7inR 11. Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information.

Описание: Рассказывает Игорь Николаев. 
Аннотация:
Many empirical studies have used numerical Bayesian methods for structural inference in vector autoregressions that are identified solely on the basis of sign restrictions. Because sign restrictions only provide set-identification of structural parameters, over certain regions of the parameter space the posterior inference could only be a restatement of prior beliefs. In this paper we characterize these regions, explicate the beliefs about parameters that are implicit in conventional priors, provide an analytical characterization of the full posterior distribution for arbitrary priors, and analyze the asymptotic properties of this posterior distribution. We show that in a bivariate supply and demand example, if the population correlation between the VAR residuals is negative, then even if one has available an infinite sample of data, any inference about the supply elasticity is coming solely from the prior distribution. More generally, the asymptotic posterior distribution of contemporaneous coefficients in an n-variable VAR is confined to the set of values that orthogonalize the population variance-covariance matrix of OLS residuals, with the height of the posterior proportional to the height of the prior at any point within that set. We suggest that researchers should defend their prior beliefs explicitly and report the difference between prior andposteriordistributionsforkeymagnitudesofinterest. Weillustratethesemethodswith a simple macroeconomic model.