Float on a Note

Under the U.S. National Banking System (NBS), in effect from 1863--1914, banks with national charters could issue notes under four main restrictions: full collateral in the form of government bonds, a per-period tax on outstanding notes, redemption of notes into (outside) money on demand, and a clearing fee per issued note that is cleared through the Treasury's clearing system. The simple and predominant view of this system appeals to arbitrage to claim that the system should have produced an upper bound on the yield on collateral: the tax rate plus the product of the clearing fee and the average clearing rate of notes. However, as is well known and puzzling, yields on eligible collateral were generally higher than such a bound. We explain the puzzle by a model of note issue that includes the main features of the NBS. In the model, note issuers choose to issue notes only in trades that both produce a low clearing rate (high float) and are subject to diminishing returns, and there exists a steady state with a yield on collateral higher than the presumed bound. There are two main ingredients in our explanation: the concern about float and the inverse association between the float rate and the size of placement opportunities. The former is dictated by the rules for note issue. The latter is consistent with the notion that large placement opportunities would have been available only in organized markets, but notes used in such markets would have quickly been turned in to other banks and then been through the clearing system. To achieve high float, notes should be offered in trade to people who are infrequently connected to such markets, and such placement opportunities give rise to diminishing returns from additional note issue. We formulate the model with most of the background environment same as that of the Trejos-Wright-Shi model. For each specialization type, there is a small portion of “bankers†while the remainder is “nonbankers." There are three kinds of assets: (outside) money, notes issued by bankers, and bonds issued by government. Each date has two stages, the "morning" and the "afternoon." The morning is reserved for the random pairwise meetings. The afternoon is reserved for bankers meeting the government and is used solely for note-clearing, bond purchases, and the levying of taxes and fees. Hence, a banker’s notes have two potential uses: to purchase eligible collateral and to purchase goods or other bankers' notes in pairwise meetings. Each use gives rise to different amounts of float. We assume that government clears all notes in inventory at the start of each afternoon. As a result, a banker does not use its own notes to purchase bonds because the potential float is not enough to overcome the redemption fee. Nevertheless, a banker does use its notes in pairwise meetings to trade for goods and to trade for other bankers' notes. This use gives rise to random and higher float, and, implies a diminishing marginal return from additional note issue.