Academic journal article Journal of Money, Credit & Banking

On Cash-in-Advance Models of Money Demand and Asset Pricing

Academic journal article Journal of Money, Credit & Banking

On Cash-in-Advance Models of Money Demand and Asset Pricing

Article excerpt

On Cash-in-Advance Models of Money Demand and Asset Pricing


A cash-in-advance constraint has become a popular device for introducing money into macroeconomic equilibrium models [see, for example, Clower (1967), Lucas (1980, 1982, 1984, 1988), Helpman and Razin (1984), Svenson (1985), Lucas and Stokey (1987), Townsend (1987), Cole and Stockman (1988), Ogaki (1988)]. The approach is interesting for at least two reasons. First, one might hope that adding money improves the disappointing performance of consumption-based asset pricing models. Second, the Clower constraint is an intuitively appealing and simple way of motivating why rational individuals may hold money, an intrinsically useless and return-dominated asset. (1)

This paper provides an assessment of these two aspects of the cash-in-advance approach. Concerning asset pricing, I argue that, although money may add some explanatory power to the consumption-based model, both barter and monetary versions should perform rather poorly. On the other hand, I show that a cash-in-advance model can easily be written in a way that yields a money demand function consistent with the empirical literature.

The main reason for being skeptical about monetary asset pricing is the low volatility of short-term nominal interest rates. The hope for an improved asset pricing model derives from the fact that monetary models do not have to satisfy the standard barter-economy Euler equations

[Mathematical Expression Omitted]

where u'([c.sub.t]) is the marginal utility of consumption, [Beta] the rate of time preference, and [r.sub.k, t + 1] the return on asset k [see, for example, Rubinstein (1976), Lucas (1978), Breeden (1979), Hansen and Singleton (1982, 1983), and Breeden, Gibbons, and Litzenberger (1989)]. Mehra and Prescott (1985) point out that equations of the form (1) cannot be successful in explaining asset prices for reasonable degrees of risk aversion (and other parameters), because consumption is just not volatile enough. This paper shows that the cash-in-advance constraint leads to an Euler equation that differs from (1) only by the inclusion of a short-term nominal interest rate. (2) Since nominal interest rates are not very volatile either, one may suspect that the monetary asset pricing model suffers from a similar problem of too low volatility as the barter-economy model. Though the monetary model may be an incremental improvement over the barter-economy model, neither of them should be expected to have high explanatory power for asset returns. This conjecture is confirmed in the empirical section.

On the other hand, the paper shows how the cash-in-advance constraint can be used to obtain a money demand function with empirically reasonable properties in a straightforward way. Empirical evidence, for example, in Judd and Scadding (1982) and Mankiw and Summers (1986), suggests that a money demand function should have at least the following properties: (1) Money is demanded even if it is dominated as a store of value. (2) Money demand is positively related to a scale variable, like aggregate output or consumption. (3) The income velocity of money is variable. (4) Velocity is positively related to interest rates on securities that compete as stores of value.

Cash-in-advance models have generally no problem with requirements (1) and (2). But simple versions lead to a quantity equation with unit income velocity of money (see Lucas 1982), which violates (3) and (4). These problems can be solved in two ways, by adding uncertainty or by introducing a distinction between money and credit goods. If there is uncertainty about the level of consumption at the time money holdings are determined, money demand will typically have a precautionary component that depends on the opportunity cost of holding money, thereby generating interest elasticity. If there are money and credit goods (defined as goods that can be purchased without money), substitution between the two goods yields interest elastic money demand. …

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