Money, output and the payment system: Optimal monetary policy in a model with hidden effort

We propose a new explanation for the observed difference in the cost of intraday and overnight liquidity. We argue that the low cost of intraday liquidity is an application of the Friedman rule in an environment where a deviation of the Friedman rule is optimal with respect to overnight liquidity. In our environment the cost of overnight liquidity affects output while the cost of intraday liquidity only redistributes resources between money holders and non-money holders. We show that it is optimal to set a high overnight rate to reduce the incentives to overuse money. In contrast, intraday liquidity should have a low cost to provide risk-sharing.