Float on a Note
From 1863-1914, banks in the U.S. could issue notes subject to full collateral, a per-period tax on outstanding notes, redemption of notes on demand, and a clearing fee per issued note cleared through the Treasury. The system failed to satisfy a purported arbitrage condition; i.e., the yield on collateral exceeded the tax rate plus the product of the clearing fee and the average clearing rate of notes. The failure is explained by a model in which note issuers choose to issue notes only in trades that both produce a low clearing rate (high float) and are subject to diminishing returns
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