verify_identification.PosteriorBSVART function

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Computes the logarithm of Bayes factor for the hypothesis of normality of the joint conditional distribution of the structural shocks via Savage-Dickey Density Ration (SDDR). The hypothesis of normality in this t-distributed shocks model is represented by restriction setting the degrees-of-freedom parameter $\nu$ to infinity: [REMOVE_ME]$H_0: \nu = \infty [REMOVE_ME_2]$

The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of logarithms of the marginal posterior distribution ordinate at the restriction less the marginal prior distribution ordinate at the same point: [REMOVE_ME]$log p(H_0 | data) - log p(H_0) [REMOVE_ME_2]$

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of the marginal posterior ordinate is done using truncated Gaussian kernel smoothing.

## S3 method for class 'PosteriorBSVART'
verify_identification(posterior)

Arguments

• posterior: the estimation outcome obtained using estimate function

Returns

An object of class SDDRidT that is a list with components:

logSDDR the value of the logarithm of the Bayes factor

SDDR the value of the Bayes factor

Description

Computes the logarithm of Bayes factor for the hypothesis of normality of the joint conditional distribution of the structural shocks via Savage-Dickey Density Ration (SDDR). The hypothesis of normality in this t-distributed shocks model is represented by restriction setting the degrees-of-freedom parameter $\nu$ to infinity:

The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of logarithms of the marginal posterior distribution ordinate at the restriction less the marginal prior distribution ordinate at the same point:

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of the marginal posterior ordinate is done using truncated Gaussian kernel smoothing.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

References

Lütkepohl, H., and Woźniak, T., (2020) Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity. Journal of Economic Dynamics and Control 113 , 103862, tools:::Rd_expr_doi("10.1016/j.jedc.2020.103862") .

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, tools:::Rd_expr_doi("10.48550/arXiv.2404.11057") .

See Also

specify_bsvar_t, estimate

Author(s)

Tomasz Woźniak wozniak.tom@pm.me