Liquidity Regulation in a Monetary Economy.

A market failure that justifies liquidity regulation lies on the incompleteness of financial markets when there is risk about the aggregate distribution of transaction types. I develop a framework in which outside (fiat, government-provided) and inside (plastic, bank-created) money co-exist as means of payment under either complete or incomplete financial markets for aggregate risk. The welfare analysis is reduced to comparing only two parameters: the currency-to-liability ratio ? which is set by the government and the fraction ? of banks’ depositors engaged in cash-only transactions (inside money cannot be accepted). In equilibrium, when ? < ? fiat currency is relatively scarce in the inter-bank market and then government bonds (which are transformed into liquid liabilities by banks) are less valuable than cash. This forces banks to offer higher consumption with plastic money to induce self-selection among depositors. Welfare is lower under incomplete markets: depositors exert a higher labor effort (precautionary motive) to accumulate more assets as perfect risk-sharing is unattainable (unlike the case of complete markets). Also, a higher cash requirement on banks is equivalent to an implicit increase in the policy parameter ? which makes bonds scarcer and more valuable in the inter-bank market. Therefore, a liquidity requirement is not welfare-improving because it reduces the likelihood of bank runs but because it increases the inter-bank market price of bonds which in turn improves risk-sharing. Finally, when the government sets ? = ? the welfare measures under complete and incomplete markets coincide as the Friedman rule holds.