estimate_bsvar {bsvars}R Documentation

Bayesian estimation of a homoskedastic Structural Vector Autoregression via Gibbs sampler


Estimates the homoskedastic SVAR using the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2021) for the autoregressive slope parameters A. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated using a 3-level hierarchical prior distribution. See section Details for the model equations.


estimate_bsvar(S, specification, thin = 10, show_progress = TRUE)



a positive integer, the number of posterior draws to be generated


an object of class BSVAR generated using the specify_bsvar$new() function.


a positive integer, specifying the frequency of MCMC output thinning


a logical value, if TRUE the estimation progress bar is visible


The homoskedastic SVAR model is given by the reduced form equation:

Y = AX + E

where Y is an NxT matrix of dependent variables, X is a KxT matrix of explanatory variables, E is an NxT matrix of reduced form error terms, and A is an NxK matrix of autoregressive slope coefficients and parameters on deterministic terms in X.

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly normally distributed with zero mean and unit variances.


An object of class PosteriorBSVAR containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:


an NxKxS array with the posterior draws for matrix A


an NxNxS array with the posterior draws for matrix B


a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution

last_draw an object of class BSVAR with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using bsvar().


Tomasz Wo┼║niak


Sampling from the generalised-normal full conditional posterior distribution of matrix B is implemented using the Gibbs sampler by:

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Sampling from the multivariate normal full conditional posterior distribution of each of the A matrix row is implemented using the sampler by:

Chan, J.C.C., Koop, G, and Yu, X. (2021) Large Order-Invariant Bayesian VARs with Stochastic Volatility.

See Also

specify_bsvar, specify_posterior_bsvar, normalise_posterior


# upload data

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)

# run the burn-in
burn_in        = estimate_bsvar(50, specification)

# estimate the model
posterior      = estimate_bsvar(100, burn_in$get_last_draw())

[Package bsvars version 1.0.0 Index]