Exact small-sample inference in stationary, fully regular, dynamic demand models

Asymptotics are known to be unreliable in multivariate models with cross-equation or non-linear restrictions, and the dimension of the problem makes bootstrapping impractical. In this paper, finite sample results are obtained by Markov chain Monte Carlo methods for a nearly non-stationary VAR, and for a differential dynamic demand model with homogeneity, Slutsky symmetry, and negativity. The full likelihood function is used in each case. Slutsky symmetry and negativity are tested using simulation estimates of partial Bayes factors. We argue that a diffuse prior on the long-run error covariance matrix helps to identify the equilibrium coefficients.