Money and Asset Prices in a Cash-in-Advance Economy
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Why does anyone hold cash, when bonds pay interest and cash pays nothing? Svensson treats money like any other asset -- priced by its own dividend, the liquidity services it provides when a cash-in-advance constraint would otherwise bind. The key twist on Lucas's earlier model is timing: consumers must choose cash holdings before they know how much they want to spend, so money becomes a buffer against uncertainty rather than a mechanical stand-in for current spending. That produces a demand for money with variable velocity, instead of the flat version most cash-in-advance models deliver, and lets the paper show how permanent versus temporary money growth move prices and rates differently.
What this paper finds — and why it matters
Svensson derives the demand for money and the pricing of nominal and real interest rates and other assets in a general-equilibrium, pure-exchange monetary economy by treating money symmetrically with other assets: money is priced by the same asset-pricing equation as a share or a bond, with its “dividend” given by the liquidity services it provides in relaxing a cash-in-advance constraint. The key modeling change from Lucas’s (1982) cash-in-advance model is timing: Svensson’s consumers must choose how much cash to hold before they observe the current state (and hence before they know their desired consumption), rather than after, so money becomes a genuine store of value held against future liquidity needs rather than a mechanical, always-binding transactions balance equal to current spending. This richer timing yields a demand for money with variable income velocity instead of the trivial unit-velocity quantity equation that afflicts most cash-in-advance models, and it lets the paper show, among other results, that permanent changes in monetary expansion move the price level and velocity by more than temporary changes do, that a temporary monetary expansion lowers real but not nominal interest rates while a permanent one raises nominal rates with an ambiguous effect on real rates, and that Friedman’s (1969) optimum monetary policy should be counter- or pro-cyclical depending on whether consumers’ relative risk aversion is low or high.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What is the central modeling innovation relative to Lucas’s (1982) cash-in-advance model, and why does it matter?
In Lucas’s (1982) model, consumers learn the current state and then trade assets and money before buying consumption goods, so in equilibrium they acquire exactly the cash they need and the cash-in-advance constraint always binds with velocity pinned at its technological maximum (unity) – money is “not held by the consumer between periods,” is not a store of value, and has no derivable marginal utility or capital-asset-pricing equation. Svensson instead has consumers choose their money holdings before they know the current state (and hence before they know planned consumption), so money is held in part for the future liquidity services it may provide; this produces, in the paper’s words, “a combined transactions, precautionary and store-of-value demand for money” for which “an asset-pricing equation for money can indeed be derived,” avoiding what the paper calls “a common pitfall of the cash-in-advance literature” – that the constraint’s structure collapses the model to a trivial, unitary-velocity quantity equation.
Q2. How is the price of money derived, and in what sense is it priced “like any other asset”?
The paper shows that the equilibrium pricing equation for money (eq. 2.9c) has exactly the same form as the standard capital-asset-pricing equation for a claim to future output (eq. 2.9d): the real price of a unit of money equals the discounted sum of expected future marginal utilities of money’s “direct return,” divided by the present marginal utility of wealth, where money’s direct return is defined as the value of the liquidity services it provides – “the value of relaxing the liquidity constraint.” A binding cash-in-advance constraint drives a wedge between the marginal utility of wealth and the marginal utility of consumption (the latter exceeding the former by the marginal utility of real balances), reflecting that “wealth is less liquid than cash”; once this wedge and money’s liquidity “dividend” are specified, money, bonds, and equity are all priced by the same underlying asset-pricing logic.
Q3. How do the demand for real balances, monetary velocity, and the price level respond to temporary versus permanent changes in monetary expansion?
The price level and income velocity of money both rise with monetary expansion, but the paper’s central comparative result is that they are “more sensitive to permanent changes in monetary expansion than to temporary” ones: a temporary increase in monetary expansion raises velocity and the price level, lowers the real interest rate, but leaves the nominal interest rate unchanged, whereas a permanent increase raises velocity and the price level by more, raises the nominal interest rate, and has an ambiguous effect on the real interest rate. The response of real balances and the price level to changes in income (output), by contrast, depends on the sign of relative risk aversion relative to intertemporal substitutability: they are increasing or decreasing in income depending on whether risk aversion (equivalently, intertemporal substitutability in consumption) is low or high.
Q4. What does the paper conclude about Friedman’s (1969) optimum quantity of money in this setting?
Applying the model to Friedman’s (1969) optimum-monetary-policy criterion (minimizing the distortion relative to a frictionless barter economy), the paper finds that the optimal (net) monetary expansion should be counter-cyclical or pro-cyclical depending on whether the degree of risk aversion (intertemporal substitution) in consumption is low or high, respectively, and – notably – that “the optimum monetary policy does not involve stabilizing nominal income, nominal prices, inflation or money growth,” contrary to several simple stabilization rules often proposed in the literature.
Q5. What does the paper find about the Fisher relation and the premium of nominal over indexed bonds?
Because the model is a full stochastic general equilibrium rather than the partial-equilibrium setups used in most of the prior literature (e.g., Fama and Farber 1979), the paper can trace the effects of the primitive stochastic processes for monetary expansion and income on the gap between nominal and real interest rates and expected inflation (the Fisher relation) and on the premium of nominal bonds over indexed bonds: a higher variance of monetary expansion and a negative covariance between income and monetary expansion both widen the gap between the nominal-minus-real interest rate and expected inflation, while the variance of income alone has no effect on that gap; the bond premium rises with the variance of income but responds ambiguously to the covariance of monetary expansion and income, and a higher variance of monetary expansion lowers the premium. The paper notes these results “differ considerably” from those of previous general-equilibrium approaches relying on the simple quantity theory, such as Kouri (1983).
Q6. How does the paper relate the cash-in-advance (liquidity-constraint) approach to the money-in-the-utility-function approach, and what is its position on whether they are equivalent?
Addressing a claim that the two approaches are “essentially identical” (citing Fischer’s 1983 comment on Lucas and Stokey 1983), the paper argues in Section 6 that they are not equivalent: money-in-the-utility-function models simply posit that real balances enter utility directly, with the marginal utility of liquidity services given by the direct marginal utility of real balances, whereas Svensson’s cash-in-advance approach derives the liquidity services of money endogenously, as the shadow value of relaxing a liquidity constraint that arises from the consumer’s actual trading/timing problem. The paper credits the liquidity-constraint tradition to Clower (1967) and its discussion to Kohn (1981), and positions its own contribution as improving on prior liquidity-services-of-money papers (Dixit and Goldman 1970; Kouri 1977; Fama and Farber 1979; Hodrick 1981; LeRoy 1982a,b; Jones 1983; Stulz 1983) by deriving a full general-equilibrium solution with an explicit microfoundation for the demand for money, rather than assuming real balances enter utility directly or working in partial equilibrium.
Q7. What is the economic meaning of the “liquidity constraint” wedge, and why can the nominal interest rate never be negative in this model?
The paper shows the nominal interest rate equals the ratio of the expected marginal utility of money’s liquidity-service (“direct”) return to the expected marginal utility of its “indirect” return (its value carried forward as cash or an equivalent bond payoff), which implies the nominal rate “cannot be negative, and it is strictly positive when the expected next period’s marginal utility of liquidity services is positive” – that is, whenever the cash-in-advance constraint binds with positive probability in some future state. This is because money and a nominal bond offer the same indirect (cash) return next period, but money additionally yields a liquidity dividend today that the bond does not, so in equilibrium the forgone interest on a nominal bond must exactly compensate for the liquidity services sacrificed by holding the bond instead of cash.
Q8. What scope conditions or limitations does the paper flag for its own analysis?
The paper is explicit that its results rest on a stochastic stationary rational-expectations equilibrium in a closed, pure-exchange, single-good monetary economy with specific timing assumptions about when consumers learn the state and choose cash holdings, and it notes (Section 7) that it discusses “some conclusions, limitations of the analysis, and directions for further research”; Appendix 1 is devoted specifically to detailing how its assumptions and resulting pricing equations differ from, and are not nested within, Lucas (1978, 1982). The paper also flags that its chosen definition of the real interest rate (via an indexed bond paying a sure unit of real wealth, not of the physical consumption good) differs from an alternative definition used by Lucas (1982, p. 346), and that the two coincide only in the deterministic case or when the price level is deterministic and constant – a technical scope condition the paper argues makes its own definition “more convenient” for the analysis at hand.
Key terms in this paper
Definitions below follow the paper's own usage.
- Liquidity services of money
- the paper's term for money's "direct return" in its asset-pricing framework -- the value of relaxing the cash-in-advance (liquidity) constraint, measured by the shadow price (Lagrange multiplier) on that constraint; this is what stands in for "dividends" in pricing money by the same equation used for other assets, and it is determined endogenously by the model rather than assumed as a primitive the way money-in-the-utility-function models assume direct utility from real balances.
- Liquidity constraint (cash-in-advance constraint)
- the requirement, following Clower (1967), that consumption purchases be paid for with cash acquired before the state (and consumption plans) are known; a binding liquidity constraint drives a wedge between the marginal utility of wealth and the marginal utility of consumption, "the existence of a binding liquidity constraint drives a wedge between the marginal utility of real wealth and the marginal utility of consumption," reflecting that wealth is less liquid than cash on hand.
- Temporary versus permanent monetary expansion
- the paper's distinction, formalized via the serial-correlation properties of the stochastic process for the gross rate of monetary expansion, between a current realization that carries no information about future money growth (temporary) and one that shifts the probability distribution of future money growth (permanent); the paper's central comparative-statics results -- on velocity, the price level, and nominal versus real interest rates -- differ sharply between these two cases.