Public Disclosure Authorized Public Disclosure Authorized
RESEARCH WORKING PAPER
Policy Lessons from a Simple Open-EconomyModel
-'MispaWdesmithowt specify, solve, and draw
Sl7antayananDevaraian-Delfin S. Go Jeffrey D. Lewis Sherman Robinson Pekka Sinko
Public Disclosure Authorized
Public Disclosure Authorized
TfheWorldBank Reseach Departmen Polic-y November1994
Summary findings Devarajan,Go, Lewis,Robinson,and Sinkoshow how two-sectormodelscan be used to derivepo'icy lessons about adjustmentin developingeconoTnies. In the past two decades, changesin the external environmentand in economicpolicieshavebeen the key factorsin the Derformanceof developingeconomies.By and large the shockshave involvedthe externalsector: terms-of-tradeshocksor ctutbacksin foreigncapital.The policy responsesmost commonlyproposed havetargeted the externalsecror:depreciatingthe real exchangerate or reducingdiscortionarytaxes to makethe economy more competitive.The authors provide a startingpoint for analyzingthe relationbetweenextemal shocksand policy responses. Startingfrom a small,one-country,two-sector,threegood (1-2-3)model, tle authors outline how the effects of a foreigncapitalinflowand terms-of-tradeshock can be analyzed.They derive the assumptionsunderlyingthe conventionalpolicyrecommendaion of real exchange rate depreciationin responseto adverseshocks.The implicationsof such trade and fiscalpolicy instruments as export subsidies,import tariffs,and domesticindirect taxes can alsobe studied in this framework. The authors show that the standardadviceto depreciatethe real exchangeratein the wake of an adverseterms-of-tradeshock rests on the condition that the incomeeffectof the extemal shock dominatesits substitutioneffect.But, dependingon the characteristics
policyresultsmay run counter to receivedwisdom.For example,when the substitutionefftct of an adverse externalshock dominates,real depreciationis inappropriate.An infusionof foreigncapitaldoes not necessarilybenefitthe nontradablesector,as the results of -Dutch disease"modelssuggest(for example,in the extremecase of nearly infinitesubstitutionelasticity betweenimportsand domesticgoods).When import tariffsare significantsourcesof public revenue,potential revenuelossesfrom tariff cuts must be offsetby other revenuesourcesto maintainthe externalcurrent account balance.The paper showsa simpleway to calculatethe necessarytax adjustment. A majoradvantageof smallmodelsis their simplicity. The examplein this paper can be solvedanalyticallyeither graphicallyor algebraically.It also can be solved numerically,usingsuchwidelyavailablePC-based spreadsheetprogramsas Excel.' The numerical implementationinvolvesonly modestdata requirements. The data that governmentsnormallyreleaseon national income,fiscal,and balanceof paymentsaccountsare sufficient 'A companionExcel-bascd model is available.Bank staff can copy
thespreadsheetfile"123.xls" fromthe Policy Research Department'snctworkdrive,[email protected]
,under the directory'models.'The filecan alsobe requestedfromthe internerelectronic mailaddress [email protected]
)'worldbank.org. Thefilewill be available on theBanksGopherin the future.
This paper - a product of the PublicEconomicsDivision,PolicyResearchDepartment- is part of a largereffort in the departmentto developtools for analyzingtax policyqCopiesof the paper are availablefreefrom the WorldBank,1818 H Srreet NW, Washington,DC 20433. Please contact Carlina Jones, room N10-063, extension 37699 (38 pages). November 1994.
of ideasabout the findingsof work inprogrssto encouragthe exchange ThePolicyResearch WorkungPaperSerwsdisseminates am lesstha fily polishedThe An objective ofthe seriesistogetthe findingsoutuicly, evenifthepresentations develpment isswute paperscarry the namesof tbeauthorsand sbould beusedand citedaccordingly. 7hefndings,interpretations,and condusionsare the authors'ownandshouldnot beattriburedto the WorldBank,its ExeutiveBoardof Directors, or anyof its member counties.
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Policy Lessons from a Simple Open-Economy Model ShantayananDevaTrajan,World Bank Delfin S. Go, World Bank Jeffrey D. Lewis, World Bank SbernanRobinson, IFPRI and University of California at Berkeley Pekka Sinko, Government Institute for Economic Research, Finland
Policy Lessonsfrom A Simple, Open-EconomyModel'
This paperdescribeshowto specify,solve, and drawpolicy lessonsfrom small two-sector,general equilibrium models of open, developingeconomies. In the last two decades, changes in the external environment and economicpolicies have been instrumentalin determiningthe performanceof these economies. Therelationshipbetweenexternalshocksand policyresponsesis complex;this paper provides a strting point for its analysis. Two-sectormodelsprovidea good startingpointbecauseof the natureof the externalshocksfaced by thesecountriesand the policy responsesthey elicit Thesemodelscapture the essential mechanismsby which externalshocksand economicpoliciesripplethroughthe economy. By and large,the shockshave involvedthe externalsector tenns of trade shocks,suchas the fourfoldincreasein the price of oil in 197374 or the declinein primarycommoditypricesin the mid-1980s;or cutbacksin foreigncapitalinflows. The policyresponsesmostcommonlyproposed(usuallyby internationalagencies)havealso beentargetedat the
'Forthcomingas achapter in Franqoisand Rein(1994). Robinson(1990)andGo and Sinko(1993).
externalsector. (I) depreciatingthe real exchangerateto adjust to an adverseterms of trade shock or to a cutbackin foreignborrowingand (2) reducingdistortionarytaxes(some of which are tradetaxes) to enhance economicefficiencyand make the economy more competitivein world markets. A "minimaliste model that captures the shocks and policies mentioned above should therefore emphasizethe externalsectorof theeconomy. Moreover,many of the problems-- and solutions - have to do with the relationshipbetweenthe external sector and the rest of the economy. The model thus should have at least two productivesectors: one producingtradable goods and the otier producingnontradables. If an economyproducesonlytwadedgoods,concepts likea real devaluationare meaningless. Sucha country will not beableto affect its internationalcompetitivenesssince all of its domestic prices are determined by worldprices. If a countryproducedonly nontradedgoods,it wouldhave beenimmuneto most of the shocks reverberatingaround the world economysince 1973. Within the categoryof tradablegoods,it is also useful to distinguishimportablesand exports. Sucha characterizationenables us to look at terms-of-tradeshocks as well as the impact of policy instrumentssuch as import tariffs and export subsidies. Theminimalistmodelthat incorporatesthese features,while small,capturesa richarrayof issues. We can examinetheimpactof an increasein the price of oil (or other importand/or export prices). In addition, this modelenablesus to lookat the use of tradeand fiscal policyinstruments:exportsubsidies,importtariffs, and domesticindirecttaxes. The implicationsof increasesor decreases in foreigncapital inflows can also be studied with this framework. While the minimalist model captures, in a stylized manner, features characteristic of developing countries,it also yields policy resultsthat cut againstthe grain of receivedwisdom. For example, it is not alwaysappropriateto depreciatethe real exchangerate in responseto an adverseinternationalterms-of-trade shock; reducing imporLtariffs may not always stimulate exports: unifying tariff ratesneed not increase efficiency;and an infusionof foreigncapital does not necessarilybenefitthe nontradablesector (in contrast to the results from "Dutch disease" models). Deapn-Go-Lwis-Roobison-Sinka
A major advantageof small modelsis their simplicity. They maketransparentthe mechanismsby which an externalshock or policychangeaffectsthe economy. In addition,the examplepresentedin this papercan be solvedanalytically- eithergmphicallyor algebraicAlly.It also can be solved numericallyby usingthe mostwidely-available,PC-basedspreadsheetprogmms hence, it is not necessaryto learna new, difficult programminglanguagein order to get started.The presentationwill introducethe approachused to solve larger,multisectormodels. Finally,theseminimalisttwo-sectormodelsbehavein a similar fashion to more complexmultisectormodels,so we can anticipatesome of the results obtainedfrom multisector models. The plan of the paper is as follows. In Section2. we presentthe simplesttwo-sectormodels. We specify the equationsand discusssome modellingissues. We then analyze the imlpactof terms-of-trade shocksand changesin foreigncapital inflows. In Section3, we describean easy way of implementingthe frameworkand use it to discusssome policy issues. The conclusion,Section4, draws togetherthe main points of the paper.
Table 1: The Basic 1-2-3CGE Model Flows
(1) X = G(E, Ds; 0)
(10) pq = f,(pa, p)
S= F(M, DD;c)
(6) Y =P-X
(14) pw nM - pwE-E= B
(8) Pe (9)
(ii) Pr*_Q pmSM
g 1 (p¶, pd)
EndogenoausVariables E: Exportgood M: Import good D5 : Supply of domestic good
Pt : Price of aggregate output Pq:Price of composite good R. Exchangerate
D0 : Demandfor domestic good QS:Supply of composite good QD: Demandfor composite good Y: Total income Pr: Domesticprice of exportgood Pm Domesticprice of import good Pd: Domesticprice of domestic good
Exogenous Variables pw': World price of export good pw'0 : World price of importgood 2: Balance of trade a: Import substitutionelasticity Q: Exporttransformationelasticity
The basic model refers to one countrywith two producing sectors and three goods; hence, we call it the "1-2-3 model." For thetime being,we ignore factor markets. The two commoditiesthat the country producesare: (I) an export good, E, which is sold to foreigners and is not demandeddomestically, and (2) a domesticgood,D, which is only solddomestically. The third good is an import M, which is not produced domestically. There is one consumerwho receivesall income. The countryis small in world markes, facing fixed world prices for exports and imports. Theequation system is presentedin Table 1. ne model has three actors: a producer, a household, and the rest of the world. Equation I defines the domestic productionpossibility frontier, which gives the maximum achievable combinationsof E and D that the economy can supply. The function is assumed to be concave and will be specified as a constant elasticity of tansfornation (CEI) function with fnsformation elasticity1. The constant, X, defies aggregate productionand is fixed. Sincethere are no intermediate inputs, X also corresponds to real GDP. The assumption that X is fixed is equivalent to assuming full employment of all primary factor inputs. Equation 4 gives the efficient ratio of exporis to domestic output (E/D) as a function of relative prices- Equation 9 defines the price of the composite commodityand is the cost-functiondual to the frst-o 3 tvr condition, equation 4. The composite good price P2 correspondsto the GDP deflator. Equation2 definesa composite commoditymade up of D and M which is consumedby the single consumer. In multisector models, we extend this tratment to many sectors, assuming that imports and domestic goods in the same sector are imperfectsubstitutes, an approach which has come to be called the Armington assumption.? Followingthis treatment, we assume the composite commodity is given by a
See I Amign
constant elasticity of substitution(CES) aggregationfunctionof M and D, with substitutionelasticity o. Consumersmaximize utility,which is equivalentto maximizingQ in this model, and equation 5 gives the desired ratio of M to D as a functionof relative prices.3 Equation 10defines the price of the composite commodity. It is the cost-functiondual to the first-orderconditionsunderlyingequation 5. The price, P.q correspondsto an aggregateconsumerprice or cost-of-livingindex. Equation6 determineshouseholdincome. Equation3 defineshouseholddemandfor the composite good. Note that all income is spent on the single composite good. Equation 3 stands in for the more complex system of expenditureequationsfound in multisectormodels and reflects an importantproperty of all complete expendituresystems:the valueof the goodsdemandedmust equal aggregateexpenditure. In Table 1,the priceequationsdefinerelationshipsamongseven prices. There are fixedworld prices for E and M; domestic prices for E and M; the price of the domestic good D; and prices for the two composite commodities,X and Q. Equations I and 2 are linearly homogeneous,as are the correspondingdual price equations,9 and 10. Equations3 to 5 are homogeneousof degreezero in prices- doublingall prices, for 4 Since only relativeprices example,leavesreal demandand the desiredexportand importratiosunchanged.
matter,it is necessaryto defne a numeraireprice; in equation I1, this is specified to be the exchange rate, R. Equations 12, 13, and 14define the market-clearingequilibriumconditions. Supply must equal demand for D and Q, and the balanceof trade constraintmust be satisfied. The complete model has 14 equationsand 13 endogenousvariables. The three equilibriumconditions,however,are not all independent. Any one of them can be dropped and the resulting model is fully determined. models. Finally, these minimalisttwo-secter modelsbehavein a similar fashionto more complex multisectormodels, so we can
In the multisecormodels. we addexpenditueficions with manygoodsbasedon utility maidmizzaion at two levels. First alkloc expcnditur amonggoods.Second, decdeonsactoralimpor ratios. In the 1-2-3modeLtheCESfunctiondefiningQ canbe reatcdasa utility hnctiondircdtly. ' For thedemandequation,onemustshowthatnominalincomedoubleswhenall pricesdouble.includingtheechdan rate. Tracingthe elementin equation 6. it is asyto denostratethatnominalincorn goesupproportionatlywith prices Dewrcjaa-Go.Lewis-Robhnsn.Sinko
anticipate some of the results obtained from multisectormodels. To prove that the three equilibriumconditionsare not independent,it sufficesto show that the model satisfies Walras' Law. Such a model is "closed" in that there are no leakages of funds into or out of the economy. First note thethree identities(i, il, and iii) that the model satisfies. The first two arise from the homogeneityassumptionsand the third from the fact that, in any system of expenditureequations, the value of purchasesmust equal total expenditure.' Multiplyingequations 12 and 13 by their respective prices, the sum of equations 12, 13,and 14equalszero as an identi-y(movingB in equation 14 to the left side). Given these identities, simple substitutionwill show that if equations 12 and 13 hold, then so wust 14. The 1-2-3model is differentfrom the standardneoclassicaltrade modelwith all goods tradable and all tradables perfect substitutes with domestic goods. The standard model, long a staple of trade theory, yields wildly implausibleresults in empiricalapplications.' Empiricalmodelsthat reflecttheseassumptions embody"the law of one price," whichstatesthat domesticrelativepricesof tradablesare set by world prices. Suchmodelstend to yield extremespecializationin productionand unrealisticswings in domestic relative pricesin responseto changesin trade policy or world prices. Empiricalevidence indicatesthat changes in thepricesof importsand exports are only partiallytransmittedto the pricesof domestic goods. In addition, such models cannot exhibit two-waytrade in any sector ("cross hauling'), which is often observed at fine levels of disaggregation. Recognizing these problems, Salter (1959) and Swan (1960), specified a two-sectormodel distinguishing "tradables" (including both imports and exports) and "nontradables." Their approach representedan advanceand thepapersstartedan activetheoreticalliteratue. However,they had littleimpact on ernpiricalwork. Even in an input-outputtable with over five hundred sectors, there are very few sectors
' In dis modelequation3 and idenLiryiii ae thesame In a multisecormodcl.as noted above.idcntity iii is a necessarypropertyof any systcm of expenditure equations. ' Enpirical problems wih tdis specificaion have beena thornin thesideof modelerssincc thecarlydays of linear programmingmodcls. For a survey,see Taylor (I975). De.arwnGo-Lewis-Robinson-Sio
which are purelynon-traded;i.e.,with no exportsor imports. Sodefined,non-tradedgoodsare a very small share of GDP;and, in modelswith 10-30sectors,therewould be at most only one or two non-tradedsectors. Furthennore.the link betweendomesticand world prices in the Salter-Swanmodel does not depend on the trade share, only on whetheror not the sector is tradable. If a good is tradable,regardlessof how small is the trade share, the domestic price will be set by the world price. The picture is quite differentin the 1-2-3modelwith imperfectsubstitutabilityand transformability. All domesticallyproducedgoodsthat are not exported(D in Table 1) are effectivelytreatedas non-tradables (or, better, as "semi-tradables'). The shareof non-tradablesin GDPnow equalsone minus the exportshare, which is a very large number,and all sectorsare treatedsymmetrically. In effect, the specificationin the 1-2-3model extendsand generalizesthe Salter-Swanmodel, making it empiricallyrelevant. De Melo and Robinson(1985) show, in a partial equilibrium framework,that the link between domesticand world pricesassumingimperfectsubstitutabilityat the sectoral level depends criticallyon the trade shares. both for exports and imports, as well as on elasticity values. For given substitution and transformation elasticities,the domesticprice is morecloselylinkedto the world price in a given sector the greater are export and import shares. In multisectormodels,the effect of this specificationis a realistic insulationof the domesticprice system from changesin world prices. The links are there, but they are not nearlyas strongas in the standardneoclassicaltrade model. Also, the modelnaturallyaccommodatestwoway trade, since exports, imports,and domesticgoodsin the same sector are all distinct. Given that each sector has seven associated prices, the model provides for a lot of product differentiation. The assumptionof imperfectsubstitutabilityon the import side has been widely used in empiricalmodels.'Notethatit is equally importantto specifyimperfecttransformabilityon the exportside.
'TTh CES forTnulation for the impon-aggregationfunctionhas beencriticizedon econometricgrounds(see Alstonet aL (1990)for an examplc). It is certainly a restrictivefonn. For example.it constrainsthe incomeelasticityof demandfor imponsto be one in every sector. Ratherthan compictercjectionof approachcsrclying on imperfectsubstitutability,this criticismwould seem to suggest that it is time to explore the many altemativefunctionalformsthat areavailable. For example,Hanson.Robinson.andTokarick(1989)estimatesectoWlimportdemandfunctions basedon the almostidealdemandsystem(AIDS)formulation.They findthat scctoralcxpenditure elasticitiesof inport demandmc generallymuch greaterthan one in the U.S. resultsconsistentwith cstimates from macroeconomnciric models. Factorsoiler than relativcpricesappearto affect Devarjan-Go-Lenuss-Robhhson-Sinko
Withoutimperfecttransformability,the lawof one pricewouldstill hold for all sectors with exports. In the 1-2-3model, both importdemandand exportsupplydependon relativeprices.'
DoMeloandRobinson(1989)analyzethepropertiesof thismodelin somedetailandargue liat it isa goodstylizationof mostrecentsinglc-country, trade-focused, computablcgeneralequilibrium(CGE) models. Productdifferentiationon both the importand expon sides is ver appealingfor applied models,
esp,ecially at thelevelsof aggregation typicallyused.Thespecification is a faithfulextensionof the SalterSwan model and gives rise to normallyshaped offer curves. 'fhe exchange rate is a well-dcfinedrelative price. If the domesticgoodis chosenas the numerairecommodity,settingPdcqual to one,thenthe exchange rate variable, R. correspondsto the rcal exchangerate of neoclassicaltrade theory: the relative price of tradables(E and M) to non-tradables(D). Trade theory models(and our characterizationin Table 1)often setR to one, with Pd then definingthe real exchangerate. Forother choicesof numeraire,R is a monotonic
functionof thereal exchangerate.9 The 1-2-3 modelcanalso be seen as a simpleprogramming model. This fornulation is given in Table 2, and is shown graphicallyin Figure 1. The presentationemphasizesthe fact that a single-consumer
generalequilibriummodel can be representedby a programmingmodel that maximizesconsumer utility, which is equivalent to social welfare.'0 [n this model, the shadow prices of the constraint equations correspond to marketprices in the CGEmodel." Wewill use the graphicalapparatusto analyzethe impact
tradeshares,andit is importanlto studywhattheymightbeandhow theyoperate.AlstonandGreen(1990)alsoestimatcd the AIDS import formulation.A relatedpaperis Shiells.Roland-Holst. andReinert(1993). ' Dervis.deMclo,andRobinson (19S2)specifya logisticexportsupplyfunctionin placeof equation 4 in Tabic 1. Theirlogisticfunctionis locallycquivalentto thefunctionthatis derivedfromtheCETspecification. Dervis,deMelo.andRobinson (1982),Chapter6. discussthisrelationship in detail. "' GinsburghandWacibmeck (1981)discuss,in detail,thegeneralcascwherca multi-consumer CGEmodelcan be represented by a programming modelmaximizinga Negishisocialwelfarefunction.SeealsoGinsburgh andRobinson(1984)for a briefsurveyof the technique appliedto CGEmodels.
" In the pwgramming model,we implicitlychooscQ asthenumeraire good,with P. a 1. In thegraphicalanalysis, we sd R a 1. DevcrajanGo-Gewis-Robinsn-Sinbo
of two shocks: an increase in foreigncapital inflow and a change in the intemationaltenns of trade.'2 We will also use this programming-modelformulation,including endogenous prices and tax instruments,to derive optimal policy rules under second-bestconditions. Table 2: The 1-2-3 Model as a ProgrammingProblem Maximize Q = F(M, DD;a)
with respect to: M, E, DD, D)S subject to: Shadow Price (I) G(E, Ds; 0)
(2) pw8 -M s pwe-E + B
(domesticsupply and demand)
D) s D)S
The transfornation function(equation I in Table I and constraint I in Table 2) can be depicted in the fourth (south-east)quadrant of the four-quadrantdiagram in Figure I. For any given price ratio pd/P., the point of tangencywith the transformationfrontierdeterminesthe amountsof the domestic and exported good that are produced. Assume,for the moment,that foreign capital inflow E is zero. Then, constraint 2, the balance-of-tradeconstraint,is a straightline throughthe origin,as depicted in the first quadrantof Figure 1. If we assumefor conveniencethat all worldpricesare equal to one, thenthe slope of the line is one. For a given level of E ptoduced,the balance-of-tradeconstraintdetermineshow much of the imported good the county can buy. [ntuitively,with no capital inflows(1]= 0), the only source of foreignexchange is exports. The secondquadrantshowsthe 'consumptionpossibilityfrontier,"whichrepresentsthe combinationsof the domesticand importedgood that the consumercan buy, given the productiontechnologyas reflected in the "rhe discussionfollowsde Mdo and Robirnon(I 98). De=Praan-Go-Lewis-Robinson-Sinko
M Bado" of Tra*
DD~ ' 7
Figere 1: The 1-2-3 Programming Model
transformation frontier and the balance of trade constraint. When world prices are equal and trade is balanced,thfe consumption possibility frontier .s the mirror image ofthe transformation frontier. Equatien 2 in Table I dcfines 'absorption,"
which is maximized in the prograrnming problem. The hngency
the "iso-absorption" (or indifference) curves and thie consumption possibility frontier will determine the amount of Dand Mthe consumer wil11demandsat price ratio pd/pm. The economyproduces at point Pand consumes at pOillt C. Now consider what would happen ifforeisgncapital inflow increased from its initial level of zero to some value iN> O). For cxample. the country gains additional access to world capital markcetsor receives
some foreign aid. Alteratively, there is a prinary resource hoomin a country where theasource
effectively an enclave,so that the only direct effect is the repatriation of export earnings." In all of these cases, we would expect domestic prices to rise relative to world prices and the tradable sector to contract relative to the nontradablesector. In short, the countrywould contract "Dutch disease."
~~~~~~~~~~~~~~~~~~~~~~~~~~~3 * I
Figure 2: Increasc in Foreign Capital Inflow That this is indeed the case can be seen by examining Figure 2. 'Me direct effect is to shif;cthe balance of trade line up by 13. This shift, in tum, will shift the consurption possibility frontier up vertically by the same Ei. Thecnew e.quilibriumpoint will depend on the nature of the imnportaggregation function (the
consumee,sutilityfiunction).In Figure2, the consumptionpointmoves from C to C*7 widi increaseddemand for both D and M and an increase in the price of the domestic good. Pl. On the production side, the relative price has shifted in favor of the domestic good and against the export -an appreciation of the real exchange " Se Benjaumiand Devarajan(1985)e-rBaliamin. Devarajan.anldWeiner11939). Devartan-C;Lwis-Robinson
rate. Will the real exchange rate always appreciate? Consider two polar extremes, which bracket the rangeof possible equilibria. Supposethe elasticity of substitution betweenimports and domestic goods is nearly infinite, so that the indifferencecurves are almost flat. In this case, the new equilibrium will lie directlyabovethe initialone (pointC), sincethe two consumptionpossibilitycurves are vertically parallel. The amountof D consumedwill not change and all the extra foreignexchange will go towards purchasing imports. By contrast, suppose the elasticity of substitution between M and D is zero, so the indifference curves are L-shaped. In this case (assuminghomotheticityof the utilityfunction),the new equiiibrium will lie on a ray radiatingfrom the originand going throughthe initialequilibriumrIn this new equilibrium,there is moreof both D and M consumed,and the price ratio has risen. Since PI"is fixed by hypothesis,pd must have increased - a real appreciation. The two cases bound the range of possible outcomes. The real exchange rate wil1appreciate or, in the extremecase, stay unchanged. Productionof D will either remain constantor rise and productionof E, the tradablegood in this economy,will either stay constant or decline. The range of intermediatepossibilitiesdescribesthe standardview of the Dutch disease. Considernow an adverseterms of trade shock representedby an increase in the world price of the imported good. The results are shown in Figure 3. The direct effect is to move the balance of trade line, although this time it is a clockwiserotation rather than a translation(we assume that initially fl = 0). For the same amountof exports,the countrycan now buy fewer imports. The consumptionpossibility frontier is also rotated inward. The new consumptionpoint is shown at C*, with less consumptionof both imports and domestic goods. On the productionside, the new equilibrium is P*. Exports have increased in order to generate foreign exchange to pay for more expensive imports, and Pc/Pdhas also increased to attract resourcesaway for D and into E. There has been a real depreciationof the exchange rate. Will there always be a real depreciationwhen there is an adverseshock in the internationaltenns of trade? Not necessarily. The characteristicsof the new equilibriumdepend crucially on the value of a, Dcwujan-Go.Lews-RohinSoninko
Figure 3: Change in World Prices
t[heelasticity of substitution beween imports and domestic goods in the import aggregation function. Consider thieextremes of a = Oand a = . In the first case, as in Figure 3, there will be a reduction in the amount of domestic good produced (and consumed) and a depreciation of the real exchange rate. In the second case, however, flat indifference curves will have to be tangent to te new consumption poss:.bility frontier to the left of the old consumption point (C), since the rotation flattened the curve. At the new point, output of D rises and the rcal exchange rate appreciates. When a = 1, thiere is no change in either the real cxchange rate or the production stnuctur of the economy. The inituitionbehind this somewhat unusual result is as follows."4 When thle price of imports rises in an economy, there are two effects: an income efrect (as the consuuner's real income is now lower) and a substitution effect (as domestic goods now become more
'' We derie
attractive). The resulting equilibriumwill dependon which effect dominates. When a c 1, the income effect dominates. The economy contracts output of the domestic good and expands that of the export commodity. In order to pay for the needed, non-substitutah'eimport, the real exchange rate depreciates. However,when a > 1,the substitutioneffect dominates. The responseof the economyis to contractexports (and hence also imports)and producemore of the domestic substitute. For most developingcountries,it is likely that a c 1,so that the standardpolicyadvice to depreciate the real exchangerate in the wake of an adversetermsof trade shock is correct. For developed economies, one might well expectsubstitutionelasticitiesto be high. In this case, the responseto a terms-of-tradeshock is a real revaluation,substitutionof domestic goods for the more expensive (and non-critical) import, and a contraction in the aggregatevolume of trade. In all countries, one would expect substitution elasticities to be higher in the long run. The long-run effect of the real exchange rate will thus differ, and may be of opposite sign, from the short-runeffect The relationshipbetweenthe responseof the economyto the tenns-of-tradeshock and the elasticity of substitutioncan also be seen by solving the model algebraically. By consideringonly small changes to the initial equilibrium,we can linearizethe model and obtain approximate analyticalsolutions. We follow this procedure to analyzethe impactof a terms-of-tradeshock.' Let a 'A" above a variable denote its log-differential- That is,
d(Inz) = dnz
differentiate equations 4. 5, and 14 in Table 1. assuming an exogenous change in the world price of the import The results are:
"'Dc McloandRobinson (19S9)derivethecioscd-ronn solutionfor the counuy'sofcr curvein the 1-2-3model.A morecompletediscussion andmathematical derivationis givenin Devarajan. Lewis.andRobinson(1993).
D = a (pfd
Mf + p6wM = E
Eliminating AM, D and E and solving for P
a -I Cy + a
Thus, whetherpdincreasesor decreasesin responseto a terms of trade shockdepends on the sign of (a - 1), confirming the graphicalanalysis discussed above. Figure 4 illustratesthe impactof a 10 percent import price shock on P' under varyingtrade elasticities,0 < a < 2 and 0 < a < 2. Note that the directionof change in P1willdeternninehowthe rest of the economywill adjust in this counterfactualexperiment. If P1falUs(the real exchange rate depreciates),exports will rise and production of the domestic good will fall. Our analysiswith the 1-2-3modelhas yielded several lessons. rirst, the bare bones of multisector g2Pneral equilibriummodelsare containedin this small model. Second,and perhaps more surprisingly, this two-sector model is able to shed light on some issues of direct concem to developing countries. For example, the appreciation of the real exchange rate from a foreign capital inflow, widely-understood intuitively and derived from more complex models,can be portrayed in this simple model. In addition, resultsfrom this small modelchallenge a standardpolicy dictum: always depreciate the real exchange rate when there is an adverseterms-of-tradeshock. The model shows the conditions under which this policy advice should and should not be followed.
Figure 4: Import Price Shock,Trade Elasticities,and DomesticPrices Of course, manyaspectsof the economy are left out of the small model. In particular, there is no government, factor markets,and intermediategoods; the frameworkis also static. Devarajan, Lewis, and Robinson(1990)discussseveralextensionsand modelingissuesin a one-periodsetting; Devarajanand Go (1993) presenta dynamicversionofthe 1-2-3frameworkin which producerand consumerdecisionsare both intra-and intertemporallyconsistent.All these extensionsrequirethat the modelbe solved numerically. We turn therefore to the numerical implementationof the 1-2-3 model, extending the basic 1-2-3 model to include the government sector in order to look at policy intrumentssuch as taxes
Table 3: The 1-2-3Model with Govemmentand Investment Real Flows
(1) X =G(E,Ds;o)
(I0)P m =(II + t").R.pw"'
(2) QS = F(M,DD;a)
(I ) PD= (l + t)-R.pW
(3) Q 0 =C+Z+G
(12) P'=(I +t')-Pq
(4) E/D = g2(pc,pd)
(14) Pq = f1(P",P')
(15) R= I
m-M (6) T = t'-RRpw
(16) Do - Ds = 0
- t4 R.pwc.E
(18) pw"-M - pw'-E - ft - re=
QD _ QS
(7) Y= P-X + tr-Pq+ re-R
(19) P'Z - S=O
(8) S i-Y + R-B+ ss
(20) T - Pqi - tr-Pq- ft*R- Sr=0
( 9) C-P'= (I - si- ty)Y
Accounting Identities (i) P._X Pc.E+ pd.DS (ii) Pq.Qs P.'M + PlOD'
E: Exportgood M: Import good D)S:Supply of domestic good DD:Demand for domestic good Qs: Supply of composite good QD: Demand for composite good P': Domestic price of export good P: Domesticprice of importgood Pd:Producer price of domestic good P': Sales price of composite good PI: Price of aggregateoutput Pq:Price of compositegood R. Exchangerate T: Tax revenue S5:Governmentsavings Y: Total income C: Aggregate consumption S: Aggregate savings Z: Aggregate real investment
pw": World price of import good pw': World price of export good tr: Tariff rate tt: Exportsubsidy rate t: sales/excise/value-addedtax rate ty:direct tax rate tr: governmenttransfers ft: foreign transfers to government re: foreign remittancesto private sector s: Averagesavings rate R: Aggregate output G: Real governmentdemand B: Balanceof trade rQ:Exporttransformationelasticity a: Import substitutionelasticity
Table 4: List of Parameters and Variables in the Excel-Based 1-2-3 Model C
Elasticityfor CET 1st) Elasticityfor CESIQIsq)
WorldPriceof Imports(wm) WorldPriceof Exports(we)
2.22 0.77 2.67
ImportTariffs(tm) ExportDuties(teo IndirectTaxes(tol
0.13 0.01 0.08
0.13 0.01 0.08
Direct Taxes tty)
9 Scalefor CET(at) 10 Sharefor CET(bi) 11 Rhofor CET(rt) 12 13
Scale for CESIQ(sql
14 Sharefor CES/QIbql 1E Rhofor CES/Q(rql
18 17 la
Savingsrate(syl (GI Govt.Consumption Govt. Transfers (trl
Foreign Grants (ft)
Net Priv Remittances(reI ForeignSaving 18) Output (XI
0 17 0.10
0.12 0.02 0.01 0.08 1.00
0.12 0.02 0.01 0.08 1.00
Supply of Domestic Good (Dsl
Demandof DomesticGood(Odl Supplyof CompositeGood(Gs) Demandof CompositeGood(0d)
0.67 1.18 1.18
0.67 1.18 1.18
1.00 1.00 1.00
TotalIncome(YI AggregateSavings(SI Consumption(Cn)
2.26 0.53 0.83
1.00 1.00 1.08 1.00 1.00 1.00
2.00 2.00 2.17 2.00 2.00 2.00
2.00 2.00 2.00 2.00 2.00 1.00
0.25 *0.01 0.00
0.25 -0.02 0.00
Import Price (Pm) Export PrIce (Pe) Sales Price (PI) Price of Supply IPqI Price of Output IPx) Price of Dom. Good (Pd)
Investment (ZI GovernmentSavings ISgi Law IZ-SI Walras
27 28 29
Table 5: List of Equations in the Excel-Based 1-2-3Model J 3
Eq.# _ 1 6 7 2 8 3 4 9 1a 6 4
26 27 28
RealFlows (CETEQ) CET Transformation Supplyof Goods(ARMG) Demand(DEM) DomesUc E10Ratio(EDRAT) MIDRatio(MDRAT)
-bt)*DsA(rt))A(lrt) =at*(bt*EA(rt)+(1 =aq*(bq'MA(_rq)+(1-bq)*DdA(-rq))A(-1/rq) =Cn+Z+G )A(1(rt-1)) =( (PelPd)/(bVl(1-bt)) )(11(1+rq)) =( (Pd/Pm)*(bql(1-bq))
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
6 7 8 9 10 11 12 13 14 15 16 17
RevenueEquation(TAXEQ) TotalIncomeEquation(INC) SavingsEquation(SAV) Consumption Function(CONS) Prices ImportPriceEquation(PMEQ) ExportPriceEquation(PEEQ) SalesPriceEquation(PTEQ) OutputPriceEquation(PXEQ) SupplyPriceEquation(PQEQ) Numeraire (REQ) Conditions Equilibrium DomesticGoodMarket(DEQ) CompositeGoodMarket(QEQ) CurrentAccountBalance(CABAL) Budget(GBUD) Government
+ te'PeE + ts'Pq'Qd + tyY = tm*wm*Er_M = Px*X+tr*Pq+ re*Er =sy*Y+Er*B+Sg =Y*(1-ty-sy)lPt
=Er'wm*(1+tm) =Er*wel(1+te) =Pq*(1+ts) =(PEIE+Pd*Ds)/X =(PmrM+Pd*Dd)tQs -1 =Dd- Ds =Qd-Os =wm*M- we*E-ft - re = Tax- G*Pt- tr*Pq+ ft*Er
As a means of evaluating economic policy or extemal shocks, general equilibrium analysis has several known advantages over the partial approach and its numerical implementation has become increasinglythe preferred tool of investigation.",So far however,CGE models are cumbersome to build, requiring extensive data, model calibration, and the leaming of a new and often difficult programming language. For that reason, tl:e-partial approach still dominates practical applications because of its simplicity. In the field of public finance, for example, it is a relativelysimple affair for non-specialiststo deal with tax ratios, the projections of collection rates of taxes and their corresponding bases, and, if necessary,to augment the analysiswith estimationsof tax elasticities.'7 Moreover,sinceonly ratiosof taxes to GDP are used, the partial approach has the further advantage of requiring the least information and offeringa quick way of lookingat the revenue significanceof taxes. Nevertheless, using fixed ratios and assumingzero-elasticitiesignoresthe feedbackintoothermarketsand the divisionofthe tax burden;it limits the investigationand leads to an incompletepicture. General equilibriumanalysisavoids these limitations but the problem has been to find an easy and convenientway of doing it. Fortunately,the simplicityof the 1-2-3modeland the availabilityof morepowerfulWindows-based spreadshecttools for the desktopPC, likeMicrosoftExcelfor Windows(Excel hereafter),'8 provideappealing and temptingalternativesfor CGE modeling. Thesetools have built-ingraphics,easy integrationwith other Windows applications,and convenientaccessto interestingadd-in programs. Being much easier to learnand
use, they make CGE analysis more accessibleto economistswho are otherwisediscouraged by unwieldy programming. A model based on a popularspreadsheetprogramcan also become an effective vehicle for
Robinson(1989) containsa survey of CGE applicationsto developing countries.
X SeeA Prmst(1962)and R. Chclliah and S. Chand(1974) fora discussionof suchan approach.
'" Mkrosoft Excel and Windows are tradcmarksof Microsoft Corporation. Denarajan-.GaLewis-Robinson-Sinko
illustrativeand educationalpurposes. While Excel is one exampleand hardlythe only software suitable for economic modeling, the robustnessand flexibilityof its solver function, which is quite capable of finding numerical solutions of systems of linear and non-linear equations and inequalities, as well as its userfriendlinessand wide distributionmake it a particularlyattractive tool for potential CGE modelers. In what follows,we describea stepwiseprocedureto implementthe 1-2-3model using Excel."' We also run a few policy simulations by applying the model to one small open economy, Sri Lanka.
3.1 The 1-2 3 Model with Government and Investment In the previous section, the discussion of the 1-2-3model focused on the relative price of traded goods relative to the price of domestic goods and how this real exchange rate adjusts in response to exogenous shocks. In order to apply the frameworkto a particularcountry however, it has to be modified to fit real data and to handle policy issues. For example,the real exchange rate is not an instrument which the governmentdirectlycontrols. Rather,most govermmentsusetaxes and subsidiesas well as expenditure policy to adjust their economies. Nor did the previous section touch on the equality of savings and investmentwhich is importantin bringingabout macroeconomicbalance or equilibrium. Table 3 presents an extended versionof the 1-2-3modelto includegovemmentrevenueand expenditureand also savings and investment. We make sure that the modifications introduced will conform to data that are commonly ivailable(see calibration below.) In the new set-up, four tax instrumentsare included: an import tariff C, an export subsidy f, ar indirecttax on domestic :ales t', and a direct tax rate P. In addition, savings and investment are included. The single household saves a fixed fraction of its income. Public savings (budgetarydeficit or surplus)is the balanceof tax revenueplus foreigngrants and governmentexpenditures (all exogenous)such as governmentconsumptionand tmnsfersto households. The currentaccount balance,
1The discussionof Excel procedurs is compatiblewith latest release.versmn 5.We also include in the footnotes whereapplicable. how to implement the samc proceduresin the previousversion of Excel
taken to representforeignsavings,is the residualof importsless exportsat world prices, adjusted for grants and remittances from abroad. Output is fixed for reasons cited in section 2.
Foreign savings is also
presently fixed, so that the model is savings-driveni;aggregate investmentadjusts to aggrcgate savings.20 In sum, we have 20 equationsand 19endogenousvariables. By Walrs' law however,one of the equations, say the savings-investmcntidentity, is impliedby the others and may be dropped.
3.2 Defining Model Components Building the i-2-3 framework in Excel requircs the usual modeling steps: (1) declaration of parametersand variables: (2) data entry; (3) assignmentof initial values to variables and parameters; and (4) specification of equations.
In addition, the model has to be precisely defined as a collection of
equations;in some cases, it may requirean objectivefunctionto be optimized. Finally,the solver is called to conduct numerical simulations. A suitable way to arrange the 1-2-3 Model in an Excel worksheet is to assign separate columns or blocks for paramneters,variables and equations. Separate columns are assigned for the base year and simulationvaluesof variables.Labelsand explanationsfor parameters, variables, and equations are easily providedin the adjacent left columnto improvereadability. We also assigna blockfor the data set with both initial and calibratedvaluesdisplayed. Thus, we are able to arrange all necessary ingredientsconveniently on a single worksheet.
323 Variables and Pammeters Table 4 is an exampleof how to organize the parametersand variables in an Excel-basedmodel. We separate out from the rest of the exogenousvariablesthe parametersrelated to the trade elasticities; the
' In thealbmativeinvestmcn:-driven closue.aggrcgatc investment is fixedandsavingsadjustthroughforeignsavings(endogenous). For a discussion of alternativemacro-closures. seetheoriginalworkof Sen(1963)or thesurves by Ratso (1982)andRobinson(1989).
tradeelasticitiesare generallydefinedat the outsetof an experimentand parameterssuch as the share and scale values of the CESand CET functionsare calibratedjust once for both the base case and the current simulation(see the calibrationsectionbelow). ColurmnA providesa briefdescriptionof each parameterand Column B lists the correspondingnumerical value. The exogenous variables (described in Column C) specify the externalor policy shocks introducedin a particularexperiment- their magnitudesare defined in ColumnE whiletheirbase-yearvaluesare presentedin ColumnD. Likewise,theendogenousvariable3 are listedin ColumnF to 1. New valuesare computedfor the endogenousvariablesduringa simulationand entered in ColumnH as Current. Column1,Cur/Base,providessimple indicesof changeof the endogenous variables. A useful featurein Excel is the capabilityto definenamesfor various modelparts. This is done by usingtheName commandand Defile optionunderthe Insertmenu?' Thecell in B6 of Table 4, for example, canbe calledby its parameternamne, st; hence,we can referto parameters,variables,or equationsby using theirdefinedor algebraicnamesinsteadof cell locations. By doing this, we makethe modelspecifications easierto readand mistakeseasier to detect. To keeptrack of thesenames, it is advisableto write themout in explanationcells adjacent to the correspondingparameters,variables,and equations. In the example shownin Table4, we writea short descriptionand put in parenihesis the Excellabel or name. Baseyearand currentvaluesof variablesare distinguishedusingthe normalconvention-in the caseof exportgood E. for example,the base year level is labelledas EOwhileE is retainedfor the simulatedlevel.
3.4 Equations Theorganizationof theequationsof ourmodelis illustratedin Table5. The equationsare numbered and listed(in ColumnJ of Table 5) in the sameorder as Table 3. ColumnK of Table 5 lists the equation descriptionsand theExcelnamesin parentheses.Thecorrespondingmathematicalexpressionsare entered 1 Priorto version 5 of Excel.
this is donc by using dheDefineNamecomnd
in te FomdJa menu.
in ColumnL. In the normalmodethe fornulas are hiddenin the backgroundand only the currentnumerical valuesare evident. The formulasare easilydisplayedby usingthe Optionscommandon the Toolsmenu, selecting(or clicking)the Viewtab, and choosingFormulasin the WindowOptionsbox.' In a spreadsheetlike Excel,a formulais typicallyenteredinto a cell by writingout just the righthand side of an equationas shown in Table 5. To completethe equation, each of these mathematical expressionshas to be matchedand set equal to a variabledefinedas above(see Solver sectionbelow). The complicatedexpressionsin ColumnL of Table 5 requiresome explanations. Equation I and 2, called CETEQand ARMG in Excel, are the right-handexpressionsof the CET and Armington(CES) functionsin the 1-2-3model,which usuallytake the followingalgebraicform:
Y = A[6-X,P + (1 - 6))Z2]J
wheretheCESsubstitutionelasticitya and CETtransformationelasticityn are givenby a = 1/(1- p);- < p