Generalized exogenous processes in DSGE: A Bayesian approach

The Reversible Jump Markov Chain Monte Carlo (RJMCMC) method can enhance Bayesian DSGE estimation by sampling from a posterior distribution spanning potentially nonnested models with parameter spaces of different dimensionality. We use the method to jointly sample from an ARMA process of unknown order along with the associated parameters. We apply the method to the technology process in a canonical neoclassical growth model using post war US GDP data and find that the posterior decisively rejects the standard AR(1) assumption in favor of higher order processes. While the posterior contains significant uncertainty regarding the exact order, it concentrates posterior density on hump-shaped impulse responses. A negative response of hours to a positive technology shock is within the posterior credible set when noninvertible MA representations are admitted.