A Model of Interbank Settlement

A settlement system is a set of rules and procedures that govern when and how funds are transferred between banks in order to finalize their customers’ transactions. Perhaps the most crucial feature of such a system is the frequency with which settlement occurs. A lower frequency allows banks to retain fewer idle reserves, and therefore economizes on financial opportunity costs. However, the accumulation of outstanding interbank liabilities under infrequent settlement introduces a large risk should a bank default on its payments. Moreover, when a bank retains fewer reserves, it is more vulnerable to external shocks. Conversely, a higher frequency of settlement decreases both the size and probability of defaults, but is more costly. This paper introduces a partial equilibrium model of a banking sector in which this tradeoff between cost and risk arises endogenously. We then complete the economy with a trading sector that has a micro-founded role for credit as a media of exchange. The result is a dynamic general equilibrium model that incorporates a sophisticated banking environment. Within this general equilibrium framework, we are able to conduct welfare and policy analysis. In particular, we study the optimal intra-day borrowing policy that the operator of a settlement system should impose on member banks. ∗I am particularly indebted to Randy Wright for his guidance throughout the writing of this paper, and to Ed Green and Ludo Viscchers for their suggestions. I thank Aleksander Berentsen, Ping He, Charles Kahn, David Mills, Deniz Selman, Skander Van den Heuvel, Neil Wallace, and members of the Penn Macro Lunch for helpful commentary. Finally, I’d also like to thank Stephen Millard and Matthew Willison for introducing me to this topic. All errors are my own.