              |
#>    Non-centred SV model is estimated              |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
#>  **************************************************|
#>  bsvars: Bayesian Structural Vector Autoregressions|
#>  **************************************************|
#>    Summary of identification verification          |
#>      H0: omega_n = 0  [homoskedasticity]           |
#>      H1: omega_n != 0 [heteroskedasticity]         |
#>  **************************************************|