S1365100599011049a

AMIXEDBLESSING

NaturalResourcesandEconomicGrowthTHORVALDURGYLFASON

UniversityofIcelandTRYGGVITHORHERBERTSSON

UniversityofIcelandandUniversityofAarhusGYLFIZOEGA

BirkbeckCollege,UniversityofLondonThispaperdiagnosesthesymptomsoftheDutchdiseaseinatwo-sectorstochasticendogenousgrowthmodel.Aproductive,low-skill-intensiveprimarysectorcausesthecurrencytoappreciateinrealterms,thushamperingthedevelopmentofa

high-skill-intensivesecondarysectorandtherebyreducinggrowth.Moreover,thevolatilityoftheprimarysectorgeneratesreal-exchange-rateuncertaintyandmaythusreduceinvestmentandlearninginthesecondarysectorandhencealsogrowth.Cross-sectionalandpanelregressionsbasedondatafor125countriesintheperiod

1960–1992confirmastatisticallysignificantinverserelationshipbetweenthesizeoftheprimarysectorandeconomicgrowth,butnotbetweenthevolatilityoftherealexchangerateandgrowth.

Keywords:EconomicGrowth,NaturalResources,DutchDisease,Learning-by-doing

Sincethesecondworldwarithasbecomequiteclearthatrapideconomicgrowthisavailabletothosecountrieswithadequatenaturalresources[italicsadded]whichmaketheefforttoachieveit.—W.ArthurLewis(1968,p.ix).

1.INTRODUCTION

Economicgrowthisacomplexphenomenon.Nevertheless,theempiricalgrowthliteratureofrecentyearshasidentifiedonlyacoupleofrobustdeterminantsofthe

TheauthorswishtothankJ.MichaelOrszag,RonSmith,FridrikM.Baldursson,andseminarparticipantsatBirkbeckCollege,QueenMaryCollege,andtheLondonSchoolofEconomicsforusefulcommentsandHaukurC.Benedik-tssonforresearchassistance.Addresscorrespondenceto:T.Gylfason,UniversityofIceland,Oddav/Sturlugotu,IS-101Reykjavik,Iceland,SNS,Stockholm,andCEPR;e-mailgylfason@hi.is.T.Herbertsson,InstituteofEco-nomicStudies,UniversityofIceland,Oddav/Sturlugotu,IS-101Reykjavik,Iceland,andUniversityofAarhus;e-mailtthh@hi.is.G.Zoega,BirkbeckCollege,UniversityofLondon,7-15GresseStreet,LondonW1P2LL;e-mailgzoega@econ.bbk.ac.uk.

c1999CambridgeUniversityPress󰀂

1365-1005/99$9.50

204

NATURALRESOURCESANDECONOMICGROWTH205

rateofgrowthofpercapitaGDPacrosscountries:initialGDPandtheratioofinvestmenttoGDP.Afewmorevariableshavebeensuggestedbysomewriters:foreigntrade,schoolenrollment,inflation,politicalinstability,corruption,inequal-ity,andthepreponderanceoftheprimarysectorintheeconomy.Wefocusonthelinksbetweenprimaryproductionandgrowth.

WecontendthatthedivisionofGDPbetweenprimaryandsecondaryproductionaffectseconomicgrowthinthelongrun.Acasuallookattheevidenceseemstosupportthisview.Thereis,forexample,astatisticallysignificantnegativecorrelationbetweentheinitialshareoftheprimarysectorinthelaborforceandtheaverageratioofinvestmenttoGDP(Figure1).Thissuggeststhatexcessiveprimaryproductionmayinhibitgrowthbyreducinginvestmentinphysicalcapital.Ifthisisthesolechannelthroughwhichprimaryproductionaffectsgrowth,however,thentheinclusionofinvestmentinacross-countrygrowthregressionshouldrendertheeffectofprimaryproductionongrowthstatisticallyinsignificant.

Ourmainhypothesisinthispaperisthatanabundanceofnaturalresourcesandacorrespondingpreponderanceofprimaryproductiontendtoinhibiteconomicgrowthbyreducinginvestmentinhumancapital.

TheroleofhumancapitalinempiricalmodelsofeconomicgrowthhasbeenemphasizedlatelybyBarro(1991),Mankiwetal.(1992),andBarroandSala-i-Martin(1995).Theideagoesback,atleast,toLewis(1955)andNelsonandPhelps(1966),whoclaimthateducatedworkersarefasterlearners,becauseeducation

FIGURE1.Relationshipbetweenaverageinvestmentrateover1960–1992andtheshareoflaborintheprimarysectorduring1965inacrosssectionofcountries.

206THORVALDURGYLFASONETAL.

teachespeopletolearn;seealsoRomer(1986,1990)andLucas(1988).Inthecontextofendogenousgrowthmodels,afasterrateoflearningandknowledgespilloversfreetheeconomyfromdiminishingreturnsandthusfacilitatesustainedgrowth.

Thispaperisintendedtoshedfurtherlightontheroleofhumancapitalinmodelsofeconomicgrowthbypointingoutthepossibleroleofsectoraldifferencesineducationinexplainingcross-countrydifferencesingrowth.Inparticular,weclaimthattheprimarysector,whichincludesagriculture,fishing,andforestry,mayneed—andalsogenerate—lesshumancapitalthanservicesandmanufacturing.1Wesuspectthat,forthisreason,countrieswithacomparativeadvantageintheproductionofprimaryoutputconsequentlymayexperiencelesseconomicgrowth.Thismayhelpexplainthesignificanceofmeasuresofhumancapitalincross-countrygrowthregressionsreportedbyBarro(1991),Mankiwetal.(1992),andBarroandLee(1993).

Whydocountriesthatspecializeinastagnantprimarysectorfailtodevelopathrivingsecondarysectorandthussustaingrowth?Aplausibleexplanationin-volvestheDutchdisease[seeCorden(1984)]:Thedominantprimaryindustrycausesthecurrencytoappreciateinrealterms,hencereducingtheprofitabilityofotherexports.Weextendthisargumentbydescribinghowafloating-exchange-rateregimecanprovideinsuranceforthedominatingprimaryexportindustryatthecostofincreasedexchange-rateuncertaintyforallotherindustries.2Theseproblemsmagnifythedistortionsintheintersectoralallocationofthefactorsofproduction,sothateconomicgrowthisreducedfurther.

Thenextsectionlaysoutasimplestochasticendogenousgrowthmodelwithatradableandanontradablesector,wheretheformerhasaccesstotwodifferentkindsofproductiontechnology,viz.,aprimarysectorandasecondarysector.Weassumethatlearning-by-doingandknowledgespilloversonlyoccurinthelatter.Wedescribetheconditionsnecessaryfortheemergenceofasecondarysector,whichescapesdiminishingreturnsandgeneratesgrowth,inthepresenceofadominantprimarysector.Section3teststheimplicationsofthemodelbasedonbothacrosssectionandapanelofcountries.Section4concludes.2.GROWTHWITHASMOTHERINGPRIMARYSECTOR2.1.PrimaryProductionandtheRealExchangeRate

T

,inaprimarysector,whereTheeconomyinitiallyproducestradablegoods,y1

outputdependsontherelativepriceoftradablegoodsintermsofnontradables,λ=pT/pN,i.e.,therealexchangerate:

T

=B1+βλ,y1

β>0.(1)

B1representsproductivityintheprimarysector,whichissubjecttoproductivity

shocksthatfollowageometricWienerprocess,dB1=σB1dW,withoutdrift.Thedomesticdemandforthetradableprimarygoodalsoisdescribedbyasimplelinear

NATURALRESOURCESANDECONOMICGROWTH207

functionoftherealexchangerate,

cT=A−αλ,

α>0,

(2)

whereArepresentsautonomousdemand.Therealexchangerateisdeterminedbytheintertemporalbudgetconstraint,whichrequirestheeconomytoexport(import)enoughtradablegoodstopay(consume)interestonforeigndebt(assets).Intheabsenceoftrendproductivitygrowth,thistranslatesintoequation(3),whereDdenotesthenoninterestexternalsurplus—measuredinunitsoftradablegoods—neededtomeetinterestpaymentsonforeigndebtinordertokeepitsstockconstant.Aconstantlevelofforeigndebtisassumed:

T

−cT=B1−A+(α+β)λ.D=y1

(3)

Equations(1–3)givetherealexchangerate,λ,asafunctionofB1,D,A,andthe

effectsoftherealexchangerateonprimarysectoroutputsupplyanddemand,βandα.Foragivenvalueofthenoninterestsurplus,takingthetotaldifferentialof(3)andusingIto’slemmagives

󰀆󰀅1

(4)σB1dW.dλ=−

α+βChangesintherealexchangeratearethusafunctionofthestochasticprocessfollowedbyB1.Thisisthesameprocessastheonefollowedbyproductivityexceptforthefirsttermontheright-handside,whichisnegative.Thusaproductivityimprovementintheprimarysectorleadstoarealappreciationofthecurrency:λfalls.TherelationshipbetweentherealexchangerateandB1iscommonlyreferredtoastheDutchdisease:Aproductiveprimarysectorcausesthecurrencytoappreciateinrealterms(i.e.,λtofall),hencemakingitdifficultforotherpotentialexportindustriestoestablishthemselvesorforexistingonestothrive.Themagnitudeoftheeffectontherealexchangeratedependsonsupply-and-demandelasticitiesofprimaryoutputoftradables,henceβandα.Ifthesetwoparametersaresmall,theeffectontherealexchangerateislarge.ThusweexpectthesymptomsoftheDutchdiseasetobeparticularlyseriousincountrieswithlowelasticities.Moreover,realexchangerateswillbemorevolatileinsuchcountries:Thevarianceterminequation(4)willbelarger.Wediscusstheconsequencesofthisbelow.

2.2.WhenCanaSecondarySectorEmerge?

Now,imaginethattradableoutputalsocouldbeproducedbyusinganalternativetechnologyinthesecondarysector.Moreover,assumethatitsshareofemploymentisinitiallysmall:l2=󰀄.Thusweimaginethatthereisonetypeof(tradable)outputandtwotypesofproductiontechnology,primaryandsecondary.Bothhavediminishingprivatereturnstolabor.However,theydifferintwowaysasfollows:(1)Notrainingoflaborisrequiredintheprimarysector,whereasinthesecondary

208THORVALDURGYLFASONETAL.

sector,hiringinvolvestraining,i.e.,investmentinhumancapital.3(2)Thereislearning-by-traininginthesecondarysector,involvinginstantaneousknowledgespillovers.Thisimpliesconstantreturnstoscaleatthesociallevelinthesecondarysector.Thisfollowsfromourpresumption,supportedbythestudiesmentionedabove,thatworkersinthesecondarysectoraremoreskilledonaverageand,forthatreason,moreopentonewproductionprocesseswhileintraining.

Theproductiontechnologyinthesecondary,tradablesectornowcanbede-scribedasfollowsfortherepresentativefirm:

Tα1−α=B2l2L2,y2

(5)

T

isoutput,B2isanexogenousmeasureoftechnologyinthesecondarywherey2

sector,l2islaborinthesecondarysector,andL2istheaggregatelaborforceusedthere.Thenumberoffirmsisn=L2/l2.TheinclusionofL2intheproductionfunctionreflectstheeffectoflearning-by-doing(training):Anewworkertrainedinthesecondarysectorincreasesaggregateknowledgeaboutproductioninthesectorthroughinstantaneousknowledgespillovers.WeassumethatB2isdeterministicandfixed.

Theexchangerateregimeandthe(initially)dominantshareofprimaryoutputinexportsreducetheriskofproductionintheprimarysector.Realexchangeratemovementsreduceuncertaintyintheprimarysector,whereastheyincreaseitinthe(hypothetical)secondarysector:StartingsecondaryproductionisriskybecausetherealexchangerateandB2arenotcorrelated.

B1andB2havenotrend,andso,theonlypotentialsourceoftechnologicalprogressislearning-by-doinginthesecondarysector.Accordingly,untilasec-ondarysectoremerges,thereisnogrowth.ThismeansthatthehigherthevalueofB1,thehigherwillbetherealexchangerate(i.e.,λwillbelower),andhencethemoredifficultitwillbeforasecondarysectortotakeoff,i.e.,forgrowthtotakeplace.Wereturntothisthemeshortly.

Becauseofthetrainingcostsinthesecondarysector,wetreatlaborinthatsectorasaquasi-fixedasset.Thedecisiontohireworkersinthatsectorisinherentlyanintertemporal(investment)decision.WeusethemethodsdescribedbyDixitandPindyck(1994)tosolvetheoptimizationproblemfacedbytherepresentativefirminthissector.WedenotethecostofhiringbyTperworker.Workersinthesecondarysectorquitwithprobabilityq.Thisisbecauseofrandompreferences,whichcauseworkerstoswitchbetweenfirmsfornonwagereasonswithafixedprobabilityperunitoftime.Becausefirms,whenhiringnewworkers,knowonlytheaveragequitratebutnotanindividual’sexposuretopersonalfactors,itisthisaveragequitratethattheytakeintoaccountwhenmakingtheirhiringdecisions.4UsingIto’slemma,wegetthefollowingBellmanequation,whichdescribesthevalueofthestockoftrained,secondary-sectorworkersl2,i.e.,thevalueofthefirm,V,whenthevalueoffuturehiresinthesectorisignored:

α1−αλB2l2L2

rV(l2,λ)=

1

−wl2−ql2Vl2+

2

󰀅

1α+β󰀆2

2σ2B1Vλλ

(6)

NATURALRESOURCESANDECONOMICGROWTH209

andristherealrateofinterestandwistherealwagemeasuredinnontradedgoods.Eachfirmissmallenoughtotakethetotalnumberofworkersintheindustry,L2,asgiven.Equation(6)isessentiallyanassetequation.Theleft-hand-sidevariableshowstherequiredreturn.Theright-handsideisthesumofadividendandanexpectedcapitalgain.Thefirsttermontheright-handsideiscurrentoutputinthesecondarysector.Thesecondtermshowsthewagebill.Thethirdtermistheexpectedlossduetoquitsofpreviouslytrainedworkers.Thelasttermistheexpectedchangeinthevalueofthefirminresponsetofuturechangesintherealexchangerate.

Thesolutiontodifferentialequation(6)containsthefollowingparticularinte-gral,VP:

󰀌∞

󰀁−qt󰀂󰀄−rt󰀃󰀁󰀂α−α

P

V(l2,λ)=E−wl2e(7)λB2l2e−qtL1edt.2

0

Thisistheexpected,presentdiscountedvalueoffutureprofitsfromthel2workers

employedattimezero,measuredbythedifferencebetweenfutureoutputandwagepayments,takingintoaccounttheconstantquitrate,q.Theequationcanberewrittenasfollows:

α1−αλB2l2L2wl2

−.V(l2,λ)=

r+αqr+qP

(8)

Tofindthevalueofthemarginalsecondary-sectorworker,5wetakethederivative

of(8)withrespecttol2:

α−11−α

αλB2l2L2w

v(l2,λ)≡Vl2(l2,λ)=−.

r+αqr+qP

P

(9)

Wealsoneedtocalculatethevalueoftheoptiontohireaworkerinthesecondary

sector,i.e.,thecomplementaryfunction.Now,definevGasthevalueoftheoptiontohirethemarginalworker,whereGdenotesgeneral,

vG(l2,λ)≡Vl2(l2,λ),

(10)

anddifferentiatethehomogenouspartofequation(6)withrespecttol2.Thisgives

󰀊󰀉󰀅󰀆2

1B1

σ2vλλ.(11)(r+q)v=−ql2vl2+

2α+βThegeneralsolutionis

vG(l2,λ)=C1󰀊γ1+C2󰀊γ2,

(12)

α−11−α

L2,γ1andγ2aretherootsofthecharacteristicequation,where󰀊=αλB2l2

andγ1>1andγ2<0.6Thenegativerootiseliminatedbecausewewantthe

210THORVALDURGYLFASONETAL.

valueoftheoptiontogotozeroastherealexchangerateapproacheszero.Thissimplifiesthegeneralsolutionto

vG(l2,λ)=C1󰀊γ1.

(13)

ThevalueofthemarginalemployedworkerinthesecondarysectoristhenequaltovPandtheoptionvalueofhiringhimisequaltovG.Thelatterispartofthecostofhiringtheworker.Whenanewworkerishiredandthedirecttrainingcosts,T,areincurred,theoptionofhiringhiminthefutureissacrificed.Themarginalcostofhiringanewworkeris,therefore,equaltothesumofTandvG.Thethresholdvalueoftherealexchangerateatwhichtherepresentativefirmstartshiringnewworkers,λH,isdefinedbythefollowingtwoconditions:Value-matchingcondition.

α−11−α

wαλHB2l2L2γ1

−=T+C1󰀊H,

r+αqr+q

α−11−α

󰀊H≡αλHB2l2L2.(14)

Theleft-handsideofthisequationisthemarginalbenefitfromhiringanew

worker.Theright-handsideisthemarginalcost,whichisequaltothesumofthedirecttrainingcostandtheindirectcostbecauseofthesacrificedoptionofhiringhimlater.

Smooth-pastingcondition.

α−11−α

L2αB2l2γ1−1α−11−α

=C1γ1󰀊HαB2l2L2.

r+αq

(15)

Thisconditionrequiresthederivativeofthemarginalbenefitandthemarginalcostwithrespecttotherealexchangeratetobeequalatthehiringthreshold.Solvingequation(15)forC1andsubstitutinginto(14)gives

󰀈󰀅󰀆󰀇

γ1(r+αq)[w/(r+q)+T]

λH=.(16)α−11−αγ1−1αB2l2L2Combiningequations(16),(1),(2),and(3)gives

󰀅󰀆󰀇󰀈

γ1(r+αq)[w/(r+q)+T]>

λ(D,α,β,B1,A)=.α−11−α<γ1−1αB2l2L2

(17)

Theimplicationsofthemodelaresummarizedbythisequation.Itdefinesathresh-oldvalueoftherealexchangerate—agrowththreshold—suchthatiftheexchange

rateishigher,noinvestmenttakesplaceinthesecondarysector,whereasifitislower,thereisinvestmentinthesector.Thus,belowthethreshold,thereisnoeco-nomicgrowth,whereasaboveit,theeconomygrowscontinuouslyintheabsenceoffurtherchangesintherealexchangerate.

Thefirsttermontheright-handsideispositiveandgreaterthanone.Itmakesthefirmwaitbeyondthepointatwhichthepresentdiscountedvalueoffuture

NATURALRESOURCESANDECONOMICGROWTH211

profitsisequaltothecostoftrainingtheworker.Thefirmwaitslonger,becauseitseeksmoreinformationaboutfuturevaluesoftherealexchangerate:Timeisofvalue.

Wecansummarizethekeyimplicationsasfollows:2.2.1.Knowledgeexternalitiesandovervaluation.Theknowledgeexternali-tiesinthesecondarysectorraisethegrowththreshold.Theprivatemarginalproductoflaborislowerthantheaverageproductoflabor,whichisthesocialmarginalproduct.Theaverageproductoflaborinourrepresentativefirmis

Ty2

=B2(L2/l2)1−α=B2n1−α≡f(n),l2

(18)

wherenisthenumberoffirmsinthesecondarysector,asbefore.Themarginalproductis

T∂y2

=f(n)−nf󰀄(n)=B2n1−α−(1−α)B2n1−α,∂l2

(19)

whichislowerthantheaverageproduct.Therefore,itwouldbeoptimalforin-vestmentinthesecondarysectortostartbeforethethresholdofequation(17)isreached.

2.2.2.Realexchangerateandprimarysectorproductivity.Theactualvalueoftherealexchangerateisafunctionofproductivityintheprimarysector,B1;theeffectoftherealexchangerateonthesupplyanddomesticdemandforprimaryoutput,βandα;autonomousdemandforprimaryoutput,A;andthenoninterestexternalsurplusrequiredtokeepthestockofforeigndebt,D,constant;i.e.,

λB1<0,

λβ<0,

λα<0,

λA>0,

λD>0.

(20)

Amoreproductiveprimarysectorcausesthecurrencytoappreciateinrealterms,hencemovingλfurtherbelowitsgrowththreshold.ThisistheDutchdisease:Growthisreducedevenfurther.Ariseinforeignindebtedness,whichmakesahighernoninterestexternalsurplusnecessary,causesarealdepreciationofthecurrency,andwemoveuptowardthethreshold.Thus,increasedexternaldebtcanspureconomicgrowthbymakinginvestmentinthesecondary(tradable)goodssectorprofitable.Finally,agivenpositivelevelofDrequiresahighervalueofλ,themoresothelowerthesensitivityoftradablegoodsoutputandconsumptiontochangesintherealexchangerate.7

2.2.3.Exchangeratevolatility.Thevalueofthegrowththresholddependsonthedegreeofexchange-rateuncertainty,[B1/(α+β)]σ,throughγ1,whereσisameasureofuncertaintyaboutfutureprimary-sectorproductivityandB1isthecurrentlevelofproductivityinthatsector.Increaseduncertaintyreducesγ1andthusincreasesthefirsttermontheright-handsideof(17):Thethresholdrises.

212THORVALDURGYLFASONETAL.

Thus,thegreaterthesizeofproductivityshocksintheprimarysector,thehigheristhegrowththreshold.Intuitively,firmswaitlongerbeforeenteringthesecondarysector,becausethefutureislesscertain:Theywaitlongerforinformationaboutfuturerealexchangerates.Becausethisisdueentirelytotheexchange-rateregime,weconcludethataflexibleexchangerateexacerbatesthemarketfailuredescribedabove:Thegrowththresholdrisesfurtherawayfromitssocialoptimum.Thisisadifferent,althoughlessnoticed,formoftheDutchdisease.Howmuchthethresholdisraiseddependsontheelasticityofsupplyanddemandoftradableoutput.Lowelasticitiesrequiregreaterchangesintherealexchangerate.

Thethresholdalsodependsonrealwages,w;trainingcostsinthesecondarysector,T;therealrateofinterest,r;theaveragequitrateinthesecondarysector,q;andtheleveloftheexogenouslygivenproductivityinthesector,B2.Highwagesmakeitlessprofitabletotrainnewworkersinthesecondarysectorand,obviously,sodoalsohightrainingcosts.Similarly,bothhighinterestratesandhighquitratesmakeinvestmentinthesecondarysectorlessprofitableandhencerequireahigherrealexchangerateforinvestmenttooccur.8Moreover,themoreproductivethesecondarysector,thelowerthegrowththreshold.Finally,themorefirmsthereareinthesecondarysector,n,thehigherisitsmarginalproductandtheloweristhethreshold.

Thequestionariseswhethergrowthcancontinueindefinitelyoncethecurrencyhasdepreciatedenough,sothatλhasreachedthegrowththreshold.Becausethereareconstantreturnstolaborattheindustrylevel,thisappearstobethecase,butnotethat,witheconomicgrowth,demandfornontradableswouldincrease,aswouldtheirrelativeprice—therealexchangeratewouldappreciate.Asthecurrencyappreciates,growthinthesecondarysectorpetersout.Therecomesatime,otherthingsbeingequal,whenthecurrencyhasappreciatedenoughinrealtermstomakeinvestmentinthesecondarysectorstop,thusstiflingeconomicgrowth.

Wehavenotdicussedtheconsumers’intertemporaloptimizationproblem[seeMerton(1975)forasolutiontothisproblemusingstochasticcalculus].However,afewcommentsareinorder:Beforeanyinvestmentinthesecondarysectortakesplace,therealrateofinterestisequaltotheworldinterestrateasdomesticcon-sumerscaninvesttheirsavingsabroad.Moreover,weassumethattheworldrealrateofinterestisequaltothepurerateoftimepreference.Forthisreason,thereisinitiallynosavingintheeconomy,consumptionisflat,andthestockofforeigndebt(assets)isfixed.

Whentherealexchangeratecrossesthegrowththresholddefinedbyequa-tion(17),thenetsupplyofdomesticoutputfallsasfirmsinthesecondarysectorstartusingworkerstotrainnewcomers:Thereisdomesticinvestmentforthefirsttime.Becausethisisinvestmentinhumancapital,weassumethatforeignersdonotlendcapitaltofinanceit.Consequently,thisincreasesinvestment,stimulatesoutputdemand,anddrivesthedomesticrealrateofinterestabovetheworldrate.Therefore,consumptiondropsinitiallyandthengrowsinthenewsteadystatealongwithoutputinthesecondarysector,atahigherratethanbefore.

NATURALRESOURCESANDECONOMICGROWTH213

3.EMPIRICALEVIDENCE

Theempiricalimplicationsofourmodelnowcanbesummarizedasfollows,wheregdenotestherateofeconomicgrowth:

−

+

−−−+

g=f(B1,D,σ,T,q,n).

(21)

Therateofgrowthofoutputisadecliningfunctionofthelevelofproductivityintheprimarysector,B1,becausealargerprimarysectorcausesarealappreciationofthecurrencyandthusreducestheprofitabilityofinvestmentinthesecondarysector.Increaseduncertaintyaboutfutureprimary-sectorproductivity,σ,raisesthethresholdandreducesgrowth,andsoalsodo(1)anincreaseinthecostoftrainingworkersinthesecondarysector,T;(2)anincreaseinthequitrate,q;and(3)afallinthenumberoffirmsinthesecondarysector,n,ceterisparibus.Thelasteffectisascaleeffect:Thereismoreknowledgeinalargereconomy.Ariseintherequirednoninterestexternalsurplus,D,reducestherealexchangerateandstimulatesgrowth.

Wefocusonthefirstthreevariablesinequation(21)bytestingtherelationshipbetweeneconomicgrowthandthesizeandvolatilityoftheprimarysector,thelatterthroughthevolatilityoftherealexchangerate,andalsotheleveloffor-eigndebt.Thekeyimplicationofthemodelisthatanexpansionoftheprimarysector,as,forexample,broughtaboutbyanimprovementinprimaryproductiontechnology,willreducetherateofgrowthbyreducinglearninginthesecondarysector,andhencealsohumancapitalaccumulation.Thiseffectmayexplain,atleastinpart,theapparentstatisticalsignificanceofhumancapitalvariablessuchasschoolenrollmentratesinthegrowthstudiesmentionedabove.Investmentinhumancapitalthroughtraininginthesecondarysectortendstohelpstrengthenformaleducation,andagoodeducationsystem,inturn,maybeconducivetothecreationofa(human-capital-generating)secondarysector.Figures2to4supportourhypothesisbydisplayingastrongandstatisticallysignificantinversecorrela-tionbetweentheinitialshareoftheprimarysectorinthelaborforceandtheinitialenrolmentrateinprimaryschools(Figure2),secondaryschools(Figure3),andtertiaryschools(Figure4).

Thesecorrelationssuggestthatprimaryproductionmaybeausefulproxyforhumancapitalincross-countrygrowthregressions.Ifso,therelationshipbetweengrowthandschoolenrollmentratesmaybespurious,simplyreflectingtheeffectofanomittedvariable—thesizeoftheprimarysector.Tofindout,weincludeschoolenrollmentratesandmeasuresofprimaryproduction,measuredbothbytheshareofprimaryproductioninthelaborforceandtheshareofprimaryexportsintotalexports,sidebysideamongotherexplanatoryvariablesinagrowthregressiontoseewhichcontributesthemosttotheexplanationofdifferencesingrowthratesacrosscountries.

214THORVALDURGYLFASONETAL.

FIGURE2.Relationshipbetweentheaverageprimaryschoolenrollment1960–1992andtheshareoflaborintheprimarysectorduring1965inacrosssectionofcountries.

3.1.Data

Weusecross-sectionaldataconstructedfromthePennWorldTablesandtheWorldDataBank.Thesampleperiodis1960–1992.Inthefirstregression(Table1),whichcorrespondstoaβ-convergenceregression,weusedatafor125countries.Aswemovetowardamoregeneralmodelspecification,thenumberofcountriesdecreasesuntil,inthefifthregression,weareleftwith65countries.Thismethodenablesustouseasmuchaspossibleoftheinformationavailableforeachmodel,butitleavesuswithparametersthatarenotdirectlycomparableacrossmodels.Foradetaileddescriptionofthedata,seetheAppendix.3.2.Cross-SectionalEstimation

Westartwiththestandardcross-sectionalregressionmodel.Theregressorsareini-tialGDP(1960),investment/GDPratio,initialshareofprimaryproductioninthelaborforce(1970),externaldebtinproportiontoGDP,real-exchange-ratevolatil-ity,initialprimaryandsecondaryschoolenrolmentrates(1965),andadummyforAfrica.

Thefirstregressionisthestandardconvergenceregression.Inregression2,weaddthetwostandardproxiesforhumancapital,theinitialprimary-andsecondary-

NATURALRESOURCESANDECONOMICGROWTH215

FIGURE3.Relationshipbetweentheaveragesecondaryschoolenrollment1960–1992andtheshareoflaborintheprimarysectorduring1965inacrosssectionofcountries.

schoolenrollmentrates;inregressions3a–5a,weadd,oneatatime,thevariablesimpliedbyourmodel,i.e.,theinitialshareoftheprimarysectorinthelaborforce,theratioofexternaldebttoGDP,andanindexofreal-exchange-ratevolatility.Inregressions3b–5b,weusetheratioofprimaryexportstototalexportsofgoodsandservicesinsteadoftheshareoftheprimarysectorinthelaborforce.Inregressions6a–8a,weaddthesamethreevariables,nowexcludingtheschoolingvariablesfromtheregressions.Andfinally,inregressions6b–8b,weincludetheratioofprimaryexportstototalexports,nowexcludingtheschoolenrollmentvariables.InTable1,wereportourfindingsontherelationshipbetweengrowthandtheex-planatoryvariables,thestandarderrorsofestimation(SE),theadjustedcoefficient

¯2),andthedegreesoffreedom(DF).9ofdetermination(R

Table2showsthecorrelationsbetweentheorthogonalcomponentsofthere-gressorsandtheper-capitagrowthratewithandwithouttheschoolenrollmentvariables.10

Thepartialcorrelationbetweenper-capitagrowthandinvestmentandexter-nalindebtednessissignificantatthe1%levelinbothequations.Thehypothesisofzerocorrelationcannotberejectedforprimaryandsecondaryeducationandtheexchange-ratevolatilityindexatreasonablelevels.Thesamehypothesisismarginallyrejectedforprimarylaboratthe5%levelinthefirstequation,but

216THORVALDURGYLFASONETAL.

FIGURE4.Relationshipbetweentheaveragetertiaryschoolenrollment1960–1992andtheshareoflaborintheprimarysectorduring1965inacrosssectionofcountries.

cannotberejectedinthesecond.Asimilarpatternisobservedwhentheshareoftheprimarysectorinthelaborforce,excludingextractionindustries,isreplacedbytheshareofprimaryexportsintotalexports,andtheestimatesbecomemoreprecise.Thegainofprecisionisunderstandableinviewofthefactthatthecor-relationbetweentheshareofprimaryexportsintotalexportsandprimary-andsecondary-schoolenrollmentratesaresmaller(−0.23and−0.52,respectively)thanthecorrelationsbetweentheshareoftheprimarysectorinthelaborforceandprimary-andsecondary-schoolenrollment(−0.41and−0.74,respectively).Thesecorrelationsinturnmaybeviewedasanindicationthatextractionindustries(mining,etc.)generallyusesomewhatbetter-educatedlaboronaveragethanagri-cultureandfisheries.Theremainderofthissectiondescribestheresultsobtainedinfurtherdetail.

3.2.1.InitialGDP.Thecoefficientsonthisvariablerepresentβ-convergencerates.TheparameterreflectsthespeedatwhichpoorcountriesconvergetorichonesintermsofGDP.Thecoefficientissignificantlydifferentfromzeroinalloftheregressions,butsmall,implyingaconvergencespeedof0.8%to1.6%peryear.Thisresultis,however,inlinewiththefindingsofNerlove(1996)andGylfasonandHerbertsson(1996)forlargepanelsofcountries.

TABLE1.Cross-sectionalresults,1960–1992Regressiona(1)(2)(3a)(4a)(5a)(3b)(4b)(5b)(6a)(7a)(8a)(6b)(7b)(8b)RegressorInitialGDPInvestment−0.008(−4.28)0.152(8.41)—————————————−0.016−0.016(−4.34)(−4.31)0.1490.149(5.16)(5.11)——−0.009(−4.04)0.137(5.47)———−0.019(−3.32)—−0.012(−4.08)0.155(4.94)———−0.020(−2.60)−0.030(−3.28)—−0.012(−3.98)0.155(4.88)———Primaryeducation1965Secondaryeducation1965Laborinprimarysector1965Exportofprimaryproducts1970Externaldebt−0.010(−4.54)0.120(5.11)0.015(3.11)0.010b(1.08)—−0.023−0.023(−1.91)(−1.89)——−0.014(−5.44)0.110(4.47)0.011(2.03)0.002b(0.24)−0.024(−2.54)—ExchangeratevolatilityConstantAfricadummySE¯2RDF0.054(4.13)−0.010(−3.14)0.0130.461210.063(4.47)−0.007(−2.40)0.0120.491090.105(4.72)−0.005(−1.69)0.0120.51107−0.016−0.016−0.009−0.011(−4.09)(−4.03)(−3.58)(−2.58)0.1460.1450.1220.149(4.39)(4.29)(4.24)(3.86)0.006b0.007b0.0140.012b(0.72)(0.74)(2.25)(1.13)0.005b0.005b−0.006b−0.010b(0.36)(0.36)(−0.50)(−0.60)bb−0.019−0.019——(−1.48)(−1.46)——−0.020−0.021(−3.44)(−2.58)−0.019−0.018—−0.026(−2.87)(−2.70)(−2.69)—0.003b——(0.30)0.1240.1250.0730.087(3.67)(3.66)(3.83)(2.84)−0.003b−0.003b−0.008−0.001b(−0.55)(−0.57)(−2.07)(−0.21)0.0130.0130.0120.0120.490.480.520.5657567941−0.011−0.013(−2.53)(−5.62)0.1490.121(3.80)(6.08)0.012b—(1.11)−0.010b—(−0.60)—−0.030(−3.49)−0.021—(−2.54)−0.026—(−2.58)0.000b—(0.00)0.0870.113(2.80)(5.33)−0.001b−0.007(−0.21)(−2.12)0.0120.0120.540.5040113−0.019−0.019(−3.29)(−3.14)—0.004b—(0.38)0.1270.1270.077(4.09)(4.08)(4.49)−0.004b−0.004b−0.010(−0.89)(−0.90)(−2.56)0.0130.0130.0120.530.480.686160820.101(4.40)−0.002b(−0.34)0.0120.5644−0.020(−2.57)−0.030(−3.18)−0.001b(−0.11)0.101(4.35)−0.002b(−0.32)0.0120.5543at-Valuesappearwithinparenthesesbelowthecoefficients.bNotsignificantatthe5%levelinaone-tailtest.Thecutoffpointfortheh0is2.33atthe1%level,1.64ina5%test,and1.28ina10%test.218

TABLE2.Partialcorrelationbetweenper-capitagrowthandregressorsaInvestmentrate0.50(4.58)0.55(5.31)0.10b(0.80)——0.05b(0.40)——−0.19b(−1.54)−0.24(−1.99)−0.36(−2.67)−0.36(−2.67)PrimaryeducationSecondaryeducationLaborshareinprimarysectorShareofprimaryexportsExternaldebt−0.34(−2.87)−0.37(−3.21)Exchange-ratevolatility0.04b(0.33)0.05b(0.40)THORVALDURGYLFASONETAL.

Withschoolingh0:r=0Withoutschoolingh0:r=0Thet-valuesappearwithinparenthesesbelowthecorrelationcoefficients.bNotsignificantatthe5%levelinaone-tailtest.Thecutoffpointfortheh0is2.33atthe1%level,1.64ina5%test,and1.28ina10%test.aNATURALRESOURCESANDECONOMICGROWTH219

3.2.2.Investment.TheparameteroninvestmentasaproportionofGDPissignificantatthe1%levelinalloftheregressions.Anincreaseininvestment/GDPfrom20%to30%fromonecountrytoanotherwould,accordingtoregressions1to8b,increasethegrowthrateperheadby1.1%to1.5%ayear,ceterisparibus.ThesefindingsrhymewellwiththoseofLevineandRenelt(1992)andSachsandWarner(1995).

3.2.3.Initialschoolenrollment.Theprimaryenrollmentrateissignificantatthe1%levelinregression2,andismarginallysignificantatthesamelevelwhenthelaborshareinprimaryproductionisaddedtotheregression;seeregression3a.Theparameterbecomesinsignificant,however,whenforeigndebtandexchange-ratevolatilityareaddedtotheregression.Thisseemstosupportourhypothesis,atleastinpart,thattheorthogonalcomponentoftheprimarylaborshareandeducationcrowdsouttheeffectsofschoolenrollmentongrowth.Thesecondaryenrollmentrateisinsignificantlydifferentfromzeroinalloftheregressions.

3.2.4.Laborinprimarysector.Thisvariableappearswiththerightsignev-erywhere.Thehypothesisofzerocoefficientsisrejectedatthe5%levelinallregressionsexcept4aand5a.AccordingtoTable2,apartialcorrelationbetweentheshareoflaborinprimaryproductionandeconomicgrowthismarginallyre-jectedwhentheeffectofschoolenrollmentisincluded.Thisrelationshipisnotrejected,however,whenschoolingisleftout.Thisgivesusareasontobelievethatthesetwoeffectsshouldnotbeincludedinaregressionmodelsimultaneously.Further,inviewofthestrongcorrelationbetweenschoolingandprimarylaborshowninFigures2to4,multicollinearityislikelyaproblem.

Theeffectoftheprimarysectorongrowthisquitestrong.Iftheshareoftheprimarysectorinthelaborforceincreasesfrom5%to30%fromonecountrytoan-other,per-capitaoutputgrowthdropsbyabout0.5%perannum,ceterisparibus.SachsandWarner(1995)reportasizableeffectofanincreaseintheshareofprimaryexportsinGDPongrowthinasampleof98countries.GylfasonandHerbertsson(1996)andGylfason(1999)alsoreportsimilarresults,basedondif-ferentdatasets:AnincreaseintheshareofprimaryexportstoGDPfrom5%to30%reducesper-capitagrowthby0.5%to1%ormore.

3.2.5.Exportofprimaryproducts.Theprimary-sectorlaborsharedoesnotincludelaborinextractionindustriesbecausetherequisitedataarenotavailable.However,wealsorantheregressionsusingtheshareofprimaryexportsintotalexportsinsteadoftheprimary-sectorlaborshare.Regressions3b–5b,nowinclud-ingextractionindustries,showthattheparametersonthisvariablearesignificantandstable.Whentheschoolenrollmentvariablesareexcludedfromtheregres-sions(6b–8b),theparametersremainsignificant.Finally,thehypothesisofequalcoefficientsinoil-producingandnon-oil-producingeconomiescannotberejectedatthe1%levelofconfidenceinaWaldtest.

220THORVALDURGYLFASONETAL.

3.2.6.Externaldebt.Theparameteronforeigndebtissignificantlynegativethroughout.Thepartialcorrelationbetweeneconomicgrowthanddebtiscorre-spondinglysignificantandlarge;seeTable2.OurmodelinSection2predictsapositiveeffectofexternalsteady-statedebtongrowth,becausemoredebtentailsalowerrealexchangerate.However,ourmodeldoesnotexplicitlyincludeaphe-nomenonthatisundoubtedlyimportantinpractice:Theeconomiesmostburdenedwithdebtmaynotbeinlong-runequilibrium.Theytypicallyhaveovervaluedcur-renciesaccompaniedbycontinuousdebtaccumulation.Inthiscase,theintuitionofourmodelwouldpredictslowergrowth.Thispossibilityseemstowarrantfurtherscrutinyinfuturework.

Anotherpossibleexplanationfortheinverserelationshipbetweendebtandgrowthcouldbethathighlevelsofexternaldebtareasymptomofeconomicmismanagementorpoliticalinstability,asemphasizedbyBarroandSala-i-Martin(1995).Toinvestigatethispossibility,weaddedtoourregressionadummyvariablederivedfromthedatausedbyAlesinaetal.(1996)torepresentcoups.Ifacouptookplaceinagivencountryduringthesampleperiod,thedummytakesthevalueone,andzerootherwise.Theparameteronthisvariableissignificantlynegativewhendebtisnotincludedintheregression(acoupthenreducesaveragegrowthby0.5%peryear),butwhendebtisincluded,thecoupdummybecomesinsignificant.Thisresultmaybeviewedperhapsasanindicationthatexternaldebtaccumulationmirrorseconomicmismanagementratherthanpoliticalinstability.

Thisimpressionbecomesstrongerwhenanothermeasureofeconomicmis-management,π/(1+π),whereπistheannualrateofinflation,isaddedtoourregression[seeGylfasonandHerbertsson(1996)].Theparameterontheinflationvariableissignificantlynegativewhetherornotthecoupdummyisincluded:Anincreaseininflationfrom5%to50%reducesaveragegrowthbyabout1%peryear,andthecoupdummybecomesinsignificant.Whenourexternaldebtvariableandinflationvariableappearsidebysideintheregression,theinflationvariablebecomesmarginallyinsignificant.

3.2.7.Exchange-ratevolatility.Thisvariableisstatisticallyinsignificantev-erywhere.Wealsoranregressions(notreported)usingboththevarianceofthelaborshareinprimaryproductionandofGDP.Bothvariablesenteredthere-gressionswiththewrongsignbutwerenotstatisticallydifferentfromzero.ThissuggeststhattheDutchdiseasemaymanifestitselfthroughtheleveloftherealexchangerateratherthanthroughitsvariability.

3.2.8.Africa.TheAfricadummyissignificantinregressions1and2,wherethelaborshareisnotincluded.In8oftheremaining12regressions,theprimarylaborshareunderminestheAfricanconnection.Wealsorantheregressionswith-outtheAfricadummy,buttheresultsobtainedinregressions3ato8bremainedvirtuallyunchanged.

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3.3.PanelEstimation

Toinvestigatethedynamicpropertiesofthedata,weemploytherandom-effectspanelmodel.11Thedataspanthesameperiodasbefore(1960–1992)andnowcompriseamaximumofseven5-yearaveragesandaminimumofoneforeachvariable.Becausethesubperiodsareonly5years,wedonottestfortheeffectsofexchange-ratevolatility,becausetheestimatedvarianceofthatvariablecanhardlybeexpectedtobeconsistentwithonlyfiveobservations.InTable3wereportourpanelregressions.12

Regressions1–3ayieldsimilarcoefficientsoninitialGDPasthecross-sectionalregressions.Whenexternaldebtisadded(regressions4aand6a),themagnitudeoftheconvergenceparameterincreasessubstantially,fromapproximately1%toalmost6%inregression4aandtoalmost4%inregression6a.Theparametersontheexportsharearelesssignificantthanbefore.Becausetheshareofprimaryexportsintotalexportsislesscloselycorrelatedwitheducationthanisthelaborshareoftheprimarysectorexcludingextractionindustries,itisnaturalthattheprimaryexportsharemakesasmallercontributionthantheprimary-sectorlaborsharetothegrowthequations.However,regressions4aand6ashouldbetakenwithagrainofsalt,becausethenumberofobservationsissmallcomparedwiththeotherregressions.

Theparametersoninvestmentareapproximatelythesameinthecross-sectionalandpanelregressions.

Theparametersonprimaryeducationseemmorerobustinthepanelinthesensethattheprimary-educationvariablesurvivestheintroductionofprimarylaborintothepanelregression.Secondaryeducationshowsupwiththewrongsigneverywhere.Moreover,thelaborshareoftheprimarysectornowsurvivestheintroductionoftheexternaldebtratiointotheregression,andrenderstheAfricadummyinsignificanteverywhere.Theparametersonthelaborshareinprimaryproductioninourpreferredpanelregressions,3aand5a,areaboutthesameasinthecross-sectionalanalysis(Table1).Theshareofprimaryexportsintotalexportshasasmallerandlesssignificanteffectongrowththantheprimarylaborshare,presumablybecausetheformerisalesssatisfactoryproxyforhumancapitalthanthelatter.Thisleadsustoconcludethatourmainresultsarequiterobust:Thesizeoftheprimarysectormattersforgrowth.4.CONCLUSION

Wehavefoundastatisticallysignificantrelationshipbetweenthesizeoftheprimarysectorandtheaveragerateofgrowthofoutputacrosscountries.Thiseffectappearstodiminishtheimportanceoftherelationshipbetweeneducationvariablesandgrowth:Theeffectsofschoolinggenerallydropinsizeandsignificancewhenprimaryemploymentorprimaryexportsareaddedtotheregressions.

Wecandrawtwopossibleinferencesfromtheempiricalrelationshipbetweengrowth,thesizeoftheprimarysector,andschoolenrollment.First,itispossible

222

TABLE3.Panelresults,five-yearintervals,1960–1992aRegression(1)(2)(3a)(4a)(3b)(4b)(5a)(6a)(5b)(6b)RegressorInitialGDPInvestmentPrimaryeducation—−0.038−0.009(−4.05)(−3.79)0.2660.188(4.83)(7.01)————−0.017(−3.71)0.24(5.44)———SecondaryeducationTHORVALDURGYLFASONETAL.

LaborinprimarysectorExportofprimaryproducts−0.065(−2.20)—ExternaldebtConstantAfricadummySE¯2RDF−0.007−0.009−0.013−0.058−0.009(−4.66)(−4.27)(−3.33)(−5.29)(−3.35)0.1640.1640.1280.2120.169(10.0)(7.84)(4.89)(3.55)(5.53)—0.0120.0350.0410.021(1.69)(4.24)(2.20)(1.97)bbb—−0.017−0.044−0.008−0.025b(−2.44)(−4.38)(−0.43)(−2.77)——−0.022b−0.099—(−1.47)(−2.58)————−0.015(−1.79)———−0.051—(−1.65)0.0460.0540.1110.4760.06(4.31)(3.76)(3.01)(4.93)(2.85)bbbb−0.002−0.001−0.0050.000−0.003b(−0.87)(−0.34)(−1.45)(0.06)(−0.76)0.0320.0300.0250.0170.0300.110.110.170.370.1285653526854311−0.023−0.010(−3.59)(−2.98)0.180.133(3.37)(5.65)0.038—(1.69)0.003b—(−0.20)—−0.021(−1.73)b−0.007—(−0.50)−0.045—(−2.84)0.1570.095(3.08)(3.04)−0.002b0.004b(−0.34)(−0.98)0.0240.0310.210.11100353−0.009b−0.013b(−1.24)(−1.02)−0.077—−0.030(−2.72)(−2.54)0.3110.060.130(3.81)(3.13)(3.39)bb0.0040.0010.000b(0.53)(0.33)(0.02)0.0250.0300.2490.260.100.1981429158aThet-valuesappearwithinparenthesesbelowthecoefficients.bNotsignificantatthe5%levelinaone-tailtest.Thecutoffpointfortheh0is2.33atthe1%level,1.64ina5%test,and1.28ina10%test.NATURALRESOURCESANDECONOMICGROWTH223

thatalargeprimarysectorbased,e.g.,onanabundantnaturalresourceinhibitsthecreationofa(human-capitalgenerating)secondarysectorthroughitseffectontherealexchangerate,therebyreducingtheneedforformaleducationasmeasuredbytheschoolenrollmentrates.Second,itisalsoconceivablethatabadsystemofeducationinhibitsthesecondarysectorbyraisingtrainingcosts.ThecontinueddominanceoftheprimarysectorthenfurthersuppressesthesecondarysectorthroughtheDutchdisease.Thesetwopossibilitiesarenotmutuallyexclusive.Ofcourse,thestatisticalrelationshipbetweengrowthandprimaryemploymentandexportscouldresultfromamechanismnotinvolvinghumancapital.Inpar-ticular,itispossiblethataproductiveprimarysectorcouldaffectwagesinthesecondarysectorbyofferinghighwagestoitsownworkers.Efficiencywagethe-orieswouldpredictthatwagesbeapositivefunctionofindustryproductivity—aswellasitsexpectedrateofgrowth.Otherindustries,however,payinglowerwagesthantheprimarysectorandhencepossiblyfacinghighquitratesasworkersleaveforthelucrativeprimarysector,maybeinducedtooffersimilarlyhighwagestocombatquits.Thismaydeterhiring,learning,andgrowth.

NOTES1.BritishandGermandataindicatethattheproportionofworkerswithlittleornoeducationishigherinagriculture,fisheries,andforestrythaninmostothersectors.Theproportionofprimary-sectorworkerswithnovocationaldegreesis76%inBritainand52%inWestGermany[Prais(1995)].InGermany,thisisbyfarthehighestproportionofless-advantagedworkers.Adistantsecondishotelsandcatering,withaproportionof42%.InBritain,afewsectorsmatchourprimarysector:distributivetrades(78%);hotelsandcatering(77%);insurance,banking,andfinance(76%);themanufacturingindustriesoffood,drink,andtobacco(74%);andtextiles,leather,andfootwear(81%).

2.Asimilarargumentwouldapplytoothersystemsofinsurance,suchasagriculturalpricesupportschemes.

3.Wemakethisassumptiononlytosimplifythemodel;itsrelaxationwouldnotaffectanyofourresults.

4.WetakeL2tobeindependentofthequitrate.Thusweassumethatquittingdoesnotreduceaggregateknowledgeintheindustrybecauseeithertheworkersquittostarttheirownfirmswithintheindustryortheypassontheirknow-howtoremainingworkersbeforeleavingforotherindustries.5.Wedonotconsidertheoptionvalueoffiringtheworkeratalaterdate.

26.Byusingequations(1–3),thecharacteristicequationis:12σγ(γ−1)−q(α−1)γ−(r+q)=0,

givensuitableparameterrestrictions.

7.ThisimplicationisreversedifDisnegative,i.e.,ifthereareforeignassets.

8.Therealrateofinterestandthequitratealsoaffectthethresholdindirectlythroughγ1.Thiseffectgoesintheoppositedirection:Firmsinvestsoonerathigherinterestandquitratesbecausetheydiscountpossiblefuturelossesatahigherrate;i.e.,theyaremorewillingtotakerisk.

9.Totestfortherobustnessofourresults,wealsotriedtheHuber(1973)robustestimator,andthusineffectimposedanormaldistributionontheresiduals.Theresults(notreportedhere)remainedvirtuallythesameasinTable1.Therefore,byvirtueofthecentrallimittheorem,wearenotconcernedwiththesensitivityofourresultstooutliers.Wealsorantheregressionsusingaconsistentcovariancematrixallowingforheteroskedasticity.Thestandarderrorsthusobtaineddidnotdeviatesubstantiallyfromtheonesreported,fromwhichweinfertheabsenceofheteroskedasticity.

10.Partialcorrelationsprovideadirectmeasureofthestrengthoftherelationshipbetweenthedependentandtheindependentvariables.Thepartialcorrelationcoefficientsareestimatedfromthe

224THORVALDURGYLFASONETAL.

sampledataasfollows:(1)FitanOLSregressionwithgrowthasdependentvariableandindependentvariablesX2,X3,...,XK;(2)fitanOLSregressionwithX1asdependentvariableandindependentvariablesX2,X3,...,XK;(3)computethesamplecorrelationbetweentheresidualsfromtheregres-sionsinsteps1and2.Thepurposeofsteps1and2istoremovetheeffectsofX2,X3,...,XKongrowthandonX1beforecomputingthesamplecorrelation.

11.UsingtheHausmanspecificationtest,wefindthattherandom-effectsestimatorisBLUE.However,theestimationresultsusingthefixed-effectsestimatorarequantitativelythesameexceptforamorerapidrateofconvergence.

12.Asinthecross-sectionalregressions,wealsorantheregressionsusingarobustestimator.Theresultsreportedremainedvirtuallyunchanged,sothatweneednotbeconcernedwithpotentialnonnormalityduetooutliers.

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APPENDIX:DESCRIPTIONOFDATA

GrowthofGDP.TheRGDPCH(realGDPpercapitaat1985internationalprices,chainindex)󰀋TistakenfromthePennWorldTables.Thisisanaverage,givenbytheformula1

[log(GDPt)−log(GDPt−1)],whereTisthenumberofobservations.Tisatleastt=1T25inthecross-sectionalanalysis,but5inthepanelanalysis.

InitialGDP.HereweuseRGDPCHfromthePennWorldTablesasdefinedabove.GDP0istheobservationintheinitialyear.

Investment.Thisisanaveragefortheperiod1960–1992oftheratioofrealgrossdomesticinvestment,privateandpublic,toGDP(fromPennWorldTables).Atleast25observationsareineachaverageinthecross-sectionalanalysis.Inthepanelanalysis,thisisafive-yearaverage.

Initialschoolenrolment.HereweuseWorldBankdata.Becausenodataareavailableforschoolenrollmentbefore1965,thatyearwasusedastheinitialyearinthecross-sectionalanalysis.Inthepanelanalysis,correspondinginitialvaluesforeachsubperiodwereused.Theprimaryenrollmentrateismeasuredbygrossenrollmentofstudentsattheprimarylevelasapercentageofschool-agechildrenasdefinedbyeachcountryandreportedtoUNESCO.Thesecondaryenrollmentrateisthegrossenrollmentofstudentsatthesecondarylevelasapercentageofschool-agechildrenasdefinedbyeachcountryandreportedtoUNESCO.Lateentryofmorematurestudentsaswellasrepetitionandbunchinginthefinalgradecaninfluencetheseratios.

Laborinprimarysector.Thisisthelaborforceinfarming,forestry,hunting,andfishingasapercentageoftotallaborforceinthecross-sectionalanalysisintheyear1965(fromWorldDataBank).

Exportofprimaryproducts.Thisisthecombinedexportoffuelandnonfuelprimaryproducts,asapercentageoftotalexportsofgoodsandservicesin1970.AlldataarefromtheWorldBank.ExportsoffuelscomprisecommoditiesinSITCRevision1,Section3(MineralFuelsandLubricantsandRelatedMaterials).ExportsofnonfuelprimaryproductscomprisecommoditiesinSITCRevision1,Sections0,1,2,4,andDivision68(foodandliveanimals,beveragesandtobacco,inediblecrudematerials,oils,fats,waxes,andnonferrousmetals).TheexportfiguresareincurrentU.S.dollars.Thefiguresaredollarvaluesconvertedfromdomesticcurrenciesusingsingle-yearofficialexchangerates.Forafewcountries,wheretheofficialexchangeratedoesnotreflecttherateeffectivelyappliedtoactualforeign-exchangetransactions,analternativeconversionfactorisused.Inthepanelanalysistheyears1970,1975,1980,1985,and1990wereusedforeachfive-yearperiod.

Externaldebt.Thisisanaveragefortheperiod1960–1992offoreigndebtindomesticcurrencydividedbyGDPatmarketpricesinthecross-sectionalanalysis.Foreigndebtconsistsoftheoutstandingstockorrecognizeddirectliabilitiesofthegovernmenttotherestoftheworld.Oftentherewereveryfewobservationsforeachcountry.GDPmeasuresarefromtheWorldDataBank.Atleastthreeobservationswereincludedineachfive-yearaverageinthepanelanalysis.

Exchange-ratevolatility.ThisisdefinedasthevarianceofthelogarithmofexchangeratedividedbytheGDPdeflatorfortheperiod1960–1992.Theexchangerate,whichisrelativetotheU.S.dollar,isreportedinthePennWorldTables.TheGDPdeflatoristakenfromtheWorldBankData.Atleast16observationsareusedforeachaverageinthecross-sectionalanalysis.