macroeconomic adjustment in externally-dependent economies with parallel exchange markets

MACROECONOMIC ADJUSTMENT IN EXTERNALLY-DEPENDENT ECONOMIES WITH PARALLELEXCHANGE MARKETSAuthor(s): Damien KingSource: Social and Economic Studies, Vol. 43, No. 1 (MARCH 1994), pp. 43-70Published by: Sir Arthur Lewis Institute of Social and Economic Studies, University of the WestIndiesStable URL: http://www.jstor.org/stable/27865941 .

Accessed: 14/06/2014 00:09

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

University of the West Indies and Sir Arthur Lewis Institute of Social and Economic Studies are collaboratingwith JSTOR to digitize, preserve and extend access to Social and Economic Studies.

http://www.jstor.org

This content downloaded from 62.122.79.69 on Sat, 14 Jun 2014 00:09:44 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=salises

http://www.jstor.org/action/showPublisher?publisherCode=uwi

http://www.jstor.org/action/showPublisher?publisherCode=uwi

http://www.jstor.org/stable/27865941?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Social and Economic Studies 43:1 (1994) ISSN: 0037-7651

MACROECONOMIC ADJUSTMENT IN EXTERNALLY-DEPENDENT ECONOMIES WITH

PARALLEL EXCHANGE MARKETS

Damien King

Abstract

This paper developes a model of the macroeconomic response to a

monetary shock in an externally-dependent economy with a black market for foreign exchange. A model of the currency substitution

genre is used to describe how monetary signals may be transmitted

through a black market rate and the supply side of the economy to real

output. The model demonstrates that monetary contraction may have an expansionary supply-side influence, and that this effect is stronger in the more dependent economies. The model also shows that devalu

ation is not neutral with respect to the black market premium.

INTRODUCTION

The purpose of this paper is to develop a model of macroeconomic

behaviour for a structuralist economy with a black market for foreign

exchange. The structuralist characteristic of interest is the dependence of the production structure in developing economies on imported intermediate inputs. The distinguishing feature of the treatment is the consideration of black markets within a complete macroeconomic

framework with an independent supply side. The model demonstrates

that expansionary money may exert abrief contractionary influence on

output in externally dependent economies with black markets, before any long run expansionary impact is felt. This result, based on differential rates of adjustment in goods and asset markets, undercuts

those of structuralist models of credit-constrained output. The model

shows also that a nominal devaluation can be contractionary and is not neutral With respect to the black market premium.

The focus of the analysis is the transmission of monetary signals to the real economy. Much has been written on the transmission of such signals via the unofficial credit (or "curb") market.1 Because of

pp 43?70



44 SOCIAL AND ECONOMIC STUDIES

poor state of financial intermediation in developing economies, and in

particular, the inadequacy of markets for equity as well as official limits placed on commercial bank credit, firms face a credit constraint

in the financing of working capital for production. Changes in the money supply can affect output via the availability of commercial credit as well as through changes in the interest rate being charged in the unorganized money market. It will be shown below that the

exchange rate regime, in particular, the presence of a parallel exchange market, introduces a transmission mechanism that can act counter to

this supply-side credit effect. The analytical content of this paper has a dual heritage, however.

In addition to being a response to the new structuralists and their working capital constraint, in modeling the transmission of monetary

signals in the presence of a black market this work is a methodological descendent of the black market literature.2 The specific mechanism

highlighted in this chapter, via the black market and the supply side, has largely been ignored in that literature because of inadequate treatment of the real side. Aizenman (1985), for example, has previ ously examined adjustment to monetary shocks and devaluation under a dual exchange rate regime. He shows that a black market exchange rate will rise in response to monetary expansion. His analysis is in a

partial equili-brium setting, however, and his concern is with the performance of the current account and how it compares to the single fixed exchange rate case. Thus, there is no analysis of the effect on the real economy.

Cumby's (1984) analysis of monetary policy in a black market economy is conducted in a general equilibrium context. He shows that an expansion of the domestic money supply, even if wealth does not increase initially, raises the black market rate. The depreciation of the black market rate itself creates a wealth effect and consequent increase in aggregate demand.

Nowak (1984) uses the Kouri stock/flow portfolio balance formulation, also in a general equilibrium context, and analyses the effect of both money growth and devaluation, largely on the price level and black market exchange rate. Output is demand determined by relative prices in the devaluation exercises, but his analysis of mone

tary changes assumes fixed output.



Macroeconomic Adjustment in Externally-Dependent Economies 45

The analysis below explicitly addresses the issue skirted bythese works ? how money affects the real economy in a black market or

dual exchange market regime. The framework employed is a simple general equilibrium model with a goods market and two financial assets. The financial assets (a domestic and a foreign asset) are

modeled as portfolio balances.3 The economy has an official fixed

exchange rate and a second (higher) black market rate, and current

transactions occur in both exchange markets. Exchange controls are

used to separate the two markets.

The structure of the paper is as follows. The basic model is constructed in the next section. In section 2, exercises are conducted to trace the effects of exogenous shifts in policy variables. The polices examined are a higher level of the nominal money stock and a

devaluation of the official exchange rate. In the final section, it is shown that the temporary contractionary effect of monetary expansion varies positively with the degree of external dependence in the economy.

1. THE MODEL

The Goods Market

A salient feature of production in LDC's is its external dependence. Production, particularly of manufactures, requires the use of interme

diate inputs not produced domestically. The elasticity of substitution with respect to diese imported intermediate inputs and raw materials

versus domestic inputs is low. Even in the long run, with capital and

therefore the technology of production variable, the choice of produc tion technique is limited because even the technology is imported, and

therefore embodies the factor endowments of an industrial economy.

Consequently, output is specified as a function of imported (?) and domestic (L) inputs. Production is governed by a concave Leontief

technology of the following form

Y = [min(?/?,L/x)]1/h (1)

where , , and h>l are positive parameters.

We make the usual 'small country assumption' that the world

price of imports and exports (P*) is given. A firm buys as much of its




imported inputs as possible at the lower official rate (e?, expressed in

"pesos" per "dollar"), the amount determined by the prevailing rules of the central bank limiting sales of official reserves. Firms then

purchase dollars on the black market (at rate e) to procure the

remainder of their imported inputs. The domestic cost of each im

ported input is therefore e?P* for the share bought at the official rate and eP* for inputs obtained with "black market dollars". Notwith

standing the presence of official currency inconvertibility, firms can

obtain as much foreign exchange as they need at the prevailing parallel

exchange rate. Domestic inputs are bought at a nominal price of w, hereafter referred to as "wages".

Profit maximisation using the production function of equation 1, and normalisation of world prices, yields an output function on the

following form.

Wages are flexible and there is no money illusion, so real wages

(w/P) adjust instantly to clear the labour market. The wage rate can

therefore be expressed as a function of the exchange rate, output price, and labour market conditions. For this reason, the wage term is omitted

from subsequent appearances of the supply function. The supply of

goods therefore varies inversely with the nominal (and real) exchange rate, and positively with the price level.4

Demand for the output of the economy is the sum of domestic consumption (C) and exports (X). Real domestic consumption is determined by real wealth (W/P).5 Aggregate demand is therefore

specified as follows:

Asset Markets

On the monetary side, wealth-holders apportion their wealth between a foreign and a domestic asset. The foreign asset is black market hard

currency, henceforth referred to as "dollars".6 The domestic asset is a

fixed-interest-bearing security, representative of and encompassing the range of domestic assets actually available, including money.

The asset demands respond to the relative rates of return.7 The

portfolio mix is determined, in general, by the interest rate differential

Y = Y(e/P, w/P) (2)

Yd = C(W/P) + X (3)




and the expected rate of depreciation of the exchange rate. The demand for a foreign asset (valued in domestic currency, eP1) can therefore be stated as follows.8

eP" = f"(r*+jc-r).W (4)

f1 is the fraction of wealth (W) that is held in the foreign asset; is the expected rate of change of the parallel exchange rate; r* (r) is the

foreign (domestic) interest rate.9 Nominal private wealth, W, is

identically equal to the sum of the nominal stock of (high-powered) money (M) and the domestic value of private foreign exchange holdings (e.F, where F is the privately-held stock of foreign ex

change). Foreign asset holdings are evaluated at the parallel rate since that is the rate on marginal transactions. Because much of foreign asset

holdings are indeed held as non-interest bearing money (all of it, by assumption here) and because we assume that domestic monetary authorities control interest rates, the interest terms become parametric and are omitted from subsequent appearances of the foreign asset demand equation. In this respect, the model is in the spirit of the

currency substitution framework.10

The supply of parallel market foreign exchange, the foreign asset, is given in the short run, and its domestic value is e.F. This

follows from an assumption that foreigners do not hold domestic

currency for speculative purposes.11 This is not an unrealistic assump tion in the context of small, developing economies with officially inconvertible currencies.12

The Black Market Current Account

In the long run, the supply of black market dollars is incremented or decremented by imbalances in the current account for transactions

conducted through the parallel market. The more depreciated the black market rate, the greater the surplus (or the smaller the deficit) in the black market trade balance. This occurs because the leakage from

export earnings is greater, and because import requirements are less

since output falls when the black market rate rises. On the export side, private foreign exchange inflow is a fraction (?) of total export earnings (P*X), with ? determined by the parallel market premium? the ration of the free and official exchange rates (e=e/e0).13 The larger




is this premium, the more likely that exporters will leak some of their

earnings to the parallel market. On the import side, private foreign exchange outflow is determined by the firms' output decision and the

amount of imported inputs required to produce that output. From the

production function, equation 1, total productive imports required will

be \ Some amount, N?, of the needed foreign exchange will be satisfied by the central bank, while the remainder, ( = ?-

?), will be

procured on the black market.

Measured in foreign currency, the current account is expressed as follows.

CA = ?(e). * - *( - N?) (5)

Imports consist entirely of imported productive inputs. Units of measurement are chosen such that world prices (P*) are unity, and so

are henceforth omitted.14

If the premium (e) rises, the inflow of privately-held dollars rises and the outflow falls, resulting in a larger private current-account

surplus. Thus, net private foreign capital inflow is equal to the parallel current account surplus, valued in foreign currency, and is denoted

by F.

Equation 5 implies a corresponding specification for the official current account. Exchange controls separate activity in the two

exchange markets in such a way that the determination of the amount

of import demand satisfied at the official rate is independent of the state of the official current account. That is, exchange control rules are

established which may or may not balance the official current account.

The government is assumed to hold the official exchange rate fixed over long periods of time, tolerating the implied erosion (or build-up) of central bank reserves.15 The assumptions made regarding the

conduct of the monetary authorities with respect to managing the

official current account has important implications for the behaviour of the parallel exchange rate, so the subject is explored in an appendix.

The Complete Model

From equations 1 to 5 and the addition of a market-clearing condition for the asset market, we derive the following 4-equation representa tion.16




where e = e/e?, ?e>0, and W = M + e.F.

Expectations of the black market exchange rate are formed with

perfect foresight, so = ?/e.

To complete the specification of the model, we make three additional assumptions and distinguish between adjustment in the short, medium, and long run. The first two assumptions are critical to

deriving the results below. First, we assume that, while assets markets

clear instantaneously, goods prices are sluggish.17 This assumption is

necessary for the short-run results. Second, we make the unusual

assumption that the monetary authority holds the official exchange rate fixed over a period of time long enough to include our "long run".

This accords with the empirical observation that official rates in

developing economies remain over-valued (even if not fixed) for long

periods. Finally, purely for expositional convenience, we assume that

exports are invariant to changes in relative prices. Since imports (N) do vary with relative prices, the trade balance is price sensitive anyway and so the assumption is harmless. The assumption merely allows the

removal of uninformative terms from the algebraic expressions.

The model adjusts in three stages, distinguished by capital flows and price adjustment. The short run is that period before goods prices equilibrate and the current account balances. Alternatively expressed, in the short run and F are given. In the medium run, F becomes

endogenous. Capital flows ensure flow equilibrium in the black market. In the long run, also becomes endogenous. Price adjustment ensures that Yd is equal to Y. While goods market adjustment should occur simultaneous with adjustment in capital flows, the present treatment ? an extreme case ? is to be viewed as an approximation to simplify manipulation.

The model laid out above can be given a simple diagrammatic

representation. The asset market is represented in e-F space. Using the

demand for the foreign asset and the wealth identity, the slope of the

Yd = C(W/P) + X

Y =Y(e,P)

(6) (7) (8) (9)

f*(7i) .W = e.F

F = ?(e). - ( - ?)




asset demand function is a rectangular hyperbola with the following

slope.

de \ ) - = - -

(10) dF F

where fd = F/O-f1). This yields a negatively-sloped relationship for every value of . The right quadrant of Figure 1 shows the locus for

=0. The supply of foreign assets, F, is a vertical line at the level of the existing stock.

In e-Y space, we map the private current account and the goods market. The positively-sloped18 line labelled "CC" in Figure 1 is the locus of points that balance the black market current account. From

equation 9 the slope of the line is

de

dY

eh5Yhl = -->0 (11)

cc x?e The positive slope reflects the fact that an increase in output

generates a greater demand for imported inputs, and consequently, a

current account outflow, in the long run, this current account deficit

can be balanced by a rise in the parallel exchange rate. Above CC, the current account is in surplus, below the line it is in deficit.




Goods market equilibrium is represented by the GG line. The slope of GG is represented by the following derivative, derived from

equations 1 and 7 for demand and supply in the goods market, and the

imposition of an equilibrium condition (for the long run). de (W/PYp) + (P/Cw) ? = --

(12) dY oo F + Ye(W/PYp)

The derivative is of ambiguous sign. While the increased cost of

imported inputs depresses output on the supply side when e rises, there is a positive wealth effect on the demand side resulting from a higher valuation of foreign asset holdings. Domestic consumption is prob

ably not affected significantly by the wealth effect from this source, so it is entirely reasonable to suppose that the supply contraction domi

nates. The sign of equation 12 is therefore taken to be negative and the

GG line is drawn accordingly.

By assumption, the goods market is not always in equilibrium. This gives rise to another (short-run) relationship between the level of output and the free rate of exchange

? the relationship that obtains before the price level adjusts to equilibrate the goods market. This

relationship, gg, is obtained from the supply equation, holding the

price level constant.

de 1 ? = ?

< 0 (13)

gg ?

where Ye is the partial derivative of supply with respect to the

exchange rate, gg is negatively sloped for the same reason that GG is,

namely, rising input costs.

It follows that GG has a steeper slope than gg. GG reflects the output response after prices have adjusted to clear the goods market.

Before price adjustment takes place, the effect on output of a change in e is exaggerated and this is reflected in the shallower slope of gg.

In the steady state, the current account balances and the goods market is in equilibrium. The steady state values of e and Y are

therefore determined by the intersection of CC and GG in the left quadrant. The steady state value of F is the level that corresponds to

the intersection of the level of e from the left quadrant and the asset market line in the right quadrant.




Dynamic Adjustment

Dynamic adjustment between steady states is analysed in two phases. The first phase describes adjustment to a medium run equilibrium under the assumption of fixed prices, and the second describes the

locus of medium run equilibria as price adjusts to the steady state.

Adjustment in the first phase, where P=0, is determined in the right quadrant and is governed by two equations. To obtain the first

equation, the perfect foresight condition, = ?/e, is inserted into

equation 8, and solved explicitly for ?.

eF e = e.f1

M+eF (14)

where f1 may take either sign, and has a positive derivative with

respect to its argument. The functional form f1 is the inverse of f*and is assumed to exist.

The movement of F is governed by the current account equation in conjunction with the level of output. Substitution of the level of

output from equation 7 into the current account equation yields

F = ?(e/e?)X - 6[Y(e,P)]h + N? (15)

Equations 14 and 15 describe dynamic adjustment in the first

phase of the model. The phase portrait in the right quadrant of Figure 2 shows the locus of points for which e=0 and for which F=0, derived

FIGURE 2




from equations 14 and 15. the e=0 line is coincident with the

previously introduced asset market demand curve for =0. The F=0

line is a horizontal line at the level of e which corresponds to the intersection of the GG and CC curves in the second quadrant.

Under certain conditions, the model displays saddlepath stabil

ity in the neighbourhood of the equilibrium.19 Adjustment towards the

equilibrium is along the stable trajectory, labeled ee.20 Substituting the

solution for the path of e from a linear approximation of the system into

the profit maximising level of output, output will adjust to its medium run equilibrium along the path,

Y = [(Tw + 6Acs* + ?)h/P]1/(1-h>, (16)

where s is the natural log base (we already use e as the exchange rate), is the eigenvalue for the stable solution (initial conditions are chosen

such that the coefficient on the term with the unstable eigenvalue is

zero), Ae is a constant, and ? = e(P,e?,X,N?) is the medium run

equilibrium solution for the black market exchange rate from equation 15. From this and the rigidity of in the medium run, the path of Y(e,P) is determined.

Adjustment in the second phase, which allows for price move

ment, is governed by P = L(Yd-Y), (17)

where the function, L, is monotonically increasing. Again using a linear approximation to characterise behaviour in a neighbourhood around the equilibrium, can be shown to follow a stable path.21 Substituting the solution for the path of into the profit maximising level of output yields the following path for the adjustment of output to its steady state value.

Y = [(xw+??)h/(ApsQt+P)]1/(lh>, (18)

where is the characteristic root of a Taylorseries linear approxima tion of equation 2 for P, Ap is a constant, and is the steady state value of P.

In summary, the short run response is determined by ee, gg, and

the given stock of foreign assets, F, in Figure 2. The medium run

solution is given by gg, CC for the current account balance, and the




asset market demand curve, e=0. And the steady state is represented

by CC, the asset market curve, and GG.

2. THE EFFECTS OF POLICY SHIFTS

This section describes two comparative equilibria exercises corre

sponding to the two major policy tools available to economic manag ers in developing countries. The exogenous shocks are: changes in the

money supply (usually induced by monetised deficit spending, though the fiscal implications are ignored here); and changes in the official

exchange rate. For both monetary and exchange rate policy, antici

pated and unanticipated policy actions are explored.

Monetary Expansion

The first exercise consists of an unanticipated once-and-for-all jump in the nominal money stock. An increase in the money supply raises

total nominal wealth and thus the demand for all assets, including foreign assets. In Figure 3, this is shown as an outward shift of the asset

market demand curve, since

dF

dM

*(0) >0 (19)

e=0

This causes an immediate jump in the exchange rate from e? to e1, and, with goods prices unchanged, produces a fall in output along gg in the left quadrant of Figure 3. The impact effect on the real side is therefore




an output decline from Y? to Y1, and the mechanism is the higher cost

of imported productive inputs. However, the current account is unbalanced, both because the

exchange rate has risen and because output has fallen (point F is above

the CC curve). After the impact response of a higher free exchange rate

and lower output, the economy begins its medium run adjustment. The current account surplus generates net dollar inflows. This increases the

supply of dollars in the black market, and the black market rate falls as the stock of privately held foreign exchange rises to fully accommo

date the increased desire for such holdings. In the medium run, both e and Y return to their original values at e2 and Y2.

The initial output contraction is a significant result which is at

variance with the economics of the new structuralist critique. Accord

ing to this literature, monetary expansion increases the availability of

credit (or reduces curb market interest rates) leading to output growth.22 While the results are contradictory, both mechanisms are distinct and

not at all mutually exclusive. Firms may simultaneous enjoy lower

curb interest rates and suffer the higher cost of imported inputs. The above result is not compromised if the monetary expansion

is anticipated. The difference is that the economic contraction now

occurs in response to the information about the forthcoming monetary

expansion, and not the expansion itself. This is illustrated in Figure 4. The announcement of a future increase in the money stock causes an

immediate jump in the black market rate (from A to B), in anticipation




of the depreciation that usually follows money growth. As before, this initial rise in e exerts a contractionary influence on the real side. At

point F in Figure 4, the current account is in surplus. The accumulating dollars and the rising black market rate move the market from to C.

At C, the fully discounted monetary expansion occurs and the market

adjusts smoothly towards the steady state at D, with a parallel rate of

e2 and Y2.

The output decline that precedes an anticipated monetary expan

sion, unlike the one that follows an unanticipated episode, does not

depend on sticky prices. In the anticipated case, the supply side contraction is sufficient to ensure some fall in output, since there is no

offsetting demand expansion until the money growth actually occurs.

After the medium run has been achieved, there is upward

pressure on prices because the demand for goods has risen in response to the wealth effect of the higher nominal money stock. Consequently, GG shifts to GO1 in Figure 5, in response to the higher money stock (excess demand is evidenced by point E being to the right of GO1). The outward shift of GG to GO1 is by the amount of the following derivative.

dY 1+f1 >0 (20)

dM GG (W/PYp) + P/Cw)

FIGURE 5

e G1 G g

c

Y 3 YO

F




The adjustment along CC and along the asset market curve to the

steady state, shown in Figure 5 as the movements from E to H and D

to S, can be viewed as the achievement of a series of medium run

equilibria.

At the steady state, there is both a higher exchange rate and

greater output, compared to the original position of the economy. The

steady state increase in the parallel exchange rate is a somewhat unusual outcome. The usual result in models of this type is for the

effects of capital account disturbances to be confined to changes in

asset stocks. Therefore, the wealth increase caused here by the

monetary expansion ought to have no long run effect on the black market exchange rate.23 The unusual result derives from the effect of

the monetary expansion on output, and the presence of output in the

current account via the need for imported intermediate inputs. The

steady state rise in output increases the demand for dollars. A higher

parallel rate is required to procure the additional foreign exchange in the steady state.

In addition to higher levels of e and Y, there is also an increased stock of black market dollars in the new steady state, resulting from the brief current account surplus.24 Departing from the extreme case

shown here in which F adjusts completely before adjustment begins, the pattern that should follow an anticipated or unanticipated jump in the money stock is a rise and then lesser fall in the black market rate, and fall and then greater rise in output.

Nominal Devaluation

Consider a nominal devaluation of the official exchange rate. The

devaluation implies a reduction in the black market premium and

therefore produces a deficit in the parallel market current account at the

existing level of the parallel exchange rate. Perfectly anticipating the

rise in the parallel rate that is required to eventually balance the current

account, wealth-holders immediately increase their demand for the

foreign asset and bid the parallel rate up, as shown in the right quadrant of Figure 6 as the movement from A to B. The rise in the exchange rate

from e? to e1 produces an initial decline in output from Y? to Y1 in the left quadrant, as the economy moves from E to F along gg. Once again, the decline in output reflects the increased cost of imported inputs.




FIGURE 6

e C1 G g

c

utat demand

g G

Y YO Y1 Y2

F

The medium run equilibrium values of e and y are, as usual, determined by the relationships in the left quadrant. The new C^C1 is above CC, from

reflecting the higher parallel exchange rate now required to balance the current account.

The impact response to the devaluation leaves the economy with

excess demand in the goods market and a deficit in the current account.

(Graphically, F is to the right of GG and below ClCK) The current account deficit produces a net outflow of black market dollars. In the

face of a declining stock of black market dollars to hold, wealth

holders bid up the black market rate (from to D in Figure 6) until the current account balances at the intersection of gg and ClC\ at

exchange rate e2.

In fixed exchange rate regimes, the conditions that precipitate devaluation are usually allowed to become sufficiently severe such

that the devaluation itself is widely anticipated. In the case of a fully anticipated devaluation of the official rate, the contraction in output

begins at the announcement of the forthcoming devaluation, rather

than at its occurrence.

de e

de0 ce

? >0

e0 (21)




The announcement of the policy causes an immediate deprecia tion in the black market rate, as wealth-holders attempt to increase

their holdings in anticipation of the new higher steady state. Figure 7 shows this as a jump from A to B. In the left quadrant, the correspond ing movement is from E to F, with a decrease in real output. At F, the current account surplus leads to an accumulation of private holdings, and the asset market moves from to C. At C, the devaluation occurs, the parallel exchange rate continues to fall having been fully dis counted, and the economy adjusts to its medium run equilibrium at D and H. The black market exchange rate is higher and output has fallen.

FIGURE 7

e

Prices adjust to achieve the steady state. The GG line is unaf fected by the devaluation since the official exchange rate does not directly affect the goods market. Nevertheless, the goods market is out of equilibrium in the medium run because of the output decline. So, in the final adjustment to the steady state prices rise to eliminate the excess demand, as shown in Figure 8 as the movement from points to T. In the new steady state (e4, Y4) there is a permanently lower level of output. This result is expected in any external dependence model which ignores the trade elasticities.25 A more unusual result is that the black market premium (e/e?) has fallen. That is, the official rate devaluation is not neutral with respect to the black market premium. Neutrality is a more common result in dual exchange rate models.26




FIGURE 8

e

4 3

The relevant elasticity is as follows,

de e? 1 -= -

(22) de? e 1 + Q

e?h?Yh-'Ye where Q = - -

> 0

X?e

Ye, the inverse of the derivative in equation 12, is the derivative of

equilibrium output with respect to e and is negative. Since Q is

positive, the derivative in equation 22 is smaller than the one shown for equation 21. The Q term accounts for the presence of output in the current account, the source of this unusual result (whereas equation 21

shows the shift of the function at a given output level). Following the devaluation of the official rate, as the parallel rate rises to restore

balance to the current account, the level of output falls. But the fall in

output reduces the demand for imported inputs and therefore the outflow of dollars through the parallel market. It follows that the

parallel rate need not rise as much in order to restore balance, as is the

case when there is no external dependence. Because of external

dependence, lower imports and hence dollar outflow helps to restore

current account balance more quickly.




If output is not dependent on imported inputs, then Ye=0 and therefore Q=0. Equation 22 reduces to

de e? - =1 (23)

de?e

This restores the neutrality of nominal devaluations on the black

market premium.

3. VARYING THE DEGREE OF EXTERNAL DEPENDENCE

The severity of the short run reduction in output following monetary expansion is a function of the size and diversity of the industrial sector.

In larger economies, with a larger and more diversified industrial

sector, the degree of external dependence will be less, and the extent

to which a rise in the exchange rate will adversely affect the supply side

of the economy will also be less.

To demonstrate this result, Ye, the partial derivative of supply with respect to the parallel exchange rate, will be used as an index of

the degree of external dependence of the production structure. High values of Ye correspond to the case where the imported input share of

output (N/Y) is large and the elasticity of substitution between domestic and imported inputs is low. In this case, we say the economy is more externally dependent.

We drop the perfect foresight assumption in favour of the

mathematically simpler case of static expectations ( =0). From equa tion 8, the wealth identity, and the information that =0, we may derive

de

dM

f*(0) = = - >0 (24) M

?o F

which provides the entirely intuitive information that, certeris paribus and with static expectations, a rise in the money supply will raise the

exchange rate.

Our entire result here depends upon the sign of eM, since the

following derivative is positive when eM is positive.




d2Y - = eM > 0 (25)

dMdYe The positive sign of the derivative in equation 25 demonstrates that the greater is the degree of external dependence (Ye), the stronger is the negative output response to monetary expansion (dY/dM).

This result can be demonstrated diagrammatically.27 The slope of gg is Ye. Larger negative values of Ye rotate the gg curve clockwise

in Figure 9, to a position such as g'g1. If a discrete jump in the money stock causes the parallel exchange rate to rise, as before, output will

fall. Note in Figure 9, however, that the larger negative values of Ye that cause the "flatter" g*g* line results in steeper output declines.

FIGURE 9

4. CONCLUSION The long run in the preceding analysis is characterised as that period long enough for goods prices to equilibrate and the current account to balance. It is not long enough for the monetary authorities to be forced to adjust the official exchange rate. Without this rigidity, in the long run purchasing power parity holds and money is completely neutral.

With the assumption that the official exchange rate remains

unchanged, the model reflects how the effects of monetary and

exchange rate policies evolve in the long run in economies where the




authorities maintain an over-valued official currency. The result

obtained is that nominal money growth is expansionary and devalua

tion contractionary even in the long run. Money growth raises the

black market rate, as does an official rate devaluation, but with a

devaluation, the black market rate rises by less than the amount of the devaluation so the premium falls.

The dynamics of adjustment are potentially of interest to the New Structuralist theorists and to policy-makers in small economies. With

differential rates of adjustment between goods and assets markets,

externally dependent economies will endure a temporary contractionary influence on output following money growth, prior to any demand side

expansionary impact. Furthermore, this contraction is greater the more

the economy ' s production structure is dependent on imported interme

diate inputs.

The analysis used an artificial and simplistic three period con

struction. This simplification is cause for caution in interpreting these

results, since the major conclusion depends crucially on the lag structure of the endogenous variables. Specifically, the conclusion

that output initially declines requires that the exchange rate respond more quickly than goods' prices. Even more important, it requires that the difference in the lag between the asset price and the goods' price

movement give enough time for producers to respond with a change in production. This latter lag, between a change in e/P and the

consequent change in output, was ignored in the above analysis. A theoretical refinement of the above framework may explore the

implications of introducing that lag explicitly. These results are likely to be of greater significance to the smaller

developing economies of Latin America and the Caribbean where the small industrial sector is dependent on imported inputs for assembly into final goods, and where die foreign exchange market more closely

matches the assumptions made in this paper.




APPENDIX: Official Foreign Exchange Flows and Nowak's Unorthodox Result This appendix explores the importance of the assumption regarding the behaviour of the monetary authorities in their management of the

official current account. As an example, Nowak (1984) illustrates a

case where an alternative assumption yields the unusual result that a

devaluation of the official rate results in a fall of the parallel rate.

The official current account specification implicit in equation 9 of the parallel current account is as follows.

= [1-?(e)] - ?

(Al)

where represents official reserves. If there are no autonomous

capital flows at the official rate, the amount of the deficit or surplus on

current account depletes or expands the stock of official reserves (P), so we set the current account equal to the rate of growth of those

reserves.

In the main text, we have made the assumption that the monetary authorities maintain values of e? and N? which may not necessarily balance the official current account. That is to say that they are not

endogenously adjusting the rules, their level of enforcement, nor the

official exchange rate, in order to balance the official current. The

reason that the assumption is made is that, over long periods of time, it is largely true. The effect is that changes in the stock of official reserves are endogenous.

The result of the assumption, as demonstrated in the main text, is to ensure that changes in the official exchange rate cause movements

in the parallel rate in the same direction. Lizondo (1987) implicitly uses a similar assumption regarding the endogeneity of the official current account to anchor his result that devaluation does not affect the

black market premium.

The alternative to assuming tolerance of reserve erosion is the

assumption that the official current account balances. Then in

equation Al is zero and there must be an endogenous variable on the left side of the equation. The most obvious candidate for an endog enous variable is e?, the official exchange rate. That is, the authorities

would adjust the official exchange rate such that the official current

balances in the long run. Macedo (1982) makes this assumption. The




objection to this assumption is that it is at variance with the observa tion that LDCs maintain officially overvalued currencies over long periods of time. Furthermore, by endogenising the official exchange rate, it removes devaluation as a policy option which can be analysed

by the model.

This leaves the export share, ?, or the provision of foreign exchange, N?, to be used endogenously to balance the official current

account, ? may be altered by changing the level of enforcement of the exchange control restrictions, or the restrictions themselves. But neither rules nor enforcement can be finely tuned to achieve balance, thus ? is a poor choice for an endogenous variable.

More reasonably, the authorities can use changes in the outflow

of official reserves, N?, to match the inflow of official reserves

[(l-?)X]. In this case, N? becomes the sought-after endogenous variable. The official current may then be exogenously set to any value, not necessarily zero. In such a case, F is set to some positive value. Endogenising N? in equation Al, therefore, accommodates the

possibility that the monetary authorities will use the value of N? to achieve any desired reserve objective, including an accumulation of

reserves.

The assumption that N? balances the official current account may

completely reverse the response of the free exchange rate following a devaluation of the official rate, as it does in Nowak (1984). The devaluation lowers the black market premium (e) and reduces export smuggling, transferring foreign exchange earnings from the black market to official coffers. In terms of our notation, ? falls. The increased inflow of reserves allows the central bank to supply more

dollars to importers at the official rate, since Nowak assumes the polar case in which the authorities choose not t? accumulate reserves (F=0).

Consequently, there are fewer importers resorting to the black market

to purchase dollars. This shows up in our equations as a rise in N?.

Forcing Nowak's model into Our notation, the changes in the black

market current account are as follows.

0 = ?(e) - ( Yh-N?) > 0

+ t t (A2)




If the fall in black market dollars being demanded by importers (6Yh-N?) is greater than the fall in dollar supply occasioned by the initial decrease in export smuggling (first term), the parallel rate decreases. Nowak ensures this outcome by the simple expedient of

differential costs of smuggling between exporting and importing. In

his model, there is a positive known cost associated with export smuggling, while import smuggling is explicitly costless. The posi tive cost of export smuggling means that the devaluation increases official exports by more than it decreases illegal exports. In equations Al and A2, total exports (X) rise, but the increase actually accrues

entirely to the official market. This allows for a "large" increase in the

share of imports met at the official rate and therefore a "large" rise in

N?. Under these circumstances, a fall in the black market rate is

required to restore balance.

NOTES 1. See Bruno (1979), Taylor (1981 and 1983), Porter and Ranney (1982), van

Wijnbergen (1983 and 1986), and Buffie (1984).

2. For a sampling, see Macedo (1982), Dornbusch (1983), Lizondo (1987), and the articles summarised in the following paragraphs.

3. See Kouri (1976) for a general portfolio balance formulation.

4. As long as the constraint imposed by the limited availability of foreign exchange at the official rate is effective, that is, as long as the firm is forced to

buy some foreign exchange at the parallel rate, then the official rate does not

appear in the supply function since the marginal cost of imported inputs is the

parallel rate.

5. "Wages" includes only income from the provision of domestic inputs, and does not include discounted income from the ownership of assets.

6. Private foreign asset holdings in Latin America are indeed largely held as

money. The most common holdings are U.S. currency in a local safety deposit box or a checking account in Miami.

7. Since the focus is on the speculative portfolio, we ignore the minimum variance portfolio by assuming that asset-holders are risk-neutral.

8. We use the wealth identity introduced below to eliminate the "n'th" asset market equilibrium equation, so we explicitly model only the asset market for

foreign currency.

9. The absence of Y from the asset demand equation requires a comment. The "domestic asset** may include demand deposits and bonds, both issued by the




banking sector. Households would satisfy a change in their transactions demand for money by shifting between demand deposits and bonds. But this would not affect the distribution of their portfolio between domestic and

foreign assets, which by assumption is affected only by changes in relative rates of return. For this reason, Y does not appear as an argument in the asset demand

equations.

10. The defining characteristic of currency substitution models is that the yield on the assets in the portfolio, usually monies, are not functions of the value of the asset, as is the case with bonds. For the general theoretical treatment of

currency substitution, see Girton and Roper (1981). For previous black market

applications of the framework, see Macedo (1982) and Dornbusch et al. (1983).

11. If foreigners held domestic assets for speculative purposes, then exchange rate movements would affect portfolio holdings of the domestic asset by foreigners. Their portfolio adjustments would augment the supply of foreign currency available for domestic residents to hold.

More formally, the portfolio-balance equation, f.W = e.F, common in cur

rency substitution models, can be shown to be a special case of the specification in Kouri (1983). The exchange rate adjusts to clear stock transactions in the

capital account for assets-holders in two currency areas, where each holds the other's currency.

f(r,r*+K).W -eF = gd(r-Jt,r*).eW*

- G

g0 is the fraction of their wealth, W*, held as domestic currency by foreigners, and G is the stock of domestic currency available to be held by foreigners. If

foreigners do not hold domestic assets, the right side of the equation is zero.

12. While it may indeed be a reasonable assumption in this narrow context, note that foreign direct investment, of which there is much in Latin America, is a violation of it.

13. Technically, the ratio of the parallel to official rates is equal to one plus the

premium.

14. Though it is a major source of dollars for the black market in Latin America and the Caribbean, private remittances are omitted from the specification for

simplicity. 15. These reserve changes are sterilised.

16. We adopt the convention of denoting partial derivatives with a subscript, except time derivatives which are represented by a dot thus: F.

17. See Dornbusch (1976) for the seminal partial-equilibrium sticky-price ex

change rate model.

18. The Y scale is decreasing from left to right.

19. The condition is that ?'X>-k, where, from the production function,

k^^a-h)^1**1-?




and is negat?ve. The characteristic roots of a linear approximation of the system are

?(M)+f1]?[[j(M)+f1]2+4j(M)(?'X-k)]1/2 e = -

2

where j(M)=f1,M/(M+l)2, which will yield roots of opposite signs if the condition is satisfied. The phase portrait representing saddlepath behaviour can be characterised by noting that, away from the ?=0 locus, ? obeys the following equation.

d? ? = f "+ flf (eF/M) de

The second term is positive, but as indicated earlier, f1 is of indeterminate sign. If it is negative and large enough, the dynamics away from a neighbourhood around the equilibrium may be different. Otherwise, d?/de will be positive. Away from the F=0 locus, F moves according to

dF (W/PY1 + (P/CW) ? = ?X + Y11"1

-

de F + Y^WTPYp)

which is positive. 20. Implicit in this type of economic formulation is the additional assumption that

the economy chooses the unique stable trajectory.

21. The characteristic root of the linearised differential equation is

Q = Yeep-L,C(l-f)1,

which is negative, where the partial derivatives are evaluated at the steady state.

22. See references in footnote 1.

23. See any of the previously cited currency substitution models.

24. In a fixed exchange rate regime, an increase in the money supply flows out

through the balance-of-payments, as a one-time loss of reserves. Because the

black market rate is flexible, however, the black market is behaving in a manner consistent with the results of flexible exchange models. The monetary expan sion leads to a current account surplus that is matched by a capital account deficit. In this case, the capital account deficit is the accumulation of foreign assets in the form of foreign currency. At the same time, the official market, with its fixed rate, will suffer a loss of reserves as imports rise.

25. See, for example, van Wijnbergen (1986). On the contractionary impact of devaluation, see also Krugman and Taylor (1978) and Buffie (1984).

26. See, for example, Macedo (1982) and Lizondo (1987). However, empirical evidence supports our result that a devaluation will reduce the premium [See Dornbusch (1983)]. Kamin (1986) has previously demonstrated that the




premium must fall, using reasons independent of the one above. For a case in which devaluation reduces, not only the premium but the level of the black market rate, see Nowak (1984) or the appendix.

27. Note, however, that the CC curve was constructed under the assumption of zero

elasticity of substitution.

REFERENCES

Aizenman, Joshua, 1985, "Adjustment to Monetary Policy and Devaluation Under Two-tier and Fixed Exchange Rate Regimes," Journal of Development Economics, 18, 153-169.

Bruno, Michael, 1979, "Stabilisation and Stagflation in a Semi-industrialised

Economy," In: Rudiger Dornbusch and Jacob A. Frenkel, eds., International Economic Policy, Theory and Evidence (Johns Hopkins University Press, Baltimore, Md) 270-291.

Buffie, Edward F., 1984, "Financial Repression, The New Structuralists and Stabilisation Policies in Semi-industrialised Economies," Journal of Development Economics, 14, 305-322.

Dornbusch, Rudiger, D.V. Dantas, C. Pechman, R. de Rezende Rocha, and D. Simoes, 1983, "The Black Market for Dollars in Brazil," Quarterly Journal of Economics, February, 25-40.

Chopra, Ajai, and Peter Montiel, 1986, "Output and Unanticipated Money with Imported Intermediate Goods and Foreign Exchange Rationing," Staff Papers, 33, December, 697-721.

Dornbusch, Rudiger, 1976, "Expectations and Exchange Rate Dynamics," Journal of Political Economy, 84, 1161-1176.

Girton, Lance, and Don Roper, 1981, "Theory and Implications of Currency Substitution," Journal of Money, Credit, and Banking, 13, 12-30.

Kamin, Steven B., 1986, "Devaluation, Exchange Controls, and Black Markets for Foreign Exchange in Developing Countries," Mimeo, MIT.

Kouri, Pentti J.K., 1976, "The Exchange Rate and the Balance of Payments in the Short and in the Long Run: A Monetary Approach," Scandina vian Journal of Economics, 78, 280-304.

Kouri, Pentti J.K., 1983, "Balance of Payments and the Foreign Exchange Market: A Dynamic Partial Equilibrium Model," in: Jagdeep S.




Bhandari, Bluford H. Putnam, eds., Economic Interdependence and Flexible Exchange Rates (MIT Press, Cambridge, Mass.) 116-156.

Krugman, Paul, and Lance Taylor, 1978, "Contractionary Effects of Devalu

ation,** Journal of International Economics, 8, August, 445-456.

Lizondo, Jose Saul, 1987, "Exchange Rate Differential and Balance of

Payments Under Dual Exchange Markets,** Journal of Development Economics, 26, June, 37-53.

Macedo, Jorge Braga de, 1982, "Exchange Rate Behaviour With Currency Inconvertibility," Journal Of International Economics, 12, 65-81.

Nowak, Michael, 1984, "Quantitative Controls and Unofficial Markets in

Foreign Exchange,** Staff Papers, 31,404-431.

Porter, Richard C., and Susan I. Ranney, 1982, "An Eclectic Model of Recent LDC Macroeconomic Policy Analyses,'* World Development, 10, 751-765.

Rojas-Suarez, Liliana, 1987, "Devaluation and Monetary Policy in Devel

oping Countries,** Staff Papers, 34, September, 439-470.

Taylor, Lance, 1981, "IS/LM in the Tropics: Diagrammatics of the New Structuralist Macro Critique,** in: W.R. Cline & S. Weintraub, eds., Economic Stabilisation in Developing Countries (Washington, The

Brookings Institution) 465-506.

Taylor, Lance, 1983, Structuralist Macroeconomics: Applicable Modelsfor the Third World (New York, Basic Books).

Wijnbergen, S weder Van, 1983, "Credit Policy, Inflation and Growth in a

Financially Repressed Economy," Journal of Development Econom

ics, 13,45-65.

Wijnbergen, S weder Van, 1986, "Exchange Rate Management and Stabilisation Policies in Developing Countries," Journal of Develop ment Economics, 23, 227-247.



macroeconomic adjustment in externally-dependent economies with parallel exchange markets

Documents