Incomplete Markets and Aggregate Demand

I study the relationship between aggregate consumption and interest rates when mar- kets are incomplete. I first provide a generalized Euler relation involving the real interest rate, current and future aggregate consumption under extreme illiquidity (no borrowing and no outside assets). This provides a tractable way of incorporating incomplete markets into macroeconomic models. When household income risk is acyclical I show that this relation coincides with that of a representative agent, al- though time-varying discount factors may potentially act as aggregate demand shocks. The same representation extends to the case with positive liquidity as long as liquidity relative to income is acyclical. A corollary of these ‘as if’ results is that forward guid- ance policies are as powerful as in representative agent models. Away from the ‘as if’ benchmark, I show that aggregate consumption becomes more sensitive to inter- est rates, especially future ones, when idiosyncratic income risk is countercyclical or when liquidity is procyclical. Finally, I also apply my analysis to a Real Business Cy- cle model, providing an exact analytical aggregation result that complements existing numerical findings.