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StructuralReformsand
EconomicGrowth:A
MachineLearning
Approach
AnilAri,GaborPulaandLiyangSun
WP/22/184
IMFWorkingPapersdescriberesearchinprogressbythe
author(s)andarepublishedtoelicitcommentsandto
encouragedebate.
TheviewsexpressedinIMFWorkingPapersarethoseofthe
author(s)anddonotnecessarilyrepresenttheviewsoftheIMF,
itsExecutiveBoard,orIMFmanagement.
2022
SEP
?2022InternationalMonetaryFund
WP/22/184
IMFWorkingPaper
EuropeanDepartment
StructuralReformsandEconomicGrowth:AMachineLearningApproachPreparedbyAnilAri,GaborPulaandLiyangSun
AuthorizedfordistributionbyIvannaVladkovaHollar
September2022
IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.
ABSTRACT:Thequalitativeandgranularnatureofmoststructuralindicatorsandthevarietyindatasourcesposesdifficultiesforconsistentcross-countryassessmentsandempiricalanalysis.Weovercometheseissuesbyusingamachinelearningapproach(thepartialleastsquaresmethod)tocombineabroadsetofcross-countrystructuralindicatorsintoasmallnumberofsyntheticscoreswhichcorrespondtokeystructuralareas,andwhicharesuitableforconsistentquantitativecomparisonsacrosscountriesandtime.Withthisnewlyconstructeddatasetofsyntheticstructuralscoresin126countriesbetween2000-2019,weestablishstylizedfactsaboutstructuralgapsandreforms,andanalyzetheimpactofreformstargetingdifferentstructuralareasoneconomicgrowth.Ourfindingssuggestthatstructuralreformsintheareaofproduct,laborandfinancialmarketsaswellasthelegalsystemhaveasignificantimpactoneconomicgrowthina5-yearhorizon,withonestandarddeviationimprovementinoneofthesereformareasraisingcumulative5-yeargrowthby2to6percent.Wealsofindsynergiesbetweendifferentstructuralareas,inparticularbetweenproductandlabormarketreforms.
RECOMMENDEDCITATION:Ari,A.,Pula,G.,&Sun,L.(2022).StructuralReformsandEconomicGrowth:AMachineLearningApproach.IMFWorkingPaper,WP/22/184
JELClassificationNumbers:E02,C54,C55,D58,O43,O47
Keywords:Structuralreforms,institutions,economicgrowth
Author’sE-MailAddress:aari@,gpula@,lsun20@cemfi.es
WORKINGPAPERS
StructuralReformsandEconomicGrowth:AMachineLearningApproach
PreparedbyAnilAri,GaborPulaandLiyangSun1
1TheauthorsaregratefultoIvannaVladkovaHollar,IppeiShibata,MarinaMendesTavaresandseminarsparticipantsattheIMFforhelpfulcommentsandsuggestions.ExcellentresearchassistancewasprovidedbySamuelVictorRomeroMartinez.Thedatasetofsyntheticstructuralscoresisavailableuponrequestfromtheauthors.Allerrorsareourown.
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Contents
I.Introduction
3
II.StructuralIndicators
5
A.Dataoverview
5
B.SyntheticstructuralscoresviaPartialLeastSquares
6
C.PLSestimationprocedure
7
D.SyntheticstructuralscoreasthepredictedvaluefromthePLSmodel
8
III.StructuralIndicators
12
A.Impactofstructuralreformsongrowth
12
B.Synergiesofstructuralreformsongrowth
17
C.Theroleofstructuralreformsduringcrises
20
IV.Conclusions
2
1
References
21
Appendix
23
A.Listofstructuralindicators
23
B.Descriptionofimputationformissingindicators
27
C.ComparisonbetweenthePLSstructuralscoreandsimple-averagescore
27
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I.Introduction
Policymakersoftenpursuestructuralreformstoaidrecoveryfromcrisesandstimulateeconomicgrowth.Thisplacestheonusonpolicymakerstoidentifywhichcombinationsandsequencesofstructuralreformswouldbethemostgrowth-enhancing(IMF,2015;Rodrik,2010).However,akeychallengeisthatstructuralreformsareinherentlydifficulttomeasureastheyofteninvolvepoliciesthataregearedtowardsimprovingefficiencyofmarkets.Commonapproachesquantifystructuralreformsbasedonthestrengthofregulatorychangesthatremoveinefficiencies(seee.g.,Alesinaetal.,2020).Whiletheseapproachesprovidevaluableinsightsontheimpactofpolicyactions,theymaynotfullyreflectreformoutcomes,whichdependonthespecificsofpolicyimplementationaswellastheenvironmentinwhichreformsareimplemented.Anotherdrawbackoftheseapproachesisthattheyhavelimitedcountrycoverageduetolimiteddataavailability.Otherapproachesrelyonsurvey-basedindicatorsofstructuraloutcomestoassesstheimpactofstructuralreformsandconductcross-countryanalysis(seee.g.,EgertandGal,2016;Egert,2017).Whiletheseindicatorsareinformativeaboutstructuralperformance,empiricalanalysisiscomplicatedbythelargenumberofindicators,thecorrelationbetweenthemandbiasesthatmayarisefromtheirsubjectivenature.
Weuseamachinelearningapproachtoconstructsyntheticstructuralscoresfromalargenumberofstructuralindicators.Ouranalysiscontributestotheexistingliteraturebyusingpartialleastsquares(PLS)toaggregatestructuralindicatorsforgrowthanalysis,insteadofsimpleaveragingoradhocweighingschemes.OurPLSweightingschemeassignshigherweightstoindicatorsthataremorepredictiveofhighGDPpercapita,therebyextractingusefulinformationfromavailabledatawhileremovingthenoiseandbiasesassociatedwithsubjectiveandsurvey-basedindicators.Ourapproachalsoaccountsforthecorrelationandredundancyamongstructuralindicators,thereforeavoidingtheduplicationbiasthatsimpleaveragingwouldsufferfrom.1
Oursyntheticstructuralscoresarebasedonarichanddisaggregateddatasetofstructuralindicators.WerelyontheIMF’sStructuralandFinancialIndicatorsdatabasewhichdrawsfromseveralsourcesandincludes275structuralindicatorsfrom126countries(Figure1).2WethengrouptheseindicatorsintosixstructuralareasidentifiedinIMF(2015):financialsystem(77),tradeandopenness(28),legalsystem(37),labormarkets(74),businessenvironment(45)andtaxpolicy(14).WethenconstructasyntheticstructuralscoreforeachstructuralareaasthePLS-weightedaverageoftheunderlyingstructuralindicators.
1OurapproachbuildsuponAriandPula(2021)whichproposestheuseofprincipalcomponentanalysis(PCA),toformsyntheticstructuralfactors.ThePCAweightsaccountforthecorrelationbetweenindividualindicatorsbutaresensitivetoduplicationofindicators,whichiscommoninourdatasetduetooverlapsindatasources.
2OuranalysisincludesindicatorsfromtheWorldBank’sDoingBusiness(DB)dataset,whichhasrecentlybeensuspendedduetoconcernsaboutdatamanipulation.Whilethisposesadrawbackforourstudyaswellasasignificantportionoftheliteratureonstructuralreforms,itisworthnotingthatthisistheformofsubjectivitybiasthatweaimtoalleviatewithourPLSapproach.
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Figure1.Structuralindicatoroverview
Sourcesofstructuralindicators
Areasofstructuralindicators
Usingthesyntheticstructuralscores,wefindsignificantgrowthimpactsfromreformsincertainstructuralareas,aswellassynergiesbetweendifferentstructuralareas.Ourfindingssuggestthatstructuralreformsintheareasofproduct,laborandfinancialmarketsaswellasthelegalsystemhaveasignificantimpactoneconomicgrowthina5-yearhorizon,withonestandarddeviationimprovementinoneofthesereformareasraisingcumulative5-yeargrowthby2to6percent.Wealsofindsynergiesbetweendifferentstructuralareas,inparticularbetweenproductandlabormarketreforms.
Thepaperisorganizedasfollows.SectionIIoverviewsthedataanddiscussesourapproachtoimputingmissingindicators.SectionIIIappliesPLStoconstructsyntheticstructuralscoresbasedontheimputedindicators,controllingforthecorrelationamongtheindividualstructuralindicators,andassigningtheweightstoreflecthowpredictivetheindicatorsareforoutput.SectionIVusesthesyntheticstructuralscorestoanalyzetheimpactofstructuralreformsongrowth.Finally,SectionVconcludes.
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II.StructuralIndicators
A.Dataoverview
Theperformanceofstructuralreformsismeasuredusingquantitativeindicators.Cross-countrydataonalargesetofstructuralindicatorsareobtainedfromtheFund’sMacrostructuralDatabase,whichcombinesdatafromseveralsources.Theseindicatorsarethencategorizedtosixbroadermacrostructuralareas,listedas:
-Legalsystem,whichincludesstructuralindicatorsrelatedtocorruption,governance,crime,theruleoflawandtheprotectionofpropertyrights.
-Financialsystem,whichcoversstructuralindicatorspertainingtofinancialdevelopment,accesstofinancialservicesandthesoundnessofthebankingsectorandfinancialmarkets.
-Productmarkets,whichcontainsstructuralindicatorsoncompetition,informality,andadministrativeandregulatoryburdensinproductmarkets.
-Labormarkets,whichincludesstructuralindicatorsrelatedtominimumwagesandotherregulationsthataffectlabormarketflexibility.
-Taxpolicy,whichcapturesdistortionsinincentivesassociatedwithvarioustaxes.
-Tradeandopenness,whichcoverstariffsandnon-tariffbarrierstotrade.
Weexcludecyclicalfinancialindicators,whichreflectthebusinesscycleratherthanqualityoffinancialinstitutions.1
Datacoveragevariesalotbycountryandyear,andthemissingpatternissystematicasopposedtomissing-at-random.Forexample,severalindicatorsareonlyupdatedeveryotheryearwhilecoverageforseveralindicatorsonlystartinrecentyears.Asafirstpassinimputing
missingvalues,wetakefive-yearaveragesofindicatorsstartingintheyearof2000.Toavoiddeflatingthevariance,weonlyretainthedataforeveryfiveyears.Wethenexcludeindicatorsthatmissingmorethan20%ofthevaluesandimputetherestofmissingvaluesbyamultipleimputationprocedureasdescribedinAppendix
0
Thereisnosimplerecommendationforamaximumproportionofmissingvaluesthatcanbeproperlyconsideredinimputationmethods.Theresultsstarttobeunstableforathresholdabove20%andweleaveittofutureresearchtogaugetheoptimalamountofimputation.
1Examplesofthecyclicalfinancialindicatorsarethevolumeoftotalsyndicatedloansissuedandavailabilityofprivatecredit.
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B.SyntheticstructuralscoresviaPartialLeastSquares
Giventhehighnumberofstructuralindicators,dimensionalityreductionisnecessarytoimproveinterpretabilityforfurtheranalysis.Wemakethefollowingobservationsontheseindicators:
-Wewanttocaptureindicatorsassociatedwithstrongeconomicperformance,whichcanbemeasuredwiththeabilitytopredicthighfuturepercapitaGDP.
-Theindicatorscanbehighlycorrelatedwithinandacrossstructuralareas.
-Wehavemanyindicatorsrelativetothesamplesize.Thereare275indicators,whichissubstantialcomparedtoasamplesizeof504(126countriesand4timeperiodsin2000-04,2005-09and2010-14,2015-19).
Theseobservationsmotivatetheappropriateapproachtodimensionalityreduction.Thena?veapproachforpredictionistoestimatealinearregressionontheseindicators,andusethepredictedvalueasthecompositescore.However,whentherearemanycorrelatedvariablesinalinearregressionmodel,theircoefficientscanbecomeunstable:alargepositivecoefficientononeindicatorcanbecanceledbyasimilarlylargenegativecoefficientonitscorrelatedindicator.LASSOimprovesuponlinearregressioninallowingforhigh-dimensionalindicators,whichassumesthereareonlyafewpredictorsfortheoutcomevariable.Whilethisassumptionismorelikelytoholdincertainsettingssuchaspredictingnon-performingloansinArietal.(2021),itisunlikelytoholdforouroutcomevariable,logoffuturepercapitaGDP(inPPP).Consequently,LASSOwouldreducethedimensiontoomuchandresultinpoorpredictiveperformance.
Anothercommondimensionalityreductiontechniqueisprincipalcomponentanalysis(PCA),whichseeksaweightedaverageoftheindicatorsthathavehighvariationacrosscountries.Thishastheadvantageofmakingfulluseoftheavailableinformationtominimizenoiserelatedtoanyindividualstructuralindicatoranditalsoprovidesaweightingschemethataccountsforthecorrelationbetweenindividualindicators.However,thisapproachperformspoorlywhenwehaveredundantindicators.2
Partialleastsquares(PLS)isaflexiblemachinelearningtechniquethatachievesbothgoalsandisappropriateforoursetting(Hastieetal.,2009).PLSimprovesuponPCAbyaddingapredictivemodel.ToreceivehighweightsunderthePLSweightingscheme,theindicatorsalsoneedtobepredictiveoftheoutcome.PLSalsoimproveslinearregressionbyaccountingforthecorrelationbetweenindividualindicators.UnlikeLASSO,PLSdoesnotassumeonlyfewindicatorsarepredictiveoftheoutcome.InAppendixC,wealsoillustratetheadvantagesofPLScomparedtoscoresthatarebasedonsimpleaveragesofstructuralindicators.BelowweprovidefurtherdetailsaboutthePLSmethod.
2Forexample,theeconomicfreedomindexfromtheFraserInstituteisconstructedbasedondatafromWDI,theWEFGCR,theWGI,andtheWBDoingBusiness.ThereforetheFraserInstituteindicatorsareredundantwhenweincludetheirsourceindicators.Whileitispossibletomanuallyremovesuchredundancybasedonacarefulexaminationofthedatasourcesoftheindicators,wefocusonadata-drivenapproach.
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C.PLSestimationprocedure
LetXtdenotethevectoroftheindicatorsincountryiattimet.Eachindicatorvectorisfromoneofthesixstructuralareasc.Lettheindexjfurtherdenotethesubcategoryoftheindicatorwithinthestructuralarea.ThePLSmethodestimatesthefollowingpredictivemodelforthefive-year-aheadpercapitaGDP(yi,t):
c
yi,t=a+∑∑em∑yjc,mXt,j+ei,t
mj
(1)
wheremindexesthenumberofcomponentsused.BecausetheLHSofEquation(1)isthefive-year-aheadpercapitaGDP,weusethelargestpossiblesamplewithindicatorsfrom2000-2010toestimateEquation(1).Howeversinceweaimforgoodpredictiveperformance,wecannotjustchoosethenumberofcomponentstomaximizethein-samplefitfor2000-2010whenweestimateEquation(1).Wethereforeuseleave-one-outcross-validationtodeterminethenumberofcomponents,whichsuggeststhateightcomponentsprovidethebestpredictiveperformance.
Unlikethelinearmethodthatminimizesthein-samplepredictionerror,thePLSmethodestimatesequation(1)usinganiterativeprocedureconsistingofthefourstepsdescribedbelow.Thisprocedureprovidesanimplicitregularizationonthemagnitudeofthecoefficients(seestep4)oftheprocedure,whichimprovesuponthelinearmethod.Operationally,weusetheRlibraryplsrtoimplementthePLS.
Initializetheright-hand-side(RHS)ofequation(1)withtheoriginaldataX=Xtandinitializethepredictedleft-hand-side(LHS)withthesamplemeanoftheoutcome=.NotetheRHS
isstandardizedtobemeanzeroandstandarddeviationone.Forthem-thcomponents,thePLSalgorithmproceedsasthefollows:
1)Formthecomponentbasedontheoriginalinputs
c
zm=∑X(2)
where=cov(Xyi,t)isthecovariancebetweentheoriginalinputsandtheoutcome;
2)CalculatethecoefficientinfronttothecomponentastheOLScoefficientofregressingthe
outcomeonthecomponent
(3)
m=
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3)Predicttheoutcomeusingallcomponentssofaras=+mzm
(4)
4)OrthogonalizexwithrespecttothecomponentzmtogettheupdatedinputxThisensuresthenextcomponentzm+1,whichisaweightedaverageofxisuncorrelatedwithzm.Thecorrelationacrossindicatorsisaccountedforinthisstep.Furthermore,theupdatedinputxisaweightedaverageoftheoriginalinputsxwithweightsreflectingthecovarianceacrosstheoriginalinputsandtheircovariancewiththeoutcome.
D.SyntheticstructuralscoreasthepredictedvaluefromthePLSmodel
Weconstructthesyntheticstructurescorefor2000-2015inagivencategorycasthepredictedvaluefromthePLSmodel(1),predictedusingthe2000-2015indicators.Specifically,thesyntheticstructuralscoreisthepredictedvalueusingthePLScoefficientestimatesmandallcomponentszm:
mzm=m∑cxm?1)(5)
whichisaweightedaverageoftheoriginalindicatorsasexplainedabove.Therefore,wecanexaminetheindicatorsthatreceivethelargestweightstoconfirmwhetherthecompositescoresareinterpretable.
Table1
tabulatesindicatorswithlargeweightsforeachstructuralarea.ThesesubcategoriesmostlycoincidewiththoseselectedbyIMF(2019)toassessstructuralperformanceintheseareas.ThisprovidescredibilitytothePLSmethodforselectinghighlyinterpretablesubcategoriesinconstructingthescores.Tomakescorescomparableacrossstructuralareas,forfurtheranalysiswestandardizeeachscoretohavezeromeanandunitvariance.Ifacountryscoresoneinthefinancialcompositebutminusoneinthebusinessenvironmentcomposite,thenthiscanbeinterpretedasitsstructuralperformanceinthefinancialareacontributingonestandarddeviationmoretoitspercapitaGDPthananaveragecountry,whiletheoppositeistrueforitsperformanceinthebusinessenvironmentstructuralarea.
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Table1.Keystructuralindicatorsinthecompositionofcompositestructurescores
Note:Greylinesrepresentsubgroupsofindicatorsthatcontributeheavilytowardthecompositescoreswithineachstructuralarea.Eachlinebelowthegreylinelistsexamplesofthestructuralindicatorinthesesubgroups.
Basedonthecompositeindicators,thereareflatteningtrendsacrossthestructuralareasasshowninFigure2.Sincestructuralcompositesareconstructedtopredictoutputlevels,anupwardtrendinthecompositecanbeinterpretedasameasureforstructuralreforms(i.e.,improvementsinstructuralperformance),andtheslopesofthesetrendscanbeinterpretedasameasureforreformspeed.Therehavebeenstructuralreformsinmostareasexceptlegalsystem,wherereformssloweddowninrecentyears.ThistrendisconsistentwithIMF(2019),whichfindsstabilizationofpoliciesinmanystructuralareasinlate2000s,andnoimprovementinthelegalsystem.Insteadofstructuralindicators,IMF(2019)measuresstructuralreformsbasedonderegulations.ThefactthatcompositescorespresentsimilarstylizedfactswithIMF(2019)lendsvaliditytoourapproachofaggregatingstructuralindicators.
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Figure2.Trendsofstructuralcompositebystructuralareas
Note:Thehorizontalaxisindicatesthefive-yearwindowthestructuralindicatorsarecollected.Thelinesplottheaverageofthecompositeacrosscountries.Thecompositesarestandardizedtohavezeromeanandunitvarianceacrossallcountriesandyears.
Thepatternofstructuralreformvariesacrossincomeregionasshownin
Figure
33.ThereisalargegapbetweenthestructuralcompositesofEMsandLICsandthoseofAEsintheareaofbusinessenvironment,labormarket,legalsystemandtradeandopenness.Despitestrongpushforreforms,thisgapsuggeststhatEMsandLICshavesubstantialreformdeficitintheseareas,inlinewiththeconclusionofIMF(2019).Nonetheless,LICshaveshownimprovementinlabormarket,reflectedinanupwardtrendinthecompositescores.
Table2
furthershowstheslowdowninlegalreformsiscommontoallgeographicregions.
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Figure3.Trendsofstructuralcompositeacrossincomegroups
Note:Thehorizontalaxisindicatesthefive-yearwindowthestructuralindicatorsarecollected.Thelinesplottheaverageofthecompositeacrosscountriesinagivenregion.Thecompositesarestandardizedtohavezeromeanandunitvarianceacrossallcountriesandyears.
Table2.Shareofcountriesthatexperienceincreasesinstructuralcomposites
Note:Redreflectslowreformactivities.Greenreflectsreformactivities.
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III.StructuralIndicators
A.Impactofstructuralreformsongrowth
Theimpactofstructuralreformsongrowthisfirstestimatedusingcross-countryregressions.Letiandtindexcountryandeachofyearwindows:2000-2004,2005-2009,2010-2015,and2016-2019.WetakethefiveyearaverageofGDPgrowthrategi,t.WeuseSttodenotethecompositestructuralscoreforeachofthesixstructuralareas.Wemeasurestructuralreformasthechangeinthestructuralcomposite,whichisdenotedwith」St?1.Sinceweareinterestedinmarginalimpactofstructuralreforminanygivenarea,holdingotherareasconstant,weestimatethe5-yearcumulativegrowthimpactusingthefollowingregressionspecification
gi,t=ai+yt+Fs」St?1+wxxi,t?1+ei,t
whereaiisavectorofcountryregionfixedeffectsanddummiesforemergingmarketeconomiesandoilexporters,3andytaretimefixedeffects.Thesetofcontrolvariablesxi,tincludesinitialeconomicconditionsasmeasuredbythepercapitaGDPlevelin2000,theVIXvolatilityindexinteractedwithexternaldebt,theVIXvolatilityindexinteractedwithcurrentaccountdeficits,andvulnerabilitytooilpriceshocksasmeasuredbytheinteractionoftheoilexporterdummywithoilprices.TheregressioncoefficientFscanbeinterpretedasthereformelasticityofgrowthforagivenstructuralarea.
Table3presentstheestimatedregressioncoefficients,andeachcolumnvariesthespecificationbyalternatingfixedeffectsandcontrolvariables.Theestimatesarerobusttovariousspecifications:onestandarddeviationincreaseinthecompositescoresforbusinessenvironment,financialandlabormarkets,legalsystemhaveasignificantpositiveimpactongrowth,rangingfrom2to6%,holdingotherstructuralareasconstant.However,tradeandtaxpolicyreformshaveastatisticallyinsignificantimpactongrowth.
3Theseareconstructe
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