verify_identification function

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

Computes the logarithm of Bayes factor(s) for the hypothesis in which the model is not identified through heteroskedasticity of non-normality using Savage-Dickey Density Ration (SDDR). The hypothesis of no such identification, $H_0$, is represented by model-specific restrictions.Consult help files for individual classes of models for details. The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of the logarithm of the marginal posterior distribution ordinate at the restriction less the log-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 the lack of identification of the structural shock through heteroskedasticity or non-normality.

verify_identification(posterior)

Arguments

• posterior: the estimation outcome obtained using estimate function

Returns

An object of class SDDRid* that is a list with components:

logSDDR a vector with values of the logarithm of the Bayes factors

log_SDDR_se a vector with numerical standard errors of the logarithm of the Bayes factors reported in output element logSDDR that are computed based on 30 random sub-samples of the log-ordinates of the marginal posterior and prior distributions.

Description

Computes the logarithm of Bayes factor(s) for the hypothesis in which the model is not identified through heteroskedasticity of non-normality using Savage-Dickey Density Ration (SDDR). The hypothesis of no such identification, $H_0$, is represented by model-specific restrictions.Consult help files for individual classes of models for details. The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of the logarithm of the marginal posterior distribution ordinate at the restriction less the log-marginal prior distribution ordinate at the same point:

Therefore, a negative value of the difference is the evidence against the lack of identification of the structural shock through heteroskedasticity or non-normality.

Examples

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

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
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_sv$new(p = 1) |>
  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

verify_identification.PosteriorBSVAR, verify_identification.PosteriorBSVARSV, verify_identification.PosteriorBSVARMIX, verify_identification.PosteriorBSVARMSH, verify_identification.PosteriorBSVART

Author(s)

Tomasz Woźniak wozniak.tom@pm.me