Assessing Bayesian model comparison in small samples

We investigate the Bayesian approach to model comparison within a two-country framework with nominal rigidities using the workhorse New Keynesian open-economy model of Martnez-Garca and Wynne (2010). We discuss the trade-offs that monetary policy characterized by a Taylor-type rule faces in an interconnected world, with perfectly flexible exchange rates. We then use posterior model probabilities to evaluate the weight of evidence in support of such a model when estimated against more parsimonious specifications that either abstract from monetary frictions or assume autarky by means of controlled experiments that employ simulated data. We argue that Bayesian model comparison with posterior odds is sensitive to sample size and the choice of observable variables for estimation. We show that posterior model probabilities strongly penalize overfitting which can lead us to favor a less parameterized model against the true data-generating process when the two become arbitrarily close to each other. We also illustrate that the spill-overs from monetary policy across countries have an added confounding effect.