Download Currency Transactions Costs and Competing Fiat Currencies*

Currency Transactions Costs and Competing Fiat
Currencies*
Merwan Engineer
Abstract
This paper develops a model in which two competing ¯at currencies may coexist
as media of exchange. Domestic currency has lower transactions costs but a higher
growth rate than foreign currency. It is used in everyday transactions and has a
higher velocity of circulation in equilibrium. In contrast, foreign currency is hoarded
for occasional high consumption shocks. A precautionary transactions demand for
foreign currency arises because it is a better store of value. The di®erent endogenous
roles for the currencies provide an explanation for the nondisappearance of the hyperin°ating domestic currency in the presence of a stable foreign currency. Though
the presence of foreign currency lowers the value of the domestic currency, it may
increase welfare when large amounts of seigniorage must be generated.
Keywords: Currency Substitution, Hyperin°ation, Precautionary Money Demand,
Transaction Costs.
JEL Classi¯cation: E31, E40, E41.
Correspondence to: Merwan Engineer, Department of Economics, University of
Victoria, PO Box 1700, Victoria, British Columbia, Canada, V8W 2Y2.
Tel: (250) 721-8536. Fax: (250) 721-6214. Email: [email protected]
*I would like to thank Alok Johri, Shouyong Shi, and seminar participants at the
Canadian Economics Association Meetings, Federal Reserve Bank of Dallas, University of Arkansas, University of Guelph, University of Victoria, and Western Macroeconomics Study Group for their valuable comments. The usual disclaimer applies.
I am grateful to the Social Sciences and Humanities Research Council of Canada for
¯nancial support.
0
1
Introduction
In many developing countries the domestic currency circulates in competition with other
currencies, in particular U.S. dollars. The coexistence of domestic and foreign currency is
puzzling because the domestic currency often dramatically loses value relative to the foreign
currency. It is particularly puzzling in countries in which agents are cut o® from trading
in international goods and money markets, foreign currency purchases are penalized, and
few taxes are levied in domestic currency.1
Independent of whether the country is isolated or hostile to foreign currency, currency
0
substitution seems to satisfy several stylized facts (e.g. Calvo and Vegh 1992). In high
in°ation countries, foreign currency ¯rst displaces domestic currency as a store of value.
As high in°ation continues, foreign currency is typically used only for large occasional
purchases, particularly durables. Domestic currency remains valuable in everyday small
transactions. The use of both currencies as media of exchange is widespread so that there
is no division between those who transact in dollars and those that do not.
This paper develops a model which captures the above puzzling features and stylized
facts. The essential ingredients that produce these results are: stochastic consumption
demand, di®erent currency transaction costs, and di®erent currency growth rates . When
domestic currency has a higher growth rate but a lower transaction cost, it is used to
make all purchases in periods in which consumption demand is low. In periods of greater
consumption demand, purchases with domestic currency are supplemented with purchases
using foreign currency. The domestic currency, if valued, is always used in exchange because
it loses value more quickly. It is a \hot potato". On the other hand, the foreign currency
is hoarded to make occasional large purchases because it is a better store of value. It does
not dominate in all transactions because of its higher transaction costs. Foreign currency
¯lls the precautionary demand for money and has a lower velocity of circulation. All agents
1 Several
communist and former communist countries ¯t this characterization. For example, U.S. dollars
have circulated in Vietnam since the late 1980s, yet citizens had e®ectively no access to international goods
or money markets. In this command economy, little tax revenue was collected in domestic currency.
1
hold both currencies as media of exchange.2
In generating these results, the use of domestic or foreign currency is not restricted
to the purchase of speci¯c goods or limited to particular quantities in the model. High
domestic currency in°ation rates are a consequence of the government's presumed need
for revenues from seigniorage. Lower domestic currency transactions costs capture the fact
that local agents are better able to recognize and handle domestic currency whereas foreign
currency is more likely to be counterfeit and costs are incurred in veri¯cation. These costs
are modeled as proportionate to the amount of currency purchased.
Both currencies are intrinsically worthless and their value and velocity are derived
endogenously. Domestic currency is not supported by taxes, and foreign currency is not
given external worth. The currencies compete. If domestic currency growth is too great,
it may cease to have value. On the other hand, low domestic currency growth may drive
out foreign currency. Nevertheless, as demonstrated in simulations, the dual currency
equilibria can be robust to dramatic di®erences in the growth rates of the currencies.
The nondisappearance of the hyperin°ating domestic currency is explained by the high
velocity of everyday small transactions relative to large occasional transactions. The lower
transactions costs of domestic currency makes it the preferred medium of exchange for
small transactions. With rapid turnover the loss in the value of domestic real balances due
to in°ation is small.
The presence of a competing currency may improve welfare depending on the strength
of opposing e®ects. A competing currency has a negative externality e®ect on the value
of the domestic currency. On the other hand, there is a positive \°exibility e®ect". Using
foreign currency allows households to purchase more goods when consumption demand is
high without having to hold precautionary stocks of domestic currency. This shifts the
2
This pattern of exchange and the ingredients that generate them were observed in both Cambodia and
Vietnam by the author in 1991-1992. The quality of both dollars and gold were usually physically veri¯ed
in transactions whereas domestic currency was accepted readily in exchange. Some of my transactions
were delayed until the dollars were veri¯ed. In other transactions, dollars were not acceptable except at a
large discount because of no ready means of verifying quality. Counterfeit dollars were common and the
governments did little to discourage their use (e.g. Kristof 1996). I was told that dollars and gold were
held as a contingency against the uncertain timing of large purchases (for emergencies as well as taking
advantage of bargains).
2
burden of the in°ation tax onto the inelastically demanded everyday small transactions
away from the more elastically demanded large occasional transactions. When seigniorage
is large, this second e®ect dominates improving welfare.
There is now a large literature on currency substitution.3 An important and somewhat
problematic early result was discovered by Karaken and Wallace (1980). They show that
if both currencies are perfect substitutes in purchasing goods, the relative price of the currencies is indeterminant, and one currency would not consistently lose value relative to the
other. Early approaches to making currencies imperfect substitutes involved either introducing the currencies in the utility function or restricted the type of goods that could be
purchased with a particular currency. Only recently have transaction costs been explicitly
modelled as the source of currencies being imperfect substitutes.
Two branches of the literature are particularly related to this paper. The a®ects of
uncertainty on the relative demands for currencies was studied early in the literature by
Stockman (1980) and Svensson (1985). Agents in the economy hold both currencies for
transaction purposes and consume both foreign and domestic goods. Uncertainty generates
a precautionary transaction demand for the currencies. However, to obtain price level
determinacy, they impose the restriction that each good be bought with its own currency.
Hence, currency substitution is e®ectively limited to the extent that there is substitution
between goods. Poloz (1984, 1986) also examines the precautionary transactions demand
for two currencies under the same restriction but using a money inventory approach.
The second branch of the relevant literature explicitly introduces transactions costs.
The papers by Chang (1994), Sturnenegger (1997) and Uribe (1997) are particularly noteworthy. Chang's paper is the closest to the current paper in approach as both papers share
the assumptions that foreign currency has a higher transaction cost and a lower growth
3
0
Calvo and Vegh (1992) and Giovannini and Turtelboom (1994) survey the literature.
Search models of money o®er a new promising line of research. Matsuyama et al. (1993) prove the
existence of dual ¯at currency equilibria in a search-theoretic model where both goods and money are
indivisible. Recently, Shi (1995) has introduced divisible goods into a dual currency search model. While
this model makes signi¯cant progress, money in the model is still indivisible, there is no seigniorage, and
agents can only hold one type of money or one type of good at a time. Trejos and Wright (1995), Head
and Shi (1996), and Zhou (1997) have further developed the dual currency search model.
Barnett (1992, 1996) examines currencies from a portfolio perspective.
3
rate. Speci¯cally, Chang examines an overlapping generations model where there are rich
and poor agents. A dual currency equilibrium exists in which rich agents incur the ¯xed
cost of acquiring foreign currency and only use foreign currency to save between periods.
Poor agents only use domestic currency.
The current paper di®ers from Chang's in several ways. First, the dual currency equilibria in this paper involve all agents holding both currencies as media of exchange. Second,
there is no uncertainty in Chang's model. Third, this paper generates currency substitution with proportional costs. Introducing proportional costs into Chang's model would not
result in a dual currency equilibrium. All agents would choose to use the same currency
because they would all face the same marginal costs. Finally, Chang ¯xes the worth of
foreign currency externally.
Instead of imposing a transaction cost on acquiring currency, Sturnenegger (1997) and
Uribe (1997) both have a transaction cost for each good purchased with foreign currency.
In both models there are a continuum of types of goods. All goods are indivisible and an
agent can only purchase one unit of any good. Goods with lower transaction costs (per unit
of foreign currency) are purchased with foreign currency. Both models endogenously derive
the division of types of goods purchased with each currency. In addition, they examine
network e®ects which lead to the division changing as the economy matures. There is no
uncertainty in the models.
The papers of Chang and Sturnenegger examine welfare. Chang shows that the domestic currency equilibrium dominates the dual currency equilibrium when both equilibria
coexist. In this case foreign currency has a negative externality externality e®ect on the
value of domestic currency which hurts all agents. In contrast, Sturnenegger shows that
currency substitution is always welfare improving because the in°ation tax falls on the
continuum of goods that are most inelastic. In the current paper, the presence of valued foreign currency yields similar positive and negative welfare e®ects but using a very
di®erent model.
The paper proceeds to detail the model in Section 2. The optimum to the model is
derived in Section 3. Section 4 describes the dual ¯at currency economy, and Section 5
4
solves for the monetary equilibria. The welfare and robustness of dual currency equilibria
are explored using simulations in Section 6. Section 7 extends the model to consider
externally valued foreign currency. Section 8 concludes.
2
The Model
This paper develops a modi¯ed Townsend (1980) turnpike economy. The model has an
absence of the coincidence of wants and goods are perishable. The spatial structure endogenously yields the cash-in-advance constraints needed for valued currencies.
The Decentralized Exchange Environment. There are N ¸ 3 di®erent types of in¯nitelylived households in our economy. Each household type consists of an identical measure z
of households. Households type i are located at node i and are each endowed with good
type i: Households i value their own good and their i + 1 neighbors goods. Markets are
located half way between the nodes as illustrated below.
i¡1
à ¡¡¡ ² ¡¡¡¡¡¡¡
j
mkt(i¡1;i)
i
¡¡¡¡¡¡¡ ² ¡¡¡¡¡¡¡
j
mkt(i;i+1)
i+1
¡¡¡¡¡¡¡ ² ¡¡¡ !
Each household consists of a team of two members. One member of household i can trade
with the i + 1 neighbors in market (i; i + 1) and the other with i ¡1 neighbors in market (i;
i ¡ 1). (The nodes may be arranged on a circle so that households type N are also type 0
agents and type N agents can trade with type 1 and N ¡ 1 agents.) Within-period trades
occur simultaneously so that households cannot use revenues from trade in one market to
augment purchases in the other market. Households are assumed to be anonymous so that
trade can not be accomplished through credit.
Endowments. In each period all households i are endowed with H units of a perishable
good i. This good is referred to as the i's home good. Household i's home good is di®erent
in kind from the good endowed to household j; j 6= i. We assume that H is su±ciently
large that equilibrium is characterized by an interior solution|households want to consume
some of their home good|given the following preferences.
5
Preferences. Households i have identical time-separable utility functions:
Ui (Hi; Xi ; s) =
1
P
t=0
¯ t[Hi;t(s t) + st ln(Xi;t (s t))] ;
where ¯ < 1 is the discount factor, Hi;t (st ) is the amount of the i home good that i
consumes in period t if state st occurs, Xi;t(st ) is the amount of the i + 1 or market
good that i consumes in period t if st occurs. We call Xi;t (st ) the market good since
@Ui=@Xi;t (st ) ! 1 as Xi;t (st ) ! 0. In what follows the subscript i is dropped.
Consumption shocks are assumed to be perfectly correlated across households, so that
si;t = s t for all i; each household simultaneously is, or is not, very hungry for its market
good.4 Shocks take on only two values: each period a low shock (st = s L) occurs with
probability ¼; 0 < ¼ < 1, and a high shock (s t = sh > sL ) occurs with probability 1 ¡ ¼:
3
The Symmetric Optimum
As the setup is symmetric, it is clear that the symmetric optimum involves each household
consuming some of their \market" good. It is straightforward to show that at the symmetric
Pareto optimum, goods are passed from i + 1 to i to equate the marginal utility of the
market good to the home good,
@U=@Xt(s t) = st (Xt¤(s t)) ¡1 = 1 = @ U=@Ht (st );
so that allocations are Xt¤(st ) = s t and Ht¤(s t) = H ¡ Xt¤(st ): More of the market good
should be consumed in the high state than in the low state.
4
The Monetary Economy
4.1
Two Fiat Currencies
In the monetary economy there are two ¯at currencies. At the beginning of period 0 each
d
household is endowed with a common initial level of domestic ¯at currency M 0 and foreign
4
Perfect correlation rules out insurance markets (arising at each node i). Assuming away insurance
markets, the analysis goes through when shocks are imperfectly correlated. The reason prices are not
a®ected is because of the linear preferences which yield a constant marginal utility of income.
6
f
¯at currency M 0 . For simplicity the foreign money supply is assumed to be ¯xed. The
domestic government generates seigniorage by creating domestic money.
Government is assumed to not observe the contemporaneous consumption shock and
therefore cannot condition the domestic money supply on the current state. The growth
rate of the money supply m (¸ ¯ ¡ 1) is assumed to be constant over time, so the money
d
d
d
created is mM t , where M t = (1 + m)tM 0 is the average per capita domestic money stock
brought into period t.
Households can purchase their market good in competitive markets with domestic and
foreign currencies. The price of i's market good in terms of domestic currency is denoted
qt (st ) and in foreign currency is pt (st ): Conversely, the prices of the domestic and foreign
currency in terms of the market good are respectively 1=qt (st ) and 1=pt (s t). Both currencies
are valued if 1=qt (st ) > 0 and 1=pt(s t ) > 0:
The government also purchases goods in competitive markets. The seigniorage revenue
d
in terms of goods per person in the representative market (i; i + 1) is Gt (s t) = mM t =qt (st ).
The negative creation of money corresponds to the government selling goods and buying
domestic money in each market. For the most part, the analysis concentrates on m ¸ 0.
Of course, if domestic money is worthless no seigniorage can be raised.
The currencies also can be acquired in a foreign exchange market. The price of foreign
currency in terms of domestic currency is denoted et (st ). The foreign exchange market
opens at the end of the period (at node i) after goods markets close. This allows agents
to adjust their currency holdings within the period knowing the shock. Engineer (1996)
shows that the results are robust to opening the foreign exchange market at the beginning
of the period before goods markets open. If foreign exchange market and goods markets
open at the same time, the results are the same with a restriction.
4.2
Frictions
This paper analyzes equilibria in which both currencies are valued but are not perfect
substitutes by relaxing the assumption of frictionless exchange. The friction in exchange
that is introduced is speci¯c to currency. It is modelled as the transaction cost of purchasing
7
foreign currency. In particular, household i incurs cost c > 0 (measured in terms of the
own good i foregone) for each unit of foreign currency purchased with its own good. As
i¡1;f
households i purchases a total of pi¡1;t Hi;t
¸ 0 units of foreign currency (in market (i ¡1;
i¡1;f 5
i)); its total transaction cost is cpi¡1;t Hi;t
.
Household i also incurs a transaction cost should it choose to purchase foreign currency
in the foreign exchange market. The total transaction cost is denoted ce Ft (s t), where ce ¸ 0
is the marginal cost (in terms of the home good i) and F t(s t) ¸ 0 is the amount of foreign
currency purchased with domestic currency. The household does not incur a transaction
cost if it sells foreign currency for domestic currency. Such sales are denoted © t(s t) ¸ 0.
Apart from physical handling costs, higher foreign currency transactions costs arise
mainly from veri¯cation costs (see footnote 2). Counterfeit currency has historically been
a major problem and required resources to verify the quality of bills. Recently, the rush to
redesign the U.S. $100 bill was to avoid counterfeit \supernotes" which were often able to
fool bank machines and bankers. 6 The dollar is a natural candidate for counterfeiters as
it is used in many foreign countries where domestic expertise in detecting bogus bills may
be lacking. Also, governments may not have a strong incentive to reducing the circulation
of counterfeit foreign bills. In this paper, government enforcement policy is treated as
exogenous to avoid another layer of analysis.
A proportional transaction cost is consistent with constant returns to scale in handling
and verifying foreign currency bills (ignoring integer constraints and di®erent denominations). 7
Indirect evidence for proportional costs is the high marginal cost (as high as 10%) of purchasing foreign currencies at exchange kiosks. Decreasing costs to verifying currency can
5
The foreign money stock is ¯xed and c is su±ciently small so that all the foreign currency can be feasibly
purchased by agents (see the propositions in Section 5). However, were the stock of money to grow over
time, then purchasing all the foreign currency might be infeasible. A transaction cost speci¯cation which
f
f
avoids this problem is the following: Átp i¡1; tHti¡1;f , where Át = cM 0 =M t . Now the total transaction cost
is stationary in a steady state. A similar speci¯cation to Át could be employed to model transaction costs
for domestic currency. This is not done to keep the model simple.
6
\Supernotes" appear to come from several sources. Kristof (1996) reports that possibly sources include
the governments of North Korea, Iran and Syria. These countries deny counterfeiting.
7
An imperfect veri¯cation technology may be optimal. This imposes a cost proportional to the number
of bogus bills accepted. Also, lost or stolen foreign currency might not receive the same attention from
the authorities. These \security" rationales for high proportional costs are not modeled in this paper.
8
be captured in this framework by introducing a ¯xed cost to purchasing a technology for
handling and verifying foreign currency.. As the results are determined by the marginal
conditions, this extension has been omitted.
4.3
The Household Problem and Market Clearing
The budget constraints on the acquisition of money and the home good faced by the
representative household i are the following:
d
Mt+1
(st ) = Mtd(s t¡1) ¡ qt (st )Xtd (st ) + qi¡1;t(st )Hti¡1;d (st ) ¡ e t(st )Ft (st ) + et (st )©t (s t);
f
Mt+1
(st ) = Mtf (st¡1 ) ¡ pt (st )Xtf (st ) + pi¡1;t (st )Hti¡1;f (st ) + F t(s t) ¡ ©t (st );
H = Ht(s t) + Hti¡1;d (st ) + Hti¡1;f (s t) + cpi¡1;t(s t)Hti¡1;f (s t ) + ceF t(s t):
Money taken into period t + 1 depends on the stock of money at the beginning of period t
less amounts spent to purchase the market good plus the amount of money purchased by
the sale of the home good plus purchases in the foreign exchange market. The endowment
of the home good is exhausted by own consumption, sales of the home good to buy money
and the transaction costs of purchasing foreign currency. It is convenient to combine the
three constraints to eliminate Hti¡1;d(s t) and Hti¡1;f (st ).
d (s )¡M d (s
d
[Mt+1
t
t¡1 )+qt(st )Xt (st )]+et (s t)F t(s t)¡et (s t)© t(s t)
t
qi¡1;t(st )
f
(1+cpt (st ))[Mt+1
(st)¡Mtf (st¡1)+pt (st )Xtf (st )]¡Ft (st )+©t(st )
¡
¡ ce Ft (st ):
pi¡1;t(st)
Ht (st ) = H ¡
Substituting into the utility function for Ht (st ) the household's problem is
max
d
Xtd (st ); Xtf (st ); Mt+1
(s t )
f
Mt+1 (st ); Ft (st ); ©t (st )
E0
1
X
t=0
¯ t fH ¡
d (s ) ¡ M d (s
d
Mt+1
t
t¡1 ) + q(st )Xt (s t)+e t(s t)F t(s t)¡e t(s t)© t(s t)
t
qi¡1;t(st)
(1 + cp
(s )) [M f (s ) ¡ M f (s
) + p (s )X f (s )¡F (s )+©t(st )]
i¡1;t t
t¡1
t t
t
t t
t+1 t
t
t
¡
pi¡1;t (st )
¡ce Ft (st ) + st ln(Xtd(s t) + Xtf (s t))g
s:t: Mtd(s t¡1) ¸ qt (st )Xtd (st )
Mtf (st¡1 ) ¸ pt (st )Xtf (s t)
d
f
with M 0; M 0 and m given. The cash-in-advance constraints require that households only
purchase their market goods with the currency they brought into the period.
There are three sets of market-clearing conditions: (i) conditions for goods Hti¡1;d(st ) =
f
d
Xi¡1;t
(s t)+G i¡1;t (st ) and Hti¡1;f (s t) = Xi¡1;t
(s t ), (ii) conditions for money qi¡1;t(s t)Hti¡1;d (st ) ·
9
d
d
f
f
d
qi¡1;t (st )Xi¡1;t
(s t )+mM t · M t+1, and pi¡1;t (st )Hti¡1;f (st ) · pi¡1;t (s t)Xi¡1;t
(st ) · M 0 ; and
(iii) conditions for foreign exchange Ft (st ) = © t(s t) for all i and t.
5
Monetary Equilibria
A competitive equilibrium for the monetary economy satis¯es household optimization and
market-clearing for goods and money. To simplify matters, the analysis is con¯ned to
competitive stationary symmetric equilibria (CSSE). Under symmetry, prices of the market
goods are the same for all i; qt(s t ) = qi¡1;t (st ) and pt (s t) = pi¡1;t(s t ). The representative
household's problem yields the following ¯rst-order necessary conditions for Xtd (st ); Xtf (st );
d (s ); M f (s ); F (s ); © (s ); ®d (s ) and ®f (s ):
Mt+1
t
t t
t t
t+1 t
t t
t t
¡¯ t + ¯t s t(Xt (st ))¡1 ¡ ®dt(s t )qt(s t) · 0
(1)
¡¯ t(1 + cpt (st )) + ¯ t st (Xt (st ))¡1 ¡ ®ft (st )pt (st ) · 0
(2)
¡¯t =qt (st ) + Et¯ t+1=qt+1(st+1 ) + Et ®dt+1(s t+1) · 0
(3)
1 + cpt (st )
1 + cpt+1(st+1)
+ ¯ t+1Et
+ Et®ft+1(s t+1) · 0
pt (st )
pt+1 (st+1)
(4)
¡¯t
¯t
1 + cpt (st )
e t(s t)
¡ ¯t
¡ ¯t c e · 0
pt (st )
qt (s t)
(5)
1 + cpt (st )
e (s )
+ ¯t t t · 0
pt (st )
qt(st )
(6)
¡Mtd(s t¡1 ) + qt (st )Xtd (st ) · 0
(7)
¡Mtf (st¡1) + pt (s t)Xtf (st ) · 0
(8)
¡¯ t
where ®dt (st ) and ®ft (st ) are the Lagrange multipliers that correspond to the cash-in-advance
constraints for the domestic and foreign currencies, and Xt(s t) = Xtd(s t) + Xtf (st ): A
10
condition holds with strict inequality when the nonnegativity condition for the respective
variable binds so that it is zero. Note (5) and (6) require © t(st )Ft (st ) = 0 so that a
household does not simultaneously buy and sell currency in the foreign exchange market.
The three types of monetary CSSE equilibria are examined below.
5.1
Domestic Currency Equilibrium
When only domestic currency is valued, 1=qt (st ) > 0, 1=pt (s t) = 0 and e t(s t) = 0, foreign currency can not be used to purchase goods, Xtf (s t) = 0, or domestic currency,
et (st )©t (s t) = 0. Condition (1) indicates that the household will want to consume positive
amounts of the market good in both states, Xtd(s t) > 0. Hence in a CSSE money will
d
be purchased in both states, Mt+1
(st ) > 0; and (3) holds with equality. When (3) holds
with equality, the domestic money price is independent of the state, qt(s t ) = qt , as it is
determined by parameters and the expectation at t of future prices which depend only on
the future state. Lagging this condition and substituting for ®dt(s t)qt (s t) from (1) yields
d
Et¡1M RSXH
= ¼sL (Xt(sL))¡1 + (1 ¡ ¼)sh(Xt (sh)) ¡1 =
qt =qt¡1
:
¯
(9)
There is a domestic monetary CSSE only if the price level grows at the same rate as
the money supply, so that qt=qt¡1 = (1 + m): Let s ´ s L¼ + sh(1 ¡ ¼):
Proposition 1 (Domestic Currency Equilibrium): A CSSE exists in which only domestic
money has value; foreign money does not have value, 1=p^t (st ) = 0 and bet (st ) = 0, and can
b (s ) = 0:
^ tf (s t) = 0 or domestic currency ebt (st )©
not be used to purchase goods, X
t t
(a) For m su±ciently small, (1 + m) · ¯s=s L, the cash-in-advance constraint does not
bind in the low state, ®^da
t (sL ) = 0. Equilibrium allocations and prices are:
^ tda (sh) = ¯sh(1 ¡ ¼) ; H^ta(s t) = H ¡ X^tda (st ) ¡ mX^tda (sh);
X^tda (sL ) = sL; X
(1 + m) ¡ ¯¼
d ^ da
q^ta = (1 + m)t q^a0 ; q^a0 = M 0=X
t (sh):
(b) For m su±ciently large, (1 + m) > ¯s=sL , the cash-in-advance constraint binds in both
11
states constraining money purchases to be the same in both states. Hence
X^tdb (st ) =
¯s
^tb(s t) = H ¡ (1 + m)X
^ tdb(s t ) = H ¡ ¯s;
; H
1+m
d
q^bt = (1 + m)t q^0b; q^b0 = M 0=X^tdb (st ):
The proof to this proposition is in the Appendix. In case (a) domestic money keeps its
value well and households hold money balances beyond what they want for consumption
in the low state. This additional money is held as a bu®er which enables households to
consume more when a high state occurs.
5.2
Foreign Currency Equilibrium
When domestic money has no value, 1=qt (st ) = 0, it cannot be used to buy goods, Xtd(st ) =
0, or foreign currency, Ft(st ) = 0. Condition (2) indicates that the household will want
to consume positive amounts of the market good in both states, Xtf (s t) > 0. Hence, in
f
a CSSE money will be purchased in both states, Mt+1
(st ) > 0; in which case (4) holds
with equality. When (4) holds with equality, the domestic money price is independent of
the state, pt (st ) = pt , as it is determined by parameters and the expectation at t of future
prices. Lagging this condition and substituting for ®tf (st )pt (st ) from (2) yields
f
¡1
Et¡1M RSX
+ (1 ¡ ¼)s h(Xt (sh))¡1 =
H = ¼sL(Xt (s L))
(1 + cpt¡1 )pt=pt¡1
:
¯
(10)
Since foreign money supply growth is zero, the CSSE prices must satisfy pt =pt¡1 = 1:
Proposition 2 (Foreign Currency Equilibrium): A CSSE exists in which only foreign
money has value; domestic money does not have value, 1=~
qt (st ) = 0 and 1=ebt (s t) = 0, and
can not be used to purchase goods, X~td(st ) = 0 or foreign currency Fbt (st ) = 0 :
(a) If 1 · ¯s=sL , the cash-in-advance constraint does not bind in the low state, ®
~ fa
t (sL ) = 0.
Equilibrium allocations and prices are:
X~tf a (sL) =
f
sL
¯sh(1 ¡ ¼)
~ fa
;
a ; Xt (sh ) =
1 + c~
pt
(1 + c~
pat )(1 ¡ ¯¼)
~ ta (st ) = H ¡ (1 + c~
H
pat )X~tf a (st )
f
f
~ tf a(s h) = M 0 (1 ¡ ¯¼)=[¯s h(1 ¡ ¼) ¡ cM 0 (1 ¡ ¯¼)];
p~at = p~a0 = M 0 =X
f
12
c < ¯sh(1 ¡ ¼)=M 0 (1 ¡ ¯¼):
(b) If 1 > ¯s=s L, the cash-in-advance constraint binds in both states. Equilibrium allocations and prices:
¯s
~ tb (st ) = H ¡ (1 + c~
~ tf b(st ) = H ¡ ¯s;
; H
pbt )X
1 + c~
pb0
f
~ tfb (st ) = M f0 =(¯s ¡ cM f0 ); c < ¯s=M f0 :
p~bt = p~b0; p~b0 = M 0 =X
~ tf b(s t) =
X
The proof is in the Appendix. The transaction cost drives up the price of the market
good and hence reduces consumption. Since the transaction cost is proportional to nominal
currency holdings, money is not neutral. Increasing the initial stock of foreign currency
involves more notes changing hands, which drives up the cost of transactions for a given c:
5.3
Dual Currency Equilibria
Now consider CSSE monetary equilibria in which both domestic and foreign currency have
value. A natural starting point would be to consider the equilibrium price paths in which
the prices are state invariant as above and increase at the same rate as the respective rates
of money growth: qt =qt¡1 = et =e t¡1 = 1 + m and pt =pt¡1 = 1:
The following proposition establishes that such dual currency equilibria exist if m and
h
p0 satisfy m 2 (m(p0 ); cp0], where m(p0 ) ´ max cp0(1 ¡ ¼¯);
s(1+cp0)(1¡¼¯)
sh (1¡¼)
i
¡ 1 : This
interval is nonempty if ¯s > s L. Whereas m is a parameter, p0 is endogenous and is the
solution to a quadratic equation:
+
p 0´
¡b + (b2 ¡ 4ad):5
¡b ¡ (b2 ¡ 4ad):5
and p0 ´
2a
2a
f
a ´ (1 ¡ ¯¼)c[¯s ¡ M 0 (1 ¡ ¯¼)c];
f
b ´ (1 ¡ ¯¼)c[(1 + m) ¡ 2(1 ¡ ¯¼)]M 0 ¡ (1 ¡ ¼)s h¯(1 + m) + ¯(1 ¡ ¯¼)s;
f
d ´ (1 ¡ ¯¼)[m + ¯¼]M 0 :
f
The restrictions c < ¯s=M 0 ; b < 0; b2 ¡4ad ¸ 0 rule out nonpositive, in¯nite and imaginary
+
+
prices. As p0> p0 implies 1=p 0< 1=p0, foreign currency is more highly valued when pt = p0.
The proposition establishes an equilibrium corresponding to each price.
Proposition 3 Two CSSE may exist in which both foreign and domestic currencies have
value: (i) A High Valued Foreign Currency Dual Equilibrium (HVFDE) exists in which
13
pt = p0 for all t if and only if m 2 (m(p0 ); cp0] :
+
(ii) A Low Valued Foreign Currency Dual Equilibrium (LVFDE) exists in which pt = p0
for all t if and only if m 2
µ
¸
+
µ
+
m( p0 );
c
+
p0
¸
;
If m 2 m(p 0); c p0 the equilibria coexist. The allocation and domestic price equations
for both equilibria di®er only because they depend on pt :
¼sL¯
; Xtf (sL ) = 0;
(1 + m) ¡ (1 + cpt )(1 ¡ ¼¯)
(1 ¡ ¼)sh¯
Xt (sh) =
; Xtf (sh) = Xt (sh ) ¡ Xtd (sh);
(1 + cpt)(1 ¡ ¯¼)
Ht (sL ) = H ¡ (1 + m)Xtd (sL);
Xt (sL) = Xtd(s L) = Xtd (sh) =
d
d
Ht (sh) = H ¡ (1 + m)Xtd (sL) ¡ (1 + cpt)Xtf (sh);
f
M0
M [(1 + m) ¡ (1 + cp0)(1 ¡ ¼¯)]
M
qt = (1 + m) q0; q0 =
= 0
; pt = p0 = f 0 :
Xt (s L)
¼sL¯
Xt (sh )
t
e
Ft (st ) = ©t (s t) = 0; et (st ) = (1 + m) e 0; e0 2 [(1 + (c ¡ c )p0)(q0 =p0); (1 + cp0)(q0=p0 )] .
t
The proof to this proposition is in the Appendix.
In each equilibrium, households use the domestic money in the low state to buy the
market good and use both domestic and foreign currencies in the high state to buy market
goods. The cash-in-advance constraint binds for the domestic currency in both states,
whereas the foreign currency cash-in-advance constraint only binds in the high state. Thus,
equation (9) holds, requiring (1 + m)=¯ · (1 + cp0)=¯ or m · cp0. The equilibria will
not exist if the domestic money supply grows at a greater rate because foreign currency is
cheaper to use in the low state. On the other hand, if the domestic money supply grows at
a su±ciently low rate, m · m(p0) households will conduct all their transactions through
domestic currency. The fact that outside the interval one currency drives the other out
demonstrates currency competition. Currency competition is also evident from the fact
that an increase in p0 causes a decline in q0, ceteris paribus. That is, as foreign money
becomes less valuable, domestic money becomes more valuable.
The possibility of two dual equilibria arises because the transaction cost is on nominal
foreign currency transactions. The higher is p0 the higher is the real transaction cost, cp0 ; of
purchasing each unit of goods using foreign currency. Conversely, the high real transaction
14
cost of using foreign currency reduces it value, forcing p0 up. Thus, expectations can be
+
self-ful¯lling, and the value of foreign currency can be either low (1= p 0) or high (1=p0) in
+
equilibrium. It follows that domestic currency is more valuable in LVFDE, 1= q 0> 1=q 0,
as agents substitute toward using domestic currency.
6
Simulations and Welfare
Dual currency equilibrium exist for a large set of parameter values. Consider parameters
d
f
¯ = :998; s L = 1; s h = 2; ¼ = :95; M 0 = 1; M 0 = 1. The high value of ¯ corresponds
to a weekly transaction period when the annual discount factor is 0:90(= :99852): A high
shock occurs on average once every 20 weeks and involves valuing the market good at
twice as much as the low shock. The money supply growth rate, m, in the following ¯gures
is relative to the one week transaction period. In annual terms the growth rate varies
from ¡:1(= :99852 ¡ 1) to 17:76(= 1:05852 ¡ 1): Seigniorage revenues are reimbursed to
households lump sum.
(Figures 1, 2, and 3 here)
6.1
Domestic and Foreign Currency Equilibria
^ intersects the vertical axis at
In Figure 1, the domestic currency equilibrium line, EU;
^ = 1009:66. This is Friedman's optimal money supply rule: m = ¯ ¡1 = ¡:002.
EU ¤ = E U
^ decreases monotonically switching from case (a)
As the money supply rate increases, E U
to case (b) at m = :048: In case (a) the cash-in-advance constraint does not bind in the
low state and extra money stocks are held between periods as a contingency against the
high shock. Utility is more rapidly declining in m (and seigniorage in Figure 2) because
the demand for money in the high state is relatively elastic. Accordingly, the initial price
level qb0 increases more rapidly with m in case (a) as illustrated in Figure 3.
The foreign currency equilibrium expected utility is lower in Figure 1a than in Figure
1b because the transaction cost is higher, c = :05 versus c = :01. As no seigniorage is
raised when domestic currency is valueless, this case is not drawn in Figure 2.
15
6.2
Dual Currency Equilibria
The dual currency equilibria exist over a wide range of domestic money growth rates and
seigniorage. For example, with c = :05 the HVFDE exists for m 2 (:003; :055) which
corresponds to annual growth rates of the money supply from 18% to 1550%: The example
illustrates the nondisappearance of the hyperin°ating domestic currency.
The ¯gures also illustrate the two dual currency equilibria: HVFDE and LVFDE. In
Figure 1a (c = :05) these equilibria coexist over a range of m; whereas, in Figure 1b
(c = :01) they never coexist. The higher transaction costs in Figure 1a increase the range
of the equilibria yielding the overlap. The HVFDE dominates, EU ¡ > EU +; as the
transactions costs of buying foreign currency is less.
d
Very similar equilibrium patterns emerge against seigniorage revenue, G = mM t =qt; as
drawn in Figure 2. This is because domestic money demand is quite inelastic with respect
to m in the dual currency equilibria. This is because domestic currency turns over every
period and is used only to purchase small quantities in the low state. The inelasticity is not
coming just from the logarithmic utility function, as the elacticity of the marginal utility
of the market good is unity.
Figure 3 plots the initial domestic and foreign currency price levels, q0 and p0; corresponding to Figure 1a. In the HVFDE, as m increases, domestic currency becomes less
valuable (q 0 increases) and foreign currency becomes more valuable (p0 decreases). In the
+
LVFDE, as m increases, domestic currency also becomes less valuable ( q 0 increases). How+
ever, foreign currency becomes less valuable ( p0 increases). The higher transaction costs
of using foreign currency in the LVFDE results in domestic currency having a higher value
+
in the LVFDE, 1= q0> 1=q0. The results for the c = :01 are similar.
6.3
Welfare
The ¯gures permit a comparison of utility across steady states. First observe that in
Figure 1a the domestic currency equilibrium dominates the HVFDE , EU^ > EU ¡, for
relatively low rates of money growth m 2 [0:0032; 0:0126), from 18% to 71% annually. As
m increases further, households are better o® in the HVFDE, E U^ < EU ¡. Indeed, they
16
are considerably better o® at the upperbound, m = cp0 = 0:055. A similar pattern emerges
in Figure 1b but for a smaller range of m.
The welfare results can be explained in terms of two opposing e®ects. Both e®ects
are present in Engineer and Bernhardt (1991) who analyze a similar model where the
alternative means of exchange (barter and gold) has exogenous worth and there is no
seigniorage. A competing currency has a negative externality e®ect. It reduces the value
of the domestic currency which is a public good in facilitating exchange. This negative
e®ect remains when the alternative means of exchange is endogenous. This e®ect is most
pronounced in the HVFDE as the drop in value of the domestic currency is the greatest
across steady states.
A competing currency positively a®ects utility through a \°exibility e®ect". In the dual
currency equilibria the foreign currency allows households to buy additional quantities of
goods in the high state without having to carry precautionary stocks of domestic currency.
This shifts the burden of the in°ation tax onto the inelastically demanded everyday small
transactions away from the more elastically demanded large occasional transactions. As a
result, more goods are purchased in the high state in the HVFDE.
The pattern of the utility di®erences can be explained by the strength of the opposing
e®ects. The negative externality e®ect is related to the drop in the value of the domestic
currency, (1=qb0) ¡ (1=q 0): This di®erence diminishes as m increases primarily because do-
mestic real balances are more elastic in the domestic currency equilibrium. The °exibility
a®ect is related to the value of the foreign currency. As m increases this value increases
(1=p0 increases). The examples in Figure 1 demonstrate that the °exibility a®ect can
dominate for su±ciently large m:
The question remains: Can the °exibility e®ect improve utility when seigniorage is a
requirement? Figure 2 demonstrates this is indeed the case for both transactions costs. As
explained earlier, similar patterns arise because of the inelastic nature of currency demands.
The range of seigniorage revenues over which the HVFDE dominates is substantial in Figure
2a but not in Figure 2b.
The analysis suggests hysteresis. Consider Figure 2b. When G > :014 (or m > cp0 =
17
:0109); agents deviate from the HVFDE by just using foreign currency. This suggests
that the foreign currency equilibrium might emerge. Thus, an increase in m may result
in an irreversible change. Banning foreign currency when m 2 (0:0109; 0:0191) is welfare
improving as households are better o® in the domestic monetary equilibrium.
7
Foreign currency with external value
This section extends the model to consider the more realistic case where foreign currency
has some external value. Generally, the higher the external value, the greater is the use of
foreign currency and the less is the use and value of domestic currency.
7.1
Minimum external value and currency controls
Suppose foreign currency has a minimum exogenous value
1
.
px
Now if m is too high,
currency substitution toward use of the foreign currency occurs. If m >m(px); households
use foreign currency in the high state. The domestic currency equilibrium does not exist
in contrast to the model without external value. If m increases further such that m > cpx
domestic currency ceases to have value and the dual currency equilibria do not exist.
Subject to the above, the dual and foreign equilibria take the same form as in the text
if the minimum value is su±ciently low,
1
p0
>
1
px
>
1
+
p0
1
px
<
1
+
p0
. If the minimum value increases such that
, the LVFDE is eliminated. Then the HVFDE remains as the unique dual
currency equilibrium, and the foreign currency displays a (black market) premium over its
minimum value,
1
p0
>
1
.
px
A minimum value for the foreign currency may emerge under currency controls. The
government prevents households from purchasing foreign currency in international markets.
However, the government stands ready to purchase foreign currency with market goods (or
equivalently with domestic currency and a government tax) at rate
1
:
px
The above cases for
dual currency equilibria obtain as no there are no government purchases in equilibrium.
The policy may serve the useful role of eliminating the LVFDE.
Instead, suppose foreign currency can be sold for foreign goods in international markets
(perhaps by smuggling) at rate
1
px :
Then the same results obtain when foreign goods are
18
perfect substitutes for domestic market goods. If m > cpx only the foreign currency equilibrium exists. Even though no purchases are made in international markets in equilibrium,
a government may want to undertake enforcement actions to increase px.
7.2
Maximum external value and the small open economy
The above scenario precludes purchases of foreign currency in international markets but
allows sales of foreign currency at rate
1
:
px
Now suppose households can also buy foreign
currency in international markets with domestic goods at rate
1
pex
¸
1
.
px
To the extent
that a wedge exists the transaction cost of acquiring foreign currency in the international
market may be less than domestically. For simplicity, however, assume that the transaction
cost is the same and that the domestic currency is not internationally traded.
The possibility of buying foreign currency puts a ceiling on its purchase price. Such a
ceiling is binding if
1
pex
<
1
p0 :
Then the equilibrium price is p = pex and allocations are like
those in the HVFDE where the stock of foreign currency held increases to be consistent with
the new equilibrium price.8 Some foreign currency is purchased in international markets
in the initial period. This purchase describes the process of dollarization.
Now let px = pex so that the minimum external value is also the maximum. It can
be shown that dual and foreign currency equilibria exist for m(px) < m < cpx and that
foreign currency equilibria exist for m > cpx: The stock of foreign currency held will adjust
to be consistent with the price px in each equilibrium.
Finally, when px = pex a domestic monetary equilibrium exist if m ·
s(1+cpx )(1¡¼¯)
sh (1¡¼)
¡
1. In this case, the nominal price of foreign currency is too high and the transaction
cost becomes too onus to purchase foreign currency. If households hold stocks of foreign
currency, they will sell them for foreign goods in initial periods. In the steady state,
households only use domestic currency for purchases.
8
There is a continuum of equilibria because households are indi®erent between purchasing foreign
currency in domestic or international markets at the same prices. This is also the case for p x = p ex .
19
8
Conclusion
This paper characterizes dual ¯at currency equilibria in a modi¯ed Townsend turnpike
model. The currencies are imperfect substitutes in equilibrium as one currency has the
lower transaction cost and the other has the lower growth rate. When consumption demand is stochastic the currencies play distinct roles. The low transaction cost currency,
domestic currency, is used for everyday small purchases; whereas, the low growth rate currency, foreign currency, is hoarded and only used for making occasional large purchases.
Simulations indicate that this transaction pattern is robust to dramatic di®erences between
the currency growth rates. Of course, if the di®erence becomes too large or too small one
currency will drive the other out.
The nondisappearance of the hyperin°ating domestic currency can be explained by its
high velocity in its role of minimizing the transactions costs of everyday small purchases.
Surprisingly, the presence of the foreign currency may increase welfare in this situation
because it provides °exibility in facilitating large occasional purchases. In contrast, the
presence of valued foreign currency lowers welfare when domestic currency in°ation is
modest. This is because the competition from the foreign currency reduces the value of
the domestic currency which has a public good aspect. The analysis also indicates that
very low rates of domestic currency in°ation are consistent with the nondisappearance of
the foreign currency when foreign currency transaction costs are low. Then actions to
eliminate valued foreign currency, such as banning it or raising its transaction cost, may
be welfare enhancing.
While the paper provides insight into some reasons for currency substitution, it abstracts away from other issues. For example, international linkages are only examined in
a simple way. The model does not fully examine trade and ¯nancial °ows. Sahay and
0
Vegh (1995) and Savastano (1996) argue that these linkages are important for explaining
dollarization in Latin America and transition economies. Introducing foreign countries,
trade °ows, and strategic monetary policies into the model are major extensions left for
future research.
20
APPENDIX
Proof of Proposition 1. First, markets are shown to clear at the proposed market prices.
d
The domestic goods market-clearing condition is Hti¡1;d (st ) = Xi¡1;t
(s t) + Gi¡1;t (st ) which
d
under symmetry implies Hti¡1;d (st ) = Xtd(s t) + G t(s t ) = Xtd(s t) + mM t =qt(st ). The dod
mestic budget constraint for domestic currency requires Hti¡1;d (st ) = Xtd (st ) + [Mt+1
(st ) ¡
^ tdb=^
^ tdb(st ) = M d0 =^
^ tdb(st ) =
Mtd(s t¡1)]=qt (st ). For case (b) M
qbt = X
qb0. Since q^bt = (1+m)t q^0b; M
d
d
d
db
^ t+1
^ tdb(s t¡1)] = mM t establishing market clearing. For
M t = (1 + m)t M 0. Hence [M
(s t) ¡ M
^ tda =^
^ tda(s h) = M d0=^
case (a) M
qat = X
qa0 , and market clearing follows by the same reasoning.
As the price of domestic currency is positive, the domestic currency money market-clearing
condition must hold at equality. Dividing by q^t yields the goods market-clearing condition. Hence, goods market clearing implies money market clearing. As foreign currency is
^ tf (st ) = 0, both of the market-clearing conditions for purchases
worthless, H^ti¡1;f (s t) = X
of goods with foreign money are satis¯ed. In the foreign exchange market, the demand for
c f : This condition is
foreign currency is less than or equal to supply, Ft (st ) · ©t (st ) · M
t
satis¯ed as Fbt (st ) = 0:
It remains to be shown that agents are optimizing. The proposed allocations satisfy
the FONCs. When the cash-in-advance constraint binds in the low state, it must also bind
in the high state so X^tdb (st ) is solved directly from (9). To derive when the cash-in-advance
^ tdb(s t) into (1) to ¯nd 1 + m > ¯s=s L. When
constraint binds in the low state, substitute X
^ tda(sL) is derived from (1).
the cash-in-advance constraint does not bind in the low state, X
^ tda(s h). Standard arguments (e.g. Townsend 1980
Substituting X^tda (sL ) into (9) yields X
or Engineer and Bernhardt 1991), demonstrating that all other allocation sequences are
inferior, apply to establish that the proposed allocation is in fact a maximum.
Proof of Proposition 2. This proof parallels the Proof to Proposition 1.
Proof of Proposition 3. First, markets are shown to clear at the proposed market prices for
the interval m 2 (m(p0 ); cp0 ]. In both equilibria the domestic cash-in-advance constraint
binds and goods markets clear as demonstrated in case (b) of the Proof to Proposition
1. Domestic money markets clear as that condition reduces to the goods market-clearing
condition when the price of domestic currency is positive. Goods markets which use foreign
21
currency clear as Hti¡1;f (st ) = Xtf (st ). As the price of domestic and foreign currency is
positive, foreign money markets clear.
Second, households are shown to be maximizing at the proposed equilibrium prices
in the interval. The no arbitrage condition et 2 [(1 + (c ¡ ce )pt)(qt =pt); (1 + cpt )(qt=pt )]
ensures that foreign exchange market is not used for arbitrage. If et 2 ((1+(c¡ce )pt )(qt=pt );
(1 + cpt )(qt=pt )) households are strictly worse o® making purchase in the foreign exchange
market. The nonnegativity conditions for FONC (5) and (6) bind, Ft(st ) = © t(s t) = 0:
If either et = (1 + (c ¡ ce )pt )(qt=pt ) or e t = (1 + cpt )(qt =pt)] households are indi®erent
between purchasing currency directly in the goods markets or indirectly through the foreign
exchange market. Hence, the presence of the foreign exchange market does not change the
households currency portfolio entering a period and Ft (st ) = ©t (st ) = 0 is consistent with
household optimization.
The proposed equilibrium consumption allocations satisfy the FONCs for an optimum
and can be derived from them as follows. Since Xtf (sL) = 0, the cash-in-advance constraint
for the foreign currency does not bind in the low state, ®ft (sL ) = 0. Solving for ®ft (s h)pt (sh)
in (2) and substituting into (4) yields Xt (sh). Substituting Xt (sh) into (9) yields Xt (sL ). As
the cash-in-advance constraint binds for the domestic currency in the low state, Xtd (sL ) =
Xtd (sh) = Xt (sL ), it follows that Xtf (sh) = Xt (sh ) ¡ Xt (sL ). Standard arguments (e.g.
Townsend 1980 or Engineer and Bernhardt 1991), showing that all other consumption
allocation sequences that satisfy the FONCs are inferior, apply to show that the proposed
allocations correspond to a maximum for households.
Third, for growth rates of the money supply outside the interval, HVFDE and LVFDE
do not exist. If m · m(p0) foreign money can not be valued if domestic money is also
valued at the proposed equilibrium prices. Suppose not, that is foreign currency is valued
and m ·
s(1+cp0 )(1¡¼¯)
s h(1¡¼)
¡ 1. Then maximizing households do not purchase goods in either
the high or low state with foreign money. Hence, there cannot be a CSSE in which foreign
money is purchased and valued. On the other hand, suppose foreign currency is valued but
m · cp0 (1 ¡ ¼¯). Then the cash-in-advance constraint on goods purchased with domestic
currency does not bind in the low state and su±cient domestic currency is hoarded in the
22
low state that all purchases in the high state are with domestic money. Again, foreign
currency is not used to purchase goods and cannot be valued in a CSSE.
Considering the other bound, if m > cp0 domestic money can not be valued if foreign
money is valued at the proposed equilibrium prices. Suppose not; that is, domestic currency
is valued. Then equation (10) but not (9) holds. Su±cient quantities are purchased with
foreign currency that no purchases are made with domestic currency in the low state and
hence high state. (1) holds with strict inequality. As no goods are purchased with domestic
currency, it cannot be valued in a CSSE.
23
References
[1] Barnett, R., 1992, Speculation, incomplete currency market participation, and nonfundamental movements in nominal and real exchange rates, Journal of International
Economics 33; 167 ¡ 186:
[2] Barnett, R. and M. Ho, 1996, Sunspots, currency substitution, and in°ationary ¯nance", Journal of International Economics 41; 73 ¡ 93:
0
[3] Calvo, G. and C. Vegh, 1992, Currency substitution in developing countries: an in0
0
troduction", Revista de Ana lisis Economico 7; 3 ¡ 27:
[4] Chang, R., 1994, Endogenous currency substitution and in°ationary ¯nance, and welfare", Journal of Money Credit and Banking 26; 903 ¡ 916:
[5] Engineer, M., 1996, Transaction costs and competing ¯at currencies, University of
Victoria Discussion Paper 96-01.
[6] Engineer, M. and D. Bernhardt, 1991, Money, barter, and the optimality of legal
restrictions", Journal of Political Economy 99; 743 ¡ 773:
[7] Giovannini, A. and B. Turtelboom, 1994, Currency substitution, in F. van de Ploeg,
ed., Handbook of international macroeconomics (Blackwell, Cambridge) 390-435.
[8] Head, A. and S. Shi, 1997, Search, in°ation and exchange rates, mimeo, Queen's
University.
[9] Kareken, J. and N. Wallace, 1981, On the indeterminancy of equilibrium exchange
rates", Quarterly Journal of Economics 96; 207 ¡ 222:
[10] Kristof, N., 1996, North Korea denies link to bogus currency, New York Times New
Services as printed in the Globe and Mail, April 20, 1996.
24
[11] Matsuyama, K., N. Kiyotaki and A. Matsui, 1993, Towards a theory of international
currency, Review of Economic Studies 60; 283 ¡ 309:
[12] Poloz, S., 1984, Transaction demand for money in a two-currency economy", Journal
of Monetary Economics, 14; 241 ¡ 250:
[13] Poloz, S., 1986, Currency substitution and the precautionary demand for money",
Journal of International Money and Finance 5; 115 ¡ 124:
0
[14] Sahay, R. and C. Vegh, 1995, Dollarization in transition economies: evidence and
policy implications, IMF Working Paper 95/96.
[15] Savastano, M., 1996, Dollarization in Latin America: recent evidence and policy issues,
in: P. Mizen and E. J. Pentecost, eds., The macroeconomics of international currencies:
theory, policy, and evidence (Edward Elgar, London).
[16] Shi, S., 1995, Money and prices: a model of search and bargaining, Journal of Economic Theory 67; 467 ¡ 496:
[17] Stockman, A., 1980, A theory of exchange rate determination, Journal of Political
Economy 88; 673 ¡ 698:
[18] Sturzenegger, F., 1997, Understanding the welfare implications of currency substitution, Journal of Economic Dynamics and Control 21; 391 ¡ 416:
[19] Svensson, L., 1985, Currency prices, terms of trade and interest rates, Journal of
International Economics 18; 17 ¡ 41:
[20] Townsend, R., 1980, Models of money with spatially separated agents, in: J. H.
Kareken and N. Wallace, eds., Models of monetary economies (Fed. Reserve Bank,
Minneapolis)
[21] Trejos, A. and R. Wright, 1995, Toward a theory of international currency, mimeo
Northwestern University.
25
[22] Uribe, M., 1997, Hysteresis in a simple model of currency substitution, Journal of
Monetary Economics 40; 185 ¡ 202:
[23] Zhou, R., 1997, Currency exchange in a random search model, Review of Economic
Studies 64; 289 ¡ 310:
26