Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Confronting Model Misspecification in Macroeconomics

Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Confronting Model Misspecification in Macroeconomics

Article excerpt

Working Paper 2010-18 December 2010

Abstract: We confront model misspecifications in macroeconomics by proposing an analytic framework for merging multiple models. This framework allows us to address uncertainty about models and parameters simultaneously and trace out the historical periods in which one model dominates other models. We apply the framework to a richly parameterized dynamic stochastic general equilibrium (DSGE) model and a corresponding Bayesian vector autoregressive model. The merged model, fitting the data better than both individual models, substantially alters economic inferences about the DSGE parameters and the implied impulse responses.

JEL classification: C52, E2, E4

Key words: merged model, misspecification, state-dependent weights, model uncertainty, parameter uncertainty, impulse responses, policy analysis

I. INTRODUCTION

A stochastic dynamic equilibrium, indexed by a pararneterized model, is a likelihood function. Given the likelihood and the prior density of model parameters, one can simulate the posterior distribution and compute the marginal data density (MDD). The MDD is then used to measure how well the model is fit to the data.

Consider the situation in which there are multiple models on the table. The conventional procedure for model selection is to compare MDDs amongst individual models. (1) Since it is not uncommon that the MDD implied by one of the models is overwhelmingly higher than the MDDs implied by others, this procedure often ends up with the selection of one model at the exclusion of others. One primary example is that a linearized dynamic stochastic general equilibrium (DSGE) model such as Smets and Wouters (2007) can easily trump a standard Bayesian vector autoregression (BVAR) model. (2) The implication is that the BVAR can be simply replaced by the DSGE model for policy analysis.

Despite such overwhelming evidence presented by the posterior odds ratios in favor of one model, economists nonetheless continue to use both the DSGE and BVAR models in macroeconomic analysis. The tension between what the conventional procedure concludes and what actually transpires is a mere manifestation of increasing concerns about model misspecification by choosing a particular model (a particular likelihood) and categorically rejecting other models. Policymakers, as well as academic researchers, recognize that models are only approximations (Hansen and Sargent, 2001; Brock, Durlauf, and West, 2003; Sims, 2003). Indeed, they seldom rely on one single model even though this model fits better than other models according to the posterior odds criterion, because they know that

We confront model misspecification by proposing a Bayesian approach to merging multiple models. The merged model assigns state-dependent weights to predictive densities (conditional likelihoods) implied by different models so that the relative importance of each model changes across time. This new methodology, built on Geweke and Amisano (forthcoming), is motived by practical policy analysis dealing with situations where there are multiple competing models and each model explains (predicts) an observed outcome better than other models but only for certain episodes. An informal way for policy analysis is to employ a different model at a different time. Unlike the conventional model-averaging method, our Markov-switching approach not only assigns a weight of relative importance to each model but, more importantly, allows researchers to trace out the periods in which the data give the most weight to a particular model.

We apply our analytic framework to two widely used models: a richly parameterized DSGE model and a corresponding BVAR model. The MDD for the DSGE model is much higher than the BVAR model. The conventional Bayesian model-averaging method would imply that the BVAR model should receive nearly zero weight, a pathology discussed in Sims (2003). …

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