Demand, wealth inequality and the business cycle

We consider a flexible price continuous-time DSGE model of a closed economy populated by heterogeneous households subject to uninsurable idiosyncratic income risk and aggregate TFP shocks. The economy produces a variety of imperfectly substitutable final goods. Our main innovation is a rich representation of household consumption and saving behavior allowing for a time-varying elasticity of substitution across varieties. Specifically, we consider a utility function displaying Increasing Elasticity of Substitution (IES). We provide a convenient approach to handle the complex dynamic programming problem implied by income heterogeneity, aggregate shocks and non-homothetic preferences. We show that IES preferences help to replicate important features of the wealth distribution observed in the data together with a plausible macroeconomic dynamics.