Technical note on "assessing Bayesian model comparison in small samples"

This technical note is developed as a companion to the paper ‘Assessing Bayesian Model Comparison in Small Samples’ (Globalization and Monetary Policy Institute working paper no. 189). Taking the workhorse open-economy model of Martínez-García and Wynne (2010) with nominal rigidities under monopolistic competition as our Data-Generating Process, we investigate with simulated data how Bayesian model comparison based on posterior odds performs when the model becomes arbitrarily close to a closed-economy and/or an economy with flexible prices and perfect competition. This technical note elaborates on three key technical points relevant for Martínez-García and Wynne (2014). First, we explain the building blocks of the open-economy model of Martínez-García and Wynne (2010). We also derive the equilibrium conditions (and the steady state) under producer-currency pricing. Second, we discuss the log-linearization of the equilibrium conditions around the deterministic steady state and our benchmark parameterization. The linear rational expectations model that results from the log-linearization is used to simulate the data under our benchmark parameterization. These simulated data is used in Martínez-García and Wynne (2014) to conduct their Bayesian model comparison exercises. Third, we describe the Bayesian estimation and model comparison techniques with special emphasis on the questions of: (a) how we elicit priors on the models themselves and the parameters of a given model, and (b) how we compute posterior model probabilities. Simultaneously, commentary is provided whenever appropriate to clarify the economic significance of the assumptions embedded in our workhorse open-economy model.