So I’ve finally posted the paper I’ve been working on — a New Monetarist model of bank money — on SSRN. Warning for non-economists: lots of Greek in this one.
Here’s the title and introduction.
The Nature of Money in a Convertible Currency World
This paper studies the nature of money in an environment where the means of payment is convertible at a fixed rate into the numeraire consumption good. By focusing on this environment we eliminate the possibility that the means of payment changes value over time, and deliberately construct a situation where the price level is disabled as a means of equilibrating the supply of money with the demand for it. To our knowledge no one else has studied such an environment in a Lagos-Wright-type framework. Our goal in this paper is to demonstrate that in this environment the first-best can still be attained – if the means of payment is effectively a naked short of the unit of account.
A naked short has the effect of creating a “phantom” supply of the shorted object that disappears when the short is closed out. We demonstrate here that banks can create this “phantom” supply of the unit of account in the form of acceptances of private debt. This type of bank liability is issued when the bank stamps a private commercial bill “accepted,” and the bank obligation is put into circulation when the borrower makes purchases. Then, when the borrower pays off the loan, the phantom supply of the unit of account along with the outstanding, but contingent, bank liability that was used to create it is closed out.
Why do we model the means of payment as a naked short of the unit of account? We argue, first, that this is the best way to understand the nature of the banking system in its developmental stages. Second, by modelling the means of payment in this way our model demonstrates the efficiency gains that can be created through the introduction of a banking system. Third, by carefully evaluating the incentive feasibility conditions for our bank money equilibria, we are able to relate the monetary system to banking stability. We find that the implementation of central bank monetary policy via interest rates can be explained by the need to stabilize the banking system. Finally, we also find support for the use of usury laws as a means by which policymakers choose amongst multiple equilibria to favor the interests of non-banks over those of banks.
The monetary system modelled in this paper is based on the 18th century British monetary system as described in Henry Thornton (1802) An enquiry into the nature and effects of the paper credit of Great Britain. Privately issued bills function as a means of payment because they are “accepted” as liabilities by the banks that underwrite the monetary system. While these bills were denominated in a gold-based unit of account, as a practical matter there was no expectation that they would be settled in gold. Instead, they were used as a means of transferring bank liabilities from one tradesman to another. Thus, bills that are simultaneously private IOUs and bank liabilities are used to make payment. The non-bank debtor pays off her debt by depositing someone else’s bank-certified liability into her account. (The 18th century monetary system was the precursor of the checking account system and operates just like a system of overdraft accounts.) The bank’s liability on a deposited bill is extinguished when funds are credited to the depositor’s account.
In our model productivity is stochastic, and as a result the demand for money is stochastic. We show that the bank-based money described in our model can accommodate this stochastic money demand so that a first best is attained. Thus, our model can be viewed as a model of the “banking school” view where money is issued on an “as needed” basis at the demand of non-banks.
We argue that the convertible currency environment forces a reconsideration of the nature of money. Typically the monetary literature views money as “an object that does not enter utility or production functions, and is available in fixed supply” (Kocherlakota 1998). Shifts in the price of money equilibrate the economy in these environments. Historically, however, stabilization of the price of money by tying it to a fixed quantity of gold was a foundation of economic success in the early modern period (van Dillen; Bayoumi & Eichengreen 1995). Thus, we consider how money functions in an environment where its price is “anchored”. We show that a solution is for the means of payment to be a debt instrument that is denominated in the anchored unit of account and is certified by a bank. This solution is based on actual market practice in the early modern period.
This approach allows us to reinterpret general results such as Gu, Mattesini, and Wright (2014)’s finding that when credit is easy, money is useless, and when money is essential, credit is irrelevant. While their conclusion is correct given their definitions of money and credit, we argue that this standard definition of money is not the correct definition to apply to an environment with banks. We argue that the means of payment in an environment with banks is a naked short of the unit of account, which would be categorized in GMW’s lexicon as “credit”.
This paper employs the methods of new monetarism. Our model combines an environment based on Berentsen, Camera, and Waller (2007) with an approach to banking that is more closely related to Gu, Mattesini, Monnet, and Wright (2013) and Cavalcanti and Wallace (1999a,b). Our model of banking is distinguished from GMMW because non-bank borrowing is supported not by collateral, but by an incentive constraint alone, and from Cavalcanti and Wallace because our banks don’t issue bank notes, but instead certify privately issued IOUs. We find that for values of the discount rate that accord with empirical evidence, such a payments system can be operated with no risk of default simply by setting borrowing constraints. We start by finding the full range of incentive feasible equilibria of the model, and then discuss how, when there are multiple equilibria, a policymaker may choose between these equilibria.
In this environment competitive banking is incentive feasible only when enforcement is exogenous. In the case of endogenous enforcement, competition in banking typically drives the returns to banking below what is incentive feasible and the only equilibrium will be autarky. This result is consistent with many other papers that have found that the welfare of non-banks is improved when there is a franchise value to banking (Martin and Schreft 2005, Monnet and Sanches 2015, Huang 2017. See also Demsetz et al. 1996).
Thus, the challenge for a policymaker is how to regulate competition in the banking sector so that banking is both incentive compatible – and therefore stable – and also meets the policymaker’s goals in terms of serving non-banks. One solution is to treat banking as a natural monopoly, allowing an anti-competitive structure while at the same time imposing a cap on the fees that can be charged by banks. This solution explains usury laws, which by capping interest rates at a level such as 5%, the rate in 18th century Britain, is able to generate both a robust franchise value for the banks that provide payments system credit and at the same time to ensure that a significant fraction of the gains created by the existence of an efficient means of payment accrue to non-banks. An alternate solution is to impose a competitive structure on the banking industry, but also to set a minimum interest rate as a floor below which competition cannot drive the price. We argue that this is the practice of modern central banks and thus that monetary policy should be viewed as playing an important role in preventing competition from destabilizing the banking sector.
Section I introduces the model of a convertible currency. Section II describes the equilibria of the model. Section III presents the equilibria using diagrams. Section IV discusses the means by which policymakers choose between the difference equilibria of the bank-based monetary system. Section V concludes.
 While it would be easy to reconfigure the means of payment to be deposits or bank notes, we believe the monetary function of bank liabilities in this paper is sufficiently different from the existing literature that it useful to present it using an unfamiliar instrument.
 For the purposes of keeping the exposition simple, assume that we model the monetary system prior to 1797 (when gold convertibility was suspended).
 Indeed, we argue elsewhere that the credit based on precisely such constraints constituted the “safe assets” of the monetary system through the developmental years of banking (Sissoko 2016). Treasury bills, the modern financial world’s safe assets, were introduced in 1877 and modeled on the private money market instruments of 19th century Britain (Roberts 1995: 155).