Essays on Money, Banking and Payments

The history of money has always been intertwined with the history of banking. Nevertheless, very few papers have studied banking in a rigorous monetary environment. This thesis demonstrates that it is crucial to integrate these two literatures. I present three theories of money and banking, each generating results that are drastically different from those of the traditional banking models without microfoundations for money. Chapter 1 addresses the problem of monitoring the monitor in a model with private information and aggregate uncertainty. There is no need to monitor a bank if it requires loans to be repaid partly with money. A market arises at the repayment stage and generates information-revealing prices that perfectly discipline the bank. The mechanism also applies when multiple banks exist. With multiple banks, a prohibition on private money issuing not only eliminates welfare-improving money competition but also triggers free-rider problems among banks. In Chapter 2, I develop a dynamic model to address the following question: when both individuals and banks have private information, what is the optimal way to settle debts? I establish two main results: first, markets can improve upon the optimal dynamic contract in the presence of private information. 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 to be settled with short-term inside money, i.e., bank money that expires immediately after debt settlement. Short-term inside money makes it less costly to induce truthful revelation and achieves more efficient risk sharing. Chapter 3 studies bank runs in a model with coexistence of fiat money and private money. When fiat money is the only medium of exchange, a bank run equilibrium coexists with an equilibrium that achieves optimal risk sharing. In contrast, when private money is also a medium of exchange, there exists a unique equilibrium where no one demands early withdrawals of fiat money and agents in need of liquidity only use private money to finance consumption. This unique equilibrium achieves the first-best outcome and eliminates bank runs without having to resort to any government intervention.Ph