Stock and Bond Return Predictability : The Discrimination Power of Model Selection Criteria

We analyze the discrimination power of well-known model selection criteria when R2 is low as in typical asset return predictability studies. We find that the discrimination power is low in this setup and in particular give another interpretation to the well-cited Bossaerts and Hillion (1999) study. We then look at model selection criteria in a testing framework and propose, as a diagnostic tool, a bootstrap based procedure to construct the class of models which are statistically undistinguishable from the best model chosen by a model selection criterion. As an empirical illustration we reanalyze the Pesaran and Timmerman (1995) results and show that the class of undistiguishable models can be large. Finally we show that the similar problems arise in a more hidden way in the context of recent model uncertainty studies such as the Bayesian model selection criteria proposed by Avramov (2002) and Cremers (2002).