IMF-結(jié)構(gòu)改革與經(jīng)濟(jì)增長(zhǎng)：機(jī)器學(xué)習(xí)方法（英）

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.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND2

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

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND3

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.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND4

Figure1.Structuralindicatoroverview

Sourcesofstructuralindicators

Areasofstructuralindicators

Usingthesyntheticstructuralscores,wefindsignificantgrowthimpactsfromreformsincertainstructuralareas,aswellassynergiesbetweendifferentstructuralareas.Ourfindingssuggestthatstructuralreformsintheareasofproduct,laborandfinancialmarketsaswellasthelegalsystemhaveasignificantimpactoneconomicgrowthina5-yearhorizon,withonestandarddeviationimprovementinoneofthesereformareasraisingcumulative5-yeargrowthby2to6percent.Wealsofindsynergiesbetweendifferentstructuralareas,inparticularbetweenproductandlabormarketreforms.

Thepaperisorganizedasfollows.SectionIIoverviewsthedataanddiscussesourapproachtoimputingmissingindicators.SectionIIIappliesPLStoconstructsyntheticstructuralscoresbasedontheimputedindicators,controllingforthecorrelationamongtheindividualstructuralindicators,andassigningtheweightstoreflecthowpredictivetheindicatorsareforoutput.SectionIVusesthesyntheticstructuralscorestoanalyzetheimpactofstructuralreformsongrowth.Finally,SectionVconcludes.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND5

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.

INTERNATIONALMONETARYFUND6

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.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND7

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=

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND8

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.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND9

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.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND10

Figure2.Trendsofstructuralcompositebystructuralareas

Note:Thehorizontalaxisindicatesthefive-yearwindowthestructuralindicatorsarecollected.Thelinesplottheaverageofthecompositeacrosscountries.Thecompositesarestandardizedtohavezeromeanandunitvarianceacrossallcountriesandyears.

Thepatternofstructuralreformvariesacrossincomeregionasshownin

Figure

33.ThereisalargegapbetweenthestructuralcompositesofEMsandLICsandthoseofAEsintheareaofbusinessenvironment,labormarket,legalsystemandtradeandopenness.Despitestrongpushforreforms,thisgapsuggeststhatEMsandLICshavesubstantialreformdeficitintheseareas,inlinewiththeconclusionofIMF(2019).Nonetheless,LICshaveshownimprovementinlabormarket,reflectedinanupwardtrendinthecompositescores.

Table2

furthershowstheslowdowninlegalreformsiscommontoallgeographicregions.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND11

Figure3.Trendsofstructuralcompositeacrossincomegroups

Note:Thehorizontalaxisindicatesthefive-yearwindowthestructuralindicatorsarecollected.Thelinesplottheaverageofthecompositeacrosscountriesinagivenregion.Thecompositesarestandardizedtohavezeromeanandunitvarianceacrossallcountriesandyears.

Table2.Shareofcountriesthatexperienceincreasesinstructuralcomposites

Note:Redreflectslowreformactivities.Greenreflectsreformactivities.

IMFWORKINGPAPERSStructuralReformsandEconomicGrowth:AMachineLearningApproach

INTERNATIONALMONETARYFUND12

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