18

Table 2
Parameter Estimates For Conditional Money Demand
Alternative Definitions of Aggregate Money
Venezuela: 1960-1980
(Numbers in parenthese are t-statistics)

M1 M2 M3

o 6.038 8.521 7.409
(2.1) (3.9) (7.4)

u 0.956 0.763 0.871
(5.4) (15.4) (7.5)

k 1.109 1.095 1,132
(20.1) (29.5) (27.)

v 0.279 0.446 0.297
(1.7) (3.9) (2.5)

6 0.900 0.900 0.900
(n.ae) (nea.) (n.a.)

2

R 0.99 0.99 0.99
DW. 1.56 1.83 1.27
h 0.668 0.442 1.926
Jarque-Bera 4.637 2.571 0.892
ARCH 0.019 -0.051 -0.095

(0.08) (-0.21) (-0.39)



ema*

(4+i)

12
Local Perfect Substitutability

o<oo
o-oo
o<a@
M
ud
c
mt" m%e, (M9*/M4)e,
(14i* )/(4+x)

Figure 3


22

ENDNOTES
* I have benefited from comments by Eric Bond, Peter B. Clark, Neil
Ericsson, Dale Henderson, Dave Howard, Karen Johnson, Karen Lewis, Marc
Miles, and Ken Rogoff. Andrew Atkeson provided invaluable research
assistance. An earlier version of this paper was presented at the Tenth
Annual Meeting of The Eastern Economic Association, March 16, 1984. Any
remaining errors are my own. 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.

An even greater depreciation (900 percent) took place in Argentina's
black market during 1975 (Calvo and Rodriguez 1977).

On the other hand, Cuddington (1983) argues that, for all practical
purposes, currency substitution models have nothing new to offer in the way
of understanding interest and exchange rate behavior since these models are
already embedded into more general portfolio models. Nevertheless,
Brillembourg and Schadler (1979) implement empirically a portfolio model to
explain exchange rate behavior for the eight most important currencies; they
find that currency substitutability is a significant phenomenom that needs
to be taken into account in explaining exchange rate behavior. For an
i960}, introduction of the issue of currency substitutability, see Marwah

1969).

Other empirical analyses focus on the role of currency substitutability
on the behavior of the exchange rate for the major currencies. For
instance, see Brillembourg and Schadler (1979), Britain (1981), Miles
(1981), McKinnon (1982), Goldstein and Haynes (1984). However, these
studies analyze exchange rate behavior for countries with a flexible
exchange rate system, whereas one of the interesting aspects of the
Venezuelan case is the existence of currency substitution in a fixed
exchange rate system. In addition to providing a rationale for the
depreciation of the Venezuelan bolivar, a currency substitution model for
Venezuela might be useful in addressing issues such as the timing of a
devaluation and the development of speculative runs on the stock of foreign
exchange (Flood and Garber 1981, and Blanco and Garber 1983). Similarly,
one of the essential features of the balance-of-payment-crises models
developed by Krugman (1979) and Obstfeld (1984) is the specification of the
money demand function, which can be derived within the framework of analysis
of currency substitution models.

4

See in particular the analyses developed by Canto and Miles (1983),
Girton and Roper (1981), Cuddington (1983), and Calvo and Rodriguez (1977).
>

The real capital stock should also be considered part of wealth, but we
have left it out for simplifying purposes.

There is not a single--and universally accepted-- definition of money
(see Osborne 1984 for a survey). Each monetary instrument has a number of
attributes that complicates the process of aggregating various instruments
into a single monetary aggregate. In aggregating linearly (adding)
different monetary instruments, we make the assumption that individua’s are


3
of the exchange rate under the rational expectation hypothesis.

The basic message from these analyses is that if two currencies are
perfect substitutes for each other, then the exchange rate between them is
indeterminate. Consequently, small changes in the expected return to
holding one currency will induce swift changes in the composition of the
portfolio with a corresponding impact on the exchange rate. Therefore, it
would seem that the sharp movements in the exchange rate that were observed
in Venezuela would be consistent with an expected depreciation of the
venezuelan bolivar provided there existed a substantial degree of currency
substitution. Our first purpose in this paper is to determine empirically
the degree of currency substitution existing in Venezuela.

The empirical evidence regarding the degree and extent of currency
substitution--as shown by Miles (1978), Ortiz (1983), and Daniel and Fried
(1983)--has focused on the case where the institutional banking structure
allows for the circulation of both domestic and foreign currency. Two of
the countries more commonly analyzed are Mexico and Canada, where U.S.
dollars have circulated as an additional medium of payments. One question
that naturally arises in this context is to what extent the existence of
banking regulations are a pre-condition for the existence of currency
substitution. In Venezuela, for instance, only domestic currency is allowed
to circulate. Therefore an empirical analysis for Venezuela might provide
some evidence regarding the need of regulatory constraints for the existence
of currency substitution possibilities.

Our second purpose is to apply duality results from production theory
in an attempt to formalize the notion of exchange rate instability. One
corollary of the analysis we develop is an alternative explanation of
exchange rate indeterminacy in the presence of perfect currency

substitutability.


19

h-statistic for serial correlation in the error process is 0.67 for Ml, 0.44
for M2, and 1.96 for M3. Of these statistics, only the value for M3 is
above the critical value (1.645) for which the hypothesis of positive serial
correlation cannot be rejected. Second, we cannot reject the hypothesis
that the error term is homoskedastic, as indicated by the ARCH value.
Finally, tne Jarque-Bera statistic (see Jarque and Bera 1980) indicates that
we cannot reject the hypothesis of a normal distribution for the error
process for any of the monetary measures considered here. All in all, we
cannot reject the assumptions made for the error term in classical
regression analysis.

Although our parameter estimates are robust to alternative measures of
money, we do not hesitate in pointing out the preliminary nature of our
results. We have used rather strong assumptions in our analysis such as
purchasing power parity, the aggregation of variables across individuals,
and especially the aggregation with respect to expectations. In particular,
we have assumed that the distribution of expectations of depreciation across
individuals is concentrated at x = (eye, 1 )/eg 4 = 0 since e,= e,_) over

the last twenty years.

V. CONCLUSIONS

The main purpose of this paper has heen to provide an economic
rationale for the 400% depreciation of the bolivar exchange rate that
occurred between March and August of 1983. We approach this question using
a currency substitution model which, when coupled with duality results from
production theory, implied that a necessary condition for the observed
exchange rate instability is the existence of a large elasticity of
substitution in currency holding.

The empirical results yield a statistically significant elasticity of


25

REFERENCES
Barnett, W. (1980). "Economic Monetary Aggregates." Journal of Econometrics
Vol. 14, No. 1:11-48,

Blanco, H. and P. Garber (1983). "The Speculative Attack on The Mexican
Peso." mimeo.

Brillembourg, A. and S. Schadler (1979). "A Model of Currency Substitution
in Exchange Rate Determination 1973-1978." IMF Staff Papers Vol. 26, No.
3:513-542.

Britain, 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 Vol. 13, No. 2:135-155.

Calvo, G. and C. A. Rodriguez (1977). "A Model of Exchange Rate
Determination Under Currency Substitution and Rational Expectations."
Journal of Political Economy Vol. 85, No. 3:617-625.

Canto, V. and M. Miles (1983). "Exchange Rates in a Global Monetary Model
with Currency Substitution and Rational Expectations." in Bhandari, J. and
B. Putnan (eds.) Economic Interdependence and Flexible Exchange Rates MIT

Press.

Cardozo, E. (1983). "A Money Demand For Brazil." Journal of Development
Economics Vol. 12, No.1/2:183-193

Cuddington, J. (1983). "Currency Substitution, Capital Mobility, and Money
Demand." Journal of International Money and Finance Vol. 2, No. 3:111-153.

Daniel, B. and H. Fried (1983). "Currency Substitution: An Empirical Study
for the U.S. Dollar." Paper presented at the 1983 North American Finance
Association Meetings: San Francisco.

Flood, R. and P. Garber (1981). "Bubbles, Runs, and Gold Monetization."

mimeo.


a

i*

21

DATA APPENDIX

Ml, M2, M3 in nominal terms; source: Banco Central de Venezuela
interest rate of commercial active banks in Caracas;

source: Banco Central de Venezuela

U.S. Treasury bill rate; source: IMF

exchange rate (bolivars/dollars);

source: Banco Central de Venezuela

nominal GDP; source: Banco Central de Venezuela


16

ll
optimal money holdings, wt, following a partial adjustment process:

: ayy
ms 5-0 (Mwy > 0 WY + ups (18)

which yields the following expression:
le
me = Mine» Ye)¥ (mop )?°¥ + (u,-(1-w)uy_y)» (16)
where y is the speed of adjustment. Substituting equation (8) into equation
12
(16), we get:

me = {140(1-6)/6]°C (144 ) (14x) /(141*) J? }92/ (1-2) gh0/ (1-0) y¥/ Hg

ay
kmy + Yee (17)
where f(y) = ay!/
k = (a/A)¥,

‘E ue > (1-v)uy y+

The statistical properties of v

(1) Ey) <0,

are:
t

2 2 2
(2) (vp) = oC1#(1-y) J - 2(1-v)E(uguy_4)s
2 2 2 2
(3) (vy yy )-E(uyUy y)-(1-way + (1) Eluy yup _p)=n(14(1-¥) )-(1- vas

Therefore, a sufficient condition for serial independence in v, is:

2 2
n= Co, (1-y)/E(14(1-9) Je

t


6

- * <p -l/

M = ALoMt  4(1-5)(E(1-8)/67 [(a44) (14x) /(144") 7? wy pe (7)
and solving for nf, we get:

Mo = {14( (1-6)/6)°((1H ) (14x) /(14i 7) JOE }/ 9) ge/ (1-2) yay, (8)

Equation (8) is the conditional demand for domestic currency, which
depends on domestic and foreign interest rates, on the expected rate of
depreciation, and on the given aggregate level of money holdings. The main
advantages of equation (8) are first, that the parameter o can be estimated
taking into account all the first-order conditions for the portfolio
allocation problem, and second, that there is no need to use unreliable data
on Venezuelans' holdings of foreign currency abroad. However, we still have
the problem that M is unobservable. For the. purposes of empirical
implementation, we will assume that the aggregate level of money holdings,
in nominal terms, is a function of the level of nominal income:

M = f(Y). (9)
Using this simplifying assumption, we express equation (8) as:

d

we MG, i2oxs Y) = Mw, YD, (10)

where w' = (i, i*, x). Combining equation (6) with equation (10), we get

the conditional demand for foreign currency:

d

uv = ww, Y)/e. (11)


subject to

-p -p -l/p
w/P = A(e(M4/P) + (1-8)(M4*yp*) ) (2)
where

C: portfolio holding costs,

i: domestic nominal interest rate,

i*: foreign nominal interest rate,

P: domestic price level,

P*; foreign price level,

x: expected depreciation of the exchange rate,

wf; nominal money demand for domestic currency,

ue: nominal money demand for foreign currency,
M: nominal (aggregate) level of money holdings,
6: distribution parameter, and

p: substitution parameter, p=(1-c)/o.

If we assume purchasing power parity, then we can form the lagrangean

as:

-p -l/p
d*)

A= (1H )ME + ((1H*)/(14x) lem) + a = Cant” + C1-ay(en”) )

where e is the exchange rate (domestic currency/foreign currency). The
first-order conditions for the cost minimization problem are:

aasam? = (144) = a(aM/aM4) = 0, (3)

ansa(eM*)= ((1H")/(14x)) = aaM/a(eM®”)=0, (4)


4

Although this issue has received some attention in the literature. the
analyses have not been exhaustive. More specifically, we show that the
range of fluctuation of the exchange rate depends, to a large extent, on
whether perfect currency substitutability is local or global.

We begin our analysis in section II where we develop a model to explain
currency substitution relevant for the Venezuelan economy. In section III
we apply duality results to derive the conditions leading to exchange rate
indeterminacy. In section IV we implement empirically our model and
estimate the elasticity of currency substitution using annual data for
Venezuela for the period 1960-1980. Finally section V contains our

conclusions.

II. A MODEL OF CURRENCY SUBSTITUTION

We will assume an economy where individuals’ wealth is mainly made up
of “money" ° We assume that money can be held in either domestic currency
or foreign currency. Since we do not allow for domestic circulation of
foreign currency, we need to assume that indi viduals have foreign currency
deposits abroad that can be exchanged for domestic currency and vice-versa.
This assumption is consistent with the absence of capitals controls in
Venezuela.

Formally, we assume that individuals follow a sequential portfolio
decision process, and that the optimal portfolio composition is obtained by
minimizing the cost of holding a bundle of domestic and foreign currency

6
subject to a given level of money holdings:

min C/P = (14i)(M4/P) + ((14i*)/(14x) MO" /P*), (1)


W7

The parameters of equation (17) are estimated using a Daviaci-Fietcher-
Powell nonlinear estimation algorithm. We find that the parameter estimates
are sensitive to the starting values. One possible reason for this
instability is the presence of exponents of the form o/(1-°), which when
coupled with the possibility of o being equal to one during the optimization
routine, induce a discontinuity in the sum of squared residuals (at o =1).
As a result: of this parameter sensitivity, we estimate equation (17) using
the value of © that minimizes the sum of squared residuals. The parameter
estimates corresponding to equation (17) are shown in table 2 for
alternative definitions of the money stock.

The estimate of the long run elasticity of substitution, », equals 6.0
for Ml, 8.5 for M2, and 7.4 for M3. All of the elasticities are
significantly greater than one. Our parameter estimates are robust to the
definition of the monetary aggregate and although the estimates of » are
less than infinite (perfect substitutability case), they point to the
existence of a significant elasticity of substitution. One implication of
our empirical results for o is that banking regulations preventing the
circulation of more than one currency (domestic versus foreign) have not
dampened currency substitution, at least in Venezuela.

The parameter u represents the inverse of the long run income
elasticity of money holdings and its estimated value ranges from 0.76 to
0.96, implying an income elasticity ranging from 1.31 to 1.04 (Cardozo 1983
obtains similar results for Brazil). The estimate of the (constant)
speed of adjustment, v, ranges from 0.28 to 0.45 which implies an estimated
mean lag of adjustment ranging from 5 to 10 months.

We have also tested the hypothesis that the error term possesses the

statistical properties assumed in classical estimation. In particular, the


7
since equation (6) is not the solution to the system of equations (3) to (5)
representing the first-order conditions. In effect, only two of these three
equations are used to estimate o, whereas the equation system that needs to

be estimated is:

ent” mt = ((1-8)/8)% (141) (14x) /(14i"))% , (6)
and

qi (l-9)/o de -(1-0)/o -0/(1-0)
M = ACM + (1-6)(eM® ) ) , (5)

and there is absolutely no guarantee that the parameter estimate of o using
only equation (6) will be equal to the parameter estimate of o using
equations (5) and (6)-

Perhaps one reason why previous empirical models have used only
equation (6) to estimate o, despite the parameter estimates being at odds
with the theory used, is that M is unobservable as it depends on the
unknown parameters & and o. However, equation (6) is not without problems,
especially for developing countries, where the possibility of capital flight
creates serious difficulties in obtaining adequate data for wa*, For
Venezuela the situation is more complex because, in contrast to the
experience of Canada and Mexico, only domestic currency is allowed to
circulate as a means of payment.

In this paper we eliminate the second of these problems by using the
conditional demand for domestic currency, which is obtainted by solving for

ie
eu? in equation (6) and substituting the result into equation (5):


23

perfectly indifferent with respect to each and every attribute of each
monetary instrument. In this paper we assume that there is an aggregate of
money holdings depending on the different monetary instruments:

* *
CC eee rr

where M.: monetary aggregate,

MP: ith domestic monetary instrument,

we: ith foreign monetary instrument.
Assuming weak separability between domestic and foreign instruments, we
get:

m= MiMt(ngs ec. md), Mame, md)

If we now assume (1) perfect substitutability among the arguments of
dgmestic ,and foreign money aggregates, and (2) strong separability between
M" and M" , then we get equation (2). Notice that as a result of our
aggregational assumptions, the term currency does not refer exclusively to
coins, bills and demand deposits, but might encompass other monetary
instruments as well, such as saving deposits.

In solving the portfolio allocation problem, Miles (1978) and Ortiz
(1983) maximize the production of money services, equation (2), subject to a
liquidity constraint. Their solution to this problem seems, however,
inconsistent with their assumption that the level of money services is
given. In effect, they endogenize the variable that is assumed exogenous.
Furthermore, although their first-order conditions are the same for a
maximum or a minimum, their empirical implementation is faulty since not all
of the constraints have been taken into account.

The main consequence of not using all of the first-order conditions is
that the marginal cost of holding money is left unspecified for a given
level of money holdings. I am grateful to Eric Bond for bringing this point
to my attention.

An exception is Barnett (1980), who examines the issue of constructing
monetary aggregates recognizing that different monetary instruments need not
be perfect substitutes for each other.
iu

Furthermore, this sizeable capital flight probably underestimates the
actual capital flight since foreign currency could be deposited outside the
U.S., and even if deposited in the U.S., it need not be registered as a
liability to venezuelans if they declare their residence to be outside
Venezuela.

‘ae

One clear limitation of this assumption is that the speed of adjustment
is the same for all explanatory variables.
ae

If we were to estimate v using the demand for money in real terms, we
would have to transform nominal income and lagged nominal holdings into
real terms. This would entail multiplying the geheqministic part of
equation (17) by a factor of the form P(t-1)P\*/"/"*, P being the GDP
deflator, and the error term by a factor of (1/P). However, notice that the


International Finance Discussion Papers
Number 242

May 1984

CURRENCY SUBSTITUTION, DUALITY, AND EXCHANGE RATE INDETERMINACY:
AN EMPIRICAL ANALYSIS OF THE VENEZUELAN EXPERIENCE

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.


emd*

(1+i)

10

Global Perfect Substitutability

M
wd
meme,
(m?yM%e,
(141*)/(44x)

Figure

2


9
TIT. EXCHANGE RATE INDETERMINACY AND DUALITY

It is somewhat surprising that despite the similarity existing between
the analysis of currency substitution and the analysis of factor
substitution in production theory, almost no attempt has been made to apply
duality results to the analysis of currency substitution.

If we substitute the optimal portfolio allocation (equations 10 and 11)

into equation (1), then we get the cost function:

C = (14 )MOGwyY) + (C144 )/(14x) Jem” WY) = ClwsY). (12)

Using equation (12), we can find the combinations of i, i*, and x for which
C is constant, defining in this way an isocost curve. We can also define an
isoholdings curve as the set of values of i, i*, and x for which aggregate
money holdings, M, are constant. The duality result relevant for our
analysis is Shephard's derivative lemma, which implies that the ratio of

optimal currency holdings equals the slope of the isocost curve:
d* ad .* Naa
eM” /MTM= {aC(.)/a((1+i )/(1+x))}/{ac(.)/a(1+i) }. (13)

One corollary of Shephard's lemma is that the curvatures of the
isoholdings curve and of the isocost curve are inversely related to each
other. Figure 2 depicts the situation where the elasticity of currency
substitution is infinite for all possible portfolio allocations, and thus
the isoholding curve is perfectly flat. Since the ratio of optimal currency
holdings equals the slope of the isocost, it follows that the isocost has a
curvature with a 90 degree angle. As a result, for any value of wt M9, the
exchange rate is indeterminate since any value of e from 0 to = is perfectly
consistent with portfolio equilibrium.

The case portrayed in Figure 2 is a rather extreme case, however, since

it is one of global portfolio perfect substitutability, resulting in


-p -l/p

anyon =M~ ACN + (1-5)(eNe*)  ) 0. (5)

Using now equations (3) and (4), we get the optimal currency ratio as:
*
en md = ((1-6)/8)% ( (141) (14x) /(1H1"))° (6)

where o=(1/l+p) > 0 is the elasticity of substitution between foreign and
domestic currency. As o+0, the two currencies become perfect complements to
each other. As o»TM, the two currencies become perfect substitutes for each
other, and as shown in section III, the exchange rate becomes

indeterminate.

According to equation (6), an increase in domestic interest rates
reduces the attractiveness of holding domestic currency and raises the ratio
em’* yu, Similarly, an expected depreciation of the domestic currency will
increase profit opportunities from holding foreign currency raising the
emtTM yd ratio. Finally, an increase in foreign interest rates will reduce
the attractiveness of holding foreign currency and, as a result, will lower
the optimal currency ratio. For the purpose of explaining the depreciation
of the venezuelan bolivar, the inclusion of interest rates is quite
relevant. If individuals expect that a fixed exchange regime will be
abandoned at some future date, x>0, then substantial capital gains can be
made by borrowing as much money as possible. And what equation (6) says is ,
that the source of borrowing depends on interest rate differentials.

Equation (6) has been used to estimate the elasticity of currency
substitution as measured by the parameter o (Miles 1978, Laney 1980, (Ortiz

7
1983). However, I would argue, that this approach is not entirely correct


20

currency substitution estimate ranging from 6 to 8. This empirical evidence
lends support to the hypothesis that the sharp depreciation of the
venezuelan bolivar in'1983 was the result of an expected depreciation of the
bolivar, probably arising out of declining nominal oi] prices and
international reserves below Venezuela's short term external obligations,

given the significant extent of currency substitution.


26

Girton, L., and D. Roper (1981). "Theory and Implications of Currency
Substitution." Journal of Money, Credit, and Banking Vol.13,No.1:12-30.

Goldstein, H. and S. Haynes (1984). "A Critical Appraisal of McKinnon's
World Money Supply Hypothesis." American Economic Review Vol.74, No. 1:217-
224,

Jarque, C. and A. Bera (1980). "Efficient Tests for Normality,
Homoscedasticity, and Serial Independence of Regression Residuals." Economic
Letters Vol. 6, No. 3:255-259,

Krugman, P. (1979). "A Model of Balance-of-Payments Crisis." Journal of
Money, Credit, and Banking Vol. 11, No. 3:311-325,

Laney, L. (1980). "Currency Substitution: The Mexican Case." Paper presented
at the meeting of the System Committee on International Research and
Analysis, Federal Reserve Bank of Philadelphia, October 23-24,

Marwah, K. (1969). "An Econometric Model of Colombia: A Prototype
Devaluation View." Econometrica Vol. 37, No.2:228-251.

McKinnon, R. (1982). "Currency Substitution and Instability in the World
Dollar Market." American Economic Review Vol. 72, No. 3:320-331.

Miles, M. (1978). "Currency Substitution, Flexible Exchange Rates and
Monetary Policy." American Economic Review Vol. 68, No 3:428-436,

Miles, M. (1981). "Currency Substitution: Some Further Results and
Conclusions." Southern Economic Journal Vol. 48, No. 1:208-217.

Obstfeld, M. (1984). "Balance-of-Payments Crises Models and Devaluations."
Journal of Money, Credit, and Banking Vol. 16, No. 2:208-217.

Ortiz, G. (1983). "Currency Substitution in Mexico." Journal of Money,
Credit, and Banking Vol.15, No. 2:174-185,

Osborne, D. (1984). "Ten Approaches to The Definition of Money." Economic
Review Federal Reserve Bank of Dallas, March.


tL

eh

St

Zt

6l

£eo6l

3lvyY SINVHOXS LOdS =

S86l ALVY ADNVHOXA LOdS VISNZANAA

L aunbLy


13

Effect of Expected Devaluation
on Currency Composition

emo*

03> 02>0,

—(14i)(14x)/(14i*), x0

—(14i)/( 147")

L_ ud

Figure 4


15
billion between 1979 until 1981. However, these liabilities more than
doubled froma level of $4.6 billion in February of 1982 to a level of $9.4
billion in May of 1982, and have remained in the $8 billion range since
then.

Thus this evidence is consistent with the hypothesis that venezuelans
expected a devaluation as it became apparent that the government, with a
level of international reserves of $12 billion, facing a decline in
international oil prices, and not being able to service its short term

external obligations, would stop selling foreign exchange at the prevailing

exchange rate at some point in the near future.

IV. EMPIRICAL IMPLEMENTATION

Central to our explanation of the large depreciation of the bolivar in
the free market is the existence of a very large elasticity of substitution
between domestic and foreign currencies. Our purpose in this section is to
estimate the value of the elasticity of currency substitution using annual
data for Venezuela for alternative monetary aggregates covering the period
1960-198).

We begin by adding an error term to the equation representing optimal

holdings of domestic currency, equation (10):

qo.
Me = Mw,» Y,) tu, (14)
é .
where ue? N(O,0,), with
n for s=l1, k 70
E(u ME kes) =

0 for sl, k 20.

In addition, we assume that actual money holdings, nf » adjust to


Currency Substitution, Duality, and Exchange Rate Indeterminacy:

An Empirical Analysis of the Venezuelan Experience

Jaime Marquez*

Board of Governors of the Federal Reserve System

I. INTRODUCTION

The Venezuelan bolivar was pegged to the U.S. dollar for over twenty
years until late February of 1983, when the monetary authorities were forced
to close the foreign exchange market to prevent a speculative run on the
stock of international reserves. The market reopened a week later with an
exchange rate system consisting of two controlled exchange rates and a
“free" market exchange rate. This last exchange rate depreciated nearly 400
percent in less than 3 months (see Figure 1), a shock greater in magnitude
than the oi] shock of 1973-74. The basic question we ask in this paper is
whether we can find an economic rationale for such a formidable
depreciation.

We address this question using a currency substitution model for
“Venezuela. Currency substitution models have heen receiving an increasing
amount of attention in the literature because of their implications for both
monetary policy and exchange rate behavior in open economies. For example,
McKinnon (1982) argues that, because of the existence of currency
substitution, the appropriate concept of money supply--and monetary policy--
is a global one. Miles (1978, 1981) discusses the implications of currency
substitution for the autonomy of monetary policy under flexible exchange
rates. Calvo and Rodriguez (1977), Canto and Miles (1983), and Girton and
Roper (1981) develop alternative theoretical models to study the

implications of different degrees of currency substitution for instability


24

error term would become heteroskedastic.

+8 To obtain the ARCH value, regress the estimated residuals on the
squared estimated residuals lagged one period. If the coefficient for this
last variable is not significantly different from zero, then we cannot
reject the hypothesis of a homoskedastic error term. The value shown in
table 2 is the coefficient of the squared residuals lagged one period, and
the number in parentheses is the t-statistic.


Title: Currency Substitution, Duality, and Exchange Rate Indeterminacy:
An Empirical Analysis of the Venezuelan Experience

Authors: Jaime Marquez

Address: Board of Governors of The Federal Reserve System, Washington,
DC 20551

Date: May 1984

Series and Number: International Finance Discussion Papers, No. 242
Pages: 26

Price: No charge

JEL Subject Classification: 311,431

Keywords: Exchange rate, Currency substitution, Venezuela

We develop a currency substitution model to explain the 400
percent depreciation of the free market exchange rate of the Venezuelan
bolivar. Applying duality theory, we find that currency substitution
is a necessary condition for such a depreciation. Using annual data for
1960-1980, we estimate the elasticity of currency substitution for
Venezuela, and we find that this elasticity is significantly greater

than one.


a
complete indeterminacy of the exchange rate. However, it is possible that
perfect asset substitutability might be only a local Property--not a global
one--of the isoholdings curve. The local perfect substitutability case is
Portrayed in Figure 3. The existence of a flat zone in the isoholdings
curve induces a kink in the isocost curve. At the kink, the exchange rate
will also be indeterminate, but now the range of indetermination is bounded
away from both zero and infinity. Given that movements in the exchange rate
of the most important currencies have been bounded, the notion of local
perfect substitutability has some appeal, at least from an empirical
standpoint.

How do these duality results relate to the original question of this
Paper, namely, is there a plausible explanation for the sharp depreciation
of the exchange rate in Venezuela during 1983? These duality results
suggest that an expected devaluation of the venezuelan bolivar will not by
itself generate an increase in foreign currency holdings. It is the
combined effect of a high elasticity of substitution between foreign and
domestic currency coupled with an expected depreciation of the bolivar
that leads to an increase in foreign currency holdings. To see this,
suppose that the initial portfolio equilibrium is given by point A in Figure
4. If the domestic currency is expected to depreciate (x>0), then the
opportunity cost of holding foreign currency decreases and induces an
increase in the demand for foreign currency from point A to point B. From
the figure we can readily see that the increase in foreign currency holding
is greater the larger is the elasticity of substitution.

Although we do not present any formal test to show that x>0, the
evidence from table 1 suggests that indeed venezuelans expected a
devaluation of the bolivar. In particular, table 1 shows that the amount of

liabilities of U.S. banks to venezuelan residents were in the order of $4


14

Table 1
Liabilities of U.S. Banks to Venezuelan Residents
Payables in U.S. dollars
(U.S.$ billion, end of period)
1979 1980 1981 1982 1983 1984

January 4.6 7.7 9.3
February 4.6 7.7 9.4
March §.1 8.2
April 8.2 8.5
May 9.4 8.6
June 9.3 8.6
duly 9.1 7.7
August 9.2 8.6
September 8.6 8.4
October 8.8 8.2
November 8.3 8.0
December 4.2 3.2 4.2 8.4 8.6

Source: Federal Reserve Bulletin, several issues.