Intrinsic Bayesian Estimation of Vector Autoregression Impulse Responses

We propose an information-theoretic alternative to the conventional Bayesian posterior mean estimator of impulse responses in vector autoregression (VAR) models. The proposed estimator is based on the intrinsic entropy loss function, which is invariant to nonlinear transformations of parameters. Consequently, intrinsic estimation of impulse responses is equivalent to that of VAR parameters. The Bayesian estimator under the entropy loss involves a frequentist expectation of regressors. We propose Markov chain Monte Carlo algorithms to simulate the posterior of the frequentist expectation of regressors and compute the Bayesian estimates. We estimate the VAR impulse responses in two applications.