A Dynamic Model of Intermediated Consumer Credit and Liquidity

We construct a model of consumer credit with payment frictions, such as spatial separation and unsynchronized trading patterns, to study optimal monetary policy across different interbank market structures. In our framework, intermediaries play an essential role in the functioning of the payment system, and monetary policy influences the equilibrium allocation through the interest rate on reserves. If interbank credit markets are incomplete, then monetary policy plays a crucial role in the smooth operation of the payment system. Specifically, an equilibrium in which privately issued debt claims are not discounted is shown to exist provided the initial wealth in the intermediary sector is sufficiently large relative to the size of the retail sector. Such an equilibrium with an efficient payment system requires setting the interest rate on reserves sufficiently close to the rate of time preference