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Policy,Planning,andResarch
WVORKINGPAPERP FnanaldiOperations The Wor!dBank September1988 WPS 84
BlackMarketsfor Foreign Exchange,Real Exchange Rates,and Inflation Overnight versus Gradual Reform in SubSaharanAfrica Brian Pinto
Inflation could rise pernanently and substantially as a result of unifying official and black market exchange rates, even if real govwrment spending remains constant.
Tle Policy. Planning, and Research Cmnplex distributes PPR Working Papers to dissaeinate the findings of work in progress and to enowuge the exchange of ideas amongBank staff andall others imtesated in devclopmenxissues Tbesepapers carrythe names of the authon, reflect only their views, and hould be used andcited accordingly.The findings, interprettions, andumclusions arethe authors'own. hey should not be attributedto the World Bank, its Board of Directors, its management, or any of its menber countries.
PolkamPbn*, and Rueswh
Finandal Opaon
The olack market foreign exchange premium is an important implicit tax on exports, creating a conflict between the fiscal goal of financing govermmentspending with a limited menu of tax instruments and the allocative goal of stimulating exports. The premium is solved for in a model that includes the portfolio balance approach to exchange rates, dual exchange markets, and seignorage for fnancing the fiscal deficit.
The steadystate and dynamic implications for inflation of floats as a vehicle for unifying official and black market rates are then analyzed. Inflation could rise substantially in the new steady state as the lost revenue from exports is replaced with  higher tax on money. Further, the conditions under which undershooting or overshooting occur are parametevized. The paper is motivated by and illustrated with recent examples from SubSaharan Africa.
This paper is a product of thieFinancial Operations Department. Copies are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Sheila Fallon, room N8061, extension 61680.
The PPR Working Paper Series disseminates the findings of work under way in the Bank's Policy, Planning, and Research Complex. An objective of the series is to get these rmdings out quickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official policy of the Bank. Copyright © 1988 by the International Bank for Reconstruction and DevelopmenttThe World Bank
TABLE OF CONTENTS
Page
I.
EXCHANGE RATE UNIFICATION AND INFLATION
.
.
1
II. MODEL.. . 4 Government Spending and Foreign Exchange Rationing . . 4 Production and Real Exchange Rate. . . 6 Inflation Tax, Portfolio Balance and the Premium . . 8 Tradeoff between Tax on Exports and Inflation Tax . . 10 Unification Through Overnight Floats and Inflation . . 13 Exchange Rate Rules.................................................17 III. EXAMPLES FROM SUBSAHARAN AFRICA Overnight vs. Gradual Reform
.. .
.
19 20
IV. CONCLUDING REHA KS.............................................. ......22
Footnotes............................................................
.........
ApDendix
References ..... Figures 1

6
..........
24 27 ............................................. 29
I. EXCHANGE RATE UNIFICATIONAND INFLATION
This paper, which focuseson exchange rate reform and inflationin the presenceof black markets for foreign exchange,is motivatedby the recent experienceof certain SubSaharanAfrican countries,althoughmany Latin American countrieswould qualify. Attempts to unify officialand black market exchange rates by officiallyfloatingthe domesticcurrencyhas in two recent instances,Sierra Leone and Zambia, led to large increasesin inflation,with an accelerationin the rate of currencydepreciationrelativeto that historicallyobserved in the black market. Such increasesin inflationhave damaged the credibilityof the economic reform and weakenedofficial commitmentto it. What causes these surges in inflation? Take Sierra Leone. Sierra Leone experimentedbriefly with a foreignexchange auction in 1982, abandoning it in favor of a fixed peg to the dollar till it floated its currency,the leone, in July, 1986. The black market exchangerate (leoneper dcllar)was roughly four times the official rate prior to floating. Inflation,which had averaged 70 percent per year ovez the previousthree years, jumped almost immediatelyto an annual rate in excess of 200 percent,at which it stabilized. Likewise, Zambia started a foreignexchange auction in October, 1985, after unsuccessfullytrying to lower the black market premium and improve externalbalance through managed exchange rate rules from July, 1983. Its curcencyhad been linked to a foreigncurrency basket and was depreciated every month at a predeterminedrate with the rationingof commercialand capital transactionsretained. The black market premium was in excess of one hundred percent when the auction started. Annual inflationrose from about 20 percent in 1983 and 1984 to 37 percent in 1985 (auctionstarted in October), attainingan estimated level of 70 percent in 1986.
2 Two basic motives have spurred the adoptionof market exchangerates: first, to minimize black market premia (unify officialand black market exchange rates) thereby increasingexports and eliminatingallocative inefficiencyand inequitythrough import license rents; and second, absorbing black markets into the officialmainstream through economic incentivesrather than unenforceablelegislation,so as to raise the credibilityof economic policy. Initial conditionshave includeda rationedofficialmarket with a managed (fixed)rate, and a black market, where the currencyfloats freely and foreign exchangeis at a premium. In contrastto the usual specificationof dual exchange rates, e.g., Lizondo (1984),Dornbusch (1986), ''mMestic currency in the dual regimes of SubSaharanAfrica is not convertiblt
ither
commercial (trade)or capital (financial)transactionsat the j:ficial exchange rate. The black market rate applies explicitlyor implicitlyto both sets of transactions,serving as the marginalcost, or implicit resale value, of foreign exchange.1/ one might reason as follows:if, in fact, the officialexchange rate is inframarginal,then floatingthe currencyofficiallyshould result in a unified rate that is pretty close to the black market rate. Further,postfloat inflation 
rate of currency depreciation 
should be no different
from that which prevailed In the black market prefloat. In seeking to allay policymakers'fears that a float will result in a 'free fall of the exchange rate' irrespectiveof fundamentals,Quirk et al. (1987) point out that the inflationaryeffects of floatinghave wdependedcruciallyon the monetary and fiscal economic policiesthat have influencedthe subsequentdirection of the exchange rate changes'. They proceed to cite the example of Uganda, where domesticprices had already adjusted to the black market rate prior to floating (which is typically
the case): "The subsequent surge of inflation
when the exchangemarkets were unified was in responseto a relaxation of fiscal policy

'.
3It will be argued here that, under plausible conditions,postunificationinflationcould rise permanentlyand substantiallyeven if the level of real governmentspendingremains constant. The surge in inflationis explained insteadby developingthe link between fiscal and exchange rate reform with high black market premia. This link is directs there is a conflictbetween the allocativegoal of stimulatingexports by loweringthe black market premilm and the fiscal goal of financinggovernmentspendingwith a limitedmenu of available tax instruments. The black market premium functionsas an implicittax on exports,serving at once as a disincentiveto export productior. and a source of hidden fiscal revenues. The fiscal deficit is financedby a combinationof seignorage(the tax on domestic money) and the implicittax on exports. With unification,the hidden export tax vanishes. As a result, there li a compensatingrise in the tax on domestic money, Inflation. The first part of the analyticalmodel focuseson productionand real exchange rates, formally interpretingthe premium as a tax on exports. In contrastto other tax rates, e.g., a 30 percent import tariff, the premium is an endogenoustax rate, being determine'by the general equilibriumof all the asset prices in the economy. Consequently,the second part of the model focuses on the determnalntsof the premium as a precursor to discussingthe tradeoffbetween the premium and rate of inflation. These determinants include fiscal,monetary and exchangerate policy, asset preferencesand the terms of trade. UnLficationthrough floats and the Implicationsfor inflation are then discussedboth dynamicallyand in the steady state. The impact of acceleratedcrawls and maxidevaluatlonsis also examined. Lastly, policy formulationand some concludingremarks are presented.
4TI. MODEL
Exchange rate reform in net Franc Zone SubSaharanAfrica, and in LDCs generally,is motivated by the linked goals of making externalbalance sustainableand increasingexportg. This requiresconsiderationof export incentives,or the real exchange rate defined as the relativeprice of exports to nontradables. There are thus two goods: exports and home goods. There is currency substitution(Calvo and Rodriguez (1977))with residentsholding two noninterestbearing assets, domesticmoney (cedis)and foreignmoney (dollars). The dynamicsof cedis are influencedby the financingof the fiscal deficit,and of dollars, by the current account. GovernmentSpendingand Foreign ExchangeRationing For simplicity,the governmentspends only on importedgoods including,importantly,interestpaymentson historicallycontractedforeign debtt no new foreign borrowing is incurred. The governmentbuys dollars from the private sector at the arbitrary rate, e, exchangin&cedis for dollars. These dollars are paid for partly from conventionaltax receipts,which the private sector pays in cedis, and partly by printing cedis, which covers the deficit. The existenceof a fiscal deficit thus permits a simultaneous examinationof the inflationtax on cedis and the implicit tax on exportsvia a choice of e (cedis per dollar). The governmentsets e arbitrarily,does not have the reservesto deplete and so rations the official foreign exchangemarket by capital controlsand restrictionson commercialtransactions. The analytical implicationis that, with some leeway,official reservesin dollars, R, can be arbitrarilychosen. We assume that they are held constant, i.e., R  O. Thus, a fractionof private sector exports is surrenderedto the governmentat rate e for cedis. The governmentuses this to finance its own spending,which

;

is exclusively on imports, giving the remainder back to the private sector also at rate e.
There is consequently no net official accumulation of
dollars. The rationing schemt 
the previous paragraph amounts to a
redistribution within the priv* e sector coupled with an 'mplicit net tax transfer to the government, the source of this tax being the premium on dollars in a black market, where the exchange rate is b 2 e.
The black
market, or free market, arises precisely because the official market is rationed. Domestic currency is freely convertible in the floating black market at rate b, which is the marginal cost of foreign exchange. Dollars obtained officially can be resold, or at an7 rate, imports purchased with official dollars are priced in domestic currency at their opportunity cost, the black market rate.
This is precisely what gives rise to
rents
in the
presence of rationing through import licenses. Exporters either ship their exports through official channels, earning the rate e, or smuggle them, at rate b.
There are no real resource
costs of smuggling, but there are private costs of smuggling. 2/
These
consist of bribes paid to various officials. The marginal cost of these bribes increases with the volume of exports smuggled. Exporters equate the marginel returns between the official and black markets in equilibrium. Consequently, the marginal return on exports is the official rate e.
This
creates an asymmetry between importers and exporters. For importers, e is inframarginal and irrelevant; for exporters, e is the marginal return. It is precisely this difference that leads simultaneously to import license rents and to the black market premium being interpreted as a tax on exports. In the above regime, e has an exogenously chosen rate of depreciation, ele  A
2 0. This, in conjunction with a given real fiscal
deficit and the assumption that R as we shall see later.

0
is equivalent to a money supply rule,
 6
Production
and Real ExchanseRate The approachhere followsKharas and Plnto
(1987). There le no
capital,and the given endowmentof labor,C, is fully eployed, being allocatedbetween two goods
an export good, and a hom good, which also
requiresintermediateImports. The privatesector spends only on hbas goods, domesticconsumptionof the exoort good being negligible. Home goods, H, with price PH, re producedby a CobbDouglas technologyusing importedInputs (oil),I, and labor, L1 . 31 Importsare valued at their marginalcost, b. Exportsare producedusing a constanttechnology,X  L. Of total *xports,X, X2 is smuggledout returnstoscale
and X3 surrenderedto the governmentat rate e. C(X2) Is a strictlyconvex functionrepresenting privatecosts of smuggiLng(bribes)in terms of exports with C()MO and C', C0>0. The privatesector solves the followingproblem, where w is the domesticcurrencywage and Px the dollar price of exports. The dollar price of importsis unity: (1) max
s.t.
pHH + bPX 2 + *PxX3 bPxC(X2 )  w(L1 + L2 + L3 )  bI
H c L xi
Li
,i,Li
I L
I, L > O
10,I) 0.e (i2,3)
(i1,2,3).
The solutionto (1) based on the FOC may be describedas follows:total exportsare distributedbetweenthe officialmarket (X3) and the black market (X2) by equatingmarginalreturns,i.e., by settingbpx(l  C'(X2)) *Px
 w.
1 . We obtain the export smugglingfunction Let c I (C')
(2) X2  c (1  1/#), where # ' b/e is the black market premium. Since c' > 0, dX2/d#
>
0, so that
7
the incentiveto smuggle increasesas the premium rises. With regard to home goods, it must be the case that in equilibrium, where k is a constantdependingon a.
PH k(a) wb,
ep1  w, it follows that PH k(e) e #
Using the FOC that
ia a Px
The current account in dollars is given by Px(X2 + X3 )  I  g, where I is intermediateimports and g is governmentspendingon imports,fixed in dollars.
Consequently, px(X2 + X3 )

I  g  F + R, the RHS of the equality
denoting foreign asset accumulation. F is the stock of dollars held in that private portfolios. Recalling that R  0, it follots (3) Px(X2 + X3 )  I + g + F. Consequently, in steady state with F  0, I  pxXg, where X  X2 + X3 is
total exports. Substitutinginto H 
a
1a I (see (1)) gives the steady state
technologicalrelationshipbetween H and X, (4) H since X 
(LE X)  L1.
(pxXa g)ia , It is easy to verify that H. < 0 so that H is a strictly
concave functionof X. Further,H  0 when X  g/ps or when X  E.
We
require that pxL > g, i.e., that the maximum feasiblesupply of dollars exceed the government'srequirements. The PPF is shown graphicallyin Fig. 1. At X  X*  (1a)E +
a(gIpx),Hx  0. Since domestic residentsconsume only home goods, it follows that
the optimal
point
to produce Fig.
at is X*, where H is maximized. 1 near here
Where does productionactuallytake place? From (1), (1  a) pHH  bI and that aPHH  wLl. with (3) yields:
we know that
Using these FOC and X2  L2 , X3  L3
(5) LI '
ap1 
+pat) 
I ,(1 a)
(PD,4.FR)
Let Xopt denote the steady state solutionto (1). Since Xopt C  Ll, using (5) with F  0, we get X(Pt
((1
 a)E + ao(g/px)](l
 a + at).
Since 0 2 1,
ft follows that XoPt 5 X*, with XOPt  X* when 0  1, i.e., the expsrt tax via
t
is eliminated. When X  XoPt, Hx  bpx(l  l1/)/pH,which is zero when
1. This expressionis merely the ratio of the marginal costs of smugp 4/ price of home goods.
So long as
t
t

g to
> 1, XOPt c X* and consumptionox home
goods is less than its maximum feasible level correspondingto X*. Not only does this capture the productiondistortionas a result of the export tax via r,
it also capturesthe notion of import compressionand its effect on lower
GDP growth as a result of stunted exports,a major preoccupationin many LDCs today. The bottomlineis that in order to stimulateexports,
t
must be
reduced. This is the allocativegoal that is pursued. In the circumstances,a natural candidate for the real exchange rate is epx/pH, the relativemarginal returns of exports and home goods. This 1 . since PH  k(a)(epx)abla. In order to raise works out to be kl(pxI1)l
the relativereturn of exports and thereby the inceAtivesto produce them,
t
must clearly be reduced,which is consistentwith our earlier observations. Propositionl: In order to depreciatethe real exchange rate and improve productionincentivesfor exports, the black market premium must be lowered. Proofs Obvious from above discussiceAnd Fig. 1. InflationTax, PortfolioBalance and the Premium Since reducing of
t.
t
stimulatesexports,we now focus on the determinants
This brings us to the monetarypart of the model. The main ideas from
the real part of the model are that
* must be reduced if exports and real
income are to be raised,which is obvious from Fig. 1. We simplify the rest of the presentationby settinga  0, i.e., home goods are producedwith
9This makes the algebra more elegant, but does not
intermediate imports only.
in any way change the results we now present on the tradeoff between the tax on exports and the inflation t x (see Kharas and Pinto (1987)). This is because these results are driven by the financing of the fiscal deficit and the asset demand for dollars. Setting a  0 means that the private sector, like the government, spenes only on imported goods, which is the assumption in Lizondo (1984) and Pinto (1986). All production, pL, lis now exported and consumption, imported. Eq. (3) can therefore be rewritten as F

pxL  g  I.
where
I
is now private consumption. Private residents spend a fixed fraction, a, of their nominal financial wealth, W

M + bF, where M is the stock of cedis in private
portfolios and F is converted from dollars into cedis at the (relevant) black market rate, b.
F

p
(6)

Fp
where m
Thus, bI  a(M + bF).
This, in conjunction with
g  I yields the dynamic equation: L  g  a(m/
+ F),
M/e, recalling that
*
b/e.
The dynamic equation for M is provided by the financing of the deficit.
ie assume that government spending, g, and taxes, t, are fixed in
dollars. The deficit is financed by domestic credit, D.
Since R

O it
follows that: (7)
M
D  e(gt),
with the deficit being converted into cedis at the official exchange rate, e. Since m E M/e, we get:
(gt'  me,
(8)
n
where
e  e/e>O is the official rate of depreciation.


10
_
The system is completedby a portfoliobalanceequation. Let A be the fractionof wealth W 11 + bF held as domesticmoney. Since interest rates are abstractedfrom, the relevantdifferentialrate of return betweenM and F is the rate of depreciation 'ofthe cedi in the black market, b=b/b. Continuousassetmarketclearingand perfectforesightyield
(9)
X(b) .
M
bF ,
()
0 if 7> 1
c 0 if v
1, i.e.,
e exceedsthe seignoragemaximizingrate, increasinge actuallyraises** (to the rightof B in Fig. 2). The intuitionis that a rise in 0 will,
in the new
steadystate, raise the differentialrate of return betweenH and F, increasingthe desirabilityof F. This by itselfwould raise *; but e also affectsthe unit inflationtax, leadingto the ambiguity.
 12 
Notice that in Fig. 2. the minimumpointon the [*(e) curve (correspondingto B on the xaxis) is less than 1. This is equivalentto assumingthat it would be feasiblefor the governmentto finance its deficit entirelyby the inflatior, tax, should it choose to. Further, in the dual regime, it is analyticallydesirable that
!> 1, owing to rationing. These
considerationstogether imply that f  1. Thus, the relevant tradeoff between 0 and # is between A and wl on the xaxis, and the segment CD on the #*(e) curve in Fig. 2. This tradeoffexists iff v < 1. Further, the model and steadystateequilibriumsolutiondo not apply between il and rh . since for an a in this interval,seignorageexceeds the deficit and foreign exchange is bought at an officialpremium, rather than discount, relativeto the black market. We shall assume the followingcotnditions are satisfiedt * f
(1,
)
(15) 0 and d#*Idpx < 0, can be formally derived from eq.(11). A precise expressionis now derived for the implicittax on exports in steady state via the premium. First, for the private sector, the real stock of cedis is M/b, and not m M/e.
Accordingly,the relevantcapital
loss from the inflationtax in steady state is (MHb).# m*.§/I. Second, from eq. (7), cedi taxes  et, so that the real tax burden is et/b  t/t* in steady state. Since the private sector'snet loss is the government'sgain, it follows that the residue is the implicittax on exporters,given by g(m*.eI/#+
t/I)

g(l  l/4). More mechanically,reorganizingeq. (13)
yieldst (17)
If
t
g  m*e
+
t
g(l
1)+
t
+ m
2 2, i.e., there is a 100 percent premium on foreign exchange in the
conventionalsenseacommon situationin SubSaharanAfricathisrevenue financesupwards of 50 percent of governmentspendingon imports and interest payments on foreign debtl UnificationThrough OvernightFloats and Inflation Assume, to start with, that there is a genuine tradeoffbetween and
e as discussedearlier in the context of Fig. 2.
t
The 'real deficit"
continues to refer to (gt), i.e, the number we would get by looking at the fiscal accountsavailable at any Ministry of Finance. Thus, revenuesfrom both the inflation tax and implicittax on exportersvia
t
are excludedin
computing the real deficit. The reason for this reminderwill become apparent.
 14 
Proposition3: Assume conditions (15) hold and that (gt) and Px are given. Then if the currency is floated overnight (rationingis eliminatedand the official rate of depreciationendogenized),post unificationinflationwill rise in the new steady state, i.e., there will be a permanent increasein inflation. Prooft Let ube denote the unified floatingexchangerate, and a denote its now endogenousrate of depreciation. The new dynamic system consists of eqs. (6), (8) ed (10),with e  u and #  1. In particular,m is redefinedas M/u, and in the new steady state, t*  1.
Considereq. (16), noting that 0 is
the rate of inflationjust before floating. Since the R.H.S. of (16) is constant, and 0* > 1 prior to the float, it must be the case that 0(a) > 9(e) if the inflationtax is to finance the deficit in the new steady state. But, from (15), 5
C
1. Therefore,a > 0. In fact, a  fl > e, where rl is shown in
Fig. 2. The intuitionis simple:by unifying, the governmentloses the tax revenuesimplicit in the premium, g(ll/) (eq. (17)). In the absence of changes in fiscal policy, it must replace this tax on exports with a higher tax on money. Obviously,the larger the tax on exports (the larger #* is, equivalently,the smaller e is) to begin with, the bigger the jump in inflationupon floating. Fig. 3 near here Fig. 3 summarizesthe outcome. Since, upon unification, (18)
e(c)3A(*).*
* .
and the R.H.S. of (18) is a constant, it follows that there are two possible steadystateequilibria,Jr and rh as shown in Fig. 3. These are the same as the fl and rh in Fig. 1 for given (gt) and Px
71 In accordancewith
standardresults (e.g.. Dornbuschand Fischer (1985)),rl is saddle point stable, and rh completelylocally stable, given rationalexpectations.8/

15

Proposition4: Assume, with given (gt) and Px' that the currency is floated overnight,unifying the officialand black market exchange rates. Of the two possible steadystateequilibria,wl and 1'h (Fig. 3), i1 (1 < 1) is saddlepoint stable, and Th (9 > 1) completelylocally stable, under rational expectations. Proof: Set #  1 in eq. (6), (8) and (10) and replace e with u. This is the new dynamic system. Redefinem as M/u, noting that it is now a jump variable. Invert (10) to yield Q  #(m/F), where
t
t'
E/(1X)1l,
0, the saddlepointstabilityof rl follows. rh can be shown to be
completelylocally stable by showing that A > 0 and the trace, given by [a + a ((1X)/v1)],negativewhen 1>1. What are the dynamicsof inflationupon floating? We assume that upon floating,the economy gravitatesto the lowinflationequilibrium,91 for the same reason as in the closedeconomyliterature:this equilibriumis saddlepoint stable (Proposition4) and thereforeimplies a unique dynamic path for the price level and inflation. Given conditions(15), inflationwill be higher in the new steady state, so that the desired steady state ratio and level of F will rise, implying a dynamic path for inflation. Fig. 4 presentsthe phase diagram in mF space for the system (19)(20). The curve FO is shown as the downward sloping line, FF, with slope 1. MMis the m=O curve. Its slope is derived in the appendix.
 16 D is the dual regime equilibriums the ratio of domestic to foreign assets \/(1)k))is higher and Inflation, lower. E is the saddlepoint stable low inflation equilibrium ('1 m*, F*), with higher inflation and therefore a lower domestictoforeignasset ratio, (rl)I(1)dr 1 ))=m*IF*. Fig. 4 near here VV is the positively sloped saddle path leading to E.
Since F is
higher in the new steady state, current account surpluses need to be generated. By (19), this requires a reduction in (m+F). With F sticky, m_M/u jumps to the point ' on VV.
The economy then converges to E along VV.
From Fig. 4, we see
that whether inflation overshoots or undershoots its new steady state level, rl, depends upon whether VV is flatter or steeper then the line OE with slope m*/F*. If the slope of VV equals m*/F*, then inflation will jump immediately to fl1 The precise condition is derived in the Appendix as eq. (25) and graphed in Fig. 5. Fig. 5 near here It turns out thac if a/sl > (lX(11 )], the inxflationrate will overshoot 'l. Otherwise, it will undershoot rl portfolio equation, \(Q) 
,e7(, X0 e (0,l).
Assume X(Q) is a Cagantype At Q* in Fig. 5, which plots
condition (25) (see Appendix), a/Q  (1  X(Q)]. Therefore, if wl < (>) Q*, we observe overshooting (undershooting). The determinants of Q* are portfolio preferences (as parameterized by
k,
and 7) and the speed at which dollars can be
accumulated (as determined by the propensity to spend out of wealth, a).
The
determinants of rl include these as well as the fiscal deficit (recall from Fig. 3 that X(r
1
).i
1

a(g  t)/(pxL  g)).
Suppose 7 goes down
(desired ratio of dollars in wealth goes down at each level of inflation) and a goes up (larger current account surpluses will be generated for a given reduction in wealth).
Then from Fig. 5, Q* goes up and from Fig. 3.
Nj
goes
down (unit inflation tax curve rises) increasing the chances of overshooting. Table 1 computes approximate values of t* for different parameter levels.
 17 
Table 1: IllustrativeComputationof Values for G* (1) Case
(2) a
(3) X0
(4) 7
(5)
*
(6)
*
(Z per year) A B C D
0.05 0.10 0.10 0.10
0.85 0.85 0.90 0.90
0.50 0.20 0.20 0.10
200 500 500 1000
21 45 53 64
Case A assumes reasonablythat 5 percent of wealth is consumed per year. At zero inflation,85 percent of wealth is held as cedis (Xo  0.85). 7 is 0.50, implyinga seignoragemaximizing rate of inflation (X*, col. (5)) of 200 percent/year. Q is roughly 21 percent/year. In case B, a is raised to 10 percent and W* to 500 percent/year,with 0* rising to 45 percent/year. Case C raises )o to 0.90. Case D is the most conservative,with a  0.10, )O  0.90 and 1*
=
1000 percent/year. Yet, 0* rises modestly to 64 percent/year. Since prevailinginflationrates prior to floatingare lowerboundsfor
w1 under conditions(15), undershootingof inflationis empiricallya distinct possibilityfor many of the empiricalcases from SubSaharanAfrica. The bottomlineof this sectionhas two partss first, in any event, inflationwill rise in the new steady state; second, to know whether inflation is going to overshootor undershoot,we must know w1 and u*. Otherwise,we cannot offer the comfort that the rise in inflationis transitoryand that inflationwill eventuallydecline. ExchangeRate Rules We now considerofficial exchangerate rules that attempt to lower the premium. From eq. (11),we see that the steadystatesolutionfor
* is
independentof the level of the officialrate, e. Oneshot devaluationswill thereforereduce the premium only temporarily.9/ The reason is that growth rates and monetary dynamicsdo not change fundamentally. Some intuition is
 18 provided for this result in Fig. 6. m  (gt)  m#.
The downward sloping line plots eq. (8),
To simplify, assume we are in steady state to start with, and
that the devaluation is unanticipated. As a result of the devaluation,m, which is usually sticky, jumps from m* to ml in Fig. 6, so that m jumps to A > 0.
Since F is sticky, # must decline to ensure portfolio balance.
However, as m returns from mi to m*, # returns to its original value (see Pinto (1986) for explicit dynamics). A devaluationwhich accompanies a reduction in g will, however, speed up adjustment to a new steady state where # is permanently lower. Fig. 6 near here In contrast, if whether
e is increased,0 will go up or down depending on
e is beyond rh, or between A and 91, to start with, in Fig. 2. This
result has already been discussed above: accelerating e will i7Th to start with, a reduction in 0 will
work only if
be unambiguouslybeneficial,
since both the premium and rate of inflation decline. 10/
It is important to
note however, that for such high inflation situations, attempts to halt inflation in its tracks through exchange rate freezes (0O) will not work unless g and (gt) are drastically reduced. Otherwise, there is no steadystate solution for m or
*, and
i
equals
G, which approximatesthe growth rate of
base money. ll/ A policy switch will be forced when
i
is hit.
In such cases,
inflationwill rise rapidly and by a large amount if the policy change includes an overnight float (see Proposition 3). Another possibility is motivated by the erroneous argument that the equilibrium exchange rate, e*, is some weighted average of b and e, rather than being determined on the margin. Thus, e* to move towards e*.

pb * (lp)e, pe(Ol). and advice is
This unwittingly links official depreciation to the
premium: e  e*e  P(be), or, 0
=
p(#l).
Such a policy could set up a
destabilizingspiral of higher premia and rising depreciation, raising inflation (see Kharas and Pinto (1987) for an example).

19

III. EXAMPLES FROh SUBSAHARANAFRICA
Why does the governmenttrade off the premiumwith the rate of inflation?
Typically,exports originate in agriculture,with the bulk of
import licensesgoing to urban manufacturing. The gainers and losers in the event of unification,are shown below: Gainers
Dual Regime
 Government  Import license
 Farmers  Domestic currency
recipients
holders
 Government
Unified Regime
Losers
 Farmers
 Former import
license holders  Domestic currency
holders
The tradeoffthus potentiallyhas strong urbanruralredistribution connotations. The distributiveeffects of the higher inflationtax upon unificationdepend upon who holds domestic currency. One could argue that the urban, rentseekingsector is able to hedge itself by acquiringdollars, so that the inflationtax is regressive,affecting the urban and rural poor. Examples of relevantcountriesare Ghana, Sierra Leone, Somalia and Uganda. 12/ Stereotypically, there is a single export, cocoa. Part of the cocoa is surrenderedthrough a commodityboard to the government,which sets prices with referenceto the officialexchange rate. The rest is smuggledout for hard currency. Equivalently,cocoa is exporteddirectlyby the producers, with some fraction surrenderedto the governmentat the officialexchange rate. For countries like Nigeria,which is a net seller of foreign exchange to the private sector, rationing impliesa real transfer from the governmentto the private sector which is proportionalto the dollar value of import licenses

20 
issued. Tax receiptsand the real deficit thereforeare not independentof the premium. In terms of Fig. 3, the horizontalline with intercept a.(gt)/(pxEg)will move downwardsupon unification,lowering71* The incentiveeffects of exchangerate reform,however, apply to nonoil exports. Hereafter,we concentrateon the more common 'net buyer" cases extension to 13/ the *net seller" case is straightforward. In terms of mechanics,exchange rate rules have not worked well. Devaluationsare not generallyaccompaniedby a relaxationof rationing. The theoreticalresult that the premium in steady state is independentof the level of the officialrate and thereforewill decline only temporarilywith onestep devaluationshas receivedconsiderableempiricalsupport: Somalia in 1985, when the goal of unifyingthe official and free rates by Decemberwas thwartedby almost immediatLequivalentupward movements in the free ratel Sudan in recent times; Zaire and Zambia in the two or three years before they adopted floating rates. Such temporarydepreciationsof the real exchange rate are not likely to stimulatenew, permanentcommitmentsto the export sector. Acceleratingthe official rate of depreciationabove prevailingrates of inflationwill work only if conditions (15) are satisfied. Thus, if prevailing inflationexceeds rh in Fig. 2, # will rise. A preemptiveshift into dollars to escape the higher inflationtax will acceleratethis process and raise inflationtoday via unpleasantmonetaristarguments (Sargentand Wallace (1984)).
Overnightvs. Gradual Reform Policymakersin countrieswith high black market premia face a dilemmat either they live with misallocatedresources,inequitabletransfers, stunted exports and lower real income;or they float, raising inflation substantiallywith high political and social costs. 14/

21 
A middle ground is provided by the recent experience of Ghana.
It
initiated a recovery program in April, 1983, when the black market exchange rate was over 60 cedis per dollar, and the official rate, a mere 2.75 cedis per dollarl Inflation was over 100 percent per year. 15/
In a nutshell,
Ghana's strategy has been one of a gradual reduction of the fiscal deficit, accompanied by an equally gradual relaxation of rationing, and supported by large, discrete devaluations to speed up adjustment to a lower premium. Rationing has been relaxed imaginatively, through the gradual transfer of commercial transactions from the official to the black market.
This was
formalized by the introduction in October, 1985, of a broadbased special import license scheme for imports through the black market.
Such recognition
of the black market is an important psychological step ln eventual unification. This was followed in September, 1986 by an auction. Through a series of maxidevaluations, the official rate had been moved from 2.75 to 90 cedis per dollar, but still represented a substantial discount relative to the black market, where the rate was roughly 180 cedis per dollar (o was reduced from over 20 in April, 1983 to 2 by September 1986).
It was therefore decided to
split the official market into a fixed rate tier and a freely determined rate through an auction with restricted access.
This step represented essentially
the continued taxation of cocoa and subsidization of petroleum. These markets were unified at the auction rate in March, 1987. Future steps involve merging the auction, which has restricted access, with the black market. In contrast to the moreorless overnight measures in Sierra Leone, Ghana's program appears painfully slow, having lasted for over four years, with unification still in process. There is an important argument in favor of such gradualismt fiscal reform is much more timeconsuming than exchange rate reform, which can be introduced instantly. The reasons are the weakness of institutional mechanisms, credibility issues and political will. 16/
 22 
Ironically,in Sierra Leone, the tax/GDP ratio declinedmonotonically from 16.5 percent in 1978/79 to 5.6 percent in 1985/86,and fiscal discipline was at its weakest when the currencywas floated. Credibilitywas low, with the arrears position so extreme that Sierra Leone was paying upto 20 percent above spot internationalprices for rice and petroleum,an almost unheardof situation. To float the currencyunder such circumstances,when # was between 3 and 4, implyinga 3ubstantialexports tax, is at least questionable(recall that the export tax is (l(l/#)).
IV. CONCLUDINGREMARKS
Paradoxicallythe first step in exchange rate reform for "high *" countriesmust be a fiscal one:
g
sting the budget to fix the size of the
implicittax revenuesfrom exports via
t.
The taxsubsidyredistribution
within the private sector as a result of foreign exchange rationing is also important. This involves identifyingthe potentialgainers (e.g., agriculture)and losers (e.g., commerce,protectedmanufacturingusing importedinputs) in the event of unification. Such identificationwill make plain the politicalpressure points likely to emerge upon unification. Three key issues arises (1) To what extent and how quickly can governmentspendingbe reduced? (2) Are existingtax instrumentsapart from the premium and rate of inflationbeing used to the hilt, or are the latter being used as the easy way out (see Aizenman (1986) for a welfare analysisof a related issue)? 17/ (3) Is there an equitabledistributionof the tax burden based on Ramseytypeconsiderations? The main policy conclusionis that if policy credibilityis low and the initial level of the premium high, with significantrevenue and redistributiveimplications,the pace of reform should be set by the feasible speed of fiscal reform. Acceleratingrates of depreciationabove prevailing

23 
inflationin the absence of credible fiscal reform could result in perverse black market premium response,jeopardizingthe survivalof both fiscal and exchange rate reform. Moreover, such policy will not succeed in real depreciationunless the premium falls. Likewise,overnight adoptionof floats is likely to meet with considerablepolitical and social oppositionas inflationrises, creatingthe possibilityof policy reversals. The *best route, consequently,might be to graduallyrelax rationing,accompanyingthis with discretedevaluations,with the pace of reform being set by the speed of fiscal reforms there are no quick fixes. Lastly, it would be incorrectto conclude from this study that an LDC should never float its currency. Thiu decisionshould )pend upon the credibilityand speed of accompanyingfiscal reform and the initial size of the premium.
 24

Footnotes 1. The recent experienceof Bolivia,Ghana, Nigeria, Somalia and Zaire suggest a wide coverageof the ideas expressedhere. Quirk et al. (1987) document the recent experienceof several developingcountrieswith floatingexchange rates. 2. The Zirst reason for ignoringresourcecosts of smuggling is that the issue has already been researched. The second is that for many LDCs, they do not seem to be e major issue: a cocoa smuggleruses the same means as the cocoa board, only he has to grease sevaral palms. 3. Home goods includeall goods and economic activitythat do not contributeto the supply of tradables. This would include commerce,e.g., the distributionand marketing of importedconsumergoods, and highly protected manufacturingthat thrives on cheap importsvia licensesat the official rate. See also Krueger (1974). 4. Intuitively,the private sector maximizes the value of home goods minus smugglingcosts. 5. This is the same as the steadystatesolution in Kharas and Pinto (1987), eqs. (18)(20),with a0o. 6. For a proof, see Pinto t1986),Appendix I. There are two predetermined variables,m and F, and one jump variable,#. 7. This explainswhy the minimum point of #*(#) in Fig. 1 is less than unity. It enables a consistentcomparisonof inflationbetween the dual and unified regimes.
8. Lizondo (1987) studiesunificationin a similar setup, but with two major differences:absence of rationing,and an exogenouslygiven growth rate for domesticmoney. Therefore,upon unification,there is a unique equilibrium and the issue of postunificationinflationdoes not arise. Lizondo focuses instead on the exchange rate and balance of payments followingunification.
 25

9. Only in the unrealisticcase of a zero fiscal deficit will a oneshot devaluationpermanentlylower the premium. Nominal domesticmoney, H, is fixed so that m permanentlydeclines (e0 since there is no inflationtax). 10. This will raise the unit inflationtax; but total revenue from inflation will continue to be (gt) in the new steady state. 11. In Ghana (Pinto (1986)),e was fixed at 2.75 cedis per dollar between 1978 and October, 1983. With foreignexchangerationingand the monetizationof deficits, b continued to depreciate,reachingabout 90 cedis per dollar by October,1983, resultingprobablyin the highest recordedpremium in historyt 12. For other examples, see Quirk et al. (1987). In Latin America, Bolivia is a classic recent case. (see Kharas and Pinto (1987)). 13. Nigeria'sexperienceis instructivefor another reason,demonstrating conclusivelythat the equilibriumexchange rate is not a weighted average of the officialand black market rates. Immeeiatelybefore its float in September,1986, the officialrate was 1.50 and the black market rate between 4 and 5 naira/dollar.Since officialoil exDorts accountedfor more than 952 of total exports; it was believed that upon floating,a rate close to 1.5 naira/dollarwould emerge. However, a rate very close to 5 naira/dollaremerged. This developmentwas consistentwith rationingand the implicit resale of officiallyallocateddollars in the dual regime. 14. With the exceptionof the Gambia, the floats in Africa have been "current account'based, with capital controlshaving been retained. In such cases, black market premia have declined from their substantialinitial levels of severalhindered percent to 1015 percent,an example being providedby Zaire. This suggestsseepage between current and capital account transactions. 15. Johnson et al. (1985) suggest that, for countrieswith a history of high inflation,people are accustomedto livingwith depreciationthat "will at
 26 
least offset inflation,and there is little problem in acceleratingthe rate slightlyto produce a real depreciation". The argumentsadvancedhere suggest that such a policy could be costly. 16. For an imaginativetreatmentof credibilityissues, see Calvo (1986) and van Wijnbergen (1985). 17. Suppose 03 to start with, implyinga tax rate of 67 percent, and that the export is bought by a commodityboard. Upon unification,the government might find it difficultto justify an explicittax of 67 percent. It may, however,decide upon a lower tax of say, 15 percent. This has the advantage of eliminatingthe misallocationcosts associatedwith cheap imports in the erstwhiledual regime, since importersmust now pay the unified rate.

27 
Appendix
Linearizing (19)(20)around the saddlepointstable, lowinflation equilibrium (91 m*, F*) givest 1
I
I
m 
I II
l ' I
(21)
I .I
i 
mp
~~F
. 2 1A)
x'
211
2 (
GX) 1
F
'
I
l
lmm*I M l
l.1
1
11
I
IF
a
I
a
PFFP*
or x  D.y, where x'  (i, F), etc., and the partial derivativesin D are evaluatedat (tl,
m*,F*). Recall that m is now defined as M/u and is therefore
equivalentto m/t  M/b in the dual regime. Shape of di 0 Curve
MQH)in Fig. 4
When di 0, it follows from (20) that (gt)  mu.
From portfolio
ba,ance,we know that m/(m + F)  \(u), X' c 0. Hence, we can write: (22)
(R ; t)
(23) Ai(u)
 _
.m
+ P
m m + F
which are parametricin u. Let t*
denote the unit inflationtax maximizingrate
(level of u which maximizesX(fi).Q). From (22),when Q  W*, (m + F) is at its minimum value. When Q > r*, X(U).C is lower and (m + F) is higher. Further,m/(m + F) falls (see (23)), so that m/F declines. Hence, this part of the di 0 is nagativelysloped and becomes asymptoticto the horizontalaxis in Fig. 4 as u When u < t*,
#A.
(m + F) grows, but so does m/(m + F), so that m/F
increases. Consequently,the mi 0 curve cuts the F  0 curve from below and asymptoticallyaproaches the line with slope io/(l X.) as (0, 1).
Au 0, 10
X(o) 6

28

Slope of Saddle Path in Fig. 4 From the phase plane in Fig. 4, we know that the saddle path is positivelysloped. Let v* denote the slope of the saddle path, VV. Then v* is the positive root of the quadratic (see (21)):
(24) Pv)
av2 + (a  1

O.
)v + ( m*)2
F*
We want to know if 1A*2 )4(lX), where x is evaluated at rl
from (24), P(X0(1  X))
X
aX
Directly from

Consequently, aa
>
(25)
P
>
(1)
. 0