Bayesian Structural VARs with Asymmetric Conjugate Priors

Implements Bayesian estimation of structural Vector Autoregressions in the asymmetric A-form of Chan (2022) , with an asymmetric Minnesota prior whose own-lag and cross-lag hyperparameters are selected by empirical Bayes via the closed-form marginal likelihood. Exact equation-by-equation posterior simulation in the structural form (independent Normal-Inverse-Gamma draws) provides posterior draws of the reduced-form parameters; structural identification through sign restrictions follows the algorithm of Rubio-Ramirez, Waggoner and Zha (2010) . Impulse responses, posterior bands, and acceptance diagnostics are computed from the accepted draws.

acpbvar

Bayesian estimation of asymmetric structural VARs in A-form, with Empirical-Bayes hyperparameter selection and sign-restriction identification.

Overview

acpbvar implements the asymmetric A-form representation of structural Vector Autoregressions following Chan (2022). The package combines

an asymmetric Minnesota prior, with own-lag and cross-lag tightness selected by Empirical Bayes through the closed-form log marginal likelihood (the intercept tightness is fixed);
exact equation-by-equation posterior simulation in the structural form, with independent Normal-Inverse-Gamma draws;
analytical recovery of the reduced-form quantities (impact matrix, lag coefficients, innovation covariance) from each posterior draw;
structural identification via sign restrictions, following the rotation algorithm of Rubio-Ramirez, Waggoner, and Zha (2010);
posterior impulse responses with credible bands.

The package has no external dependencies beyond base R.

Installation

# install.packages("devtools")
devtools::install_github("ursillofederica/acpbvar", build_vignettes = TRUE)

Quick start

library(acpbvar)

# Simulate a small structural VAR with known sign pattern
sim <- simulate_var_example(T = 200, seed = 42)
Y   <- sim$Y

# Posterior simulation under the asymmetric A-form prior
mcmc <- post_sim(Y, p = 1L, R = 1000L)

# Sign restrictions: supply (y+, pi-), demand (y+, pi+), monetary (y-, pi-, r+)
S <- rbind(
    supply   = c( 1, -1,  0),
    demand   = c( 1,  1,  0),
    monetary = c(-1, -1,  1)
)

accepted <- sign_restrict(mcmc, S, n_id = 3L, max_tries = 1000L)

# Impulse responses
irfs <- collect_irfs(accepted, n = 3L, p = 1L, H = 12L)
plot_irfs(irfs,
          var_names   = sim$var_names,
          shock_names = sim$shock_names)

The vignette acpbvar_workflow documents the full workflow, including diagnostics and recovery of the true structural impact from the simulated data-generating process.

References

Chan, J. C. C. (2022). Asymmetric conjugate priors for large Bayesian VARs. Quantitative Economics, 13(3), 1145-1169.
Rubio-Ramirez, J. F., Waggoner, D. F., & Zha, T. (2010). Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference. Review of Economic Studies, 77(2), 665-696.