Although leptokurtosis is fairly common in macroeconomic time series,
agreement over what non-normal distributions are plausible, is rare. The paper
proposes a linear model that allows for trend versus difference stationarity and
asymmetric behavior over the business cycle along with several distributional
alternatives for the disturbance terms. It proposes computationally feasible Markov
Chain Monte Carlo methods to perform Bayesian computations, applies the model to
industrial production data of seven industrialized countries, and relies on prior
predictive densities to compare models with Student-t, symmetric stable, EGARCH,
exponential power family and finite-mixture-of-normals errors. The relationship
between unit root inference, asymmetry and leptokurtosis is examined in detail using
the exact, finite-sample posteriors corresponding to the different models.