Modeling the monetary aggregates in general equilibrium has been a challenge. There are some examples such as Chari et al. (1996), and Gordon et al. (1998), who present models that are compared to Base money. Ireland (1995) presents one that he relates to M1-A velocity. These models have been employed as ways to explain the actual monetary aggregate time-series evidence. However, McGrattan (1998), for example, argues that the simple linear econometric model in which velocity depends negatively on the nominal interest rate may do just as well or better in explaining the evidence.
The article here takes up the topic by modeling a nesting of the aggregates that uses a set of factors that expands from the nominal interest rate by including the production of banking services. Through this approach the productivity factor of banking enters, as well as a cost to using money, sometimes thought of as a convenience cost. With this general equilibrium model, and its comparative statics, an explanation of velocity is provided that depends in part on the nominal interest rate, similar in spirit to McGrattan (1998). Also using technology factors, we explain U.S. evidence on monetary base velocity, M1 velocity, and M2 velocity, as well as for the ratios of various aggregates. This more extended explanation than previous work highlights the limits to a nominal interest rate story, while revealing a plausible role of technological factors in determining the aggregate mix.
The original literature on the welfare cost of inflation, well-represented by Bailey (1992), assumes no cost to banks in increasing their exchange services as consumers flee from currency during increasing inflations. (1) Similarly, Johnson (1969) and Marry (1969) assume no real costs for banks in producing "inside money." (2) The approach here builds on the more recent literature of Gillman (1993), Aiyagari et al. (1998), and Lucas (2000) that assumes resource costs to avoiding the inflation tax by using alternative exchange means. In particular, we specify production functions for banking instruments, both demand deposits (inside money) and credit, that require real resource use. This gives rise to the role of banking productivity factors in explaining the movement of aggregates. (3)
The next section reviews Haslag's (1998) model and shows how it is sensitive to the distribution of the lump sum inflation proceeds. This sensitivity makes tentative the growth effect of inflation with the model. The demand for reserves can be made insensitive to the distribution of the inflation tax transfer by framing it within a model in which the bank must hold money in advance as in the timing of transactions that is pioneered in Lucas (1980). This is done in section III using Haslag's (1998) notation, Ak production technology, and full savings intermediation. The resulting real interest rate depends negatively on the nominal interest rate, so inflation negatively affects the growth rate, similar in fashion to the central result of Haslag (1998). A parallel consumer cash-in-advance demand for goods is also added, as in Chari et al. (1996), to give a model of reserves plus currency.
The article then expands the model to give a formulation of the demand for the base plus non interest-bearing demand deposits, or an aggregate similar to M1. (4) Following a credit production approach used in a series of related works (see Gillman and Kejak 2002; Gillman et al. 2003; Gillman and Nakov 2003), we then add credit, or interest-bearing demand deposits, to give a formulation for an aggregate similar to M2.
II. SENSITIVITY TO LUMP TRANSFERS
In Haslag (1998), all savings funds are cost-lessly intermediated into investment by the bank. The bank must hold reserves in the form of money. This gives rise to a bank demand for money to meet reserve requirements on the savings deposits. The consumer-agent does not use money, although the lump sum inflation tax is transferred to the agent. …