Private Saving and Terms of Trade Shocks

Private Saving and Terms of Trade Shocks: Evidence from Developing Countries Author(s): Jonathan D. Ostry and Carmen M. Reinhart Source: Staff Papers - International Monetary Fund, Vol. 39, No. 3 (Sep., 1992), pp. 495-517 Published by: Palgrave Macmillan Journals on behalf of the International Monetary Fund Stable URL: http://www.jstor.org/stable/3867471 Accessed: 02/09/2010 23:20 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. 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REINHART* Therelationshipbetweentemporarytermsof tradeshocksand household savingin developingcountriesis examined.It is first shown that,from a theoreticalstandpoint,this relationshipis ambiguous:privatesavingmay rise or fall in responseto a transitorytermsof tradeshock, dependingon the values of the intertemporalelasticityof substitutionand the intratemporalelasticityof substitutionbetweentradedand nontradedgoods. Empiricalestimatesof thesetwoparametersare obtainedusingdatafrom a sampleof 13 developingcountries,and then used to drawimplications for the response of private saving to transitoryterms of trade shocks. [JEL E21, F32, F41, 010, 053, 054, 055] T OFTRADEhavehistoricallybeen one of the most important HETERMS exogenous determinantsof the external positions of developing countries.Overthe past two decades,sharpfluctuationsin worldmarket prices for primarycommoditiesand two oil shocks, which substantially increasedthe price of importedenergy productsfor non-oil developing *Jonathan D. Ostry, an Economist in the Research Department, holds a doctoratefrom the Universityof Chicago,as well as degreesfrom the London School of Economics and Political Science, Oxford University, and Queen's University. CarmenM. Reinhartis an Economistin the ResearchDepartment.She holds a Ph.D. from ColumbiaUniversity. The authorswish to thank Mike Gavin, Mohsin S. Khan, Leo Leiderman, EnriqueMendoza, Peter Montiel, Assaf Razin, and Peter Wickhamfor useful comments. 495 496 JONATHAND. OSTRYand CARMENM. REINHART countries,were associatedwithincreasedvariabilityin the saving,investment, and currentaccountbehaviorof these countries. The theoretical literatureon the relationshipbetween the terms of trade and the currentaccount has focused almost exclusivelyon how terms of trade changes affect private saving, ignoring any additional effects on investmentand publicsaving.' The traditionalexplanationassociatedwith the namesof Harberger(1950)andLaursenand Metzler (1950)-suggests that an improvementin the terms of trade raises a country'sreal income level, measured as the purchasingpower of its exportsin worldmarkets,andhence, on the assumptionthatthe marginal propensityto consumeis less than unity, raisesprivatesaving.Thus, the Harberger-Laursen-Metzler (HLM) effect, as it has become known, that improvementsin a country'stermsof tradewould be hypothesized associatedwithincreasesin privatesaving,andconversely,adverseterms of trade shocks would reduce saving. Thisview went largelyunchallengedfor nearlythree decades, andwas generallysupportedby the availableempiricalevidence. (See, for example, KhanandKnight(1983).)In the early1980s,however,severalstudies re-examinedthe theoreticalunderpinningsof the HLM effect, a crucial buildingblock of whichwas the Keynesian(static)relationshipbetween consumption(or saving)andincome.These studies,including,for example, those by Sachs(1981, 1982)and Svenssonand Razin (1983), argued that household saving decisions should be derivedfrom solutions to a dynamicoptimizationproblemof choosingconsumptionlevels at different points in time. As far as the HLM effect was concerned, the key insightprovidedby these models was that the relationshipbetween the terms of trade and savingdependedcruciallyon the expected duration of the terms of trade shock. For example, if households expected an improvementin the terms of trade to be permanent,then they would revise upwardtheir estimate of permanentincome in proportionto the increasedpurchasingpowerof theirincometoday. Underthe hypothesis thatthe marginalpropensityto consume(save)out of permanentincome is unity(zero), a permanentchangein the termsof tradewouldtherefore have no effect on saving, contraryto the HLM view.2By contrast,in a situationin which the improvementin the terms of trade was expected to be only temporary,the increasein permanentincomewouldbe smaller than the increasein currentincome, and savingwould accordinglyrise. 1Fora discussionof investmenteffectsof termsof trade changesin a somewhat different context, see Corden(1988). 2 The view that permanenttermsof tradeshockshaveno effect on the current accounthas been disputedby Obstfeld(1982),Ostry(1988),and, more recently, by Gavin(1990). PRIVATE SAVING AND TERMS OF TRADE SHOCKS 497 Therefore,the HLMhypothesiswassatisfiedfortransitorytermsof trade disturbances,but apparentlynot for permanentones. At the sametime, the view thattransitorychangesin the termsof trade haveunambiguouseffectson privatesavingis misleadingfor two reasons. When a countryexperiencesa temporaryadverseterms of trade shock that raises the price of currentimportsrelativeto future imports,consumershave an incentiveto postpone their purchases-that is, to save considerations-the basis for more. So, while consumption-smoothing the HLM effect-imply thatprivatesavingshoulddeclinein responseto the temporaryreal income decline, the so-called consumption-tilting motivesimplythatprivatesavingshouldincreaseas agentsreducecurrent consumptionin line with the increase in its relative price.3On these groundsalone, therefore, what happens to saving is theoreticallyambiguous and depends on the relative magnitudesof the consumptionsmoothing and tilting motives. The parameter governing this latter motive is the intertemporalelasticity of substitution.Relatively large values of this parameterimply that, in responseto a given (transitory) movementin the termsof tradeand, hence, in the intertemporalrelative price (consumptionrate of interest),consumersincreasetheir savingby a relativelylarge amount;it follows that the largeris this elasticity,the greateris the increase(the smallerthe fall) in privatesavingin response to a transitoryadverseshock to the terms of trade. In addition, however, when there are nontradedgoods, an adverse terms of trade shock will lead consumersto substituteawayfrom relativelyexpensiveimportsin favorof home goods, therebybiddingup their relative price. If the terms of trade shock is temporary,the resulting temporaryreal appreciationwill contributeto a furtherincreasein the consumptioninterestrate and, hence, a furtherincreasein saving.4The parametergoverningthe switchfromimportsto home goods and, hence, the magnitudeof the temporaryreal appreciationand increase in the consumptionrateof interestis the intratemporalelasticityof substitution between tradables and nontradables.A relatively large value of this parameterimpliesa largeincreasein the consumptionrateof interestand a commensuratelylarge rise in saving. It may be concluded,therefore, 3A transitoryadverseshock to the terms of trade raises the cost of current consumptionrelativeto futureconsumption(the consumptionrate of interest) becauseit temporarilyraisesthe relativeprice of imports,whichentersinto the consumerprice index. The latter, however,returnsto its trend level once the termsof tradereturnto theirtrendlevel. Forfurtherdetailson the consumption rate of interest, see Dornbusch(1983). 4 See Ostry (1988). The reasonis the same as given in the previousfootnote. The transitoryrise in the relativepriceof nontradablesraisesthe consumerprice indextemporarily,makingcurrentgoodsmoreexpensiverelativeto futuregoods. 498 JONATHAN D. OSTRY and CARMEN M. REINHART that the largerare either the intertemporalor intratemporalelasticities of substitution,the greaterwill be the increase(the smallerthe decrease) in private saving in response to a temporaryadversemovementin the termsof trade. The outcome in any case is an empiricalmatterthat can only be addressedthroughestimationof these two criticalparameters. The approachtaken in this paperinvolvesestimatingthe "structural" parametersof a representativehousehold'sutilityfunction.The basisfor suchan approach,in preferenceto the alternativeof estimatingreducedform consumptionor savingfunctions,is related to the Lucascritique. As is well recognized,the Lucas critiqueimpliesthat there may not be anythingthat could properlybe called a consumptionor savingfunction, in the sense of a stable functionalrelationshipthat is independentof the wider macroeconomiccontext.5In contrastto previousstudies, we employ a disaggregatedcommodity structureaccordingto which agents consumeboth tradedandnontradedgoods. Disaggregationpermitsestimationof the two parametersof interest:the intertemporalelasticityof substitutionandthe intratemporalelasticityof substitutionbetweentradables and nontradables.The data set employedis also suitablefor comparingourfindingsto those of previousstudiesthatemployeda one-good structure.In contrastto many such studies, we find evidence that the intertemporalelasticityof substitutionis significantlydifferentfromzero and lies in the 0.3 to 0.8 range, dependingon the region considered. Intratemporalsubstitutionelasticitiesare estimatedto be significantly higher, and indicate that this parameter-which to our knowledgehas been entirelyignoredin previousEulerequationestimationsfor developing countries- playsa criticalrole in determiningthe signandmagnitude of the HLM effect in these countries. Finally, althoughthe empiricalresults of this paper can be used to analyze a variety of other issues-including the effects of permanent terms of trade shocks and the impactof trade reforms(which alter the internalterms of trade of the countrythat undertakesthem)-we focus in what follows on temporaryterms of trade shocks, mainly because recent empiricalevidence relatingto the developingcountriessuggests thatthe transitorycomponentof suchshocksis quantitativelyimportant.6 For instance, Cuddingtonand Urzua (1989) found that fully 60 percent of all shocks to commodity prices were of a temporarynature, and Mendoza (1992) reporteda similarresult relatingto the terms of trade of developingcountries. 5See Hall (1988, p. 340), for an elegant restatementof this view. On the usefulnessof our estimatesto the issue of permanenttermsof trade shocks, see, for example, Ostry (1988), Gavin (1990), and Edwardsand Ostry (1992); on their applicabilityto trade reform issues, see Calvo (1987), Ostry 1990, 1991, 1992), Edwardsand Ostry (1990), and Ostryand Rose (1992). 6 PRIVATESAVINGAND TERMSOF TRADESHOCKS 499 The remainderof thispaperis organizedas follows.SectionI illustrates the role of preferenceparametersin the HLM effect in the context of a simple two-periodmodel that admits closed-formsolutions. For the purposesof empiricalimplementation,however,SectionII considersthe stochastic,infinite-horizonversion of this model and presentsthe optimalityconditionsfor an intertemporalequilibriummodelin whichhouseholds consumeboth tradedand nontradedgoods. Section III describes the approachto estimationand presentsthe empiricalresults.The main conclusionsare containedin Section IV. I. A SimpleModel of the HLM Effect Considera small open exchange economy where the representative household derives utility, C, in each period accordingto the following constantelasticityof substitution(CES) function:7 - C = (am - 1/ + nl 1/e) 1, a, > O, (1) wherem (n) denotesconsumptionof importables(nontradables).Agents are assumedto live for two periods.8Intertemporalconsumptiondecisions maximizethe followingCES utilityfunctionsubjectto constraints specifiedbelow: U = (C - + pC -l/) 1 , a > 0, p < 1, (2) where the subscripts1 and 2 denote periods 1 and 2, respectively,and where 3 denotes the subjective discount factor. In equation (1) the parameterEdenotes the intratemporalelasticityof substitutionbetween tradables(importables)and nontradables.Largervaluesof this parameter imply greater responsivenessto relative price (real exchange rate) changes. A value of unity correspondsto the logarithmicutility case, while values above (below) unity imply gross substitutability(complementarity).In equation (2) the parametercrdenotes the intertemporal elasticityof substitution.Largervalues of this parameterimply greater 7 The model of this section is a simplified version of the one developed in Ostry (1988). A stripped-down version is presented here only for the purposes of illustrating the role of preference parameters in the HLM effect. The model to be estimated empirically is presented in Section II. 8 As is well known, the two-period assumption is not restrictive here, since the second period may represent the aggregation of a large (possibly infinite) number of future periods. The motivation for the two-period structure is that it allows us to obtain closed-form solutions for the response of private saving to terms of trade shocks, something that is precluded in the infinite-horizon version of the model developed later. 500 JONATHAN D. OSTRY and CARMEN M. REINHART responsivenessto movementsin intertemporalrelativeprices(consumption rates of interest). Equation (2) collapses to a logarithmicutility function when oC= 1. Perfectcapitalmobilityis assumed,and thereforethe countryfaces a given (in terms of the numeraire)world interest rate.9 All debts are requiredto be repaidby the end of the secondperiod.These assumptions imply that the representativehouseholdmaximizesequation (2) (given equation(1)), subjectto the constraintthat the presentvalue of expendituresnot exceed the presentvalue of resources.The latter, whichwe referto below as lifetimewealth,is assumedto take the formof a stream of endowmentsof tradable(importableandexportable)andnontradable goods. The solutionto this optimizationproblemyields demandsof the form mi = m [pi, q, Pi C,(R, W)] (3a) ni = n[pl, ql, P1C(R, W)] (3b) m2 = m2 [P2, q2,P2 C2(R, W)] (3c) n2= n2[P2, q2,P2 C2(R, W)], (3d) wherepi andqidenote, respectively,the relativepriceof importablesand nontradables,and Pi denotes the consumerprice index in period i; R is the consumptiondiscountfactor,whichis givenby R = 1/(1 + r), where r is the consumptionrateof interest;andWis realwealth.1'The consumption discount factor, R, is related to the world discount factor, R*, accordingto R = R*P2/P,. (4) Thus, the consumptiondiscountfactortakes into accountthat the relevant interest rate for intertemporalconsumptiondecisionsdepends on the evolution of the relative price structurethrough time. Since the consumerprice index in any period depends on the relative prices of 9Withoutloss of generality,the numeraireis takento be the exportablegood. Forrecentevidencesupportingthe viewthatdevelopingcountries,in general,can be ocharacterizedas financiallyopen economies,see Haque and Montiel(1991). to obtain explicit solutionsfor the demand Although it is straightforward functionsin this case, there is no particularinterest in doing so. In equations (3a)-(3d), we havemadeuse of the factthatthe optimizationproblemas specified satisfiesthe assumptionsnecessaryfortwo-stagebudgeting(GoldmanandUzawa (1964)). Accordingly,demandsin a given perioddependonly on relativeprices in thatperiodand aggregatespendingin thatperiod.The realvalueof aggregate spending,in turn, depends only on lifetime wealth and on the intertemporal relativeprice,R (the consumptiondiscountfactor,whichis equalto 1 over 1 plus the consumptionrate of interest). PRIVATESAVINGAND TERMSOF TRADESHOCKS 501 importablesand nontradables,the consumptionand worlddiscountfactorswill differfromone anotherwheneverthe termsof trade(the relative price of importables)or the real exchange rate (the reciprocalof the relativepriceof nontradables)is not expectedto remainconstantthrough time. To close the model, market-clearingconditionsfor nontradable goods are specified: n [pl, ql, PI C1(R, W)] = nf n2[p2, q2,P2C2(R, W)] = n2, (5a) (5b) where nifrepresentsthe endowmentof nontradablegoods in period i. Finally,we can define the ratioof privatesavingto GDP (grossdomestic product)(s) as follows:" x1 - l (ml i) + + m nl X1 pi qi (6) wherewe have used the market-clearingconditionsfor home goods and whereYx,mi representthe endowmentsof the exportableandimportable goods, respectively,in the first period. Considernow the effect of a transitorydeteriorationin the terms of trade-that is, a rise in pl, withp2 constant.To simplifythe analysis,it is convenientto consideran initiallystationaryequilibriumin which all pricesandquantitiesare constantovertime. Differentiatingequation(6) aroundan initialequilibriumwiths = 0, andusing(5a) and (5b) to solve for the effects on ql and q2gives b (1 - k)E¢T )E dss = b(1 d log p- bE + (1 - b)r - b (1 k)X, (7) where b is the initialexpenditureshare on importables(a positive fraction), k is the ratioof currentto lifetimespendingor wealth, and Xis the ratioof exportsto productionof tradables.12The firstterm on the righthandside of equation(7) representsthe intertemporalsubstitutioneffect, whichis equal to (minus)the productof the elasticityof currentspending with respect to the consumptiondiscountfactor, (1 - k)cr,and the change in the discount factor, be/(be + (1 - b)a). This expression is increasingin both e and c, which shows that savingrises by more, the "Under the assumptionof no historicaldebt commitments,this ratio is also equal to the ratio of the currentaccount balance to GDP, since there is no investmentor governmentsavingin the model. 12Clearly,bothk andXarepositivefractions.If the horizonof householdswere infinite,a good proxyfor k wouldbe the realinterestrate. It shouldalso be noted that if there is no domesticproduction(or endowment)of importsubstitutes,X is equal to unity. 502 JONATHAN D. OSTRY and CARMEN M. REINHART larger are either the intratemporal or intertemporal elasticities of substitution. For a given rise in the consumption interest rate, larger values of o( imply larger increases in saving. For a given elasticity of saving, larger values of e imply larger increases in the consumption rate of interest and, hence, larger increases in saving. The second term on the right-hand side of equation (7) represents the consumption-smoothing effect, which depends on the initial volume of exports. With real income falling below its trend level, the consumption-smoothing effect tends to reduce private saving. Equation (7) summarizes the main result of this section, namely that private saving will increase by more (fall by less) in response to a temporary deterioration in the terms of trade, the larger are either intertemporal or intratemporal elasticities of substitution. II. The Stochastic Euler Equations The model of Section I was presented in order to illustrate the role of preference parameters in the HLM effect. With a view toward empirical implementation, however, we need to generalize that model by allowing for uncertainty and more than two periods. Accordingly, consider an economy with an infinitely lived representative household whose objective is to choose a consumption stream that maximizes [(r/(a - 1)] Eo E p(aml - 1/ + nl 1/ -le) t=O a, 3, E, ( > , p < 1, (8) subject to the series of budget constraints ptmt + qtnt = ptmt + qt it + Xt + At - (l/R*- 1)At- 1, and the transversality condition13 t lim (1/R*)At = 0, t-- 00i = o t > 0, (9) (10) where Eo is the expectations operator conditional on information available at time 0; At denotes the real level of debt carried from period t to period t + 1;14 (1/R*) - 1 = r* is the real interest rate (in terms of 13 See ChamberlainandWilson(1984)for a fullerdiscussionof the appropriate no ponzi-gameconstraintin an infinite-horizonconsumptionmodelunderuncertainty. 14We assume that the inheritedlevel of debt, A_1, is given and, for convenience, set equal to zero. PRIVATESAVINGAND TERMSOF TRADESHOCKS 503 the numeraire)on the debt;15and remainingnotation is as specified in Section I. The problemof the consumer,then, is to choose an optimalsequence (m,, nt,At) thatmaximizesequation(8), subjectto equations(9) and(10). The first-ordernecessaryconditionsfor an optimumare I -m RPt Ct +l- aml - lI + n' - /e_ + Et P,-+ +l R*pt +-am1-+e + n'1-,e a (n,/m)' a(C-1) - m, t+1 , nMt 1(- l (. 3 -1 =ptIqt. 1 (13) Equation (11) is the intertemporalEuler equation associatedwith importables consumption in two consecutive periods; it states that the marginalutilitycost of givingup one unitof m at time t shouldbe equated to the expectedutilitygainfromconsumingone more unit of m at t + 1. Equation (12) is the analogous condition relating the marginal rate of substitutionbetweenconsumptionof good n at t andt + 1to the relevant intertemporal relative price. Finally, equation (13) is the nonstochastic first-ordercondition equating the intratemporalmarginalrate of substitution between importablesand nontradablesto the corresponding relativ pe itc ratio. It can be verified that equations(11)-(13) are not ither of the two reindependent. Specifically, combining (13) wmoe or te ivnat nonstochasmainingequationsyieldsthe ttha . tic first-ordercondition holds, equations (11) and (12) do not provide independentrestrictionson the evolutionof consumptionthroughtime. It is perhapsworthemphasizingthe differencesbetweenequations(11) nd and (1on2)tradabs corresponding () and the correportables model.'6 In such a model, the relative price ratio that is relevant for transformingpresentinto futureconsumptionis the real interes ratethat is, the nominalrate deflatedby the rate of changeof the aggregate price index. When relative prices are not constant, however, as when there are terms of trade shocks, the appropriateintertemporalrelative price ratio needs to take account of such changes. This is why, for example,in equation(11) the priceratiothat premultipliesthe marginal rate of substitutioninside the expectationsign is the real rate of interest Clearly,then, R * is the associatedworldreal discountfactor. 16This is particularly relevant, since estimation of consumption Euler equations for developing countries has been confined to environments in which there is a single consumption good; see, for example, Giovannini (1985) and Rossi (1988). 504 JONATHAN D. OSTRY and CARMEN M. REINHART 1 , adjustedfor the rate of change of the in terms of the numeraire,1/R*, termsof trade over time, Pt/Pt+1 (that is, the "own"rate of interest).If the relativepriceof importsis expectedto declinethroughtime, current importablesconsumptionis expensiverelativeto futureimportablesconsumption. In consequence, offsetting changes in the marginalrate of substitutionare requiredin preciselythe same directionas would occur if the worldrate of interestwere to rise (R* were to fall). An analogous interpretationcarries over to equation (12), wherein the appropriate relativeprice for the purposeof determiningthe marginalrate of substitution between nontradables consumption in consecutive periods involvesthe real exchangerate ratio, q,/q,+ i. Giventime-seriesdata on importablesand nontradablesconsumption and on interest rates and import, export, and nontradablesprices, it is possible to estimate the system consistingof equations (11)-(13) and recoverthe mainparametersof interest.Since (13) musthold identically (in the absence of measurementerror),and since (11) and (12) are not independent,given that (13) holds, it is sufficientin the estimationto considerequation (11) alone. The restrictionson the joint behaviorof consumptionof importablesand nontradables,the terms of trade, and the relevantrate of returnimpliedby the maximizationof the expected utilityfunctiongiven by equation(8), subjectto the constraintsgiven in (9) and (10), are summarizedin equation (11). In addition, given the assumptionof rationalexpectations,we can use equation(11) to define the disturbance ut PPt= R amt;1 amt t +1am -1 + + 1n}^^m/ r(E + n -m Mt + 1 e +1 1 14) m, whereutmustbe uncorrelatedwithanyvariablethatis in the information set of agents at time t. III. Empirical Results The parametersof the representativehousehold'sutilityfunctionoutlined in the previoussectionswere estimatedusing annualpooled timeseries, cross-sectiondata for 13 developing countries. The countries examinedin the analysisincludefourAfricancountries-Egypt, Ghana, Cote d'Ivoire, and Morocco; five Asian countries-Sri Lanka, India, Korea, Pakistan, and the Philippines; and four Latin American countries-Brazil, Colombia, Costa Rica, and Mexico. PRIVATE SAVING AND TERMS OF TRADE SHOCKS 505 Data Issues Data coverage for each country begins in 1968 and ends anywhere between 1983and 1987;see the Appendixfor a list of the sampleperiod for each countryand the sources of the data. As equation (14) highlights,estimationof the intertemporaland intratemporalelasticitiesof substitutionrequiresdata on householdconsumptionof tradedand nontradedgoods and the termsof trade. While time series on the terms of trade are readilyavailable(see Appendix), consumptiondata are generallynot disaggregatedinto tradedand nontradedcomponents.Guided by the theoreticalframework,these series were constructedusing data from a varietyof sources.17 The time series for consumptionof importableswas constructedas follows. The agricultural,mining, and industrialsectorsproducetraded goods;GDP originatingin these sectorsthusdefinesdomesticproduction of traded goods. Private and public services comprise the nontraded goods sector. Domestic productionof importsubstitutesis calculatedas domesticproductionof tradedgoodsless exports,on the assumptionthat exportablesare not consumedat home.l8If marketsclear, all domestic productionof importsubstitutesis consumedat home. Consumptionof importsubstitutesplus consumergoods imports,whichare total imports less importsof intermediateand capital goods, make up the series of interest-consumption of importables.Nontradedgoods consumptionis residuallycalculatedas total privateconsumptionless consumptionof importables.19 The relevantprice deflatorsfor the consumptionof traded and nontraded goods are price indices for imports and services, respectively. Deposit ratesof interestwereusedwhen available,and, in theirabsence, a moneymarketrate. All consumptiondataare convertedto a per capita basis by dividingthe aggregatesby the existingpopulation. Methodology Weestimatethe parametervector,x = [, E,or]by fittingthe first-order condition defined in equation (14) to the panel data using Hansen's 7 All series are availableupon request. inthecaseof somecountries, bea restrictive Thismayadmittedly assumption butunfortunately, thedatadonotpermitusto disaggregate further. consumption all the seriesusedto disaggregate 19Toensureconsistency, into consumption its tradedandnontradedcomponents(GDPby sector,privateconsumption, exports,andimports)areon a nationalincomeaccounts(NIA)basis. 18 506 JONATHAND. OSTRYand CARMENM. REINHART (1982) generalized method of moments (GMM).20 The residuals in the estimated equation are partly forecast errors, which, by the assumption of rational expectations, are uncorrelated with any variable in the agent's information set at time t; in technical terms, those errors are orthogonal to any chosen instrument known to agents at time t. The assumption that all available information is used in forecasting future consumption and prices (that is, m, + 1, n, + 1, qt + 1, and p + 1) allows us to use a large number of instruments to estimate a smaller number of parameters. That excess of instruments over estimable parameters yields a testable set of overidentifying restrictions. In reality, however, the error term may also include measurement error. Any systematic part of that noise-say, owing to serial correlation-should be allowed for in the estimation. Simply, it may be more efficient to fit the orthogonality condition less tightly in those periods when it is known measurment error swells the composite residual. Understanding the complex nature of the disturbances-that is, the ut-is critical to the estimation strategy. Serial correlation among the u, may arise for a variety of reasons. First, as illustrated by Hayashi and Sims (1983), current values of consumption, m, and n,, may not be observed before expectations of future consumption (m,+1, n, +) are formed, implying some lagged values of u, are not in the information set; this may make today's forecast error correlated with last period's yet unobserved error.21 Second, the nature of the measurement error may make the residuals serially correlated; time aggregation problems in annual consumption data, as discussed in Hall (1988), introduce a first-order moving average process with a known parameter in the error term. Since the moving 20The parametera is some positivenumberthat denotes the weightattached to the importedgood in the periodutilityfunction.In the analysisthat follows, a (whichis not ofimmediateinterest),is not jointlyestimatedwiththe remaining parameters.Instead, the followingvalues were used: 0.85 for Africa, 1.14 for Asia, and 0.58 for LatinAmerica.These valueswere obtainedby estimatingthe nonstochasticfirst-ordercondition(equation(13)) using ordinaryleast squares (OLS). Since we tested for and found cointegrationamongrelativeprices and consumptionof importablesand nontradedgoods, we know that OLS provides consistentparameterestimatesfor a. By imposingin the subsequentestimation the values of a, we increase the efficiency of the estimates of the remaining parameters.The estimatesof e obtainedby applyingOLSto (13) were also used as the startingvalues in the subsequentGMM estimation. 21This problemis not likely to arise with pricesand interestrates, whichare generallyavailablemonthlywith little or no lag. However, for the consumer makingtwo-periodforecastsof consumption,it is not unlikelythatoverestimating (underestimating)today'sconsumptionlevel leads to a similarerrorin the subsequent period, makingthe two correlated. 507 PRIVATE SAVING AND TERMS OF TRADE SHOCKS averageparameteris known, the constraintthat the disturbancesfollow a first-ordermoving average process is taken into account by quasidifferencingthe relevantseries.22In addition,becauseof the diversityof countriesincludedin our sample, as well as the fairlylong periodof coverage considered,we allow for the presence of more general forms of heteroscedasticityin the disturbances. The estimationproceeds under the assumptionthat the parameters that characterizehousehold preferencesare identical across countries and regions.Although, as we will latershow, homogeneityof tastes may be a restrictiveassumption,it economizeson the numberof parameters to be estimatedand allowsfor the maximumdegreesof freedom.23Two differentsets of instrumentsare employed. Neither instrumentset includesvariablesmeasuredat time t, since the movingaverageprocessin the errorterm would result in these variablesbeing correlatedwith the residual,ut. The selection of instrumentsis not trivial, since the use of instrumentsthat are correlatedwiththe residualwouldresultin inconsistent estimates.The most recentpermissibleinstrumentis one laggedtwo periods. The first vector of instrumentalvariables zl/ = [constant, mt -/mt-2, nt-1lnt-2, Pt -2(R*-2pt-1), r- , nt- 1], uses six instruments.This implies that there are six orthogonalityconditions; with three parametersto be estimated, there are three overidentifyingrestrictions.The second instrumentset replacesthe levels of consumptionof importablesand nontradedwith their ratio z2/ = [constant,mt- /m- 2, lt- 1lt- 2, Pt- 2 (R- 2pt- 1), mt - 1 nt- 1]. In the latter case there are five instruments,three free parameters(as before), and, therefore,two overidentifyingrestrictions.While the variationin the instrumentset is slight,comparisonof the estimatesproduced by each set sheds light on which parametersare most sensitive to the choice of instrumentsor, in other words,whichparameterestimatesare more robust.24 22 Fora completediscussionof howthe movingaverageparameteris calculated, see Working(1960) and Hall (1988). 23This assumptionwill be relaxedlaterwhen regionalestimatesof the preference parametersare estimated. 24A commonprocedurein the existingliteratureon estimationof Euler equations is to allowthe instrumentset to varyby introducingmorelags, considering instrumentsets suchas z3' = z lt,, zl - l]. If one is workingwith time seriesfor a singlecountry,the addedlaginvolvesthe loss of 1 degreeof freedom.However, in the presentanalysisthe addedlagwouldentailthe loss of 13degreesof freedom (1 for each country).For this reason, we consideronly the most parsimonious instrumentsets. 508 JONATHAN D. OSTRY and CARMEN M. REINHART Estimation Results Table1 reportsthe parameterestimatesfor eachinstrumentset andthe minimizedvalueof the objectivefunction,J, whichHansenandSingleton (1982) showedto be a test statisticfor the validityof the overidentifying The parameterestimatesfor 3,e, ando aresimilarfor both restrictions.25 instrumentsets and are economicallymeaningful.The discountfactor, P, falls in the 0.96-0.99 range. The intertemporalelasticityof substitution, ca, is in the 0.38-0.50 range but is large relative to its standard The intratemporalelasticityof substitutionlies in the 1.22-1.27 errors.26 range, indicatingthat importablesare gross substitutesfor nontraded goods.27The J-statisticsare smallrelativeto the degreesof freedom(for either instrumentset), indicatingthat the overidentifyingrestrictions imposed by the model are not rejected by the data; that is, the three parametersestimated do a good job of satisfyingeither the five or six orthogonalityconditionsthat depend on the instrumentset. The quasidifferencing of the data and the correction for heteroscedasticity producedregressionresidualsthat are white noise. Of notable interest is the fact that, in contrastto previous workincludingGiovannini(1985) and, to a lesser degree, Rossi (1988)for the developingcountries,and Hall (1988) for the United States-the intertemporalelasticityof substitutionis estimatedto be significantlydifferent from zero. This means that, in responseto shifts in real (consumptionbased) rates of interest, householdswouldbe expectedto alter the time profile of their consumption,increasingthe growthrate of the latter in response to an increasein real rates of return. A possible explanationof our findingof a statisticallysignificantdegree of intertemporalsubstitutionrelates to the restrictiveassumptions Specifically,for the mostpart,these employedby previousresearchers.28 studies either assumed the existence of a single consumptiongoodmakingno distinctionbetweenconsumptionof tradableandnontradable goods; or they assumedthat standardconsumptionandpriceserieswere 25The J-statisticis distributedas X2(n) underthe null hypothesis.The degrees of freedom, n, are equal to the numberof overidentifyingrestrictions. 26Interestingly,these estimatesare consistentwithvaluesin the 2.5-3.0 range for the coefficientof relativerisk aversion(the reciprocalof the intertemporal elasticityof substitution)used in calibratingreal businesscycle models:see, for example, Stockmanand Tesar(1990). 27Thisis slightlyhigherthan the estimatesobtainedby Backus, Kehoe, and Kydland(1991) for the United States. 28Of relatedinterestare recent empiricalpapersthat have includedmoneyin modelingthe consumer'schoice problem:see, for example, Arrau (1990) and Ecksteinand Leiderman(1992). 509 PRIVATE SAVING AND TERMS OF TRADE SHOCKS Table 1. Estimatesof the Model PoolingAll Regions for AlternativeInstrumentSets Parameters e All Countries Instrumentset I Instrumentset II 1.279 1.223 (0.154) (0.351) a 0.383 0.504 [3 (0.087) 0.955 (0.033) (0.228) 0.991 (0.041) Memorandumitems: J-statistic 5.707 2.590 (0.127) (0.274) Numberof observations 208 208 Note: The data and sample periods covered are describedin detail in the Appendix. Standarderrorsare shown in parentheses.For instrumentset I the 0.95 criticalvalue of the J-statistic,whichis distributedas X2(3)underthe null hypothesis,is 7.815. Forinstrumentset II the relevantcriticalvalueis 5.991. The probabilityvalues of the J-statisticappearin parentheses. reasonable proxies for the "true" utility-based indices.29Either assumption is likely to prove too restrictive in the case of developing countries, which are frequently subjected to terms of trade shifts and which commonly experience large movements in real exchange rates that alter the relative price between importables and home goods. The practice in previous literature of computing the real interest rate that is relevant for consumption decisions as the nominal rate divided by (one plus) the rate of change of a standard aggregate price deflator-that is, a deflator for which the correct utility-based weights have not been used-may thus potentially imply a serious misspecification, especially when the profile of relative prices (terms of trade and real exchange rates) is not constant through time. For the most part, researchers in the past have used a linearized version of the Euler equations considered here for the particular case of a single consumption good:30 Ac, = a + or, + e,, 29 (15) Correctaggregationwouldapplyutility-basedweightsto the varioustypesof goodsconsumed.However,availableaggregatepriceindicesdo not employsuch a methodology. 3Notice thatthe assumptionof linearityitself involvesa numberof additional restrictions(particularlyon the joint distributionof consumptionand rates of return),relativeto the model estimatedin this paper. 510 JONATHAN D. OSTRY and CARMEN M. REINHART where c, is (the natural logarithm of) aggregate consumption, r, is the (conventionally measured) real rate of interest, and et is a random disturbance. The coefficient on the real interest rate, a, is the intertemporal elasticity of substitution. Giovannini (1985) found no systematic relationship between changes in consumption and the real interest rate. Rossi (1988), who allowed for liquidity constraints, also failed to detect a relationship in many of the regions considered. Using the countries in our sample, we estimated the more restrictive version of the model given in equation (15). As in Giovannini (1985), the estimates obtained by applying instrumental variables techniques yielded no systematic relationship between consumption changes and the real interest rate. This, of course, highlights that our finding, summarized in Table 1, of a statistically significant intertemporal elasticity of substitution is not a product of the choice of countries or period covered in our sample. It rather suggests that, in estimating the parameters of consumer preferences, it is important to relax some of the assumptions underlying a specification such as (15). Specifically, in our case, it indicates the importance of disaggregating between traded and nontraded goods. A future line of research, particularly relevant for developing countries, would retain the multigood setting employed here, but would also relax the assumption of a perfect capital market and allow for the existence of liquidity constraints, as in Rossi (1988). Table 2. Estimatesof the Model UsingPanel Data for 13 DevelopingCountries:InstrumentSet I Parameters Africa 1.279 (0.474) e a~(xT~ P Memorandumitems: J-statistic ~0.451 (0.159) 0.945 Asia 0.655 (0.105) 0.800 (0.201) 0.995 Latin America 0.760 (0.172) 0.373 (0.111) 0.995 6.492 8.333 6.928 (0.080) (0.165) (0.140) SSR 2.857 7.451 1.234 Numberof observations 62 81 65 Note: See note to Table 1. The value of (3chosenis that whichminimizesthe sumof squaredresiduals(SSR);J is the valueof the criterionquadraticfunction. The 0.95 criticalvalue of the J-statistic,whichis distributedas X2(4)underthe null hypothesis, is 9.488. The probabilityvalues of the J-statistic appear in parentheses. PRIVATESAVINGAND TERMSOF TRADESHOCKS 511 Thus far, we have imposed the restriction that preference parameters are identical across the three regions in our sample, a restriction that we feel is unlikely to be satisfied in practice. We now present a set of results that relax this assumption by allowing for possible regional variation in taste parameters. To offset the loss of degrees of freedom when the sample is broken up, we economize on the number of parameters to be estimated. Rather than estimate the parameter vector ,L = [p, e, o], as before, we confine our estimation instead to the parameters e and a. This is in keeping with our overall objective of shedding light on the HLM effect, since the parameter e will not play a critical role in this context (see Section I). Using the same estimation technique as before, we estimate e and a over a range of feasible values for p. Given the estimates of p presented in Table 1, the search was conducted over the range 0.900-0.995 at intervals of 0.005. The value of P presented in Tables 2 and 3 is that which minimized the sum of squared residuals (SSR). This search procedure not only allows us to pinpoint p for each region, but by imposing its value (as well as imposing the relevant value for a) in the estimation of e and a, it increases the efficiency of these estimates. The results for instrument sets I and II are summarized in Tables 2 and 3, respectively. In general, the parameters are estimated with precision in all regions, and the overidentifying restrictions imposed by the model are not rejected by the data. However, interesting regional differTable 3. Estimatesof the Model UsingPanel Data for 13 DevelopingCountries:InstrumentSet II Parameters E a e3 Memorandumitems: J-statistic Africa 1.441 (0.771) 0.443 (0.178) 0.940 Asia 1.152 (0.270) 0.803 (0.235) 0.990 Latin America 1.107 (0.383) 0.430 (0.135) 0.995 3.731 3.679 5.019 (0.292) (0.298) (0.170) 1.658 1.661 3.506 SSR 65 81 62 Numberof observations Note: See note to Table1. The valueof B1chosenis the one thatminimizesthe sumof squaredresiduals(SSR);J is the valueof the criterionquadraticfunction. The 0.95 criticalvalue of the J-statistic,whichis distributedas X2(3)underthe null hypothesis, is 7.815. The probabilityvalues of the J-statistic appear in parentheses. 512 JONATHAN D. OSTRY and CARMEN M. REINHART ences in preferencesemerge. Irrespectiveof the instrumentset used, the intertemporalelasticityof substitutionis estimatedto be about 0.80 for Asia, and to be roughlyhalf as large for Africa and LatinAmerica.31In effect, estimatesof o do not appearto be very sensitiveto the choice of instrumentsin any of the regionsconsidered.The value of P that minimizes the sum of squaredresidualsis around0.94 for Africaand around 0.995 for Asia and LatinAmerica,indicatingthat futureconsumptionis discountedmore heavily in the African countriesconsidered. Tables2 and3 also revealthatimportablesandnontradablesare closer substitutesin Africathanin Asia or LatinAmerica.Partof these regional differencesmay be accountedfor by regional differencesin the commodity compositionof tradablesand nontradables.In particular,the shareof durablesin importablesis lowerin Africathanin other regions, and since nontradablesare overwhelminglynondurable(that is, serin Africa. vices),thismayaccountfor the higherdegreeof substitutability For instrumentset I (Table 2), we find gross substitutabilitybetween importablesandnontradablesfor the Africancountriesonly, whereasfor the second instrumentset (Table3), gross substitutabilityis obtainedin all three regions. IV. Conclusions The traditionalexplanationof the relationshipbetween the terms of trade and the external current account balance has, for many years, rested on the Harberger-Laursen-Metzler hypothesis.Accordingto this hypothesis,an improvementin the termsof traderaisesa country'sreal incomelevel, andsincepartof thatincreasein realincomewillbe devoted to saving, the improvementin the terms of trade improvesthe current account. This paper has presented a first attempt to obtain quantitativeestimates of the main parametersthat determinethe response of private savingto transitorytermsof tradeshocksfor a cross-sectionof developing countriesin the context of a fully articulatedintertemporaloptimizing model. The main resultsof our study are as follows. First, the estimatedparametersthat describeconsumerbehaviorin a 31Rossi (1988) arguedthatestimatesof the intertemporalelasticityof substitution are biaseddownwardif liquidityconstraintsare not takeninto account.The regionaldifferencesin estimatesof o may reflectthis omission,since empirical evidence (see Haque and Montiel (1989)) indicatesthat the Asian countriesin our sampleare less liquidityconstrainedthantheirAfricancounterparts.Unfortunately,the Haque-Montielsampledoes not includeanyof the LatinAmerican countriescoveredby this study. PRIVATE SAVING AND TERMS OF TRADE SHOCKS 513 simple three-good setting (the intertemporaland intratemporalelasticities of substitution, and the discount factor) are all economically meaningful,irrespectiveof the choice of instrumentsemployed and/or the region considered.Disaggregationof the panel data allowed us to detect interestingregional differences.The overidentifyingrestrictions imposed by the model are not rejected by the data. Second,the estimatesof the intertemporalelasticityof substitutionare significantlydifferentfromzero in all the regions.This findingcontrasts withpreviouswork, includingGiovannini(1985)and, to a lesser degree, Rossi (1988)for the developingcountries,andHall (1988)for the United States. The implicationof our findingis that, in responseto shiftsin real rates of interest, householdsin developingcountrieswill generallyalter the time profile of their consumption,increasingthe growthrate of the latter in response to an expected increasein real rates of return. Third, our estimates of the intratemporalelasticity of substitution suggestthatsubstitutionbetweentradablesandnontradablesis an important channel through which terms of trade shocks are transmittedto private saving and the currentaccount. In particular,our results are consistentwith the view that termsof tradeshocksare likelyto generate substantialfluctuationsin real exchangerates, which in turn alter consumption rates of interest, thereby affecting saving behavior and the allocationof total expenditurebetween traded and nontradedgoods. Fourth,the estimatesfor all the regionsconsideredcast doubt on the view that consumptionsmoothingis the only relevantfactor governing the response of households to transitoryterms of trade shocks. An importantimplicationof our estimatesis that transitoryterms of trade shocks should give rise to intertemporalshifts in consumptionboth directly and through the movementsin real exchange rates that they induce. Calibrationof a dynamicstochasticequilibriummodel usingthe econometricestimatesof this paper(see, for example,Mendoza(1992)) should enable one to obtain reasonable quantitativeestimates of the effects of transitorytermsof tradeshockson privatesaving.Preliminary evidencein this regardsuggeststhat, althoughprivatesavingis likely to declinein responseto transitoryadversetermsof tradeshocks,the magnitudeof this decline is likely to be muchsmallerthan wouldhave been predictedon the basisof previousestimatesof the intertemporalelasticity of substitution.A policyimplicationis that the need to "finance"transitory adverse movements in the terms of trade may be smaller than previouslybelieved. Given the estimatedparametervalues, this conclusion is likely to be especiallytrue for the Asian countriesin our sample and less so for the Latin Americanand Africancountries. Finally,whilethe paperhasfocusedexclusivelyon the effectsof transi- 514 JONATHAN D. OSTRY and CARMEN M. REINHART tory terms of trade shocks, the parameter estimates obtained here should prove useful in a variety of other contexts, including the assessment of the effects of trade reforms and fiscal policies. APPENDIX Description and Sources of Data This Appendixprovidesa descriptionof the data analyzedin Section III and lists the sourcesused. Description of Data Country Africa Egypt Ghana Cote d'Ivoire Morocco Asia Sri Lanka India Korea Pakistan Philippines Latin America Brazil Colombia Costa Rica Mexico SamplePeriod 1968-87 1968-83 1968-85 1968-87 1968-86 1968-85 1968-87 1968-87 1968-86 1968-86 1968-87 1968-85 1968-87 Numberof Observations 74 20 16 18 20 96 19 18 20 20 19 77 19 20 18 20 Series and Sources InternationalFinancialStatistics(InternationalMonetaryFund) Gross domesticproduct(GDP) Privateconsumption(nationalincome accounts(NIA)) Exports(NIA) Imports(NIA) Interestrate Exchangerate Population WorldEconomic Outlook(InternationalMonetaryFund) Importunit values Export unit values PRIVATE SAVING AND TERMS OF TRADE SHOCKS 515 WorldTables, 1988-89 (WorldBank) GDP by sector of origin Deflator for services TradeData System (United Nations) Importsof consumergoods Providedby the authors Domestic productionof tradedgoods Domestic productionof importsubstitutes Consumptionof tradedgoods (importables) Consumptionof nontradedgoods Description of Series Constructed by the Authors Domestic productionof tradedgoods (NIA basis) = GDP originatingin the agricultural,mining,and industrialsectors. 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