Bayesian Framework for Finding Relevant Macro Factors in Affine Term Structure Models

We address the question of which unspanned macroeconomic factors are the best in the class of macro-finance Gaussian affine term structure models. To answer this question, we extend Joslin, Priebsch, and Singleton (2014) in two dimensions. First, following Ang and Piazzesi (2003) and Chib and Ergashev (2009), three latent factors, instead of the first three principal components of the yield curve, are used to represent the level, slope and curvature of the yield curve. Second we postulate a grand affine model that includes all the macro-variables in contention. Specific models are then derived from this grand model by letting each of the macro-variables play the role of a relevant macro factor (i.e. by affecting the time-varying market price of factor risks), or the role of an irrelevant macro factor (having no effect on the market price of factor risks). The Bayesian marginal likelihoods of the resulting models are computed by an efficient Markov chain Monte Carlo algorithm and the method of Chib (1995) and Chib and Jeliazkov (2001). Given eight common macro factors, our comparison of 2^8=256 affine models shows
that the most relevant macro factors for the U.S. yield curve are the federal funds rate, industrial production, total capacity utilization, and housing sales. We also show that the best supported model substantially improves out-of-sample yield curve forecasting and the understanding of the term-premium.