Heterogeneity in Macroeconomics and the Minimal Econometric Interpretation for Model Comparison

This paper formally compares the fit of various versions of the incomplete markets model with aggregate uncertainty, relying on a simple Bayesian empirical framework. The models differ in the degree of households' heterogeneity, with a focus on the role of preferences. For every specification, empirically motivated priors for the parameters are postulated to obtain the models' predictive distributions, which are interpreted as being the distributions of population moments. These are in turn contrasted with the posterior distributions of the same moments obtained from an atheoretical (Bayesian) econometric model. It is shown that aggregate data on consumption and income contain valuable information to determine which models are more likely to have generated the data. In particular, despite its generality, a model with both risk aversion and discount factor heterogeneity displays a very low marginal likelihood, and should not be employed for the design of macroeconomic policies and welfare analysis. It is also found that the other models display similar posterior odds, with the Bayes factors ranging between 1 and 3. Finally, it is shown that practitioners in the field should carefully calibrate the values of the unemployment rate in booms and expansions, as they heavily affect the autocorrelation of aggregate consumption and the correlation between consumption and income. This finding suggests that the magnitude of welfare effects computations is likely to be influenced considerably by these two parameters.