Resolving the National Banking System note-issue puzzle

Under the National Banking System, 1863-1914, national banks that deposited sufficient collateral could issue notes provided they paid a tax on notes in circulation: 1 percent per year before 1900 and 1/2 percent thereafter. Because note issue was far below the allowed maximum, an arbitrage argument predicts that short-term nominal interest rates should have been bounded above by the tax rate. They were not. That is the note-issue puzzle. Our resolution takes the form of a model in which notes play a role, but in which the profitability of note issue is not tied to anything that resembles a market rate of interest.