V7
Venezuelan residents. Thus no allowance is made for liabilities of non-U.S.
foreign banks to Venezuelan residents, liabilities of foreign banks to
Venezuelans not registered as residents, and non-financial assets of
Venezuelans abroad. To the extent that excluding these components,
underestimates the increase in foreign money balances, the change in the
exchange-rate risk computed here might represent a lower bound to such risk.
Secondly, the computations rest on the validity of the model used, on the
constancy of the estimated elasticity of currency substitution, and on the
exchange rate model assumed for its estimation. With these caveats in mind,

the exchange-rate risk estimates obtained in this paper should be seen as

tentative.

4. Conclusions

The purpose of this paper has been to determine empirically the extent
to which domestic money balances in Venezuela have been influenced by
foreign exchange considerations. To this end, individuals are assumed to
face a relatively simple optimization problem the solution of which yields
the specification of domestic money holdings. This specification is
implemented empirically, and the results yield statistically significant
estimates of the elasticity of currency substitution estimate ranging
between 6 and 8. This empirical evidence lends support to the idea that
foreign exchange considerations are important for modeling money demand
behavior in Venezuela and, as result, for the design of monetary and
exchange rate policies.

Given the elasticity estimates, the currency substitution model is used
to estimate changes in the out-of-sample conditional exchange-rate risk for
the period prior to 1983. The estimates suggest that the expectation of a
devaluation of the Venezuelan bolivar became increasingly more likely

towards the end of 1982. Because these estimates are preliminary, further


11
associated with reduced-form coefficients.

Finally, the design and implementation of monetary policy benefit not
only from knowledge of the existence of currency substitution, but also from
knowledge of its magnitude. However, much of the existing literature?! has
been devoted almost exclusively to the issue of statistical significance.
Even if cross-partial interest elasticities of 0.001 and 5.0 were equally
significant, differences in their magnitudes carry different implications
for monetary policy and exchange rate determination which cannot be left

unidentified. The present formulation avoids this difficulty by focusing on

both the magnitude of o and its statistical significance.

3. Empirical Implementation
3.1 Econometric Considerations

As it stands, the parameters of equation (10) are not suitable for
econometric estimation because first M* is unobservable and second, both
dynamic considerations and stochastic influences have not been recognized.

The level of optimal aggregate monetary services, M*, is not observable
because it depends on o, which is not known a priori. To circumvent this
difficulty, it is assumed that there exists a behavioral relationship
between the unobservable M* and an observable variable. This paper relies
on a nonlinear version of the Cambridge equation: 12
(12) we = f(y) = avl/H,
where Y represents nominal income and a represents the liquidity preference.
The parameter » represents the inverse of the income elasticity of aggregate
money services M*. If u = 1, then equation (12) implies a constant velocity
of circulation of domestic money holdings.

Dynamic adjustments are recognized here by adopting the widely used

assumption that the difference between the actual demand for domestic money,


ral

12 While this is clearly an ad-hoc procedure, it is at least consistent
with the idea that a given level of output requires a certain amount of
Monetary services. Note that this adhocness is not needed in general.
Specifically, one could measure M* as a divisia index of domestic and
foreign balances; such an index is a second order approximation to any
functional form (see Barnett 1980). However, this approach requires data on
balances denominated in foreign currency which, in the Venezuelan case, are
difficult to obtain.

13 Besides not being the solution to an intertemporal problem, one clear
limitation of this assumption is that the speed of adjustment is the same
for all explanatory variables. See Corbo (1982) for a dynamic adjustment
based on a disequilibrium hypothesis.

14 The algorithm minimizes the sum of squared residuals iteratively. The
parameter vector at the kth iteration by is

= “lye ' -1
Dem Bea = “ty (H Dg, = =ty (pd, + S(b.)) gps

where t is the step length, H, is the Hessian, % is the gradient, J is
the Jacobian, and S(.) is a function of the residuals. The Gauss-Newton
algorithm ignores this last term, whereas the Newton algorithm computes it
at each iteration and it is extremly slow and expensive. The method used
here computes S(.) iteratively according to

Sorte = Jor (Ulbpyy) - lb, )), where u'= (u,,..., Up).

IT
For further details, see Dennis et. al. (1981). This algorithm is available
in the computer software known as TROLL.

15 The empirical evidence of Meese and Rogoff need not apply to the
Venezuelan case. However, the random-walk hypothesis for exchange rate
expectations might be applicable for Venezuela during the period under
consideration because of both the commitment of her monetary authorities to
support the fixed exchange rate system and the large international reserves.
The Venezuelan exchange rate remained fixed at 4.292 bolivars/US$ for the
period 1976-1982. For the earlier period, it was also fixed at a slightly
different value (see data appendix).

16 For further evidence on the anomalies associated with the post-1980
period, see Sachs' comments to Diaz-Alejandro (1984), especially pp. 395-
396. Sachs argues that the years 1981-1982 were very atypical.

17 The empirical results for the portfolio balance model, equation (11),
for the period 1961-80 are (t-statistics in parentheses):


2
her institutional banking structure has not allowed onshore holdings of
monetary balances denominated in foreign currency. Previous studies have
analyzed the experience of Argentina, Mexico, and Ecuador, where balances of
both domestic and foreign currency can be held onshore. Consequently, it is
possible to establish if banking regulations are a pre-condition for the
existence of currency substitution. As it turns out, they are not.
Secondly, this paper might be useful in analysing whether the 1983 exchange-
rate collapse in Venezuela had been anticipated by the public at large, or
whether it was an entirely unexpected phenomenom.

Besides examining the Venezuelan experience, the present paper also
extends the currency substitution literature in another direction.
Specifically, most empirical studies of currency substitutability rely on
cross-partial elasticities of reduced-form money demand specifications.
Unfortunately, such specifications do not always permit identification of
the extent to which currency substitution occurs? As a result, it is
possible to accept the null hypothesis of no currency substitution when it
is false. The present analysis avoids this identification problem by
relying on a specification of domestic money holdings derived as the
solution to an optimization problem.

In addition to the issue of estimation, the present study might be of
relevance to ongoing work on both government seigniorage and crises of
balance of payments? As these analyses reveal, central to their conclusions
is the existence of a money demand function depending on foreign exchange
considerations. Because these functions have not been formally derived, the
present analysis might be seen as providing one possible formal
justification for their use.

The analysis begins in section 2 with the formulation of a simple, but

formal, theoretical model where firms decide the composition of transactions


18
work is needed before their tentative nature can be removed. Specifically,
it is important to determine the sensitivity of the elasticity estimates to
changes in the underlying assumptions about the transactions technology, the
dynamic adjustment, and the model of exchange-rate expectations. Analyses
that relax or eliminate these assumptions are certain to enhance our

understanding of the importance of currency substitution.


24

Table 1
Parameter Estimates For Conditional Money Demand
Alternative Definitions of Aggregate Money
Venezuela: 1961-1980
(Numbers in parentheses are t-statistics)

M1 M2 M3

Elasticity of Currency Substitution: o 6.038 8.521 7.409
(2.1) (3.9) (7.4)

(Inverse of) Income Elasticity: u 0.956 0.763 0.871
(5.4) (15.4) (7.5)

Speed of Adjustment: v 0.279 0.446 0.297
(1.7) (3.9) (2.5)

K 1.109 1.095 1.132
(20.1) (29.5) (27.0)

2

R 0.99 0.99 0.99
D.W. 1.56 1.83 1.27
Durbin's h . 0.668 0.442 1.926
Normality test?: Jarque-Bera (aB-y (2)) 0.902 0.723 0.360
Heteroskedasticity test”: Arch-t 0.080 -0.21 -0.39
Serial Correlation AR(8)°: F(8,4) 0.380 0.470 0.430

Data Sources: Mq = M1, M2, and M3 in nominal terms: Banco Central de
Venezuela. ig = interest rate charged by commercial banks in Caracas:
Banco Central de Venezuela. i¢ = U.S. Treasury bill rate: IMF. e =

exchange rate (bolivar/US dollar): Banco Central de Venezuela. Y = nominal
GDP: Banco Central de Venezuela.

a. Significance level at which the normality hypothesis is rejected.

b. t-statistic; if it exceeds a value of 2, the homoskedasticity hypothesis
is rejected.

c. Significance level at which the serial independence hypothesis is
rejected.


2
Choudhri assume that the ratio of domestic to foreign balances can be :
expressed as a function of real income and interest rates. They find that
the coefficient on income is significant which would invalidate the CES as a
functional form for Canada. However, these tests rest on the validity of
postulated demand funetions and on the assumed normality of the regression
residuals. These demand functions correspond to the solution of an
unspecified optimization problem which need not be consistent with the CES
formulation. Furthermore, they do not test for normality in the residuals;
if these fail to be normal, then their statistical inferences would net be
valid. Boughton derives asset demand functions from an objective function
which includes the CES as special case; his empirical results indicate that
half of the cases examined support the CES functional form. (He also tests
for normality of the errors.) Because the financial market in Venezuela is
significantly “less mature” than the financial markets in the U.S. and
Canada, it might be possible (as Boughton has indicated to me) that the CES
might provide a useful first approximation to the transaction technology in
Venezuela. It is certainly possible for the transactions technology to be
typified by some other functional form, and the sensitivity of our results
to alternative transaction technologies ought to be the subject of further
investigation.

8 One way to test for the existence of purchasing power parity, suggested
by Genberg (1978), is to regress the logarithm of the real exchange rate,

eP ¢/P > on a time trend. If the coefficient on this variable is
significant, then it is not possible to accept the null hypothesis of PPP.
Using annual data for Venezuela for the period 1961-1980, I obtain the
following results (t-statistics in parentheses):

In(e,Pe4/P 4, )25-960 + O.O03TINE; R@* -0.12, DWH2.14, SER=0.103, rho=0.578,
tft dt’ 53.7) (0.4)

where e=bolivars/$US; P= Venezuela's import price; and Paz Venezuela's GDP
deflator. This evidence, while consistent with PPP for the perfed 1961-
1980, is far from being a substitute for a more sertous study of whether PPP
holds in Venezuela. As evidenced in the papers of the Symposiua on
Purchasing Power Parity (Journal of International Economics, May 1978), this
task is beyond the scope of this paper. Unfortunately, the papers contained
in that symposium do not examine the Venezuelan experience.

9 Specifically, 1 = 1 is an admissible value which implies, by duality,
that o = 1. Thus the value of o is being assumed rather than being
estimated. I am grateful to Eric Bond for bringing this point to my
attention.

10 See Khan and U1-Haque (1985) who offer a model of capital flight and
discuss problems associated with #ts measurement.

11 For example, see Blejer (1978), Cuddington (1983), Nickelsburg (1984),
and Ortiz (1983).


15

the Jarque-Bera statistic for the normality test indicates that it is not
possible to reject the hypothesis of a normal distribution for the error
process for any of the monetary measures considered here.29 Secondly, as
indicated by the ARCH value, the hypothesis that the error term is
homoskedastic cannot be rejected 2° Finally, the hypothesis of 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 8
are equal to zero. The values for the F-test suggest that the estimated
residuals do not exhibit any sign of serial correlation. All in all, the
assumptions embodied in the error term are not rejected by the available

data.

3.4 Implications of Currency Substitution:
Could The 1983 Exchange-Rate Collapse Have Been Anticipated?

After supporting a fixed exchange rate regime for over twenty years,
the monetary authorities in Venezuela closed the foreign exchange market in
February of 1983 to prevent a speculative run on international reserves.

The purpose of this section is to use the empirical results obtained above
to estimate the out-of-sample exchange risk prior to the 1983 collapse.

The exchange-rate risk, 6, is defined here as the difference between
the exchange rate expected to prevail next period and the forward rate for
that period. Because of the commitment of the monetary authorities during
the 1981-2 period to support a fixed exchange rate system, the forward rate
in Venezuela would simply be the official exchange rate, e*. Logarithmic

differentiation of the short-run version of equation (8) yields?2

(15) Ae = A(In Meg 7 19 Mgp J/( yo) + alIn(1 + i,)-In(1 + ig).

where


(5) aA/ aM, = (1444) - AC aM*/ aM) = 0,

(6) a/ a( eMe)= ((14i -)/(148( de) /e) ) - AaM*/ 3( eM) = 0, and

-e -p -1/p
(7) aA/aa = Me = ACM, + (1-6)(eM) = 0,

Equilibrium requires first that the value of the marginal Productivity of
each type of money be equal to its borrowing cost and second, that the
resulting optimal money balances render a level of monetary services equal
to M*.

Division of equation (6) by equation (5) yields
(8) Me /My = ((1-8)/8)% (141 4) (14E( ne) /e)/(14ig)) ,

which is the optimal mix of money balances. According to equation (8), an
increase in domestic interest rates raises the cost of borrowing
domestically and thus increases the ratio of foreign to domestic balances.
Similarly, if firms expect a depreciation of the domestic currency--that is,
E( Ae)/e>0--then total financing costs can be reduced by increasing holdings
of foreign money. Finally, an increase in foreign interest rates raises the
cost of foreign borrowing and, as a result, lowers the optimal ratio of
foreign to domestic money holdings.

Equation (8) has been estimated by Ortiz (1983) and Miles (1978).
However, the resulting parameter estimates are open to criticism because
equation (8) does not represent the solution to the associated first-order
conditions, which is given by solving simultaneously equations (7) and (8).

From a theoretical standpoint, the main consequence of not using all of the


demand, Journal of International Money and Finance, 2, 111-153.

Daniel, B. and H. Fried, 1983, Currency substitution, postal strikes, and
canadian money demand, Canadian Journal of Economics, 16, 612-626.

Darby, M. and A. Stockman, 1983, The Mark III international transmission
model: Estimates, in M. Darby and J. Lothian, (eds.), The international
transmission of inflation (NBER, Chicago).

Dennis, J., D. Gray, and R. Welsch, 1981, An adaptive nonlinear least-
squares algorithm, ACM Transactions on Mathematical Software, 7, 348-368.

Diaz-Alejandro, C., 1984, Latin american debt: I don't think we are in
Kansas anymore, Brookings Papers on Economic Activity, 2, 335-403.

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

Fischer, S., 1982, Seigniorage and the case for a national Money, Journal of
Political Economy, 90, 295-313.

Genberg, H., 1978, Purchasing power parity under fixed and flexible exchange
rates, Journal of International Economics, 8, 247-276.

Girton, L. and D. Roper, 1981, Theory and implications of currency
substitution, Journal of Money, Credit, and Banking, 13, 12-30.

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

Jarque, ©. and A. Bera, 1980, Efficient tests for normality,
homoscedasticity, and serial independence of regression residuals, Economic
Letters, 6, 255-259.

Khan, M. and L. Ramirez-Rojas, 1984, Currency substitution and government
revenue from inflation, International Monetary Fund, DM/84/58.

Khan, M. and N. Ul-Haque, 1985, Foreign borrowing and capital flight: A
formal analysis, International Monetary Fund, DM/85/39.

King, D., B. Putnam, and D. Wilford, 1978, A currency portfolio approach to
exchange rate determination: Exchange rate instability and independence of
monetary policy, in B. Putnam and D. Wilford, (eds.), The monetary approach
to international adjustment, (Praeger, New York).

Krueger, A., 1983, Exchange rate determination, (Cambridge University Press,
Cambridge).

Krugman, P., 1979, A model of balance-of-payments crisis, Journal of Money ,
Credit, and Banking, 11, 311-325.

Levich, R., 1985, Empirical studies of exchange rates: Price behavior, rate
determination, and market efficiency, in R. Jones and P. Kenen, (eds.),
Handbook of International Economics (North-Holland, Amsterdam).

McKinnon, R., 1982, Currency substitution and instability in the world


4
transact in international markets for which they maintain offshore balances
of foreign money, the level of which depends on relative financing costs.
But firms might also substitute currencies indirectly. For example, a firm
whose financing and production decisions are made domestically could be
substituting currencies indirectly through domestic financial intermediaries
that obtain funds from both domestic and foreign sources.

While the role of financial intermediaries is clearly important for
currency substitution, an analysis of their influence is outside the scope
of the present paper. For our purposes, it is assumed that domestic
financial intermediaries are owned by non-financial firms. The latter are
assumed to borrow their working capital in domestic and foreign markets at
the beginning of the year. At the end of the year, the firm is assumed to
pay back both the principal and the associated interest payments.

Consequently, the financing cost incurred is

(1) C= (147) (M,/P 4) + ((1H ¢)/(14€( de) /e) )(Me/P.),
where
C : portfolio holding costs,

domestic nominal interest rate,

a

f? foreign nominal interest rate,

My : holdings of domestic money by domestic residents,
Me : holdings of foreign money by domestic residents,
Pa : domestic price level,

Pe : foreign price level, and

e : exchange rate, (domestic currency/foreign currency).

The first term on the right-hand side of equation (1) represents the cost of

borrowing domestically; the second term represents the cost of foreign


3
balances that minimizes the borrowing costs associated with a given level of
monetary services. The solution to this problem yields a closed form money
demand function allowing open economy considerations. Section 2 also points
out the advantages of the approach taken in this paper relative to competing
empirical models of currency substitution.

Section 3 implements empirically the money demand function derived in
section 2 and presents estimates of the elasticity of currency substitution
using data for Venezuela. The empirical findings point to the existence of
a relatively high elasticity of currency substitution. Section 3 also
presents estimates of the exchange-rate risk implied by the currency
substitution model developed here. The results suggest that the probability
attached to a devaluation of the Venezuelan bolivar experienced a
substantial increase by the end of 1982. Finally, section 4 contains our

conclusions.

2. An Empirical Model of Currency Substitution
2.1 Optimizing Behavior

The point of departure of this analysis is the empirical observation
that the public--that is, firms and individuals--maintains balances of both
domestic and foreign currency.4 Specifically, multinationals and investment
corporations maintain balances in more than one currency because, by
arbitraging interest rate differentials and fluctuations in currency rates,
they reduce the financing cost associated with a given level of output (see
Levich 1985). Clearly, the extent to which firms can take advantage of
interest rate differentials depends, as indicated by King et. al. (1978), on
the degree of integration of world capital markets.

The kind of currency substitution that firms undertake by themselves

might be denoted direct currency substitution. For example, oil companies


16
8 = (Eleg,)) - e*)/e* = Ele,,,- e*)/e*.

Equation (15) gives the out-of-sample, or "revealed," exchange-rate risk
conditioned on the currency substitution model developed here. Note that,
according to (15), perfect currency substitutability (o + ~) is a sufficient
and necessary condition for interest rate parity between two currencies. 22

Table 2 presents data on domestic and foreign money (offshore)
balances and on domestic and foreign interest rates. With this information,
it is possible to compute a rough estimate of the exchange-rate risk for the
years 1981-1982 using the parameter estimates for the Ml money aggregate.
For the purposes of this computation, it is assumed that the exchange-rate
risk in 1980 is zero, an assumption that is consistent with the analysis of
Diaz-Alejandro (1984)23

As table 2 reveals, the exchange-rate risk associated with the
Venezuelan bolivar increased by 46.4 percent in 1981 and by a further 43.3
percent in 1982, giving a 117.1 percent overall increase. These results
suggest that the probability attached to the expected devaluation of the

Venezuelan bolivar rose quite substantially after two years.24

Such
expectations might have been triggered by declining nominal oi] prices and
by a level of international reserves below Venezuela's short-term external
obligations. Given the relatively large estimate of the elasticity of
currency substitution, acting on the increased probability of a devaluation
entailed a depletion of international reserves to the point where the
monetary authorities were forced to close the foreign-exchange market in
February of 1983. 26
Provocative as it may be, the preceding analysis is subject to a number
of qualifications that might limit its applicability to other circumstances.

First, the data available for Mp are based on liabilities of U.S. banks to


6
parameter estimates is such that neoclassical properties of optimizing
behavior are met globally.° Second, alternative hypotheses about the extent
of currency substitution can be tested depending on the value of the
elasticity of substitution, o. Specifically, as o +0, the two currencies
become perfect complements to each other; thus the currency mix does not
respond to changes in relative financing costs. AS o + », the two
currencies become perfect substitutes for each other. Consequently, small
changes in relative costs induce swift changes in the currency composition.
When o <1, the two currencies are said to be complements, whereas if o >1,
then the two currencies are said to be substitutes. 7

Because of the constant-returns-to-scale property common to aggregator
functions, and by an appeal to the small country assumption--that is,

Pa = Pes equation (3) can be expressed as

-p -p -l/p
wes ACM, + (1-8)(eM,) :

which is a convenient characterization of technology .®

2.2 Derivation of Optimal Domestic Balances

The optimizing problem faced by the firm can be summarized by the

Lagrangean function A as

(4) He Je (141 g)Mg + ((14i¢)/(148( 2e)/e) )(eM,) +

-p -p -1/p
+ A{ME - ACM, + (1-6)(Me) )

The first-order conditions associated with this problem are


22

dt = 9-592 + 1.084 InY,- 5.343 ig - 0.199 (ig + E(Ae)/e) + 0.123 TP ge
(2.7) (6.6) (-2.6) (-1.0) (0.6)

w2
-0.690 AlnPat + 0.234 In M 3 R =0.99 DW=1.49 SSE=0.046
(-2.7) (1.7) d,t-1 JB=0.19 ARCH-t=0.25 AR(8)=0.19;

In M

the monetary aggregate is Ml; Y is nominal GDP; other definitions are found
in table 1 and in footnote 8. Note that commodity inventories are treated
as an alternative asset, which could justify inclusion of the inflation
rate. Also, the coefficient for the price level is (1 - a,), which is very
close to zero. This finding implies that the income elasticity is not
different from one, as can be tested directly using the above estimates.

On the basis of this evidence, one would conclude that foreign exchange
considerations do not influence domestic money holdings in Venezuela.
However, using Branson's result--that is, ap = c(ay - o), one finds that o =
6.975 (=5.343/(1-0.234)) with Var(o)=4.22, which suggests that foreign
exchange considerations do influence domestic money holdings.

18 For example, Ortiz (1983) obtains an income elasticity ranging between
1.4 and 1.5; the income elasticity estimates of Blejer (1978) are also in
the neighborhood of one.

19 Testing for the hypothesis that the errors behave according to the
normal distribution relies on the Jarque-Bera statistic (Jarque and Bera
1980), JB: 2 3 2 2. 2
JB = T(w3/(6u2) + (1/24) (uy/(u2- 3)°)~x (2),

where T = sample size, and uy = hairs the first term of the JB statistic
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.
20 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

E(U§]d4.1) = yp + yy0% 43

the null hypothesis of homoskedastic errors cannot be rejected if y,=0,
which is tested with a t-statistic.

21 ‘The short-run version of equation (8) is
Aln(eMe/Mq) =yo Aln((1 + ig)(1 + E(ae)/e)/(1 + if).

Note that use of this equation does not involve any inconsistency if the
parameter estimates are obtained using all the first-order conditions.


International Finance Discussion Papers

Number 265

October 1985

MONEY DEMAND IN OPEN ECONOMIES: A CURRENCY SUBSTITUTION
MODEL FOR VENEZUELA

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.


9

Of these comparative-static results, the increase of optimal domestic
balances in response to higher foreign interest rates is less traditional,
and it stands in contrast to the implications of the portfolio-balance model
(see Cuddington 1983). The difference between the two approaches lies in
the different roles assigned to domestic money balances. In the portfolio-
balance model, domestic money is the riskless asset with zero return.
Consequently, higher foreign interest rates increase the opportunity cost of
holding such balances, which implies a decline in optimal domestic money
balances. In the present paper, domestic and foreign money are held because
they render the monetary services needed to support a given level of
transactions. To the extent that the monetary services of domestic and
foreign money are substitutable for each other in the production of monetary
services, an increase in the cost of foreign money services leads to an
increase in domestic money holdings. Thomas‘ (1985) theoretical model of
currency substitution has the same comparative statics as those presented

here.

2.3 Advantages of the Present Formulation

Equation (10) possesses an number of important advantages over
competing currency substitution models. First, from an estimation
standpoint, it represents the solution to an optimizing problem.
Consequently, the estimate of o is internally consistent with the underlying
theory. This consistency would be lost if the estimate of o were to rely
only on equation (8) because no allowance would be made for the restrictions
arising from the transaction technology, equation (7). Furthermore,
estimation of o by relying on equation (8) alone--as in Miles (1978) and
Ortiz (1983)--faces serious data difficulties, especially for developing

countries, because the prevalence of unrecorded capital flights complicates


8
first-order conditions is that the user cost of aggregate money M*, \, is
left unspecified.? From an empirical standpoint, an estimate of o relying
only on equation (8) is inconsistent with the one given by the solution to
equations (7) and (8).

These difficulties can be avoided by using all of the first-order
conditions. To this end, solve first for eM, in equation (8) and substitute

the result into equation (7) to obtain

p -p -1/p
(9) Me = AEM, #(1-6)(L(1-8)/8]° C(1+ig)(14E( ae)/e)/(141-)I7M,) of,

which is used to solve for optimal domestic money balances, MG > as

(10) Mj = {1+((1-8)/6)9((144g)(14E( ae) /e) /(14i g) JOE fe) 99/(1-9) (ea),

As equation (10) reveals, optimal domestic money balances depend on
domestic and foreign interest rates, on the expected rate of depreciation,
and on the aggregate level of optimal money services. The comparative

statics associated with equation (10) are
* . * * . *
aM,/ aig <0, aM,/a(E( se) /e) <0, aMy/ aig >0, and aM4/aM* >0.

An increase in either the domestic interest rate or the rate at which the
exchange rate is expected to depreciate reduces optimal domestic money
balances because of the associated increase in the relative cost of
borrowing domestically. An increase in either the foreign interest rate or

in the given level of monetary services raises optimal domestic money

balances.


Milt

60
76

M2t
60
68
76

MSL

60

68
76

Logarithm of money supply,

1.914560
-1.419010

0.117652

Logarithm of money supply,

1.997750
1.433650

0.215658

Logarithm of money supply,

2.156740
1.514400

0.233988

PRICE_PGDP75 -

60 0.497068

68 0.548037

76 1.055350
INTEREST_R -

60 8.100006

68 9.000000

76 10.000000

INTEREST_RUS  —

GDPNL

60
68
76

2.940000
5.350000
4.990000

3.349500
4.500000
4.289750

1.887500
-1.330360
0.348806

-2.052180
-1.325170
0.442856

~2.211180
1.395080

a aenenn

GDP deflator, 1975=1;

0.498270
0.541396
1.137980

8.300000
9.600000
9.800000

-1.925360
89880
39280

-2.036720

2.183400

71.296450

A. ©80575

0.499247
0.560969
1.208690

8.200000
10.300000
10.100000

DATA APPENDIX

1.860340
08420
04041

-1.877930
-1.089490

71.734410
0.982554
32767

-1.720520
88293
-916956

-2.011350  -1.843218
-1.106860 — -0.883940
0.648890 © 0.846281
Venezuela.
0.508934 0.513904
0.597704 0.622997
1.476560 1.827360

9.100000
10.100000
11.600000

U.S. 90-day Treasury Bill.

2.780000
6.440000
7

3.160000
4.340000
10.040000

8.400000
10.100000
12.900000

3.550000
4.070000
11.620000

Exchange rate, bolivars/$US; Venezuela

3.350000
4.499250
4.292000

3.349750
4.498250
4.292390

3.349500
4.500750
4.292000

4.501250
4.400500
4.292000

Logarithm of nominal GDP, 1975=1; Venezuela.

1.527730
-0.966837
0.134587

1.477220
0.935325
0.276030

1.387990
0.815867
0.365563

-1.301400
0.722662
0.573623

-1.199590
0.649151
0.770011

M1, 1975=1; Venezuela.

-1

M3, 1975=1; Venezuela.

-l.
-0.

644560
778841

M2, 1975=1; Venezuela.

651550

704302

769570
690209

515614

0.698218

8.
10.

Nw

aD

-1,

-0

- 9500
- 0300

300000
100000

se
so

-499750
. 304750

137580

476042

-1.620460
0.432851

653060

-1.760260
0.410505

- 524301
007530

Interest rate charged by commercial banks; Venezuela.

-600000
.100000

rr

4.880000
7.870000

4.498500

-1.096250
-0.050013

-1.514760
-0.000000

-1.524530
-0.000000

-1.621900
-0.000000

0.531888
1.000000

8.700000
0.100000

1

4.330000
5.820000

4.500000
4.285000

-1.044470
-0.000000


28
dollar market, American Economic Review, 72, 320-331.

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

Melvin, M., 1985, Currency substitution and western european monetary
unification, Economica, 52, 79-91.

Miles, M., 1978, Currency substitution, flexible exchange rates and monetary
policy, American Economic Review, 68, 428-436.

Miles, M., 1981, Currency substitution: Some further results and
conclusions, Southern Economic Journal, 48, 208-217.

Nickelsburg, G., 1984, Inflation, expectations, and qualitative government
policy: Ecuador 1970-1982, mimeo, University of Southern California.

Nickelsburg, G. and V. Canto, 1983, Towards a theory of currency choice and
currency crises, mimeo, University of Southern California.

Nickelsburg, G. and V. Canto, 1984, Dominant currencies, currency
substitution, and monetarism: A case study of Argentina, mimeo, University
of Southern California.

Obstfeld, M., 1984, Balance-of-payments crises models and devaluations,
Journal of Money, Credit, and Banking, 16, 208-217.

Ortiz, G., 1983, Currency substitution in Mexico, Journal of Money,
Credit, and Banking , 15, 174-185.

Simos, E., 1981, Real money balances as a productive input. Further
evidence, Journal of Monetary Economics, 7, 207-225.

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

Thomas, L., 1985, Portfolio theory and currency substitution, Journal of
Money, Credit, and Banking, 17, 347-356.


5
borrowing. Note that the cost of borrowing one unit of foreign money is
modeled as the foreign interest rate adjusted by the expected capital gains
(or losses) resulting from expected fluctuations in the exchange rate,
E(ae)/e.

The objective of the firm is to find the mix of money balances that
minimizes the borrowing costs of supporting the given level of aggregate
monetary services consistent with the firm's profit maximizing output level.
As Barnett (1985) has shown, if the firm's transformation function is
quasiconvex and if the technology is weakly separable over time, then the
intertemporal optimizing behavior of the firm with respect to factor
demands, production levels, and net asset holdings, yields an optimal level
of monetary services, M*, which is related to the available monetary

instruments via a transactions technology u:?

(2) MH/P 4 = U(M4/P qs Me/Pe)«

The structure of the transactions technology U(.) determines the extent
to which foreign money can substitute domestic money, and its estimation
constitutes the focus of attention of this paper. To this end, it is
assumed that the transactions technology obeys a CES aggregator function:

-p -p -l/p
lel = -
(3) M 1P4 A(6(M4/P 4) +1 8)(Mg/P ) ) ’
where
6 : distribution parameter, and

p : substitution parameter, p=(1-0)/o, o 0.

The choice of a CES might be justified for two reasons. First, the space of


19

ENDNOTES

1 One of the first papers in the area of money substitutes is Chetty
(1969). For more recent theoretical analyses see Canto and Miles (1983),
Krueger (1983), Girton and Roper (1981), Cuddington (1983), Calvo and
Rodriguez (1977), Boyer (1978), King et. al. (1978), Nickelsburg and Canto
(1983), Calvo (1985), and Thomas (1985). For empirical analyses focusing on
currency substitutability and the behavior of the exchange rate for the
major currencies, see Brillembourg and Schadler (1979), Britain (1981),
Miles (1981), and Melvin (1985). For the role played by currency
substitution in the international transmission of inflation see McKinnon
(1982), Goldstein and Haynes (1984), and Darby and Stockman (1983). For the
literature focusing on developing countries, see Tanzi and Blejer (1982),
Nickelsburg (1984), Nickelsburg and Canto (1983), Ortiz (1983), and Blejer
(1978).

2 See the analyses of Ortiz (1983), Cuddington (1983), Nickelsburg
(1984), Nickelsburg and Canto (1984), Tanzi and Blejer (1982), Blejer
(1978); Canto and Miles (1983) and Miles (1978) are exceptions in this
regard.

3 For Balance-of-payments-crisis models see Krugman (1979) and Obstfeld
(1984). For analyses of government seigniorage, see Fischer (1982), and
Khan and Ramirez-Rojas (1984).

4 For Venezuela, these balances can be held offshore only. For data on
US$ balances of Venezuelan residents, see the Federal Reserve Bulletin.

Data on liabilities of German banks to Venezuelan residents are published by
the Deutsche Bundesbank (Balance of Payments Statistics, table 7d); only
recent information is available. Data on liabilities to Venezuelan
residents from other countries are scant.

5 The model developed here is analogous to Thomas' (1985) model, except
that he determines the level of output (consumption C in his model)
endogenously, whereas it is exogenously given in this paper. This
separability assumption is needed for consistent aggregation; see Barnett
(1980, 1985). Clearly, the empirical validity of the separability
assumption should be tested in future research.

6 The space of parameter estimates of well-known flexible functional
forms, such as the translog (Simos 1981) or the generalized Leontieff, do
not satisfy globally the restrictions imposed by neoclassical optimizing
behavior, Note, however, that the CES is not the only functional form
satisfying these neoclassical properties. I have benefitted from comments
by William Barnett and James Boughton on this regard.

7 Bordo and Choudhri (1982), and Boughton (1981) criticize the validity
of the CES function for Canada and for the U.S., respectively. Bordo and


25

Table 2
Out-of-Sample Conditional Exchange-Rate Risk
Venezuela: 1981-1982

1980 1981 1982

Balances of Foreign Money®

Me (mill. $US) 3476 = 6342, s«:11667

AMe/Me — (%) 82.5 84.0
Balances of Domestic Money”

Mq (mill. bolivares) 49915 53482 49013

aM y/My (%) 7.2 -8.4

Domestic Interest Rates®

ig (%) 12.9 13.7 16.9

ty (2) 0.8 3.2
Foreign Interest Rates?

ig (%) 11.6 14.1 10.7

aig (%) 2.5 -3.4

Exchange-Rate Ri sk®
Ae (2) 0 46.4 48.3

Official Exchange Rate
e* = (bolivars/US$) 4.30 4.30 4.30

a. Liabilities of U.S. banks to Venezuelan private residents.

b. Ml monetary aggregate.

c. Interest rate charged on loans by commercial banks in Venezuela.

d. U.S. Treasury bill rate.

e. The exchange-rate risk is computed using the following approximation to
equation (15):

Ao = (aM. /M, - AMM )/(¥o) - A(iy - i,), where o = 6.038, = 0.279.

d


1. Introduction

The purpose of this paper is to examine the extent to which domestic
money holdings are influenced by foreign exchange considerations--an
influence that has been labeled currency substitution. Intuitively, one
would expect such considerations to influence holdings of domestic money
because, in a highly integrated world capital market, individuals face a
choice not only between holding domestic money and domestic bonds, but also
between holding domestic money and foreign money. To the extent that these
holdings are interdependent, a change in either foreign interest rates or
exchange rate expectations would exert an influence on the composition of
optimal money holdings with a corresponding impact on domestic money
holdings.

Knowledge of the extent to which foreign exchange considerations affect
domestic money holdings is important for the design of both monetary and
exchange rate policies. For example, the intended effect of a monetary
contraction could be offset if the public has access to foreign money
balances. In addition, if the domestic currency is expected to depreciate,
then individuals will increase their holdings of foreign money in an attempt
to avoid the associated capital losses. A persisting substitution of
domestic balances by foreign balances--the so-called dollarization--results
in a loss of government seigniorage and could precipitate a balance-of-
payments crisis.

Because of the importance attached to currency substitution, it is not
surprising that this subject has attracted a good deal of attention in the

literature. 1

However, existing studies have not examined the Venezuelan
case, which is the focus of attention of this paper. In addition to filling

this gap, an analysis of Venezuela's experience might be of interest hecause


12
Mate and its desired level, Mate is eliminated with a constant speed of

adjustment y within the period of observation: !3

(13) M yb,

= v
at = Ge)” Ma tea
Substitution of equation (10) into equation (13), and adding an error term

Ups yields a domestic money demand equation suitable for parameter

estimation:

(14) Mgg = (1#((1~8)/8)°((144 g (Elegy V/eg)/(14i g) EPH Ee)

xg¥o/ (1-0) (/*) (my ee + Ug,

2
where uy~ N(O, o,), Elup. Uy ;)=0 for j >0, and K = (a/A)¥.

One of the salient features of this last equation is its intricate
nonlinearity in the parameters. As a result, the estimation of these
parameters rests on nonlinear least squares; the algorithm employed here is
an adaptive quasi-Newton iterative approach developed by Dennis et. al.
(1981) .24

3.2 Exchange-Rate Expectations

Although the theory of exchange rate determination has been the subject
of an increasing amount of attention in the literature (see Krueger 1963),
the predictive power of existing theoretical exchange-rate models has been

challenged recently by Meese and Rogoff (1983). According to their


14
whether it is the result of the events leading to the financial crisis of

February 1983.16

If anything, their inclusion would bias the results in
favor of the currency substitution hypothesis.

The results displayed in table 1 reveal that the estimate of the
elasticity of currency substitution in Venezuela ranges from a value of 6.0
for Ml to a value of 8.5 for M2. Given the wide range of values that o can
take, the range of elasticity estimates obtained here is relatively narrow.
Furthermore, even though these elasticity estimates are less than infinite
(perfect substitutability case), they are substantially greater than one,
which is the (generally accepted) benchmark value above which currencies are
said to be good substitutes for each other)” One implication of these
empirical findings is that the absence of onshore balances denominated in
foreign currency is not a necessary condition for the existence of currency
substitution. For Venezuela, currency substitution might be arising from
both the relative importance of firms with international transactions and
the absence of capital controls.

The parameter y represents the inverse of the long-run income
elasticity of money holdings and its estimated value ranges from 0.76 to
0.96. A test for the null hypothesis of » = 1 reveals that it is not
possible to reject this hypothesis for the monetary aggregates Ml and M3,
whereas it is not possible to accept it for the M2 money aggregate. The
estimates of » imply an income elasticity ranging from 1.04 to 1.31 which is
similar to estimates obtained by other investigators!® The estimate of the
(constant) speed of adjustment, y, ranges from 0.28 to 0.45 implying that
half of the adjustment takes place in a year.

Table 1 contains also several statistical diagnostics aimed at

determining the validity of the maintained assumptions for the error term--

namely, normality, homoskedasticity, and serial independence. Specifically,


Money Demand in Open Economies:
A Currency Substitution Model for Venezuela

Jaime Marquez

July 1985
(Revised)

International Finance Division
Board of Governors of the Federal Reserve System
Washington, D.C. 20551

This paper investigates the extent to which domestic money balances in
Venezuela are influenced by foreign exchange considerations. To this end,
individuals are assumed to choose the levels of foreign and domestic money
that minimize the borrowing costs associated with a given level of monetary
services. The solution to this optimization problem yields a closed form
domestic money demand function. This specification is estimated and the
results point to an elasticity of currency substitution in excess of one.
Conditioned on these estimates, the paper presents estimates of the out-of-
sample exchange-rate risk for the period 1981-1982, prior to the collapse of
the fixed exchange rate system in 1983.

This paper was presented at the Tenth Annual Meeting of The Eastern Economic
Association, March 16, 1984, New York, and at the Fifth Meeting of the
Econometric Society in Latin America, Bogota, Colombia, July 24-27, 1984. 1
have benefited from comments and criticisms by William Barnett, Mario
Blejer, Eric Bond, Guillermo Calvo, Peter B. Clark, Vittorio Corbo, John
Cuddington, Betty Daniel, Neil Ericsson, Edward Green, Dale Henderson, David
Howard, Karen Johnson, Mohsin Khan, Jacques Melitz, Marc Miles, Gerald
Nickelsburg, and Kenneth Rogoff. Andrew Atkeson provided valuable research
assistance. James Boughton's comments helped in eliminating several errors
in an earlier version of this paper. 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.


23

22 Note that, for assets that are’ perfect substitutes for each other, the
portfolio-balance model yields this interest parity condition. The reason
why these two alternative models yield the same result is because the cost
minimization problem is the dual to the wealth maximization problem.

23 Diaz-Alejandro (1984), relying on time-series evidence, points out that
in retrospec, Venezuela did not required drastic policy adjustments in 1980.
Furthermore, he argues that the 1979-80 of] price shocks were perceived as
permanent improvements in the terms of trade. On these accounts, it seems
reasonable to assume that exchange-rate risk in Venezuela is zero in 1980.
Finally, note that the estimated residuals of the money demand equations of
table 1 show no sign of serial correlation.

24 The growth rates for M2 during 1981 and 1982 are 20.2 and 3.6 percent,
respectively; the ex-post exchange-rate risk of the bolivar with M2 data is
43 percent. The growth rates for M3 during 1981 and 1982 are 15.8 and 3.2
percent, respectively; the ex-post exchange-rate risk associated with M3
data is 81.5 percent.

25 Note that U.S. liabilities to Venezuelan residents, valued at the
official exchange rate, are very close to the value of M1 holdings.


ABSTRACT
This paper investigates the extent to which domestic money balances in
Venezuela are influenced by foreign exchange considerations. To this
end, individuals are assumed to choose the levels of foreign and
domestic money that minimize the borrowing costs associated with a given
level of monetary services. The solution to this optimization problem
yields a closed form domestic money demand function. This specification
is estimated and the results point to an elasticity of currency
substitution in excess of one. Conditioned on these estimates, the
paper presents estimates of the out-of-sample exchange-rate risk for

the period 1981-1982, prior to the collapse of the fixed exchange rate

system in 1983.


26

REFERENCES

Barnett, W., 1980, Economic monetary aggregates, Journal of Econometrics,
14, 11-48.

Barnett, W., 1985, The microeconomic theory of monetary aggregation, in W.
Barnett and K. Singleton, (eds.), New Approaches to Monetary Economics,
(Cambridge University Press, Cambridge).

Blejer, M., 1978, Black-market exchange-rate expectations and the domestic
demand for money: Some empirical results, Journal of Monetary Economics, 4,
767-773.

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

Boughton, J., 1981, Money and its substitutes, Journal of Monetary
Economics, 8, 375-386.

Boyer, R., 1978, Currency mobility and balance of payments adjustments, in
B. Putnam and D. Wilford, (eds.), The monetary approach to international
adjustment, (Praeger, New York).

Branson, W., 1972, The trade effects of the 1971 currency realigment,
Brookings Papers on Economic Activity, 1, 15-69.

Brillembourg, A. and S. Schadler, 1979, A model of currency substitution in
exchange rate determination 1973-1978, IMF Staff Papers, 26, 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, 13, 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, 85, 617-625.

Calvo, G., 1985, Currency substitution and the real exchange rate: The
utility maximizing approach, Journal of International Money and Finance, 4,
175-188.

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, Cambridge).

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

Corbo, V., 1982, Monetary policy with an overrestricted demand for money
equation: Chile in the 60's, Journal of Development Economics, 10, 119-126.

Cuddington, J., 1983, Currency substitution, capital mobility, and money


10
considerably the measurement of um, 10 For Venezuela the situation is more
complex because, in contrast to the “dollarization" experience of other
Latin American countries, monetary balances denominated in foreign currency
can be held offshore only. Estimates of o based on equation (10) avoid
reliance on data for Mee

Second, from a theoretical standpoint, the present formulation
distinguishes the cross-partial interest elasticity from the elasticity of
currency substitution. The importance of this distinction can be seen by
considering the specification of optimal domestic real balances typically

found in empirical analyses of currency substitution (see endnote 2):

(11) In(M4/P 4) = aye aji,-a

a lig + E( se)/e) ) -a

gig t agin(y/P,),
where i, represents the return on a third alternative asset. Accordingly,
currency substitution is said to exist if the cross-partial interest
elasticity ay is statistically significant. But as Branson (1972, p.29) has
demonstrated, if the underlying transactions technology is characterized by
a CES function, then the cross-partial interest elasticity, the direct
interest elaticity, a, and the elasticity of substitution are related to
each other according to the following expression:

a = clo - a),
where c lies bewteen zero and one. Consequently, to accept the null
hypothesis that ay equals zero--that is, no currency substitution--is not
equivalent to accepting the null hypothesis that o is equal to zero; on the

contrary, it implies that o = a The present study avoids this difficulty

1
by relying on a specific structural model. Alternative, and more general,

structural models would also avoid the potentially misleading implications


13

analysis, the exchange rate model with the greatest predictive power is one

where the exchange rate this period is expected to prevail in the following

period as well:
Fey 41) = &>
which implies that the exchange rate follows a random walk:

2
Cea = + Yeo where YE N(O,0,), E(v,. Vp_)70 for j >0.

The present paper adopts the random walk model of exchange-rate
determination on the basis of its superior forecasting power. 1° This choice
of expectation model is also motivated by the regression results of Diaz-
Alejandro (1984), which reveal that the two most important determinants of
the real exchange rate in Venezuela are an intercept and a dummy with a
value of 1 for 1983, the year of the collapse of the fixed exchange rate
system. Notice that the empirical tests of currency substitution are
conditional on the validity of the exchange-rate expectation model adopted
here,

The forecasting power of theory-based exchange rate models might
improve in the future with the development of alternative theories, more
data collection, and more sophisticated estimation techniques. Until then,
however, the present analysis rests on what seems now to be strong empirical

evidence in favor of the random walk hypothesis for exchange rate behavior.

3.3 Empirical Results
The data used for estimation are annual covering the period 1961-1980.
Inclusion of post-1980 data would not allow us to determine whether currency

Substitution is a general characteristic of the Venezuelan economy or