Paper Abstract
I study aggregate consumption dynamics under incomplete markets, focusing on the relationship between consumption and the path for interest rates. I first provide a general aggregation result under extreme illiquidity (no borrowing and no outside assets), deriving a generalized Euler relation involving the real interest rate, current and future aggregate consumption. This provides a tractable way of incorporating incomplete markets in macroeconomic models, dealing only with aggregates. Although this relation does not necessarily coincide with the standard representative-agent Euler equation, I show that it does for an important benchmark. When this is the case, idiosyncratic uncertainty and incomplete markets leave their imprint by affecting the discount factor in this representation, but the sensitivity of consumption to current and future interest rates remains unaffected. An immediate corollary is that “forward guidance” (lower future interest rates) is as powerful as in representative agent models. I show that the same representation holds with positive liquidity (borrowing and outside assets) when utility is logarithmic. Away from these benchmark cases I show that consumption tends to become more sensitive to interest rates, especially future ones, when idiosyncratic income risk is countercyclical or if the ratio of asset prices to income is procyclical. Finally, I also apply my approach to a Real Business Cycle model, providing an exact analytical aggregation result that complements existing numerical results.

Ivan Werniong. Ph.D. in Economics, University of Chicago.  Professor at MIT Department of Economics.