Banking, Inside Money and Outside Money

This paper presents an integrated theory of money and banking. I address the following question: when both individuals and banks have private information, what is the optimal way to settle debts? I develop a dynamic model with micro-founded roles for banks and a medium of exchange. I establish two main results: first, markets can improve upon the optimal dynamic contract at the presence of private information. Market prices fully reveal the aggregate states and help solve the incentive problem of the bank. Secondly, it is optimal for the bank to require loans be settled with short-term inside money, i.e., bank money that expires immediately after the settlement of debts. Short-term inside money makes it less costly to induce truthful revelation and achieve more efficient risk sharing.