Monetary Policy and Asset Prices

Abstract

The purpose of this paper is study the effect of monetary policy on asset prices. We study the properties of a monetary model in which a real asset is valued for its rate of return and for its liquidity. We show that money is essential if and only if real assets are scarce, in the precise sense that their supply is not sufficient to satisfy the demand for liquidity. Our model generates a clear connection between asset prices and monetary policy. When money grows at a higher rate, inflation is higher and the return on money decreases. In equilibrium, no arbitrage amounts to equating the real return of both objects. Therefore, the price of the asset increases in order to lower its real return. This negative relationship between inflation and asset returns is in the spirit of research in finance initiated in the early 80's. (Copyright: Elsevier)

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Review of Economic Dynamics 10 (2007) 761–779
www.elsevier.com/locate/red
Monetary policy and asset prices
Athanasios Geromichalos, Juan Manuel Licari, José Suárez-Lledó∗
Department of Economics, University of Pennsylvania, Philadelphia, USA
Received 1 December 2006; revised 19 March 2007
Available online 4 May 2007
Abstract
The purpose of this paper is study the effect of monetary policy on asset prices. We study the properties
of a monetary model in which a real asset is valued for its rate of return and for its liquidity. We show
that money is essential if and only if real assets are scarce, in the precise sense that their supply is not
sufficient to satisfy the demand for liquidity. Our model generates a clear connection between asset prices
and monetary policy. When money grows at a higher rate, inflation is higher and the return on money
decreases. In equilibrium, no arbitrage amounts to equating the real return of both objects. Therefore, the
price of the asset increases in order to lower its real return. This negative relationship between inflation and
asset returns is in the spirit of research in finance initiated in the early 1980s.
© 2007 Elsevier Inc. All rights reserved.
JEL classification: E31; E50; E52; E58
Keywords: Liquidity; Monetary policy; Inflation; Asset pricing; Asset returns
1. Introduction
We know that monetary policy controls the money supply, which determines the rate of infla-
tion, and hence the rate of return on (or the cost of holding) currency.1However, we also know
that agents often manage portfolios with assets other than money in their daily transactions. Even
*Corresponding author at: University of Pennsylvania, Department of Economics, 160 McNeil Building, Philadelphia,
USA.
E-mail addresses: geromich@econ.upenn.edu (A. Geromichalos), licari@econ.upenn.edu (J.M. Licari),
jlledo@econ.upenn.edu (J. Suárez-Lledó).
1In simple models, in steady state the growth rate of the money supply pins down the inflation rate, and through the
arbitrage condition known as the Fisher equation, this pins down the nominal interest rate; it does not matter if policy
controls money, inflation or the interest rate, since any one determines the other two.
1094-2025/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.red.2007.03.002

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though these assets may differ in various properties, like liquidity or rate of return, and they may
appear not even to be designed for transaction purposes, different assets in a portfolio maybe
related in several ways. Lucas (1990) already points out possible interactions between liquidity
and interest rates in an economy. Therefore, the intuitive concern arises: could monetary policy
indeed affect the price or return of other assets in the economy? And if so, what would be the
precise mechanism through which those effects would take place?
We use a model in the tradition of modern monetary theory, extended to include real assets
in fixed supply just like the standard “trees” in Lucas (1978). However, these assets are not only
stores of value in our model. They also compete with currency as a medium of exchange. We
show that money is essential (i.e. monetary equilibria Pareto dominate non-monetary equilibria)
if and only if real assets are scarce, in the precise sense that their supply is not sufficient to satisfy
the demand for liquidity. In this case, real assets and money are concurrently used as means of
payment, and an increase in inflation causes agents to want to move out of cash and into other
assets. In equilibrium, this increases the price of these assets and lowers their rates of return.
Hence, the model predicts clearly that inflation reduces the return on other assets, which is
something that has been discussed extensively in the finance literature for some time. Examples
of papers that report this negative relationship are Fama (1981), Geske and Roll (2001), and
Marshall (1992). Geske and Roll, for example, characterize the connection between asset returns
and inflation as a puzzling empirical phenomenon that does not necessarily ascribe causality one
way or the other. An early attempt to explain this finding in a general equilibrium framework
was made by Danthine and Donaldson (1986), where money is assumed to yield direct utility. It
does not seem right to analyze asset prices by putting assets in the utility function - would we
take seriously as a “solution” to the equity premium puzzle a model where people “like” bonds
more than stock? As opposed to this reduced-form monetary model we choose a setting in which
the frictions that make money essential are explicitly described. Building on Lagos and Wright
(2005), we provide a model based on micro foundations within which the effects of monetary
policy on asset prices can be analyzed.
Several models based on Lagos and Wright (2005) have been created to study different ques-
tions related to the coexistence of multiple assets as media of exchange. For example, Lagos and
Rocheteau (2006) allow capital to be traded in a decentralized market and focus on the issue
of over-investment. They introduce real capital that can compete with money as a medium of
exchange. Part of this capital may be productive but not liquid (in the sense that it cannot be used
as a medium of exchange). Therefore, it will only be valued by its direct return derived from a
storage technology. However, the other fraction can be used in decentralized trade and valued
both for being productive and for its role as a medium of exchange. The object that we introduce
is not related with returns due to productivity. Instead, our object is a real financial asset and all
of it can be taken into the decentralized market. Thus, the main difference in our model lies in
the asset-pricing implications. In their framework the price of the liquid capital has to be equal to
that of the general good in the centralized market. In contrast, the price of our real financial asset
will be determined endogenously and independently in equilibrium. This price reflects now both
its return as a financial asset in terms of consumption and its role as a medium of exchange. They
also conclude that when the return from the storage technology is higher than that as a medium
of exchange agents tend to overaccumulate capital. This does not arise in our model.
Lagos (2005) builds an asset-pricing model in which financial assets (equity shares and one-
period government risk-free real bills) are valued not only as claims to streams of consumption
but also for their liquidity. In his model the price of an asset will be higher when is held for its
exchange value, and its rate of return will be lower than it would if the asset was not used as

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a medium of exchange. However, that framework is explicitly designed to address the risk-free
rate and equity premium puzzles identified in Mehra and Prescott (1985), and more importantly,
does not offer implications for monetary policy.
Like these papers, we allow alternative assets to compete as media of exchange, but our focus
is on the competition between fiat money and real financial assets, and the implications of mon-
etary policy on the price of and the rate of return on these assets. Assets are valued for what they
yield, which includes direct rate of returns, as is standard in finance, and potentially some liq-
uidity services, as is standard in monetary theory.2This paper provides a tractable model where
money and other assets coexist, and where monetary policy affects equilibrium prices and rates
of return on these assets in a straightforward and empirically relevant way.3
The rest of the paper is structured as follows. In Section 2 we describe the baseline model.
In Section 3 we consider an economy without money and study the equilibrium properties of a
model where the financial asset serves as the only medium of exchange. Section 4 introduces
money and allows us to study the link between monetary policy and asset prices. Section 5
concludes.
2. The model
Time is discrete and each period consists of two subperiods. During the first subperiod trade
occurs in a decentralized market, whereas in the second subperiod economic activity takes place
in a centralized (Walrasian) market. There exists a [0,1] continuum of agents who live forever
and discount future at rate β ∈ (0,1). Agents consume and supply labor in both subperiods.
Preferences are given by U(x,h,X,H) where x and h (X and H) are consumption and labor in
the decentralized (centralized) market, respectively. Following Lagos and Wright (2005), we use
the specific functional form
U(x,h,X,H) = u(x)−c(h)+U(X)−AH.
We assume that u and U are twice continuously differentiable with u(0) = 0, u?> 0, u?(0) = ∞,
U?> 0, u??< 0, and U??? 0. To simplify the presentation we assume c(h) = h, but this is not
important for our substantive results. Let q∗denote the efficient quantity, i.e. u?(q∗) = 1, and
suppose there exists X∗∈ (0,∞) such that U?(X∗) = 1 with U(X∗) > X∗.
During the first subperiod, economic activity is similar to the standard search model. Agents
interact in a decentralized market and anonymous bilateral trade takes place. The probability
of meeting someone is α. The first subperiod good, x, comes in many specialized varieties.
Agents can transform labor into a special good on a one-to-one basis, and they do not consume
the variety that they produce. When two agents, say i and j, meet in the decentralized market,
there are three possibilities. The probability that i consumes what j produces but not vice versa
(single coincidence meeting) is σ ∈ (0,1
i produces but not vice versa is also σ. Finally, the probability that neither of the agents likes
2). By symmetry, the probability that j consumes what
2Applications of earlier monetary theory to finance include Bansal and Coleman (1996) and Kiyotaki and Moore
(2005). In the former, the authors examine the joint distribution of asset returns, velocity, inflation, and money growth.
In the latter, the analysis focusses on the interaction between liquidity, asset prices, and aggregate economic activity.
3Recent work by Lester et al. (2007) extends our framework by modeling different acceptabilities for the underlying
assets. Since their model builds on ours, the main results in our paper are also verified in Lester et al. However, their
main contribution is to go a step further and obtain acceptability endogenously. Therefore, in equilibrium, assets have
different liquidity properties.

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what the other agent produces is 1 − 2σ. In a single coincidence meeting, if i consumes what j
produces, we will call i the buyer and j the seller.
During the second subperiod agents trade in a centralized market. With centralized trade it is
irrelevant whether the good comes in one or many varieties. We assume that at the second sub-
period all agents consume and produce the same general good. Agents in the centralized market
can transform one unit of labor into w units of the general good, where w is a technological
constant. We normalize that constant to w = 1 without loss of generality. It is also assumed that
both the general and the special goods are non-storable.
There is another object, called (fiat) money, that is perfectly divisible and can be stored at
any quantity m ? 0. We let φ denote its value in the centralized market. The key new feature
of our model is the introduction of a real asset. One can think of this asset as a Lucas tree. We
assume that this tree lives forever, and that agents can buy its shares in the centralized market
at price ψ. Let T > 0 denote the total stock of the real asset. We assume that T is exogenously
given and constant. As opposed to fiat money, the asset yields a real return in terms of the general
consumption good. We let the gross return (dividend) of the asset be denoted by R > 0. An agent
that owns shares of the tree can consume the fruit (which here is just the general good) and sell
the shares in the Walrasian market. She can also carry shares of the tree into the decentralized
market in order to trade. Hence, in this economy money and the asset can potentially compete as
a media of exchange.
3. Equilibrium in a model without money
We first consider an economy without money. Analyzing this simpler version of the model,
provides intuition for the next section, where money and the asset can coexist as media of
exchange. We begin with the description of the value functions, treating the prices and the distri-
bution of asset holdings as given. These objects will be endogenously determined in equilibrium.
Agents are allowed to keep any positive quantity of assets at home before they visit the decen-
tralized market.4The state variables for a representative agent are the units of the asset that she
brings into the decentralized market, b, and the units of the asset that she keeps at home, a. To
reduce notation we define ω ≡ (a,b). First, consider the value function in the centralized market
for an agent with portfolio ω. We normalize the price of the general good to 1. The Bellman’s
equation is given by
?U(X)−H +βV(ω+1)?
s.t.
X +ψ(b+1+a+1) = H +(R +ψ)(b +a),
where b+1, a+1are the units of the asset carried into the next period’s decentralized market and
left at home, respectively.5It can be easily verified that, at the optimum, X = X∗. Using this fact
and replacing H from the budget constraint into W yields
?U(X∗)−X∗−ψ(b+1+a+1)+(R +ψ)(b +a)+βV(ω+1)?.
W(ω) = max
X,H,ω+1
W(ω) = max
ω+1
(1)
4As opposed to money, the asset here serves as a store of value. Moreover, the terms of trade for an agent may depend
on the amount of the asset that she carries into the decentralized market. Therefore, it may be prudent to keep some assets
at home. As we shall see in what follows, this is precisely what happens in equilibrium, whenever the supply of assets is
sufficiently large to satisfy the demand for liquidity in the economy.
5We impose non-negativity on all the control variables except H, which is allowed to be negative. Once equilibrium
has been found, one can introduce conditions that guarantee H ? 0 (see Lagos and Wright, 2005).

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This expression implies the following results. First, the choice of ω+1does not depend on ω. In
other words, there are no wealth effects. This result relies on the quasi-linearity of U. Second, W
is linear,
W(ω) = Λ+(R +ψ)(b +a).
We now turn to the terms of trade in the decentralized market. Consider a single-coincidence
meeting between a buyer and a seller with state variables ω and ˜ ω, respectively. We use the
generalized Nash solution, where the bargaining power of the buyer is denoted by θ ∈ (0,1]. Let
q represent the quantity of the special good and dbthe units of the asset that change hands during
trade. The bargaining problem is
?u(q)+W(a,b −db)−W(ω)?θ?−q +W(˜ a,˜b +db)−W(˜ ω)?1−θ
subject to db? b. Using the linearity property of W, the problem simplifies to
?u(q)−(R +ψ)db
subject to db? b. Clearly, the linearity of W implies that the solution to the bargaining problem
does not depend on the variables a, ˜ a,˜b. It depends on b only if the constraint binds. The solution
to this problem is a variation of the standard bargaining result obtained in this type of models.
max
q,db
max
q,db
?θ?−q +(R +ψ)db
?1−θ
Lemma 1. The bargaining solution is the following:
?q(b) = ˆ q(b),
If b ? b∗,
then
db(b) = b∗,
where b∗solves (R + ψ)b = z(q∗) = θq∗+ (1 − θ)u(q∗), ˆ q(b) solves (R + ψ)b = z(q), and
z(q) is defined by
z(q) ≡θu?(q)q +(1−θ)u(q)
θu?(q)+(1−θ)
Proof. It is straightforward to verify that the suggested solution satisfies the necessary first-order
conditions, which are also sufficient in this problem .
If b < b∗,
then
db(b) = b.
?q(b) = q∗,
(2)
.
(3)
2
Lemma 2. For all b < b∗, we have ˆ q?(b) > 0 and ˆ q(b) < q∗.
Proof. See Appendix A.
2
Next, consider the value function of an agent in the decentralized market. Let F(b) be the
distribution of asset holdings in this market. We set ξ ≡ ασ. The Bellman’s equation is6
6The first term is the payoff from buying q(b) and going to the centralized market with state variables (a,b −db(b)).
The second term is the expected payoff from selling q(˜b) and going to the centralized market with state variables (a,b+
db(˜b)). Both expressions reflect the fact that the only relevant variable for the determination of the terms of trade is
the amount of assets that the buyer brings into the decentralized market. The last term is the payoff from going to the
centralized market without trading in the decentralized market.