17

where r. = ith divisia monetary aggregate:

t
Spe peje Me Meee}
Tse = current-period user cost of the jth component;
Te = px(R,- v5 Ct TLR, tT
Py = true cost-of-living index;
R. = maximum available expected holding-period yield in the economy ;
THe = own current~period holding yield on component j;
T = marginal tax rate; and
Me = jth component of the ith monetary ageregate!?

According to equation (12), the growth rate of the divisia monetary aggregate is
a weighted-geometric average of the growth rates of the different components
included in the aggregate; the weights change over time and they represent the
expenditure share of the jth monetary component in the ith monetary aggregate.

The data for divisia monetary aggregates are available from the Federal
Reserve Board on request; estimates of monthly divisia monetary aggregates for
the period 1969-1980 can be found in Barnett and Spindt (1982). Data for nominal
GNP, its deflator, and the 90-day U.S. CDs interest rate come from the data files
of the Multi-Country Model of the Federal Reserve Board. The definition of

foreign return used in this paper, r*, is the foreign interest rate plus the

expected depreciation of the domestic currency:

rs (C+i# TE Ce. d/e,) - 1,

where


34

where o. = variance of the log of monetary holdings across individuals,
Oe = variance of the log of nominal income across individuals, and

oe = variance of the log of the price level across individuals.

It seems plausible to postulate that changes in a, are positively correlated with
the variance of inflation, and the latter is in turn positively correlated with

the inflation rate (Marquez and Vining 1984). Thus if one = BAlnP , then

ain) 5 ,)/Ped = a+ a, Ain[()¥,,)/P] - a,A InP
j j

where a = (l-a,)a + or. /2 - ayo. /25 a> B(1-a,)0 provided that a,<5

and n=growth rate of population.


ll

and currency substitution is said to exist if the coefficient associated with
exchange rate expectations is significantly below zero.

Cuddington (1983) has tested the narrow version of the currency substitution
hypothesis, equation (6), and has rejected this hypothesis for both the U.S and
the U.K., while accepting it for Germany. However, Cuddington's empirical
analysis suffers from serious drawbacks raising questions about the generality of
his conclusions. First, expectations of future exchange rates are assumed to be
equal to today's forward rate, which implies that the exchange risk is zero. In
addition, the work of Hansen and Hoddrick (1981) casts serious doubts on the
validity of the forward exchange rate as an expectation model. Second, the
estimated coefficient on the lagged dependent variable is equal to one; this
estimate implies a zero speed of adjustment, or alternatively, that changes in
money holdings are related to the levels of the explanatory variables. These
findings are inconsistent with the underlying’ theory, even if we adopt the (very
narrow) definition of money as a non-interest bearing asset.

Finally, the test for the currency substitution hypothesis involves a joint
test for the hypotheses of no currency substitution and that the imposed exchange
rate expectation mechanism is indeed valid. Cuddington's rejection of the
hypothesis of currency substitution, seems not to recognize the joint nature of
his tests. Recognition of the serious shortcomings of Cuddington's empirical
analysis clearly limits the power of his conclusions.

Given the amount of research that has been devoted to defining money, it
seems thal: using money in its narrowest possible sense (non-interest bearing
asset) may be overlyrestrictive. There is a number of interest bearing assets
which perform the same functions that money, in its narrowest sense, performs.

Because of the restrictive nature of this definition of money, a broader view of


21

Table 1 (cont.)

Notes
4 Foreign return equals expected exchange rate depreciation.

b Foreign return equals expected exchange rate depreciation plus nominal
interest rate.

© Jarque-Bera statistic 62@)) for test of normality hypothesis; if it
exceeds 0.95, then this hypothesis is rejected.

4 p-statistic for serial independence hypothesis; if it exceeds 0.95, then
this hypothesis is rejected.

© t-statistic for homoskedasticity; if it exceeds 1.645 then this hypothesis
is rejected.

£ chow test for stability of parameters after 1980.


(1977a) studies the behavior of money demand in both Germany and the U.K. finding
that this behavior is strongly influenced by movements in foreign interest rates.
Relying on Chetty's work, Miles (1978) applies a production of monetary services
model to Canada and finds that canadians treat U.S. dollars as a good substitute
for canadian dollars; Brittain (1981) models the velocity of circulation as a
function of domestic and foreign interest rates and concludes that theic
inclusion in the explanation for velocity eliminates part of the observed
instability in its behavior; Arango and Nadiri (1981) include foreign interest
rates and exchange tates as explanatory variables in modeling money demand
behavior for several countries, and they find empirical support for the inclusion
of these open economy variables in their specification*

Although these papers have examined the question of currency substitution in
different ways, all of them rely on official estimates of money holdings which,
as the work of Barnett indicates, imply an infinite elasticity of substitution
between different monetary assets. In particular Barnett (1980, 1981) argues
that for a monetary aggregate to be economically meaningful, it must rest on
economic optimization principles. Consequently, the measurement of money
balances ought to recognize that individuals minimize the cost of obtaining a
given level of monetary services provided by a variety of assets by trading off
the different attributes of several assets, given their associated ovportunity
costs. The resulting optimal asset holdings are (functionally) aggregated to
obtain what Barnett denotes economic monetary aggregates. Only under very
special circumstances the economic monetary aggregate is equal to a linear
unweighted sum of asset values, which is the type of aggregation rule used for
officially published estimates of money holdings. Barnett (1980, 1981) and

Barnett, Offenbacher, and Spindt (1984) have investigated the behavior of money


32
TABLE A4

Parameter Estimates for U.S. Money Demand
Broad Interpretation of Currency Substitution
Rational Expectation Model
1974.1 - 1982.3
(t-statistics)

Divisia Aggregates

Explanatory Variables 1 2 3
Constant 0.017 0.028 0.026
(3.5) (5.6) (5.9)
Income 0.126 0.259 0.254
(1.0) (2.1) (2.3)
Domestic return -0.001 -0.002 -0.002
(-0.5) (-2.2) (-2.1)
Foreign return® -0.003  -0.007 0.006
(-1.8) (-4.4) (-4.3)
Inflation -0.985 1.678 71.559
(-4.1) (-6.8) (-7.1)
z 0.42 0.75 0.76
D.W. 2.26 1.39 1.66
S.E.R. 0.008 0.008 0.007
Normality: (JB) 0.91 0.21 0.20
Serial Independence: F(4,28) 0.44 0.80 0.64
Homoskedasticity: ARCH-t 0.05 -0.21 -0.79
Chow Test: F(8,23) 0.20 0.93 0.63

4Foreign return is defined here as the (rational expectation)
realized depreciation of the dollar plus the foreign interest
rate.


18

i* = foreign interest rate index;
Y
we nh 4
2g
i” = 90-day interest rate of country &

Ee (ena) = one period ahead expected exchange rate based on today's information;

es a
7 MEE) Ds

E,(ery) = 90-day expected exchange rate (dollar/currency 2) for country 2%;
e = spot exchange rate index;
wo
= mee?*) an
g .
eft = spot exchange rate (dollar/currency £) index for country 23

4.3 Testing of Error Properties

Nearly all econometric analyses of money demand behavior rest on the notion
that the classical properties for the error tern do indeed hold. While the
hypothesis of serially independent errors is usually tested, the hypotheses of
homoskedasticity and normality are generally taken for granted. This paper tests
for the validity of the classical assumptions for ordinary least squares— ,
namely, normality, serial independence, and homoskedasticity. In addition to
these tests, the paper also presents Chow tests for the hypothesis of structural
stability of the parameters.

Testing for the hypothesis that the errors behave according to the normal
distribution relies on the Jarque-Bera statistic (Jarque and Bera 1980), which
compares the extent to which the skewness and kurtosis of the distribution of

estimated residuals represent significant deviations from the normal


24

by using the economic monetary aggregates developed by Barnett.

Relying on a traditional formulation of money demand holdings for open
economies, our empirical analysis suggests that money demand behavior in the U.S.
for the period 1974-1982 has been strongly influenced by foreign interest rates
and expected movements in the value of the dollar. Thus it would seem that
foreign exchange considerations could potentially influence the conduct of
monetary policy to the same degree that domestic considerations do.

This conclusion, provocative as it may be, is preliminary because our
analysis rests on a number of simplifying assumptions which need not hold in
practice. Specifically, the assumed absence of simultaneity biases and the
postulated within-one-quarter response of money holdings are restrictive enough
to limit the generality of our findings; further research in these areas Is

clearly needed.


20

Table 1
U.S. Money Demand
Estimate of Currency Substitution Parameter
Narrow and Broad Interpretation
Forward and Rational Expectation Models
(t-statistic)

Statistical Diagnostics

Foreign

Return x2

z.pS___s.14 _arcu® —cnow’

Narrow Interpretation®

Forward Market

Ty -0.002 9.41 0.93 0.11 0.59 0.52
(-0.4)
T) 0.002 0.60 0.42 0.76 0.34 0.63
(0.3)
T3 0.002 0.62 0.61 0.49 0.34 0.38
(0.4)
Rational Expectations
Ty -0.075 0.45 0.88 0.55 0.51 0.51
(-2.2)
Tr -0.064 0.62 0.12 0.71 0.48 0.77
(-1.5) .
Ty -0.058 0.64 0.06 0.38 0.31 0.48

(-1.5)

Broad Interpretation”
Forward Market

Ty -0.004 0.48 0.89 0.46 0.19 0.33
(-2.1)

QT) -0.007 0.73 0.05 0.75 -0.30 0.98
(-4.0)

qT; -0.006 0.73 0.01 0.41 -0.70 0.77
(-3.7)

Rational Expectations

T! -0.003 0.42 0.91 0.44 0.05 0.20
(-1.8)

TT) -0.007 0.75 0.21 9.80 -9.21 0.93
(-4.4)

Ts; -0.006 0.76 0.20 0.64 -0.79 0.63

(-4.3)



33
Appendix B

Aggregation of Micro Money Demands: An Application of Envelope Aggregation
Assume for simplicity that the individual's demand function is
lot .. 2 + al InY, + (l= .
jit satay nye (1 aj )inP Bel

where j subscript refers to individuals.

Aggregation across Ne individuals yields

C/N.) et ie =a) + a QM) LIO¥ 5, + (oa UMM) La 5g B.2

However, the aggregate money demand equation subject to estimation is

CN )19C )ea+ 21 (1/N,) IRC j-) + Ca) C/N, Ine.

One possible way to reconcile both specifications is by assuming that Tie Yee

and Paes are lognormally distributed. The resulting aggregate money demand

equation is

ral CF, /P I = [a

2 2
+ (i-a,) IAN, + (oe /2) - ao, /2)] + B.3
j

0

2
+ ata i/?) - (vay )oo/2,


15

delivery in t+l, and e.

+1 is the realized spot exchange rate index in period ttl.

According to the first expectation mechanism, the forward exchange rate ef is

ttl
the best predictor of future exchange rates. This approach has been criticized
on the basis that it does not recognize the existence of risk premium, among
other reasons (see Tryon 1983). Nevertheless, it is considered here because of
its widespread use in the literature!” The second mechanism rests on the rational
expectations hypothesis, where today's expectations are unbiased predictors of
future exchange rates. The rational expectation model of exchange rate
determination has been empirically used by Symansky, Haas, and Hooper (1981) and
Dooley and Isard (1982).

The second difficulty in estimating equation (8) is the sensitivity of the
results to the spurious correlations characteristic of most time-series data. In
addition, the construction of divisia indexes induces serial correlation in the
error term. This difficulty is handled here by differencing equation (8), which

yietds!8

(9) Aln(T, ./P.) = ay + a, Aln(¥,/P,) + aaryt aA((1+1*)(E (e.,, /e,)) +
+ a, ACE, Ce, 4, )/e,) + a, InP, + Ve

Finally, earlier attempts at estimating an equation like (9) have
encountered milticollinearity problems because of the intercorrelation between
the three rates of return. To avoid this problem, the present analysis follows
Daniel and Fried (1983) and imposes covered interest arbitrage to eliminate one
race of return.

The final specification for money demand behavior under the assumption that


b= (dy seresds)s and

6(D) = functional aggregator of monetary services of domestic assets.

The solution to this problem yields a set of domestic asset demand equations,
df = 4, (ty » 5*), the parameteres of which can be estimated because data on Na
and D are available. These parameter estimates are then used in the functional
aggregate, 6(D), to obtain an estimated time series of 5((D*Cx,)) = ge » and to
estimate the user cost of domestic monetary services, 1; mW).

Although estimates of 6* could be used to test the currency substituion
hypothesis, they rely on the choice of a specific functional form for 6(D). As a
result, it might be difficult to establish whether the influence of foreign
variables on domestic money holdings is due to recognition of individuals'
optimizing behavior or whether it is due to the choice of a specific functional
form for 6. To avoid this “identification” problem, Barnett introduces the
divisia monetary aggregate, which is a second approximation to any aggregate

function in discrete time:

8(D*)

TOD*, ta)>
where [(D*, ty ) = divisia aggregate of domestic monetary servies.®

Data problems are particularly serious for monetary services rendered by
foreign assets. In principle, an optimizing problem similar to (4) would yield a
set of foreign asset demand equations which could be used to estimate the
associated parameters. However, this approach requires time series for data on
countries’ bilateral holdings of foreign assets, which are not generally
available; although the total (accounting) aggregates for domestic holdings of
foreign assets are known, use of these would imply an infinite elasticity of

substitution accross all foreign assets.


30
TABLE A2

Parameter Estimates for U.S. Money Demand
Narrow Interpretation of Currency Substitution
Rational Expectation Model
1974.1 - 1982.3
(t-statistics)

Divisia Aggregates

Explanatory Variables 1 2 3
Constant 0.018 0.031 0.028
(3.8) (5.0) (5.3)
Income 0.134 0.266 0.261
(1.1) (1.7) (1.9)
Domestic return -0.001 -0.003 ~0.003
(-0.7) . (-2.6) (-2.4)
Foreign return? -0.075 -0.064 -0.058
(-2.2) (-1.5) (-1.5)
Inflation 1.044 1.811 1.672
(-4.4) (-6.0) (-6.9)
2 0.45 0.62 0.64
D.W. 2.49 1.24 1.45
S.E.R. 0.007 0.009 0.098
Normality: (JB) 0.88 0.12 0.06
Serial Independence: F(4,27) 0.55 0.71 0.38
Homoskedasticity: ARCH-t 0.51 0.48 0.31
Chow Test: F(8,22) 0.51 0.77 0.48

4Foreign return equals the (rational expectation) realized
depreciation of the dollar.


27

19, The construction of the ith divisia index includes only the monetary
components of the ith official monetary aggregate. For example, TY includes the

same components that Ml does.

Federal Reserve Board.

The construction of weighted averages for foreign
variables rests on the methodology developed for the Multi-Country Model of the

The weights used here are

4& Country Yg Mee

1 Canada 0.165 share of U.S. imports from Canada
2 England 0.215 share of U.S. imports from England
3. Germany 0.375 share of J.S. imports from Germany
4 Japan 0.165 share of U.S. imports from Japan


these issues are handled axiomatically--that is, based on certain properties
(liquidity, interest earning, maturity), monetary instruments are classified as
belonging to one monetary aggregate or to another. These components are then
added up and the resulting total equals the estimate of money holdings for the
aggregate®

The chief drawback of these estimates is that they rest on the assumption
that individuals' preferences over assets possess an infinite elasticity of
substitution, an unduly restrictive assumption for monetary policy analysis. To
this end, Barnett (1980) has developed monetary aggregates that rest on
individuals' optimizing economic behavior and thus eliminates the need for using
the assumption of infinite elasticity of substitution in estimates of money
holdings. Our purpose here is to apply Barnett's approach to deriving an open
economy money demand function.

The point of departure of our analysis is the assumption that individuals
optimize labor supply decisions, commodity purchases, and asset holdings subject
to an intertemporal budget constraint under a weakly separable utility function.
As Barnett (1981) has formally shown, this optimizing behavior yields an optimal
level of monetary services, *, which is related to the available monetary assets

: : 7
via a functional aggregator U :

(1) Me Wd ye dos Cyrene bie dD,

where

d. = domestic holdings of the ith domestic monetary asset, i = l,...,s;
i

c5 = domestic holding of country j's non-interest bearing monetary asset,

b, = domestic holdings of country j's interest bearing monetary assets, where

jel,...,n.


demand using economic monetary aggregates by examining a number of issues

including causality between money and income, structural parameter stability, and
the dynamic specification of money demand behavior. However, these analyses rest
on closed--economy explanations of money demand behavior with no allowance for
foreign exchange considerations.

Even though the work on both economic monetary aggregates and currency
substitution has enhanced our understanding of the behavior of money demand, the
research effort in these two areas has proceded independently of each other. On
the one hand, proponents of the economic monetary aggregates give little or no
consideration to the influence of foreign variables in modeling money demand. On
the other hand, the literature on currency substitution treats monetary
aggregates as if individuals’ elasticities of substitution among different assets
were infinite. This paper combines both approaches into a unified explanation of
money demand behavior. To this end, section 2 applies the framework of economic
monetary aggregates to develop a domestic money demand function allowing for
foreign exchange considerations. Section 3 reviews the existing empirical work
on money demand modeling for open economies. Section 4 presents empirical
estimates of money demand behavior for the U.S. using economic monetary
aggregates while recognizing open economy considerations. The empirical findings
indicate that currency substitution is an important consideration in explaining

U.S. money demand behavior. Finally, section 5 contains our conclusions.

2. DIVISIA MONETARY AGGREGATES AND CURRENCY SUBSTITUTION

The definition of money has been the subject of extensive research over the
years. Specifically, issues such as what serves as money, what are different
degrees of moneyness, and what are the alternative money substitutes play an

important role in the design and implemetaion of monetary policy? In practice,


16

money earns no explicit interest (narrow interpretation of currency substitution)

is
(10) ain(T, ./P,) sat a, 4In(¥, /P,) + ay dr +
+ a, 4B, (e.4,)/e,) + a A InP, + Yeo

where a, < 0 indicates the existence of currency substitution. If the definition
of money is relaxed to include interest bearing assets (broad interpretation of

currency substitution), then the specification is

(11) aln(T,,/P,) = dy + B, Aln(yY, /P.) + 8, ar, +

+ B,dmax {((141*)(E,(e,,,)/e,))s CE, (e.4,)/e,) } + 6,4°10P tv,

and currency substitution is said to exist if By is significantly less than
zero. As indicated earlier, the tests for either interpretation of currency
substitution are conditional on the validity of the expectation model assumed

during estimation.

4.2 Data Construction
The construction of the ith divisia monetary aggregate rests on the work of

Barnett (1980), and is computed according to the following expression:

fa. fm (1/2)(s 4+ Sy e-1

(12) rat je eV ,

wes


6
where Ts = user cost of monetary services provided by domestic assets, and

TM% = user cost of monetary services provided by foreign assets.

The solution to this problem yields the optimal level of monetary services of
both domestic and foreign assets, 6* and $* respectively, and the user cost of

aggregate monetary services, mW

o* = S(m, 7, Me),

ar)

oe = O(m5, 1, MH),

TM = (1s, ", ).

If data on monetary services 5* and $* were available, then one could estimate
the parameters associated with these two functions to determine the extent of
currency substitution. Although these monetary services are unobservable, the
monetary aggregation framework of Barnett permits us to separate the problem of
measuring these services from the problem of modeling their behavior.
Specifically, it is possible to apply Barnett's monetary aggregation framework
while recognizing the influence of open economy considerations on the behavior
of 6*,

To estimate 6*, individuals are assumed to find the minimum cost portfolio
of domestic monetary assets subject to the constraint that the resulting

aggregate level of monetary services is at least as high as 6*, Formally,

i '
min "4 D

(4) subject to:
8(D)>6*,

where Ty = vector of opportunity costs for domestic assets,


22
rate expectations models--forward and rational. Also shown in table 1 are the
statistical diagnostics to test the maintained hypotheses associated with the
error term--normality, serial independence, and homoskedasticity, and a Chow test
for the hypothesis that the parameters have remained stable over the last two
years of the estimation period. Tables Al through A4 of appendix A display all
the coefficient estimates associated with each specification shown in table 1.

According to the results of this table, the narrow view that foreign
currency is held for speculative purposes is not supported by the data when the
exchange rate expectations rely on the forward market. More specifically, the
currency substitution coefficient is not significant and it has the wrong sign in
two of the three cases. This lack of support for the currency substitution
hypothesis is broadly consistent with Cuddington's (1983) findings. However, if
exchange rate expectations are assumed to be rational, then the narrow
interpretation of the currency substitution hypothesis receives strong support
from the data; the sign of exchange rate expectations is negative for each
divisia monetary aggregate, and quite significant for the aggregate T, which
includes only currency and highly liquid assets. Furthermore, according to the
values taken by the statistical diagnostics, the maintained hypotheses about the
statistical properties of the error term cannot be rejected by the data; also,
according to the Chow test, the specifications display structurally stable
parameters.

The results for the broad interpretation of currency substitution, shown in
table 1, are also highly supportive of the currency substitution hypothesis.
Specifically, the coefficient for the foreign return variable is negative and
highly significant for each divisia monetary aggregate and for each of the
exchange rate expectation models considered here. Thus the empirical results are
fairly robust. Furthemore, it is not possible to reject the hypothesis that the

residuals in each equation behave according to the maintained assumptions of


International Finance Discussion Papers

Number 257

July 1985

CURRENCY SUBSTITUTION AND THE NEW DIVISIA
MONETARY AGGREGATES: THE U.S. CASE

by

Jaime Marquez

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished materials)

should be cleared with the author or authors.


been the subject of considerable empirical research!” However, it is only
recently that foreign exchange considerations have gained significant attention
in empirical analyses of money demand behavior.

Intuitively, the greater interdependency of the world economy and the advent
of a flexible exchange rate system, has induced individuals to maintain a
portfolio including more than one national currency in order to minimize the cost
of carrying out international transactions. As a result, financial developments
abroad affecting either foreign interest rates or exchange rates (and their
expectations), will affect the optimal portfolio mix which includes holdings of
domestic money. Consequently, in the presence of currency substitution, monetary
policies abroad could influence domestic monetary policy not through fluctuations
in the domestic money supply but rather by shifting the (closed-economy) money
demand function. This point, first suggested by Miles (1978), has served as the
basis of McXinnon's proposal for worldwide monetary policy coordination!!

While the notion of currency substitution is intuitively plausible in
principle, the empirical literature is sharply divided on its importance in
explaining aggregate money demand behavior. This disagreement stems from the
absence of a commonly accepted definition of currency substitution and by the
different empirical implementations of whatever definition is adopted.
Specifically, the possibility of currency substitution has been examined in two
different contexts. In the first, developed by McKinnon (1982), currency
substitution is said to exist if the growth in world money supply is a better
predictor of U.S. price inflation than is U.S. money growth!? In the second,
which is the focus of this paper, currency substitution is embedded in a
portfolio balance model along with other domestic and foreign assets (see
Cuddington 1983). In this context, currency substituion is said to exist if

foreign exchange considerations--that is, foreign interest rates and


To bypass this data problem, the present analysis relies on duality theory.

Specifically, it is assumed that the economic aggregate of foreign assets obeys a

Cobb-Douglas specification

a Yi m vi m
gaat oo sal (ci +b)", with J y= 1,
isl isl isl

which implies, by duality theory, that the user cost for monetary services of

foreign assets is (Barnett 1981, p.210)

a Yo:
TM, = BM (min(n., m )) +,
> : c. b.
i=l 1 L
where
TM,. TM user cost of holding non-interest bearing monetary assets of country i,
i
TMm = user cost of holding interest bearing monetary assets of country i.
i
In other words, individuals are assumed to hold the asset with the lowest user
cost, or alternatively, the asset with the highest return. Notice that the
assumption of infinite elasticity of substitution between domestic holdings of
country i's money and country i's bonds does not imply that assets of country i

are perfect substitutes for assets of country j, or that domestic assets and any

: 9
country's assets are perfect substitutes for each other.

3. MONEY DEMAND MODELING IN OPEN ECONOMIES
One of the key behavioral relationships of macroeconomic analysis is the
willingness of individuals to hold domestic money balances. Because of its

importance for the design of stabilization policies, the demand for money has


29

TABLE Al

Parameter Estimates for U.S. Money Demand

Narrow Interpretation of Currency Substitution
Forward Market Expectation Model

1974.1 - 1982.4
(t-statistics)

Divisia Aggregates

Explanatory Variables Ty QT) Ts;
Constant 0.021 0.029 0.027
(4.2) (5.0) (5.2)
Income 0.093 0.274 0.273
(0.7) (1.7) (2.0)
Domestic Return -0.001 -0.004 -0.003
(-1.0) (-2.8) (-2.6)
Foreign return® -0.002 0.002 0.002
(-0.4) (0.3) (0.4)
Inflation 1.145 1.762 1.615
(-4.6) (-6.0) (-6.2)
x 0.41 0.60 0.62
D.W. 2.25 1.26 1.43
S.E.R. 0.008 0.010 0.009
Normality: (JB) 0.93 0.42 0.61
Serial Independence: F(4,28) 0.11 0.76 0.49
Homoskedasticity: ARCH-t 0.59 0.34 0.34
Chow Test: F(8,23) 0.52 0.63 0.38

Foreign return equals the forward premium


28

APPENDIX A

Parameter Estimates of Alternative Money Demand Specifications

This appendix provides a brief description of the Parameter estimates for
all the money demand equations presented in table 1. All of the parameters have
the expected signs, except in table Al where the sign of the coefficient
associated with the foreign return is positive. The income elasticity ranges
from 0.09 to 0.27, which differs significantly from Goldfeld's results. Indeed,
it would be very surprising if using a fundamentally different monetary aggregate
one were to obtain the same estimates as those using linear unweighted sums of
monetary components. Moreover, our results are particularly close to those of
Barnett, Offenbacher and Spindt (1984), who employ divisia monetary aggregates.
Furthermore, using the same estimation period the latter encounter negative
income elasticities, a result that is reversed here by the inclusion of foreign
exchange considerations. Also, as pointed out by Benjamin Friedman, the
coefficient associated with the foreign return generally exceeds the coefficient
associated with the domestic return. This is because the computation of the
domestic monetary divisia aggregate already internalizes substitution effects

resulting from changes in interest rates. Consequently, the domestic interest

rate effect could be smaller than the foreign interest rate effect.


The aggregate M* is not observed directly because the parameters associated
with U(.) are not known a priori: thus they need to be estimated. To this end,
individuals are assumed to select their portfolio in a multistage decision
process. In the first stage, individuals determine the aggregate levels of
monetary services provided by both domestic and foreign asset holdings;
subsequent optimizing stages determine the precise portfolio mix. In other
words, optimizing behavior is assumed to begin with decisions about broad
aggregates, such as domestic and foreign asset holdings, and to terminate with
decisions about holding assets with detalied characteristics, such as a 90-day
bond issued in country j with an interest rate r(j).

As the first step in this sequential process, it is assumed that the
arguments of the function U can be partitioned in such a way as to yield the

following weakly separable functional aggregator:
(2) Me = U(S(d),.-..4.), G1 (oy, Byes oie» b 1).

where 6 = functional aggregator for monetary services provided by domestic

assets, and

= functional aggregator for monetary services provided by foreign assets.

To determine the optimal levels of monetary services provided by both
domestic and foreign asset holdings, 6 and $ respectively, individuals are
assumed to minimize the cost associated with holding such assets, subject to the
condition that the resulting aggregate of monetary services does not fall below
M*:

min 155 + To

(3) subject to:

uCé, $) > M*,


19

distribution. In particular,

2 3 2 2 2
JB = Tlus/(6uz) + (1/24) (uy/u2-3) ] ~ x (2),

T ,
where T = sample size, and yp, = ) a? / T; the first term of the JB statistic
t=1

represents the skewness and the second represents departures of the estimated
kurtosis from the kurtosis associated with the normal distribution; both measures
are derived for the empirical distribution of the residuals, u.

The test for homoskedasticity rests on the work of Engle (1982) on
autoregressive conditional heteroskedasticity (ARCH) disturbances. Specifically,
the model used to test for homoskedasticity is

ea fi Deyey a;
tl t-1 9 L t-1
the null hypothesis for homoskedasticity cannot be rejected if Y,70, which is
tested with a t-statistic. Finally, serial independence in the residuals is
tested with an F-statistic for the null hypothesis that all the coefficients in

an autoregressive form of order four are equal to zero.

4.4 Empirical Results

The parameters associated with equations (10) and (11) are estimated using
ordinary least squares with quarterly data from 1974-1 to 1982-4 for the U.S.,
which includes the period of floating exchange rates. Table 1 displays the
coefficients associated with the two interpretations of currency substitution--
narrow and broad, for each of the three divisia monetary aggregates--I,, Ty, and

Ts, and for each of the exchange


36

Enzler, J., L. Johnson, and J. Paulus, 1976, Some problems of money demand,
Brookings Papers on Economic Activity, 1; 261-280.

Ewis, N., and D. Fisher, 1984, The translog utility function and the demand for
money in the United States, Journal of Money, Credit, and Banking, 16, 34-52.

Feige, &., and D. Pearce, 1977, The substitutability of money and near-monies: A
survey of the time-series evidence, Journal of Economic Literature, 15, 439-469.

Friedman, B., 1978, Crowding out or crowding in? Economic consequences of
financing government deficits, Brookings Papers on Economic Activity, 2, 593-
641.

Friedman, B., 1985, Portfolio choice and the debt-to-income relationship,
American Economic Review, 75, 338-343.

Godlfeld, S., 1973, The demand for money revisited, Brookings Papers on Economic
Activity, 3, 577-638.

Goldfeld, S., 1976, The case of the missing money, Brookings Papers on Economic
Activity, 3, 683-730.

Goldstein, H., and S. Haynes, 1984, A critical appraisal of McKinnon's world
money supply hypothesis, American Economic Review, 74, 217-224.

Hamburger, M., 1966, The demand for money by households, money substitutes, and
monetary policy, Journal of Political Economy, 74, 600-623.

Hamburger, M., 1977a, The demand for money in an open economy: Germany and the
U.K., Journal of Monetary Economics, 3, 25-40.

Hamburger, M., 1977b, Behavior of the money stock: Is there a puzzle? Journal of
Monetary Economics, 3, 265-288.

Hansen, L., and R. Hodrick, 1981, Forward exchange rates as optimal predictors of
future spot rates: An econometric analysis, Journal of Political Economy, 88,
829-853.

Jarque, C.E., and.A. Bera, 1982, Efficient tests for normality, homoskedasticity,
and serial independence of regression residuals, Economic Letters, 6, 255-259.

Judd, J., and J. Scanning, 1982, The search for a stable money demand function,
Journal of Economic Literature, 20, 993-1023.

Johnson, K., 1982, The demand for swiss monetary assets, International Finance
Discussion Papers, no. 210, Board of Governors of the Federal Reserve System.

King, D., B. Putnam, and D. Wilford, 1978, A currency portfolio approach to
exchange rate determination: exchange rate stability and independence of monetary
policy, in B. Putnam and D. Wilford, eds., The Monetary Approach to International
Adjustment, (Praeger, New York).

Leamer, E., and R. Stern, 1970, Quantitative International Economics, (Allyn and


37
Bacon, Boston).

Marquez, J., and D. Vining, 1984, Inflation and relative price behavior: A survey
of the literature, in M. Ballabon, ed., Economic Perspectives: An Annual Survey
of Economics, 3 (Harwood Academic Publishers, New York).

McKinnon, R., 1982, Currency substitution and instability in the world dollar
standard, American Economic Review, 68, 428-436.

McKinnon, R., 1984, An international standard for monetary policy stabilization,
Policy Analysis in International Economics, no. 8, (Institute for International
Economics, Washington, D.C.).

Meese, R., and K. Rogoff, 1983, Empirical exchange rate models of the seventies:
Do they fit out of sample? Journal of International Economics, 14, 3-24.

Miles, M., 1978, Currency substitution, flexible exchange rates, and monetary
policy, American Economic Review, 72, 320-333.

Radcliffe, C., A. Warga, and T. Willet, 1984, Currency substitution and
instability in the world dollar standard, American Economic Review, 74, 1129-
1131.

Samuelson, P., 1983, Rigorous observational positivism: Klein's envelope
aggregation; thermodynamics and economic isomorphisms, in F.G. Adams and B.
Hickman, eds., Global Econometrics: Essays in Honor of Lawrence Klein, (MIT
Press, Cambridge).

Stekler, L., and P. Isard, 1985, U.S. international capital flows and the dollar:
Recent developments and concerns, mimeo, Board of Gevernors of the Federal
Reserve System.

Symansky, S., R. Haas, and P. Hooper, 1981, Empirical tests of exchange rate
determination in a portfolio balance model under alternative expectation
hypotheses, paper presented at the Winter Meetings of the Econometric Society,
‘ashington, D.C.

Tanzi, V., and M. Blejer, 1982, Inflation, interest rate policy, and currency
substitution in developing economies: A discussion of the major issues, World
Development, September, 781-790.

Tryon, R., 1983, Small empirical models of exchange market intervention: A review
of the literature, Staff Studies no. 134, Board of Governors of the Federal
Reserve System.

Varian, H., 1984, Microeconomic Analysis, (W.W. Norton, New York).

Willms, M., 1971, Controlling money in an open economy: The German case, Federal
Reserve Bank of St. Louis Economic Review, 4, 10-27.


25
Footnotes

1. See McKinnon (1982); King, Putnam, and Wilford (1978); Boyer (1978); and
Miles (1978). Although one would expect currency substitution to be intimately
related to the effectiveness of official intervention in the foreign exchange
market, this interconnection has not been established yet. An issue not
investigated here is the extent to which substitution between domestic debt and
domestic equity affects currency substitution. The former type of substitution
has been the subject of analysis by Friedman (1978, 1985).

2. See Feige and Pearce (1977) who survey the work on the extent to which
domestic assets are substitutes for each other; also, the literature on money
demand instability, surveyed by Judd and Scadding (1982), argues that one of the
reasons for the observed demand instability is the high degree of
substitutability between money and the more recent financial instruments such as
NOW accounts, Repurchase Agreements, etc.

3. Nevertheless, Leamer and Stern (1970), and Willms (1971) recognized the
influence cf foreign exchange considerations on the behavior of domestic money
demand.

4. Cuddington (1983) and Bordo and Choudri (1982) have examined the currency
substitution hypothesis for a number of countries without finding empirical
support for it. Goldstein and Haynes (1984) and Radcliffe, Warga, and Willet
(1984) have also rejected the hypothesis of currency substitution for the U.S.

5. See Barnett (1980) and Hamburger (1977b).

6. There are exceptions to this proceedure: Ewis and Fisher (1984), Chetty
(1969), and Miles (1978).

7. Although the original formulation of the theory behind economic monetary
aggregates excluded foreign monetary assets, the theoretical arguments are
general enough to include these assets.

8. Notice that the aggregator of monetary services, 6(Q), depends only on
quantities of monetary assets whereas T(Q, 44) depends on both prices and
quantities. However, since [ = 6 and the latter follows from optimizing, then [
will change only when the quantities of monetary assets change.

9. An implication of this assumption is that individuals’ holdings of non-
interest bearing monetary assets will be zero, since the returns to holding them
(the expected depreciation of the domestic currency) is always smaller than the
return to holding interest bearing assets. This assumption is also used by
Dornbusch and Fischer (1980). The empirical evidence presented by Stekler and
Isard (1985) reveals that banks' claims payable in foreign currency at the end of
1984 was $10.7 billion, which probably includes interest bearing assets, is the
highest since 1981, This is a very small number when compared to the stock of
financial assets.

10. This research has focused primarily on establishing the quantitative
importance of income and relative rates of returns of domestic assets in


1. INTRODUCTION

The purpose of this paper is to examine the extent to which the behavior of
aggregate money holdings is influenced by foreign exchange considerations, an
influence that has been labeled as currency substitution. Intuitively, one would
expect foreign exchange considerations to influence domestic money holdings
since, as a result of the greater {ntegration of international financial markets,
individuals generally face a choice not only between domestic money and domestic
bonds, but also between foreign assets and domestic assets. Because holdings of
these assets are interdependent, changes in either foreign interest rates or
exchange rates would affect the optimal portfolio mix with a corresponding impact
on domestic money holdings. .

Knowledge of the extent to which monies of different countries can
substitute for each other is important for the design and implementation of
monetary policy. For example, it is conceivable that the intended effect of an
open market operation would not materialize because of offseting portfolio
changes taking place through currency substitution! That individuals could
rebalance their portfolio to offset a monetary policy decision has been
recognized in the literature for some time? But the focus of much of the
literature has been limited to substitutability between domestic money and other
domestic assets without recognizing that foreign assets can also serve as
substitutes for domestic money?

With the advent of both the flexible exchange rate system and the apparent
instability of money demand behavior in the U.S., some investigators have argued
that failure to recognize the influence of foreign exchange considerations in
explaining money demand behavior might result in a misspecified money demand

equation which could potentially be responsible for the large errors in

forecasting aggregate money demand. Specifically, Hamburger


12
. : : . 13... :
currency substitution has emerged in the literature which, in effect, assumes
that interest and non-interest bearing assets of country i are highly
substitutable from the domestic agent's point of view. Consequently, aggregate

domestic money holdings are modeled as
(7) T/P = f(r, max(i* + x, x) y) = €(r, i* + x, y),

where i* + x is the rate of return on foreign assets. In this context, currency
substitution is said to exist if the influence of the foreign return on domestic
money holdings is significantly below zero.)*

One common feature of all existing empirical analyses of currency
substitutability, with the exception of Ewis and Fisher (1984), is their reliance
on official estimates of money holdings--that is, unweighted sums of monetary
assets. To the extent that the literature on curréncy substitution aims at
establishing the extent to which domestic and foreign assets are substitutes, it
seems inappropiate to impose the condition that all domestic assets are perfect
substitutes for each other, but something less than perfect substitutes for

foreign assets.

4. EMPIRICAL ANALYSIS
4.1 Functional Form

The simplest, and perhaps most convincing way of establishing the existence
of currency substitution is to take a well-known functional form and estimate it
allowing for foreign exchange considerations. Thus the empirical implementation
of our analysis takes Goldfeld's (1973) specification of aggregate money demand
behavior and extends it here to include foreign exchange considerations. One
possible way to carry out this extension is to postulate that aggregate money

holdings behave according to


14

associated with an increase in the dispersion of relative prices, which reflects
greater price uncertainty and thus a higher financial risk associated with
holding money. Second, if individuals adjust their money holdings according to
an error correction mechanism, then the inflation rate will be part of the
specification (Baba, Hendry, Starr 1985).

The inclusion of the inflation rate as an explanatory variable here rests on
the application of an envelope aggregation theorem (Samuelson 1983) to
individuals’ money demand functions. The application of this theorem is
developed in appendix B to this paper.

Three difficulties arise in estimating the parameters associated with
equation (8). First, the estimation requires information on exchange rate
expectations, which are not observable directly. Although the modeling of these
expectations has been the subject of a considerable amount of research, both
empirical and theoretical, an analysis of the existing literature reveals that
little conseasus exists as to what is the most appropriate expectation mechanism
for exchange rates}? As a result, the test for currency substitution involves a
joint test for the hypotheses of currency substitution and for the validity of
the model for exchange rate expectations.

Although the present analysis does not resolve this identification problem,
it examines the sensitivity of the parameter estimates for two expectation

mechanisms y6

£
(1) Forward market: Elena) = hyp and

(ii) Rational Expectations: Ee) = eup

£
where rel is the forward exchange rate index (U.S. $/foreign currency) for


Abstract

The purpose of this paper is to examine the extent to which the
behavior of aggregate money holdings is influenced by foreign exchange
considerations, an influence that has been labeled as currency
substitution. Knowledge of the extent to which monies of different
countries can substitute for each other is important for the design and
implementation of monetary policy. However, existing empirical analyses
of currency substitutions rest on official estimates of money holdings
which imply an infinite elasticity of substitution between different
monetary assets. Analyses of ecomomic monetary aggregates do not impose
the assumption of infinite elasticity of substitution, but no foreign
exchange considerations are allowed. This paper combines both approaches

into a unified explanation of money demand behavior.


35

References

Arango, S., and M. Nadiri, 1981, Demand for monéy in open economies, Journal of
Monetary Economics, 7, 69-83.

Baba, Y., D. Hendry and R. Starr, 1985, U.S. money demand: 1960-1984, paper
presented at NBER Conference on Money and Financial Markets, April 26, 1985.

Barnett, W., 1980, Economic monetary aggregates: An application of index number
and aggregation theory, Journal of Econometrics, 14, 11-48.

Barnett, W., 1981, Consumer demand and labor supply: Goods, monetary assets, and
time, (North-Holland, Amsterdam).

Barnett, W., and P. Spindt, 1982, Divisia monetary aggregates: Compilation, data,
and historical behavior, Staff studies no. 116, Board of Governors of the Federal
Reserve System.

Barnett, W., E. Offenbacher, and P. Spindt, 1984, The new divisia monetary
aggregates, Journal of Political Economy, 92, 1049-1085.

Blejer, M., 1981, The dispersion of relative commodity prices under very rapid
inflation, Journal of Development Economics, 9, 347-356.

Bordo, M., and E. Choudri, 1982, Currency substitution and the demand for money:
Some evidence for Canada, Journal of Money, Credit, and Banking, 14, 48-57.

Boyer, R., 1978, Currency mobility and balance of payments adjustment, in B.
Putnam and D. Wilford, eds., The International Approach to International
Adjustment, (Praeger, New York).

Brittain, B., 1981, International currency substitution and the apparent
instability of velocity in some western european economies and in the United
States, Journal of Money, Credit, and Banking, 13, 135-155.

Chetty, V., 1969, On measuring the nearness of near-moneys, American Economic
Review, 59, 270-281.

Cuddington, J., 1983, Currency substitution, capital mobility, and money demand,
Journal of International Finance, 2, 111-133.

Cukierman, A., 1980, Relative price uncertainty, wage indexation, and the theory
of indexed bonds, working paper no. 17-80, Foerder Institute for Economic
Research, Tel-Aviv University.

Daniel, B., and H. Fried, 1983, Currency substitution, postal strikes, and
Canadian money demand, Canadian Journal of Economics, 16, 612-624.

Dooley, M., and P. Isard, 1982, A portfolio-balance rational expectations model
of the Dollar-Mark rate, Journal of International Economics, 12, 257-276.

Dornbusch, R., and S. Fischer, 1980, Exchange rates and the current account,
American Economic Review, 70, 960-971.

Engle, R., 1982, Autoregressive conditional heteroskedasticity with estimates of
the variance of the United Kingdom inflation, Econometrica, 50, 997-1008.


23

classical least squares, which strengthens the validity of the statistical
inferences made here. The results also indicate that in five out of six cases,
the hypothesis of structurai stability cannot be rejected.

Finally, limiting our attention to the rational expectation case, the
results suggest that the proper interpretation of currency substitution--that is,
narrow or broad-~may depend on the monetary aggregate considered. To be
specific, the narrow interpretation is not supported in the higher level divisia
aggregates Ty .and iy but it is strongly supported for the divisia aggregate Mh
which includes only highly liquid components and thus it is the most appropriate
characterization of currency holdings. On the other hand, the broad
interpretation of currency substitution, general! associated with international
capital mobility, is not strongly supported for the Ty aggregate, but it is
strongly supported for the higher level divisia aggregates r and T3- The bulk
of these aggregates is made up of interest-sensitive components and therefore

they are closely associated with the notion of capital mobility.

5. CONCLUSIONS

The purpose of this paper has been to determine whether the conduct of
monetary policy in the U.S. should be influenced directly by the behavior of
foreign interest rates and exchange rates. To address this issue, the present
analysis studies the response of domestic money holdings to movements in both
exchange rates and foreign interest rates~-that is, ~hether currency substitution
ie an important consideration.

Although this issue has been treated in the literature, the existing
analyses rest on official estimates of money holdings which assume perfect
substitutability between different components. The present analysis removes this

assumption and therefore extends the existing literature on currency substitution


Currency Substitution and
The New Divisia Monetary Aggregates:

The J.S. Case

Jaime Marquez
International Finance Division
Federal Reserve Board
Washington, D.C. 20551

May 1985

The purpose of this paper is to examine the extent to which the behavior
of aggregate money holdings is influenced by foreign exchange
considerations, an influence that has been labeled as currency
substitution. Knowledge of the extent to which monies of different
countries can substitute for each other is important for the design and
implementation of monetary policy. However, existing empirical analyses
of currency substitution rest on official estimates of money holdings
which imply an infinite elasticity of substitution between different
monetary assets. Analyses of economic monetary aggregates do not impose
the assumption of infinite elasticity of substitution, but no foreign
exchange considerations are allowed. This paper combines both approaches
into a unified explanation of money demand hehavior.

I have benefitted from comments by William Barnett, Renjamin Friedman,
Ronald McKinnon, Peter Tinsley, and Neil Wallace on an earlier version of
this paper. This paper was presented at the conference on New Approaches
to Monetary Economics, The University of Texas at Austin, May 23-24,
1985. I have also benefitted from the participants at the International
Macro Workshop of the Federal Reserve Board. Suggestions and criticisms
from Karen Johnson, Lois Stekler, Peter Isard, and Neil Ericsson are also
gratefully acknowledged. I retain sole responsibility for remaining
errors. This paper represents the views of the author and should not be
interpreted as reflecting the views of the Board of Governors of the
Federal Reserve System or other members of its staff.


31

TABLE A3

Parameter Estimates for U.S. Money Demand

Broad Interpretation of Currency Substitution
Forward Market Expectation Model

1974.1 - 1982.4

(t-statistics)

Explanatory Variables

Divisia Aggregates

1 2 3

Constant 0.019 0.026 0.024
(4.0) (5.3) (5.4)

Income 0.091 0.250 0.250
. (0.7) (2.0) (2.2)
Domestic return -0.004 -0.002 -0.002
(-0.4)  (-2.0) — (=1.8)

Foreign return? -0.004 -0.007 -0.006
(-2.1) (-4.0) (-3.7)

Inflation 1.061 -1.600 1.480
(-4.5) (-6.5) (-6.7)

x 0.48 0.73 0.73
D.W. 2.08 1.34 1.57
S.E.Re 0.008 0.008 0.007
Normality: (JB) 0.89 0.05 0.01
Serial Independence: F(4,28) 0.46 0.75 0.41
Homoskedasticity: ARCH-t 0.19 -0.30 -0.70
Chow Test: F(8,23) 0.33 0.98 0.77

aPoreign return is defined here as the covered interest

rate.


26

determining aggregate money holdings; another, and closely related area, of
extensive research is the structural stability of money demand equations.
Examples of this empirical work include the influential papers by Goldfeld (1973,
1976), Hamburger (1966, 1977b), Barnett, Offenbacher, and Spindt (1984), and
Enzler, Johnson, and Paulus (1976).

11. See McKinnon (1982, 1984) and the debate in the December 1984 issue of the
American Economic Review.

12, For empirical tests rejecting McKinnon's currency substitution hypothesis,
see Goldstein and Haynes (1984), and Radcliffe, Warga, and Willet (1984).

13. See Dornbusch and Fischer (1980), Tanzi and Blejer (1982), Arango and Nadiri
(1981), and Brittain (1981).

14, Clearly, differences in approaches that rest on either a narrow or a broad
interpretation of money is not a satisfactory state of affairs. A preferable
approach is to follow Ewis and Fisher (1984) or Johnson (1982). Both of these
studies examine the behavior of specific asset demands allowing for the
possibility of currency substitution. The former paper uses the framework of
economic monetary aggregates with the stock of foreign assets defined as the sum
of different foreign asset holdings. However, the rate of return to these assets
is defined as the average rate, whereas it should have been the maximum rate;
also, exchange rate changes are excluded from the return for foreign assets. The
work of Johnson eliminates these difficulties, but it rests on official estimates
of money holdings. The ultimate goal of the present research effort is to
integrate both views. .

15, Meese and Rogoff (1983), Hansen and Hodrick (1991), and Tryon (1983).

16. A third mechanism is the static expectation model: Ele. 4) )=e- It has been
observed that this expectation model has the largest predicting power among a
variety of more sophisticated models (see Meese and Rogoff 1983). However, it is
observationally equivalent to a model where the coefficient for expectations of
the exchange rate is zero. Results not shown here, but available on request,
indicate that foreign interest rates do exert a strong influence on the behavior
of aggregate domestic money demand. Another complication arises for the rational
expectations case. Specifically, if Cee eta tHe where o is the forecasting
error, then

Ye = Ue > Upay + Cay /e, la - Ce, /eg_) a, _1]

Clearly there is no a-priori reason to suspect that Vv, obeys any of the
properties of classical estimation. Of these, we test for normality, serial
independence, and homoskedasticity leaving for the revised version of this paper
the test for exogeneity.

17, For example, see Cuddington (1983) and Daniel and Fried (1983).
18. Differencing the equation is potentially troublesome. Specifically, the

characterization of long run money demand is not unique since it will depend on
the initial condition for the solution of the differential equation.


10

exchange rate expectations--contribute significantly towards explaining domestic

money demand behavior. Accordingly, domestic money holdings are modeled as

(5) T/P = f(r, i*, x, y),
- - = +

where [ = divisia monetary aggregate,
P = price level,
r = domestic interest rate,
ix = foreign interest rate,
x = expected depreciation of domestic currency, and

y = scale variable, generally real income.

Although there is little disagreement in the literature ahout the choice of
arguments in (5), there is considerably less agreement about the proper
specification of their influences. Greatly simplified, two avproaches have been
developed to specify (5): a narrow approach and a broad approach. According to
the former, money is defined as that asset earning no explicit interest, which
implies that the oaly reason to hold foreign currency is an expected depreciation
of the domestic currency. As a corollary, one must distinguish between currency
substitution and capital mobility. Currency substitution is motivated only by
depreciation of domestic currency--that is, a purely speculative motive for
foreign currency holdings--whereas capital mobility is assumed to respond to
changes in both foreign interest rates and exchange rate expectations. According

to this narrow interpretation, the Proper specification of (5) is

(6) T/P = £(r, ik + x, x, y),
- - - +


13

(8) 1n( T,./P,) =a

‘0 + a, In(y,/?.) +a, t +

2

+a re +aek
tt 348, Ce

3 dle, +a AlnP + ue

t+1 5

where a,?0, a,<0, a,<0, a,<0, a,<0;

2 3 4 5
Mee = monetary services provided by the ith (divisia) monetary aggregate,
ry = price deflator for Gross National Product,
%, = Gross National Product in nominal terms,
my nominal 90-day U.S. interest rate,
** = nominal 90-day foreign return,
* -

= (CH4*)[E Ce. )/e.1) - 1,

i* = foreign interest rate index,

e = exchange rate index (U.S.$/foreign currency),

Ee.) = one period ahead expected exchange rate based on today's information,

+Vv
t Ment t’
2

u, ~ NCO, 94)» E(u,- up) = 5

t-1

2
% ~ NC, 0),

2 2
E(v.vey) = 2ro, = 0 if neo/2.

According to (8), aggregate money demand responds to changes in real income
and domestic interest rates, as the traditional formulation suggests; this demand
also responds to changes in the foreign return from holding foreign assets and to
“the expected changes in the exchange rate. The inclusion of the inflation rate
in the specification is less traditional but not less important. In particular,
several. arguments have made for this inclusion. First, it has been observed

(Blejer 1981, Cukierman 1980) that an increase in the inflation rate is generally