The present study makes two contributions to the Bayesian Vector-Autoregression (VAR) literature. The first contribution is derivation of the Bayesian VAR estimator under the intrinsic entropy loss. The Bayesian estimator, which is distinctly different from the posterior mean, involves the frequentist expectation of a function of VAR variables. We find that the condition that allows for a closed-form expression of the frequentist expectation is violated even when the VAR is stationary, making it difficult to compute the Bayesian estimates via standard Markov Chain Monte Carlo (MCMC) procedures. The second contribution of the paper concerns MCMC simulation of the Bayesian estimator without using the closed-form expression of the frequentist expectation. A novelty of our MCMC algorithms is that they jointly simulate the posteriors of frequentist moments of VAR variables as well as the posteriors of VAR parameters. Numerical simulations show that the algorithms are surprisingly efficient
