Bayesian comparison of econometric models

This paper integrates and extends some recent computational advances in Bayesian inference with the objective of more fully realizing the Bayesian promise of coherent inference and model comparison in economics. It combines Markov chain Monte Carlo and independence Monte Carlo with importance sampling to provide an efficient and generic method for updating posterior distributions. It exploits the multiplicative decomposition of marginalized likelihood into predictive factors, to compute posterior odds ratios efficiently and with minimal further investment in software. It argues for the use of predictive odds ratios in model comparison in economics. Finally, it suggests procedures for public reporting that will enable remote clients to conveniently modify priors, form posterior expectations of their own functions of interest, and update the posterior distribution with new observations. A series of examples explores the practicality and efficiency of these methods. This paper was initially prepared as the inaugural Colin Clark Lecture, Australasian Meetings of the Econometric Society, July 1994. I wish to acknowledge helpful comments made at this meeting, in seminars at Cambridge University, Federal Reserve System Board of Governors, Harvard-M.I.T., University of Kansas, University of Minnesota, Northwestern University, University of Pennsylvania, Princeton University, and University of Virginia, and at the 1994 summer and 1995 winter North American meetings of the Econometric Society, the 1994 North American and world meetings of the International Society for Bayesian Analysis, and the 1995 Bath international workshop on model comparison. The paper has benefited from discussions with Jim Berger, Gary Chamberlain, Jon Faust, Bill Griffiths, Peter Phillips, Christopher Sims, Mark Steel and Arnold Zellner. Remaining errors and shortcomings are entirely the author’s. Zhenyu Wang provided research assistance. This work was supported in part by National Science Foundation Grant SES-9210070. The views expressed in this paper are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.