Shadow Exchange Rate in an Economy With Trade Restrictions

8/2/2019 Shadow Exchange Rate in an Economy With Trade Restrictions

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The Shadow Exchange Rate in an Economy with Trade RestrictionsAuthor(s): Trent J. BertrandSource: Oxford Economic Papers, New Series, Vol. 26, No. 2 (Jul., 1974), pp. 185-191Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2662220

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THE SHADOW EXCHANGE RATE IN ANECONOMY WITH TRADE RESTRICTIONSByTRENT J. BERTRAND1

IT is widely rgued hat n less developed economies the official oreignexchange rate does not reflect he social value of foreign xchange becauseof widespread restrictions n trade. Accordingly, t has been suggestedthat a 'shadow' exchange rate be calculated foruse in project evaluationsand other government decision-makingprocesses. In this paper, thetraditional ormula or he shadow' exchangerate s derivedfor neconomywithtrade restrictionssection ) prior o showing hat the appropriatenessof thisformuladepends cruciallyon the underlying bjectives ofgovern-ment tradepolicies (section I). The methodology mployed s to set outan explicitoptimization roblemwhich s first sed to derive he traditionalformula or heshadow rate. This alsopermits bjectivesof hegovernmentunderlyingtrade policies to be explicitly introduced into the analysisthrough dditional constraints nd the model adjusted in this way permitsthe derivation f n adjusted shadow exchangerate wherein hoseobjectivesare taken into account. IWe firstderive a formula for the 'shadow' exchangerate that closelycorresponds to that suggested in the Unido guidelines [7] and in thewritings f Balassa [2], Harberger [5], Schydlowsky 6], and Bacha andTaylor [1].It is assumed that welfare,U, is a functionof consumptionof n com-modities: U U(= ) .., (1)whereCi is the consumptionof the ith commodity.The level ofgross outputs n theeconomy s constrained y the assumeddifferentiable ross productionpossibilityfrontier :

T(X.1) ...,)Xn) < ?- (2)The relationshipbetween gross and net outputs is defined n relation 3):[I-A]X = x (3)

whereI is the identitymatrix,A is the nx n matrix of input-output co-efficients, is a vector ofgross outputs,and x is a vector of net outputs.The net productionpossibilityfrontierr s therefore(x1- a.,,...,Xn-nj ) = r(x1,...,xX)0< (4)1 Financial upportnwritinghis aper sacknowledgedrom he nstitute fEconomicResearch, ueen'sUniversity.


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186 THE SHADOW EXCHANGE RATEwhere-rs obtainedby subtracting utputused as intermediatenputsfromthe gross outputs.'The budget constraintn relation 5)

EPi i Pi Xi- Pj aji Xj+8 (5)indicates that with interindustry lowsand trade, the value of the con-sumptionbundle evaluated at world prices in foreign xchange units,Pi,cannot exceed the value of the gross output minus the value of inter-mediate inputsplus the value of an exogenously determined mount offoreign xchange S. The variable 8 is introduced into the budget con-straint to permit the effectsof a small variation in foreign exchangeavailabilityto be analysed.Denoting value added per unit in the productionprocess of the ithcommodity s 7ri again measured n foreign xchangeunits) we havepTi ~Pi- ajiPj; (6)

substituting elation 6) into relation 5), we obtainE i Ci < E riXi+S; (7)

but since thevalue ofnet output equals the sum of total factorpayments(7) can also be written sE iC, E, xis+S; (8)i isince the difference etween consumption nd net outputgives the amountofimports fpositiveand exports fnegative,relation 8) may be read asthe balance of payments constraintfor the economy.Domestic prices in domestic currencyunits, pd, and domestic values

added, rra are defined n relations 9) and (10):2d1 i1 t) (9)-rd r7Tj(1?+z) (10)wherer is the official ate of exchange and tj and zi are the percentagedifferences etween world and domestic prices and values added withconversion t the official xchangerate. If there are no foreign xchangecontrols,no prohibitivetariffs,no quotas and if import activities are

competitive, hentj is the nominalimport or export) tariffor subsidy)and zi is the effectivemport or export) tariffor subsidy). Otherwise, jand zi are the actual priceand value added distortions.1 The assumption of (a) fixed input-output coefficient,b) constant returnsto scale,(c) concave-contouredproductionfunctions, nd (d) that no efficient actor ntensity anbe written s a linear combinationof efficient actor ntensities or othergoods, is sufficientto assure the functionsT and i- employedhere. See Ethier [4] fora discussionof the im-plicationsofrelaxing a).


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T. J. BERTRAND 187With social welfare definedby relation (1) with consumption evelsconstrained by the two alternativesets of constraints (2) and (7) or (4)and (8)) dependingon whetherwe deal with net or grossoutputs, changesin social welfare dW) may be written s

dW = UidC,-A1( rPdCi- ,rPidx rd8) A2(Eidx) (11)ordW = z UUC,-A1( E rP.dCi- rridXi-rdi)-A2( TidXi) (IIa)

whereAl and A2 are the Lagrangian multipliersdefining he impact ofmarginalvariations in budget and productionpossibility constraintsonthe objective function.Welfaremaximizationby consumers nd profitmaximizationby pro-ducers assure that1 Ui AlrPi(1?+t), (12)A rPi(1?ts) (13)2

Ti A rjvi(l+Zi). (14)2Definingdy as themoney measureof the change n real income that is,dW/A, dy), we canuse (12-14) in (11) and (I Ia) to determine he shadowrate offoreign xchange:

dy [ E d3M] (15)or dy = i r + pi dti E 7r dX ] (16)Thus the shadow' rateofexchangediffers rom he official ate ofexchangeby a percentage mountequal to a weighted um ofpricedisparities,wherethe weights are changes in trade flows2relation15) or consumption ndgrossoutputchanges relation16)brought boutbythemarginal hange nforeign xchangeavailability.

1 Consumersfacingperfectly ompetitivemarketswillmaximize U(Ci,..., Cn) subject togivenconsumptionpossibilities. FormingtheLagrangian expression nd settingthe partialderivativewithrespectto a change in CQyields (12) since the Lagrange multiplier n thisproblemwill give the marginal utilityof income which is assumed equal to the socialevaluation given by A1.Similarlyproducersoperating nperfectly ompetitivemarketswillmaximize the value ofnet outputsEPi(1 +ti)xi subject to the net productionpossibilitiesset or value added EvT(l +zi)Xi subject to the gross production possibility set. TheLagrangian multiplier n theseproblemsgivesthe dollar uniteffect feasing the productionpossibility onstraintwhichequals A2/A1.

2 Trade flowsare denoted byMi = C -xi. Note that by the balance ofpaymentscon-straint 8), 1 PI(dMi/d5) = 1 so that the weightsattached to the price disparities n (15)isum to unity.


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188 THE SHADOW EXCHANGE RATEWhile,on the assumptionsmade, (16) is equivalentto (15), it is includedto aid the comparisonwith the revisedestimate of the shadow' rate whenobjectives of trade policies include affecting esource allocation in thedomesticeconomy. Relation (15) correspondsmost closely to the usualcalculation of a shadow rate. Differences n these formulations suallyturnon thederivationof the weights. Schydlowsky uggests hat a work-able approximation s that marginalimportswill be identical to averageimports nd thus the latter can be used in weighting rice differences6].Balassa [2], Harberger 5], and Bacha and Taylor [1] suggest that elasti-cities be estimated to define he effects f exchange rate changesresultingfrom he altered supply of foreign xchange. The UNIDO guidelines 7]

require n estimate of how the foreignxchange will be used, butthe detailsofhow theweighting chemeis to be derived are leftunspecified. n thispaper, concern swithhowtakingtheobjectivesoftradepolicies nto con-siderationaffects he shadow rate formulasrather han with theproblemofderiving he weighting cheme.IIThe preceding analysis does not allow in any way for the objectives

underlyingtrade tax or subsidy policies that lead to the divergencesbetween domesticand world price levels. In this section, illustratethenature of the required adjustment to the formulawhen the rationale ofpolicies underlying ariffs s explicitly ntroduced. For thesepurposes, tis assumed that trade restrictions re employedboth to alter the patternofconsumption nd to affect he allocation of resources. Specifically,t isassumed that the government eeks to restrict onsumptionofparticularcommoditiesthat may be termed uxury goods and are denoted by thesubscript I and desires to encourage a specified evel of value added inpriorityndustriesdenoted by the subscripth.These policy objectives can be introducedas additional constraints othe equation sets (1), (4), and (8) to yieldmax U =U(C1, .....C.), .(17)S. . ErPi Ci -, r,7iXi rS O. (18)i i

T7(Xl) .... ,Xn) -< 0,...... (19)rP1C, K1, (20)

z r7rTXh1 K2. (21)hFormingthe Lagrangian and settingthe partial differentials ithrespectto consumption f necessaries i.e. non-luxury oods denotedby subscriptin), consumptionof luxuries, gross output of priorityand non-priority


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T. J. BERTRAND 189(denoted by subscriptg) industries qual to zero,we obtain the first-orderconditions formaximizingsocial welfare:

Um Al Pm 0 . (22)U- AlrP A3rP, = 0, (23)Al Th?+A4rTh -A2 T 0, (24)

Al 7Tg A2i = 0. (25)Using these first-orderonditions,we obtainUM rP(+I (26)U, rP,( +A3/Al)

and _ r7T~l (27)Th rlTh(l1?A4/Al)which, nconjunctionwithrelations 12) and (14), show that f eronominaland effective ariffs re applied to non-luxury goods and non-priorityactivities heoptimal evel of tariffo affect onsumption na luxurygood,t,,equals A3/Alndthe optimal evelofeffectiveariffate onpriorityndus-tries to affect esource allocations,Zh, equals A4/Al.These results re of nterestn themselves. If it is possibleto groupfinalgoods or productionactivities by priority ank accordingto governmentobjectives of alteringconsumptionor resourceallocation,these relationsshow that an equal nominal rate ofprotection hould be applied to con-sumergoods nthesamepriority roup nd an equal effectiveate ofprotec-tion should be applied to activities n the same priority roup.' Althoughonlytwogroupshave beenused for onsumption nd production ctivities,thistreatment ould easilybe extendedwithas manyrankings s desiredusing a consumption or production constraint for each group with itsLagrangian multiplierdefining he optimalnominal or effective ariffnthe manner established hereforthe two-priorityase.We can again define he change in welfare s

dW = 2 UidCi-A,( rPidC- E r7TidXi-rd )-A2( E TidXi)3( IdC1)-A4( 4 rlThdXh) (28)

and by substitutionfrom relations (12) and (14), solve for the shadowexchangerate

dy _rs=r '1+ Pi(ti-t*) d= 7i Zi-z*) do ] (29)Relation (29) is centralto our analysis. In contrastto the traditional1 Extensionsfor hisresult on the optimalstructure feffectiveatesondifferingssump-tionsconcerning he resourceallocation objective are discussedin [3].


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190 THE SHADOW EXCHANGE RATEformulas,t is not appropriateto use priceor value added divergences oweight marginaltrade flowsor consumption nd productionchanges forthe exchange rate adjustment when rational objectives underlie traderestrictions.These objectivessupportan optimalsystemof tariffsnd therelevant adjustmentto the market exchangerate must be carriedout byweightingwiththe distortions etween actual prices and values added inthe domestic conomy nd the evelsthatwould resultfrom he applicationof an optimaltrade policy.In the traditionalformulas, t is thereforemplicitly ssumed that alltrade restrictions re sociallyharmful. f thealternative xtreme ssump-tionthatthe government as instituted fully ptimal set of traderestric-tions s made, relation 29) indicatesthatno adjustmentto themarketrateofexchange s required. n reality,neither fthese two conditions s likelyto hold. The adjustmentthencan onlybe made on the basis of knowledgeorassumptionof theoptimal structure ftrade restrictions.However, itwould seem preferable o set out explicitlywhat is assumed about theoptimality f these othergovernment oliciesrather han to leave hiddentheassumption f omplete rrationalitymplicitn the traditional ormula.'Since the issue raisedhere concerns he optimality f traderestrictions,it should be notedthat this is not the same issue discussed n the UNIDOguidelines s to whether he weighting chemeused should reflect ctualchanges in consumptionor should reflectchanges that the governmentwouldview as desirable. The formuladerivedhere is not in conflictwiththe positiontaken in the UNIDO guidelineson this latter question.

Project analysis should in our view, reflect what will (or, more realistically, whatis likely to) happen, not what ought to happen. The shadow price of foreign exchangethus depends on how increments of foreign exchange will be divided among alter-native uses, not on the wishful thinking of the project analyst who perceives (ormisperceives) the irrationality of the overall policy framework in which he operates.[7, p. 218]Whileour argument greesthat the actual ormost-likely hangesin con-sumptionand productionmust be used, the project analyst should notignorethe benefits elt to be achieved by the tariff ystem. Thus, in theUNIDO guidelinesan example is givenwhere the shadow priceofforeignexchange is set very highbecause there is a large domestic-worldpricedifferenceor he luxurygood cognacand a large share ofmarginalforeignexchangeis directedtowardsimportsof thisgood. This gives rise to the

1 Several limitations to the above formula should be noted. These mainly involvesimplification f the problem by ignoring a) otherqualificationsforgovernment-inducedpricedistortions uch as optimaltariff rguments, b) otherpolicymeasuresby which thegovernmentmight nfluence onsumptionsand productiondecisions such as consumptionand productiontaxes and subsidies as opposed to trade taxes, and (c) the implicationsofnon-tradedcommoditieswhich would make the identification f price distortions morecomplex.


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T. J. BERTRAND 191anomalythatforeign xchange s valued more highly he greater s its usefor mportswith very wide price divergences esulting rom fforts y thegovernment o restrict hese imports. In the formulation uggested here,the lowersocial valuation placed on consumption fluxury goods under-lying hepolicyconstraint20) leads to a social discounting f heconsump-tion benefits ndicated by market prices by the amount of the optimaltariff * whichwill correctly educe the social value offoreign xchangedirectedtowardsthese commodities.JohnsHopkins University

REFERENCES1. BACEA, E., andTAYLOR, ., Foreignxchange hadow rices: criticaleviewof current heories',Q.J.E., May 1971.2. BALASSA, B., 'Estimating the shadow price of foreign xchange in projectappraisal' (mimeo.,Oct. 1972).3. BERTRAND, T. J., 'Decision rules for effective rotection n less developedeconomies', A.E.R., Sept. 1972.4. ETHIER, W., 'General quilibrium heory ndtheconceptof effectiverotection'in Grubel and Johnson eds.], Effectiverotection heory,Geneva, 1971.5. HARBERGER, A., 'Survey of literatureon cost-benefitnalysis for industrialproject evaluation', in Evaluation of IndustrialProjects,New York, UJNIDO,

1968.6. SCHYDLOWSKY, D., 'On the choice of a shadow price forforeign xchange',Harvard University Development Advisory Service, Economic DevelopmentReport No. 108, 1968.7. UNIDO (P. Dasgupta, A. K. Sen, and S. Marglin),GuidelinesorProject valua-tion,New York, 1972.

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