Priors for Macroeconomic Time Series and Their Application

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This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter which can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odds ratios using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson-Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.