EconomicModelling
journalhomepage:www.elsevier.com/locate/ecmod
Humancapitalandeconomicgrowth:Amacroeconomicmodel forPakistan
FaisalSultanQadri a,⁎,AbdulWaheed b
a GovernmentPremierCollegeNo1,NorthNazimabad,Karachi,Pakistan b DepartmentofEconomics,UniversityofKarachi,Karachi,Pakistan
articleinfo
Articlehistory: Accepted6May2014 Availableonlinexxxx
JELclassification: E24 O40 I20 C51 Keywords: Humancapital Economicgrowth Education Modelconstructionandestimation
1.Introduction
abstract
ThepaperpresentsasmallmacromodelforPakistaneconomyfocusingtheimpactofinvestmentinhuman capitalonthekeymacroeconomicvariables.ThedemandsideismodeledalongtheKeynesianlineswhilethe supplysideismodeledasperneoclassicaltheoryofproduction.Thisframeworkallowsanalyzingtheeffectsof investmentinhumancapitalonsupplysidevariables(likelabor,physicalandhumancapital)anddemand sidevariables(likeconsumptionandinvestment)atthesametime.
Themodelhassmallforecastinghorizoninwhichthreealternativescenariosregardinggovernmentspendingon educationareevaluatedfrom2012to2016.Themodelshowsthatthelinkbetweenhumancapitalandlabor marketisweakhoweverachangeineducationspendingaffectsoutputthroughenhancingproductivityand throughmultiplier-acceleratorprinciple.Thoughthemodelissmallinsizeandforecastinghorizon,itcanhelp inevaluatingthefuturepathsofkeymacroeconomicvariablesassociatedwitheducationspending.
©2014ElsevierB.V.Allrightsreserved.
Theroleofhumancapitalintheeconomicgrowthofacountryis considerednothinglessthannecessary.Therearenumerousstudies basedonpanel,crosssectionalandtimeseriesdatathatfoundhuman capitalasoneofthemostimportantfactorsingrowthprocess.Most ofsuchstudiesareconductedinthelastfewdecades(Wilsonand Briscoe,2004 )becauseoftheavailabilityoflargecrosscountrydata whichallowedtheresearcherstoempiricallytestthemodelsbasedon differentsetsoftheories.1 Variouscrosssectionalstudiesalsoilluminatedtheroleofhumancapitalintheincomeconvergenceacrosscountries.2 InthecaseofPakistan,thehumancapital–economicgrowth linkagesareinvestigatedthroughvariousstudiesconductedusing timeseriesdata.3 However,whenitcomestomodellingthistheoretical andempiricallytestedrelationshipinmacroeconomicmodelingframework,verylittleworkhasbeendonesofar.
Macromodelinghasbeenusedasaneffectiveframeworkforpolicy analysisandforecastingthepathsofkeymacroeconomicvariablesfora countryorregion(likeEuropeanUnionandOrganizationforEconomic
⁎ Correspondingauthor.Tel.:+9239278285. E-mailaddresses: faysalsultan@yahoo.com (F.S.Qadri), waheedku@yahoo.com (A.Waheed).
1 See SianesiandReenen(2000) or Temple(2000) foradiscussiononsuchstudies.
2 See NelsonandPhelps(1966), Barro(1991) ,Mankiwetal.(1992)or Qadriand Waheed(2013) fordetails.
3 See Abbas(2000and2001) or QadriandWaheed(2011) fordetails.
http://dx.doi.org/10.1016/j.econmod.2014.05.021 0264-9993/©2014ElsevierB.V.Allrightsreserved.
CooperationandDevelopment).Macroeconomicmodelingframeworkdoesallownotonlytheanalysisofhumancapitalcontribution ingrowthprocess,butalsotherunningofpolicysimulationstoanalyze theeffectsofinvestinginhumancapitalonkeymacroeconomicvariableslikeoutput,employment,consumption,investmentandprices.
Therearevariousmacromodelsavailablethatarebuiltkeeping differentsegmentsofmacroeconomyinconsiderationhowever,none ofthemexplicitlydiscusstheroleofinvestmentinhumancapitalfor economicgrowth.Spendingoneducation(investmentonhumancapital)affectsoutputthroughatleastthreechannels.First,itincreasesthe productivityoflaborsooutputrisesbecauseofhighproductivity. Second,anincreaseinthelaborproductivityleadstoanincreasein thedemandforlaborandoutputrisesbecauseofmoreemployed workers.Third,anincreaseinthestockofhumancapitalattractsphysicalcapitalinflowfromothercountries(Abbas,2000,2001)andoutput risesbecauseofincreasedforeigninvestment.
1.1.ThemacroeconomicmodelsforPakistaneconomy
ThereisverylimitedliteratureavailableonmacroeconomicmodelinginthecaseofPakistaneconomy.Mainly,therearelargemacro modelslike Naqvietal.(1983),including NaqviandAhmad(1986) and Chistietal.(1992).Allofthesemodelsarelargesized,desegregated modelscoveringdifferentsectorsincludingproduction,labormarket, andmonetary, fiscalandforeignsector.Anotherinfluentialworkhas beendonebySPDCinmakingalargesizedmacromodel(Pashaetal.,
1995)connectingthemacroeconomywiththesocialsectorinPakistan. KhanandDin(2011) isasmallsizeddynamicmacromodelwhich coveredthelinkagesbetweenaggregatesupply,aggregatedemand, monetary, fiscalandforeignsectorsofPakistan. Hanifetal.(2011) isa smallsizedmacromodelanalyzingtheimpactofmonetarypolicyon keymacroeconomicvariables.Since,thesupplysideisnotconsidered inthemodelbuilding,themodelimplicitlyassumesthatachangein outputandpricesismainlybecauseofachangeinaggregatedemand whichisinappropriateinthecaseofasupplyconstraintcountrylike Pakistan.Aggregatedemandstimulationcancausein flationinthe presenceofsupplyconstraints(Hirsch,1977)insteadofincreasingthe outputandemploymentinaneconomy(Mallick,1999).Allthemacro modelsenlightenedthelinkagesbetweenmacroeconomicsectorshowever;noneofthemodelsexplicitlydiscussedtheroleofinvestingin humancapitalineconomicgrowth.Thisisthe firstmodelwhichilluminatestheeffectofsuchspendingonkeymacroeconomicvariablesin caseofPakistan.
2.Characteristicsofthemodelanddata
Themodelisasmallsized,comprehensivemacromodelwhichis comprisedofthreeblocks.Twoofwhicharerecursivewhileoneissimultaneousblock.Thereare12equationsinthemodeloutofwhich, 08arebehavioralequationsand04areidentities.Thereare20variables intotal.Outofwhich,12variablesareendogenouswhile08areexogenous.Theexogenousvariablesarefurtherclassifiedaspolicyandnonpolicyvariables.Thereare03policyvariablesnamedgovernmentconsumption,governmentinvestmentandspendingoneducationaspercentageofGDPand05non-policyvariables.
Thedatasetisannualwhichistakenfromvariouspublicationsof PakistanBureauofStatics(Former,FederalBureauofStatistics).The unitforallmonetaryvariablesismillionrupeesinconstantprice (1999–00)exceptforworldGDPwhichismeasuredinmillionUSdollar inconstantprice(1999–00),takenfromWorldDevelopmentIndicators.4
Thevariablecapitalstock(K)iscalculatedthroughperpetualinventorymethod.Thedatasetusedformodelcalibrationisfrom1981to 2011exceptfortheprivateconsumption.Thedatasetforprivateconsumptionisfrom1975to2011inordertogetthebest fi tvaluesfor modelcalibration.Thedatasetformodel'ssolutionisfrom1981to 2011.
3.Structureofthemodel
ThismodelcomplementstheexistingmacromodelswhichilluminatesthemacroeffectsofinvestmentinhumancapitalinPakistan. Themodelfollowstheframeworkadoptedby Welfe(2005and2011) whichused finaldemandequationsalongtheKeynesianlinesbut theoutputgenerationismodeledthroughneoclassicaltheoryofproduction.Thisframeworkallowsanalyzingtheeffectsofinvestment inhumancapitalonsupplysidevariables(likelabor,physicaland humancapital)anddemandsidevariables(likeconsumptionandinvestment)atthesametime. 5 ThepureKeynesianmodelisgenerally criticizedbecauseofitsinabilitytocoverthesupplysideoftheeconomy whichisveryimportantespeciallyinthecaseofunderdevelopedcountrieswhichgenerallyfacesupplyconstraints.Moreover,themodeldoes notcovertheroleofthemoneymarket,relativepricesandexpectations effectively(Valadkhani,2004).Apureclassicalmodelisalsocriticized becauseofnotcoveringthedemandsideoftheeconomy.Themodel under Kleinetal.(1999) , Bodkinetal.(1991) and Whitley(1994) frameworkovercomestheproblemsassociatedwithpureclassicalor
4 http://databank.worldbank.org/ddp/home.do?Step=12&id=4&CNO=2,lastaccessed onJuly2012.
5 See Kleinetal.(1999), Bodkinetal.(1991) and Whitley(1994) regardingstudieson similarframework.
Table1
Keycharacteristicsofthemodel.
Numberofindependentblocks3 Numberofrecursiveblocks2 Numberofsimultaneousblocks1 Numberofequations12 Behavioralequations8 Identities4 Endogenousvariables12 Exogenous(policyvariables)3 Exogenous(non-policyvariables)5
Keynesianmodel.Keycharacteristicsofthemodelarepresentedin Table1
Aspresentedin Table1,themodelclassifi esexogenousvariables intopolicyandnon-policyvariables.Theexogenousvariableson whichgovernmentenjoysasigni fi cantdegreeofcontrolareexogenouspolicyvariables. 6 Governmentconsumption,governmentinvestmentandeducationspendingaspercentageofGDParetaken aspolicyvariablesinthemodel. 7 Thecoef ficientsofallindependent variablesinthe08behavioralequationsarethelongrunequilibrium valuesofthevariablesasperEngle –Grangertwostepprocedure. 8
4.Demandblock
Thedemandforproductsandservicescomprisesofconsumption demand,investmentdemand,inventoryandnetexports.
4.1.Consumptiondemand
Consumptiondemandisthesumofprivateconsumptiondemand andgovernmentconsumptiondemand.Governmentconsumptiondemandistakenasapolicyvariablewhiletheestimatedcoefficientsand relevantparametersofprivateconsumptionarestatedbelow.
4.1.1.Privateconsumption
Inordertogetthebest fitconsumptionfunctionforPakistaneconomy,differentspecificationshavebeenused.Inanalternativespecification,lagofconsumptionwasfoundtobestatisticallyinsignificant rejectingtheexistenceofadaptiveexpectations.Therelationshipbetweeninterestrateandconsumptiondependsontherelativemagnitudes ofincomeandsubstitutioneffect.Generally,anegativerelationship betweeninterestrateandcurrentconsumptionisexpected.However,interestratealsoturnedouttobestatisticallyinsignificantintheregression whichimpliesthatinterestratehasverylimitedornoroleintheintertemporalconsumptiondecision.
Equation1 log(PC)=6.854+0.329 ∗ log(Y)+0.212 ∗ log(M2)AdjustedR2 t-Statistics5.6302.7955.273 0.996 Prob(t-stats)(0.000)(0.008)(0.000) DWstatistics1.624 F-Statistics4507.348
However,thebest fitregressionindicatesthatKeynesianconsumptionfunctionandwealtheffectexplaintheconsumptionbehaviorsufficiently.InEq.(1),YrepresentscurrentincomeandM2istakenasa proxyfor financialwealth.9
6 See RaandRhee(2005) fordetails.
7 Fordetailsofvariablesandtheirdescription,see Appendix1
8 SeeTablesin Appendix1and2.Tablesshowthatallthevariablesinthe08behavioral equationsareI(1)andthattheresidualseriesobtainedfromall08equationsareI(0).
9 See Hanifetal.(2011) forasimilarspecification.
4.2.Investmentdemand
Investmentdemandisthesumofprivateandpublicinvestment, governmentinvestmentandinventoryinvestment.Government investmentistakenasanexogenouspolicyvariablewhileinventory investmentasanexogenousnon-policyvariableinthemodel.
4.2.1.Privateandpublicinvestment
Equation2 log(INVAB)= 0.911+0.945 ∗ log(Y)AdjustedR2 t-Statistics 0.3485.3240.952 Prob(t-stats)(0.735)(0.000) DWstatistics1.475F-Statistics299.525
Similartotheprivateconsumptionequation,differenttheoretically acceptablespecificationsweretestedforthesecondimportantcomponentofaggregatedemand,investment.Interestratewasfoundtobeinsignificantinthisregressionwhichrejectstheexistenceofclassical investmentdemandfunction.Governmentinvestmentwasalsoincludedinanotherspecificationtocheckthecrowdingoutphenomenonbut thatalsoturnedouttobeinsignificant.Finally,inthebest fitregression, thevariationinprivateandpublicinvestmentcanbeexplainedsufficientlybythevariationinincomeasstatedintheKeynesianaccelerator principle.
4.3.Tradeblock
The finalcomponentofaggregatedemand,netexportsisdeterminedthroughtradeblock.10 Thisblockiscomprisedofexportand importfunctionswhichareconnectedthroughthenetexportidentity.
4.3.1.Productandserviceexport
Pakistan'sexporttotheworldistakenasafunctionofworld'sincomewhichsufficientlyexplainsthevariationinPakistan'sexports.
Equation3 log(EXPORT)= 33.679+1.513 ∗ log(WGDP)AdjustedR2 t-Statistics 1.8902.6460.966 Prob(t-stats)(0.069)(0.013) DWstatistics1.970F-Statistics432.757
Intheotheralternativespecifications,realexchangerateisfoundto beinsignificantinexplainingexportvariation.Similarly,lagofexport wastakenasanindependentvariabletocapturethepartialadjustment effecthowever,itwasalsofoundtobestatisticallyinsignificant.
4.3.2.Productandserviceimport
groupandchemicalgroup.Allofthesearepositivelyrelatedtodomestic incomewithincomeelasticitygreaterthanunity.Thecoefficientofpartialadjustmenteffectisfoundtobestatisticallysignificantinthemodel.
5.Supplyblock
Supplysideofthemodelrepresentstheneo-classicaltheoryofproductionasdiscussedinthesubsequentsubsections.
5.1.Productionfunction
Theproductionfunctionwiththreevariableinputsisusedinthe modelnamely,labor,physicalcapitalandhumancapital.
Equation5 log(Y)=4.611+0.375 ∗ log(EL)+0.558 ∗ log(K)+ 0.136 ∗ log(H( 1)) AdjustedR2 t-Statistics6.6252.8107.0881.719 0.998 Prob(t-stats)(0.000)(0.009)(0.000)(0.097) DWstatistics1.411 F-Statistics3203.238
Inthefunction,laborinputiscapturedthroughemployedlabor,capitalstockisusedinordertocapturecapitalinputandgrossenrolment rateinsecondaryeducationistakenasaproxyforhumancapital inputinthefunction.Allofthesearefoundtobepositivelyandsignificantlyrelatedwithoutputastheoreticallyexpected.
5.2.Demandforlabor
Labordemandfunctionismodeleddifferentlyfromconvention. Laborforceandthelagofhumancapitalareusedasexplanatoryvariables.Asneo-classicaltheoryoflabordemandexplains,theincreased laborforcewoulddecreaserealwagesandtherebyincreasethequantity demandedforlabor.InacountrylikePakistanwherelaborforcehas beenincreasingveryfast,thisvariableseemsmoreappropriatein explainingthelabordemand.
Equation6 log(EL)= 101.752+1.260 ∗ log(L)+0.063 ∗ log(H( 1))AdjustedR2 t-Statistics 0.00910.1193.0730.999 Prob(t-stats)(0.992)(0.000)(0.005) DWstatistics1.795F-Statistics10209.34
Theoryofproductionandlabordemandexplainsthatincreasedproductivityoflaborwouldleadtoincreaseinthedemandforlabor. Humancapitalisalsoexpectedtobepositivelyrelatedwiththedemand forlaborbecauseitincreasesthelaborproductivity.
5.3.Humancapital
Equation4
log(IMPORT)= 16.041–0.510 ∗ log(RER)+1.701 ∗ log(Y)+ 0.412 ∗ log(IMPORT( 1)) AdjustedR2 t-Statistics 2.393 2.3442.9242.5870.899 Prob(t-stats)(0.024)(0.027)(0.007)(0.015) DWstatistics1.524F-Statistics85.529
Intheimportdemandfunction,realexchangerate,11 domesticincomeandlagofimportareusedasexplanatoryvariables.Astheoreticallyexpected,thecoefficientofrealexchangerateisnegative.Thekey componentsofPakistaniimportsbelongtoPetroleumgroup,machinery
Inempiricalstudies,humancapitalisgenerallyproxiedthroughan educationstockor flowindicator.Atthesametime,therearestudies whichemployedhealth,nutritionandexperienceasanindicatorof humancapital.Therearestudieswhichfoundthecoefficientofhuman capitalasstatisticallyinsignificantorevennegativelyrelatedtothe growthprocess.12 Theempiricalstudiesshowthatthedirectionand magnitudeofhumancapitaltoaffecteconomicgrowtharesensitive withrespecttotheproxyused.Thisstudyusedanarrowdefinitionof humancapitalandemployededucationindicatorasaproxyforhuman capitalbecauseoftheavailabilityofofficialdataandalsobecausethisindicatorisundermoredirectcontrolofgovernmentthenanyofthebroad indicatorlike ‘learningbydoing’ . 10 See ChristodoulakisandKalyvitis(1998) forsimilarspecification. 11 RER=IMPPRICE/CPIwhereIMPPRICE=unitvalueofimports ∗ exchangerate. 12 See BenhabibandSpiegel(1994) or Pritchett(2001)
Inlinewithconventionandtheory,humancapital(grossenrolmentrateinsecondaryeducation)ismodeledasafunctionof domesticincomeandgovernmentspendingoneducationaspercentage ofGDP.
Equation7 log(H)= 1.061+0.154 ∗ log(ES)+0.161 ∗ log(Y)+ 0.545 ∗ log(H( 1)) AdjustedR2 t-Statistics 2.0332.1992.7724.0030.933 Prob(t-stats)(0.052)(0.036)(0.010)(0.000) DWstatistics1.925F-Statistics139.859
Asexpected,thecoefficientsofdomesticincomeandgovernment spendingoneducationaspercentageofGDParefoundtobepositively andsignificantlyrelatedwithhumancapital.Thecoefficientofpartial adjustmentmechanismisalsofoundtobestatisticallysignificant.The otherrelevantvariableslikeurbanizationarefoundinsignificantin explainingthemodel.
6.Priceblock
Inlinewiththetheoreticalexpectations,consumerpriceindexis foundtobeapositivefunctionofimportpricesandthebroadmoney relativetothedomesticincome.
Equation8 Log(CPI)=2.694+0.265 ∗ log(IMPPRICE)+0.357 ∗ log(M2/Y)AdjustedR2 t-Statistics6.3526.0663.955 0.998 Prob(t-stats)(0.000)(0.000)(0.000)
DWstatistics1.496 F-Statistics5128.391
Importpriceistheproductofunitpriceofimportandnominal exchangerate.Ifunitpriceofimportincreasesordomesticdirectexchangerateincreases(orbothfactorsincreasesimultaneously),the domesticpricesareexpectedtoincrease.InacountrylikePakistan, wherethebiggestcategoryofimp ortispetroleumproducts,anincreaseinimportpricesismorelikelytoincreasethedomesticprices signi ficantly.
7.Diagnostictests
Priortosolvingthemodel,itisnecessarytocheckwhetherthe coef fi cientsformodelcalibrationareestimatedthroughastatisticallyreliableprocedureornot.Therearedifferentteststocheck whetheranindividualequationisreliableenoughtobechosenfor modelcalibrationornot.The fi ndingsofsuchtestsarereportedin Table2.
Inthissection,thediagnostictestsbeginwithBG/LMwhichisused tocheckifthereisanexistenceofautocorrelationinanyequation.None ofthequestionshavefoundtohave firstorsecondorderautocorrelation.Whitetestisusedtochecktheexistenceofpureorspecification
Table2
Diagnostictests.
Source:Authors'estimation.
EquationBG/LMtestProbWhitehet.testProbChowforecasttestProb
10.9750.3881.0930.3841.1210.454 21.0110.3783.6320.040.5850.81 30.0190.9811.5920.2211.5860.398 40.7190.4973.7430.0070.1590.994 52.0460.1511.0220.4551.540.572 61.0570.3621.2430.31957.7910.017 70.0580.9440.8060.6164.5130.197 81.8110.1843.5210.0157.8990.118
basedheteroscedasticity.Theestimatedcoef fi cientsofEqs.(2), (4)and(8)areobtainedthroughtheprocedureknownas “White heteroscedasticityconsistentstandarderrorsandcovariance” because theseequationswerefoundtohaveheteroscedasticity.
Chowforecasttestisusedtoseewhethertheparametersarestable duringthesampleperiod.1987,1999and2007arechosenasbreak pointsbecausethesearethetransitionyearsfromamilitaryperson's ruletodemocraticruleorviceversa.Theemploymentparameteris foundtobeaffectedinthedifferentkindsofregimes.
8.Forecastingperformance
Themainobjectiveofthismodelistopredictdifferentpathsofmacroeconomicvariablesassociatedwithdifferentpolicyscenariosregardinggovernmentspendingoneducation.Priortostartingthescenario experiments,themodelisalsoevaluatedforwithinthesampleand outofsampleperformance.
8.1.Within-sampleforecastperformance
Thewithinsampleforecastperformanceisevaluatedthroughconventionallyusedstatisticsnamedrootmeansquarepercentageerror (RMSPE),meanabsolutepercenterror(MAPE)andTheilinequalitycoefficientwhileoutofsampleperformanceisevaluatedthroughstochastic simulations. Table3 presentsthevaluesofrootmeansquarepercentage error(RMSPE),meanabsolutepercenterror(MAPE)andTheilinequality coefficient.
Thetableshowsthatthemodelperformswellinstaticanddynamic simulationsespeciallyinthecaseofpredictingtheGDPandemployment. AllRMSPEvaluesarelessthan05inthecaseofstaticsimulationandless than06inthecaseofdynamicsimulationexcepttheprivateandpublic investment.InthecaseofMAPE,allstatisticsarelessthan04instatic andlessthan05indynamicsimulationsotherthanprivateandpublic investment.AllvaluesofTheilinequalitycoefficientareclosetozeroindicatingsatisfactoryforecastingabilityofthemodel. Fig.1 presentsactual valuesagainstthepredictedvaluesestimatedthroughstaticanddynamic simulationsforthekeyvariablesinthemodel.Thegraphsshowthatthe modelcantrackthehistoricalvalueswithremarkableaccuracyespecially inthecaseofGDP,employment,privateconsumptionandCPI.
8.2.Out-of-sampleforecastingperformance
Outofsampleperformanceisconventionallyevaluatedthrough stochasticsimulations.Thedynamicdeterministicsimulationpredicts thefuturepathofendogenousvariablesasasinglepointateachobservationhowever;theprocedureofpredictionthroughstochasticsimulationisquitedifferent.
Thestochasticsimulationsincorporateuncertaintyinthepredictionsthroughaddingrandomshocksintoeachestimatedequation.In thiscase,themodelpredictsacompletedistributionofendogenous
Table3
Forecastingaccuracyofthekeyvariables.
Source:Authors'estimation.
RMSPEMeanabsolute percenterror Theilinequality coefficient StaticDynamicStaticDynamicStaticDynamic Y1.8182.8171.4952.1350.0090.016 H4.6165.7243.6454.5630.0230.028 EL0.7161.0200.4670.8080.0030.004 PC3.028 a 2.354 a 0.016 a CPI2.9385.0042.4473.9580.0180.031 INVAB8.50010.7596.9509.1350.0440.051
a Nodynamicsinequation.
Fig.1. Staticanddynamicsimulation.
variablesateachobservation.Sincethemodelislinear,meanandstandarddeviationsareappropriatestatisticstodescribethedistribution sufficiently.
TheMonteCarloapproachisusedtoestimatethedistributionofendogenousvariablesintheforecastperiod.IntheMonteCarloapproach, themodelissolvedseveraltimeswithsimulatedrandomnumbers substitutedforunknownerrorsateverysolution.
Fortheout-of-sampleperiod,thevaluesfortheexogenousvariables aregeneratedthroughdynamicforecastingbyusinganautoregressive componentintheequationofINVC,GC,M2andLF.Thevaluesfor IMPPRICE,INVENTORYandWGDPareassumedtogrowatthelast 05year'saveragegrowthrate.ThefocusedpolicyvariableH(government
spendingaspercentageofGDP)isassumedtobe fixedataround2.2% (theaveragepercentagevalueforthelast10years).
Fig.2.presentsthegraphsforthekeyvariablesforout-of-sampleperiod.The figurepresentsthreecurvesforeachvariable.Thecurveinthe middlerepresentsthemeanofdistributionateachobservationandthe othertwolinesshowthe95%confidenceinterval.The figureshowsthat themodelperformanceissatisfactoryfortheout-of-sampleperiod.
9.Scenarioanalysis
Afterestablishingthebaselinepathforthekeyvariables,theimpacts ofthreepolicyscenariosareanalyzed.Inallthethreescenarios,aone
Fig.2. Stochasticsimulationforout-of-sampleperiod.
timeorsustainedshockwouldbegiventothecorepolicyvariable,governmentspendingoneducationaspercentageofGDP.Ithasbeen discussedthatthechangeinspendingeffectshumancapital fl owin theeconomywhicheffectsoutputinthreedistinguishedways. First,itincreasesoutputduetohigherproductivity.Second,it increasesoutputduetoincreasedemploymentandthird,duetoincreasedforeigncapitalin fl ows.Inthisstudy,the fi rsttwochannels havebeenmodeled.
9.1.Scenario1:Educationspendingas4%ofGDPfrom2012to2016
The firstshockisasustainedlevelofeducationspendingas4%ofGDP throughouttheforecastperiod.Asshownin Fig.3,thisshockincreased enrolmentrateby9.5%fromthebaselineinthesameyear.Thedeviation
ofenrolmentratefrombaselinehasbeenincreasingthroughouttheforecastperiodandreached22.28%in2016eventhoughthemarginalenrolmentratehasbeendeclining.Theprivateandpublicinvestment respondstothisshockin2013andtheinvestmentdeviates1.41%from baseline.Thisdeviationfurtherincreasedinthelateryearsbecauseof themultiplier–acceleratorprocessand finallyreached3.18%in2016. Theincreasedhumancapitalaffectsthelabordemandandemployment in2013.A0.57%increaseinemploymentascomparedtothebaselineis recordedin2013whichincreasedfurtherinthesubsequentyearsand reached1.2%in2016.TheimpactofthisshockaffectsGDPin2013and GDPincreasedby1.52%frombaseline.ThedeviationofGDPfrombaselineincreasedfurtherduetoemploymentandmultiplier–accelerator principle.In2016,thisdeviationreached3.45%frombaseline.Aninterestingthingisthatthoughtheoveralleconomicactivitieshavebeen
Base line Scenario1 Percentagedevia onfrombaseline
Fig.3. Scenario1.
increasinghowever,CPIfallsrelativetothebaseline.ThedeviationofCPI frombaselinehasbeenincreasingthoughwithdecreasingrate.This mightbebecauseinPakistan,theCPIdependsmoreonimportprices andmoneysupplyrelativetoGDPandGDPgrowsfasterinscenario1 thereforemoneysupplyrelativetoGDPdeclines.TheincreaseinGDP affectsprivateconsumptionpositivelyin2013andprivate consumptiondeviatesfrombaselineby0.49%.Thisdeviationreaches 1.12%in2016.
9.2.Scenario2:Startingfrom3%in2012,agradual0.5%increaseinthe educationspendingaspercentageofGDPfrom2013to2016
Fig.4 presentstheresponsefromkeyvariablestothesecondshock. Thisshockisagradual0.5%increaseintheeducationspendingas
percentageofGDPthroughouttheforecastperiodstartedfrom3%in 2012.Thisshockincreasedtheenrolmentrateby4.84%fromthebaselinein2012.Thedeviationofenrolmentratefrombaselinehasbeenincreasingthroughouttheforecastperiodandreached26.75%in2016. Theprivateandpublicinvestmentrespondstothisshockin2013.The investmentincreasedby0.72%frombaselineandendedat3.17%in 2016.Employmentrespondedin2013tothisshock.A0.29%increase inemploymentfrombaselineisrecordedin2013whichreached 1.22%in2016.ThisshockincreasesGDPby0.78%frombaseline in2013whichreached3.43%frombaselinein2016.CPIfallsrelative tobaselineby0.27%in2013andcontinuedtofallthroughtheforecastingperiod.Inresponsetotheshock,privateconsumption increasedfrombaselineby0.25%in2013.Thisdeviationreaches1.11% in2016.
Baseline Scenario1 Percentagedevia onfrombaseline
Fig.4. Scenario2.
9.3.Scenario3:Educationspendingas5%ofGDPin2012than3%ofGDP throughoutfrom2013to2016
ThethirdshockisaonetimeincreaseintheeducationspendingaspercentageofGDPin2013an dthenasustainededucation spendingaspercentageofGDP.Accordingtothisshock,theeducationspendingaspercentageofGDPis5%in2012thana sustainedincreaseof3%ofGDP,throughouttheperiod2013 –2016. Fig.5 presentstheresponsefromkeyvariablestothis shock.Enrolmentraterespondedtotheshockbyanincreaseof 13.4%fromthebaselinein2012.Thedeviationofenrolmentrate frombaselinedeclinesslowlywithtimeandreached11.91in 2016.Theprivateandpublicinvestmentrespondstothisshock in2013.Theinvestmentincreasedby1.94%frombaselineand
thisdeviationremainsquitestablethroughouttheforecasting period.A0.79%increa sefrombaselineinemploymentisrecorded in2013whichdeclinedinasmoot hmannerandreached0.71%in 2016.ThisshockincreasesGDPby2.1%frombaselinein2013and thedeviationincreasestill2015.In2016,thedeviationfrombaselineremains2.1%.CPIfallsrelativetobaselineby0.74%in2013 andthisdeviationremainsalmostunchangedthroughouttheforecastingperiod.
10.Conclusionandpolicyimplications
Thepaperbuildsandsolvesacomprehensivemacromodel forPakistaneconomy.Thisisthe fi rstmodelforPakistan economythatexplicitlydiscussedtheroleofeducationspendingin
Base line Scenario1 Percentagedevia onfrombaseline
Fig.5. Scenario3.
determiningthekeymacroeconomicvariables.Themodel has12equationsintotaloutofwhich04areidentities.The demandsideofthemodelisconstructedinlightofKeynesian frameworkandthesupplysideismodeledinneoclassicallines.The modeldifferentiatespolicyvariablefromordinaryexogenous variablesbecausethesevariablesareunderdirectcontrolof governmentpolicies.ThecorepolicyvariableinthemodelisspendingoneducationaspercentageofGDPandthreescenarios associatedwithdifferentpathsofeducationspendingarediscussedin thepaper.
Calibrationofthemodelisdonethroughordinaryleastsquare andthemodelissolvedthroughGauss – Seidelprocedure.The modelperformsquitewellintrackingthehistoricalpathsofthe keyvariables.Thewithinsampleperformanceisevaluatedthrough conventionalstatisticsRMSPE,MAPEandTheilinequalitycoef ficient
whichareestimatedforboththestaticanddynamicrunsofthe model.Theoutofsampleperformanceisevaluatedthroughstochasticsimulations.
Thepolicyscenariospredictdifferentfuturepathsofthekey macroeconomicvariables.Thesimulationsshowthatthelinkbetweeneducationandlabormarketisquiteweak.Intheallthree scenarios,eventhoughtheeducationspendingincreasedmore thanthehistoricalpathhowever,themaximumchangeintheemploymentassociatedwithsuchspendingis1.22%frombaselinein the5thyear.Themaximumoutpu tandinvestmentdeviationare 3.45%and3.18%frombaselineresp ectively,whichismainlybecauseoftheproductivityeffectandthroughmultiplier–accelerator principle.
Forsmallforecastingspan,thismodelcanbeusefulintakingthe decisionsregardingeducationspending.
Testforstationarity
ADFtest Level
Firstdifference VariablesCC&TCC&T
Y1.622 1.063 3.050** 3.676** L2.773 0.552 5.139* 5.265* K2.3480.000 3.068** 3.995** H 0.514 1.811 5.374* 5.293* ES 2.211 2.165 3.380** 3.231*** EL2.452 0.424 5.087* 6.476* PC2.017 0.744 5.699* 4.716* M2 0.931 2.514 3.777* 4.679* CPI1.083 2.363 3.199** 3.581*** WGDP1.463 2.644 5.159* 5.369* INVAB0.208 2.540 6.120* 5.989* IMPORT 0.746 2.872 5.760* 5.672* EXPORT 0.486 2.543 5.780* 5.618* IMPPRICE 1.700 3.164 5.654* 5.789*
Note:Criticalvalueswithintercept(C)andinterceptandtrend(C&T)onlevelat10%are 2.625and 3.225respectively. *,**and***showsthestatisticalsignificanceofthevariablesat1%,5%and10%respectively. Source:Authors'estimation.
Appendix2
Variable Description
Exogenous(policyvariables)
Spendingoneducation ES GovernmentspendingoneducationaspercentageofGDP
Governmentconsumption GC
Governmentconsumptioninmillionrupees(constantpricesof1999–2000)
Governmentinvestment INVC Governmentinvestmentinmillionrupees(constantpricesof1999–2000)
Exogenous(non-policyvariables)
Laborforce LF Laborforceinmillion M2 M2 Millionrupees Inventory INVENTORY Inventoryinmillionrupees
Importprice IMPPRICE Inrupees
WorldGDP WGDP InconstantUSdollar(2000)
Endogenous
GDPatconstantmarketprice Y
GDPatconstantpricesof1999–2000
Grossenrolmentratio(Secondary) H Ratio
Employedlabor EL Inmillion
Privateconsumption PC
Inmillionrupees(constantpricesof1999–2000)
Privateandpublicinvestment INVAB Inmillionrupees(constantpricesof1999–2000)
Consumerpriceindex CPI Ratio
Totalinvestment INV
Inmillionrupees(constantpricesof1999–2000)
Totalconsumption TC Inmillionrupees(constantpricesof1999–2000)
Netexports NX
Inmillionrupees(constantpricesof1999–2000)
Imports IMPORT Inmillionrupees(constantpricesof1999–2000)
Exports EXPORT Inmillionrupees(constantpricesof1999–2000)
Capitalstock K Inmillionrupees(constantpricesof1999–2000)
Listofidentities
TC=PC+GC 1 INV=INVAB+INVC+INVENTORY. ..2 K=K( 1) ∗ 0.95+INVAB+INVC .3
NX=EXPORT IMPORT……………….………..4
ADFtest Level
VariablesCC&T
U1 43.553* 40.924*
U2 5.081* 4.981*
U3 4.570* 4.462*
U4 3.972* 4.348*
U5 4.620* 4.681*
U6 5.309* 4.991*
U7 5.188* 5.108*
U8 7.426* 6.833*
ThevariablesU1toU8representtheresidualseriesofEqs.(1)to(8)respectively.
Note:Criticalvalueswithintercept(C)andinterceptandtrend(C&T)onlevelat1%are 3.670and 4.340respectively.
*showsthestatisticalsignificanceofthevariablesat1%.
Source:Authors'estimation.
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