Robust Bayesian Model Selection
نویسندگان
چکیده
This paper extends the robust Bayesian inference in misspeci ed models of Müller (2013, Econometrica) to Bayesian model selection of a set of misspeci ed models. It is shown that when a model is misspeci ed, under the Kullback-Leibler loss function, the risk associated with Müllers posterior is less (weakly) than that with the original posterior distribution asymptotically. Based on this new result, two new information criteria are proposed for model selection under model misspeci cation. Su¢ cient conditions are provided for the risk associated with Müllers posterior to be strictly smaller. JEL classi cation: C11, C12, G12 Keywords: Model selection; Model misspeci cation; Arti cial posterior distribution, Sandwich-covariance matrix; Markov chain Monte Carlo. Essentially, all models are wrong, but some are useful. (George Box) 1 Introduction Economic theory often makes strong predictions on certain aspects of economic behavior while at the same time is silent on other aspects. One of the best known cases is that economists are often agnostic about the form of the distribution, especially when distributions are not normally distributed. As a result, robust statistical inference of economic models has received a great deal of attention from econometricians and empirical economists. In frequentists paradigm, seminar methodological contributions include Huber (1967), Hansen (1982), White (1982), Gourerioux, et al. (1984a, 1984b). For a long time, robust Bayesian analysis has focused on investigating the sensitivity of posterior distributions to prior distributions, leaving aside the issue of adequacy of the Yong Li, Hanqing Advanced Institute of Economics and Finance, Renmin University of China, Beijing, 1000872, P.R. China. Jun Yu, Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business. Yu would like to acknowledge the nancial support from Singapore Ministry of Education Academic Research Fund Tier 2 under the grant number MOE2011-T2-2-096. Email for Jun Yu: [email protected]. URL: http://www.mysmu.edu/faculty/yujun/.
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