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PolicyResearchWorkingPaper10991

TheOnlyWayIsUp?

EconomicMobilityinMalaysiainthe21stCentury

GertonRongenPeterLanjouw

WORLDBANKGROUP

PovertyGlobalDepartmentDecember2024

PolicyResearchWorkingPaper10991

Abstract

Thisstudydocumentsshort-termeconomicmobilityinMalaysiaoverthefirsttwodecadesofthetwenty-firstcen-tury,atthepopulationlevelandforvarioussubgroups.Thefindingsshowbroadandsteadyimprovementsinwell-being,asevidencedbylargedecreasesinchronicpovertyandsig-nificantincreasesinpersistenteconomicsecurity.Thestudyemploysasyntheticpanelapproachbasedonnationallyrepresentativemicro-leveldatafor2004–22,witharefine-mentthatallowspresentingbootstrappointestimatesandstandarddeviations.Inaddition,thestudyinvestigatessev-eralpovertyandvulnerabilityscenarios,aswellasrelativemobility.First,theresultsindicatethatchronicpovertyhasdecreasedto2–3percentofthepopulation.Nevertheless,

progressisnotuniform:around15percentofthepopula-tioninruralEastMalaysialivesinchronicpoverty.Second,thestudyfindsconsiderableincreasesinsustainedeconomicsecurity—theextentofimprovement,however,dependsontheapproachandincomethresholdsthatareusedtodefinesecurity.Moreover,ethnicandregionaldifferencesinsecurestatusaresizableathigherincomeclassthresholds.The

largestdifferencesareofaregionaldimension:anindivid-ualinurbanPeninsularMalaysiaismorethanthreetimesmorelikelytoliveineconomicsecuritythansomeoneinruralEastMalaysia.Altogether,thestudyobservesupwardmovementacrosstheboardbutlittleevidenceofdramaticchangesintherelativepositionsofsocietalgroups.

ThispaperisaproductofthePovertyGlobalDepartment.ItispartofalargereffortbytheWorldBanktoprovideopenaccesstoitsresearchandmakeacontributiontodevelopmentpolicydiscussionsaroundtheworld.PolicyResearchWorkingPapersarealsopostedontheWebat

/prwp.Theauthorsmaybecontactedata.g.m.j.rongen@vu.nl

.

ePolicyResearchWorkingPaperSeriesdisseminatesthendingsofworkinprogresstoencouragetheexchangeofideasaboutdevelopmentissues.Anobjectiveoftheseriesistogetthendingsoutquickly,evenifthepresentationsarelessthanfullypolished.epaperscarrythenamesoftheauthorsandshouldbecitedaccordingly.endings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.eydonotnecessarilyrepresenttheviewsoftheInternationalBankforReconstructionandDevelopment/WorldBankanditsaliatedorganizations,orthoseoftheExecutiveDirectorsoftheWorldBankorthegovernmentstheyrepresent.

ProducedbytheResearchSupportTeam

TheOnlyWayIsUp?EconomicMobilityinMalaysiainthe21stCentury

GertonRongen*aandPeterLanjouwa

JELcodes:C53,D31,D63,I32,O53

Keywords:Povertydynamics,incomemobility,ethnicinequality,regionalinequality,Malaysia,syntheticpanels

ThispaperwascommissionedbytheWorldBank’sPovertyandEquityGlobalPractice,EastAsiaandthePacificUnit(EEAPV)forthereportAFreshTakeonReducingInequalityandEnhancingMobilityinMalaysiaundertheprojectMalaysiaEquityandInclusion(FY23-25).ThereportwasledbyLauraRodriguez,RirinPurnamasariandMatthewWai-Poi.

Acknowledgments:theauthorswouldliketothankChrisElbersforhisinvaluablesuggestions,as

wellasLauraRodriguez,RirinPurnamasariandMatthewWai-Poifortheircommentsandreflections.

*Correspondingauthor:a.g.m.j.rongen@vu.nl

aVrijeUniversiteitAmsterdam;AmsterdamInstituteforGlobalHealthandDevelopment

1.Introduction

ThisstudyanalyzespovertydynamicsandeconomicmobilityinMalaysiaovertheperiod2004-2022.Wemakeuseofasyntheticpanelbasedonnationallyrepresentativecross-sectionalmicrodatatoinvestigatethemovementsofMalaysianhouseholdsacrosstheincomedistribution.Wetakethreeperspectives:first,westudymobilityatthelowerendofthedistributionbyfocusingonpovertydynamics.Second,wetakeabroaderviewofeconomicmobilitybydividingthedistributionintothreegroupsandanalyzingupwardanddownwardmobilityalongthosedimensions.Finally,weassessrelativemobilitybyconsideringtransitionsacrossquintilesovertheentireincomespectrum.

ThisstudybuildsonthefindingsofRongenetal.(2024)infourways.First,itextendstheanalysisbyincludingsurveydataon2019and2022.Second,ittakesanexpandedviewbyexplicitlyanalyzingvariousscenariosforsettingthepovertylineandforincorporatingtheconceptsofvulnerabilityandeconomicsecurity.Third,itgivesthefirstestimatesofrelativemobilitybasedonthesemicrodata.Lastly,weintroduceamethodologicalrefinementsuchthatweareabletopresentbootstrappointestimatesforalltransitions,whereasthepreviousstudyestimatedupperandlowerboundsonmobilityonly.

WeconcludethatthepictureofeconomicmobilityinMalaysiaovertheperiod2004-2022isgenerallypositive,withlargereductionsinchronicpovertyandagrowinggroupthatweclassifyaseconomicallysecure.However,thesegainsarenotuniformanddependonhowwedefineincomegroups,andonwhichpopulationsubgroupweconsider.ChancesofremainingpoorandoffallingintopovertyarehighestinruralEastMalaysia.Moreover,attainingeconomicsecuritythroughsustainedupwardmobilityisparticularlydifficultinruralEastMalaysiaandforEastMalaysiaBumiputeras,twogroupsthatoverlaptoanimportantextent.Downwardmobilityseemstohaveincreasedforthesegroups.Lastly,relativemobilityresultsshowconsiderablepersistenceinthepositionofsizeablegroupsateitherthebottomorthetopofthedistribution.Overourstudyperiod,wedonotobserveepisodesofgreaterrelativemobility–theorderingofMalaysiansocietyasexpressedthroughitsincomedistributiondidnotexhibitmajorchanges.

Thepaperproceedsbydiscussingmethodologyanddatainthenextsection.Thereafter,weprovideresultsin

section3,

whichconsistsofthreesubsections.Wedrawsomeconclusionsinthefinalsection.

1

2.Methodologyanddata

1

2.1.Boundestimatesforpovertydynamics

ThissectionsummarizestheapproachpresentedinDangetal.(2014).Ouraimistoestimatejointandconditionalprobabilitiesofpovertydynamics.Forexample,wewishtoknowthelikelihoodthatanindividualispoorinsurveyround1andnon-poorinround2,ajointprobabilitywhichwecanwriteasfollows,denotingpercapitaincomebyyiandthepovertylinebyz:

P(yi1≤z1andyi2>z2).

Alongsideevidenceonjointprobabilities,wearealsointerestedinconditionalprobabilities.Forinstance,wemightwishtoestimatethelikelihoodofmovingoutofpoverty,conditionalonbeingpoorinitially.Suchaconditionalprobabilitycanbewrittenas

andcanbecomputedstraightforwardlyfromthejointprobabilities,astheright-handsideoftheequationshows.PaneldataarenotavailableinMalaysia.Intheabsenceofsuchdata,wedonotobserveincomesinround1andround2forthesameunitiandwouldnormallynotbeabletoestimatetheseprobabilities.However,themethodwedescribebelowdrawsoncross-sectionaldataandyieldsbothupperandlowerboundsforeachofthefourpossibleoutcomesofthedynamicprocess,inbothconditionalandunconditionalterms.

Wemodelthelogarithmofpercapitaincomeineachroundasalinearfunctionoftime-invarianthouseholdcharacteristicsandanindividualerrorterm.Schematically:

yi1=βxi1+εi1

and

yi2=βxi2+εi2.

Thebasicideaofthemethodistousetime-invarianthouseholdcharacteristicsxitopredicthouseholdpercapitaincomefortheyearinwhichtheactualobservationislacking.Suchcharacteristicswillbe

1ThissectionislargelybasedonthedescriptionofmethodologyinRongenetal.(2022).

2

unchangedacrossthetworounds.Mostly,theywillbecharacteristicsofthehouseholdhead,suchastheyearofbirth,educationalattainment,ethnicityorreligionandbirthdistrict.Inaddition,ifthesurveyincludesretrospectivequestions,thesecouldalsobeincluded,e.g.,ifthehouseholdownedacarortelevisionatthetimeoftheprevioussurvey.Aswehavedataforeachsurveyround,weestimatethecoefficientvectorβonthesetime-invariantexplanatoryvariables.

Inpracticalterms,wepredicttheround1incomeforhouseholdsintheround2surveybymultiplyingthecoefficientvectorresultingfromtheround1regression(β1)withthecharacteristicsofhouseholdsinround2(xi2).Thispredictionlooksasfollowsfortheobservationsiofround2,withtheadditionofanerrortermestimate:

一

i1=βxi2+i1.

Weturnfirsttotheassumptionsunderlyingthisapproachandwillthendiscusshowestimatesfortheerrortermareobtained.

Themethodforestimatingboundsonpovertytransitionquantitiesispredicatedontwoimportantassumptions.First,weneedtoassumethattheunderlyingpopulationfromwhichthedataaresampledisthesameinbothsurveyrounds.Thisimpliesthatthemethodcannotbeappliedincaseswheretherearelargeshockstothepopulation,forexample,ifthereweremassivemigrationintooroutofthecountry.Moreprecisely,wewanttoensurethattheincomemodelcoefficientsthatweestimateinround1aregoodpredictorsforwhattheround1incomeofthehouseholdssurveyedinround2wouldhavebeen.Hence,toensurestabilityofthereferencepopulation,weonlyincludehouseholdswhoseheadsarebetween25and60yearsinsurveyround1.

2

Second,weneedtomakeassumptionsabouttherelationshipbetweentheerrortermsεi1andεi2.Specifically,weassumethattheseare,onaverage,positivelycorrelatedovertime.Inthepresenceofhousehold-specificeffectsandpersistenceofshocks,thisdoesnotseemtobeanunreasonableassumption.Insettingswherepaneldataareavailable,thecorrelationcoefficientoflogincomePcanbeestimateddirectly,andindeedstudiesreportvaluesbetween0.53and0.89acrossavarietyofcountries(Dangetal.(2014);Colgan(2023,2024).Wedonotmakefurtherassumptionsabouttheshapeofthedistributionoftheerrortermsfortheseboundestimates;inthatsense,theresultingboundsonpovertytransitionsarenon-parametric.

Theupper-andlower-boundestimatesformobilityderivefromtwoextremecasesoftheassumedrelationshipbetweentheerrorterms.Itisimportanttonotethatupperboundsofmobility

2Thisagerangeischosensothatformationofnewhouseholdsanddissolutionofexistinghouseholdsshouldbeataminimum.Moreover,itensuresthatinround1headswillgenerallyhaveobtainedtheirmaximumlevelofeducation.

3

correspondtothelowerboundofimmobility,i.e.,remainingpoororremainingnon-poor,andviceversa.Throughoutthepaper,upper-boundestimateandlower-boundestimaterefertoupperandlowerboundsofmobility.

Atoneextreme,weconsiderthecaseofP=0,whichcorrespondstotheupper-boundmobilityestimate.Inthisscenario,theerrorsareuncorrelatedandmobility,givenhouseholdcharacteristics,willbeatamaximum,bothoutofpovertyandintoit.Becauseweassumethaterrorsinfactarepositivelycorrelated,onaveragetheupperboundwillbestrictlylargerthanactualmobility.Predictedupper-boundround1incomeforhouseholdisurveyedinround2willbe:

u=′xi2l1,

~

wherel1isaresidualrandomlydrawnfromtheactualdistributionofresidualsresultingfromestimatingtheincomemodelontheround1data.

3

Basedonthepredictionsthusobtained,wecanestimatetheprobabilityofeachpovertytransitionforeachobservation.Aggregatingthesequantitiesatthepopulationlevel,weobtainthecountry-levelpovertydynamics.

4

Duetotherandomnatureofthisprocess,thesestepsarerepeatedRtimes,withR=100inthisapplication,andaveragedtoobtainarobustestimateoftheupperboundofmobility.

Attheotherextreme,ourlower-boundestimatesassumeaperfectpositivecorrelation

betweentheerrors:P=1.Inthiscase,averagemobilitywillbeatitsminimum.Fortheestimation,thismeanswesimplytaketheestimatedround2residual,scaleitbyY,andaddittothefittedround1income:

5

L=′xi2+Yi2.

Analogoustotheupper-boundscenario,butwithouttherepetition,weobtainthelower-boundpopulation-levelpovertydynamicsestimates.Conditionalprobabilitiesaresubsequentlycomputedfromthepopulation-orsubgroup-leveljointprobabilityestimates.

3IncontrasttoRongenetal.(2024),wedoapplypopulationweightsindrawingthisrandomsampleofresiduals,inresponsetoadiscrepancywefoundbetweenthepreviouslyestimatedboundsandproposedbootstrappointestimatesthatwediscussfurtherdown.Theresultingchangestoboundestimatesareminor,andmobilitytrendsremainunaffected.

4Inouranalysistheregressionsareatthehouseholdleveltakinglogpercapitahouseholdincomeasthedependentvariable.Transitionprobabilitiesforeachhouseholdarepopulation-weightedwhenweaggregate,sothatthecountry-levelfiguresrepresentpopulationproportions.

5WeuseascalingfactorY=ε1⁄ε2toadjustforthedifferenceinerrorvariancebetweenthetworounds(εisthestandarderroroftheresiduals).

4

2.2.Bootstrappointestimates

WeproposeaBayesian-inspiredinnovationtothesyntheticpanelmethodthatallowsustopresentpointestimatesoftransitionquantities.

6

Ourpointofdepartureisasfollows:wedonotknowtheactualdegreeofhouseholdincomecorrelationinMalaysia,butseveralpanelstudieshavedocumentedsuchcorrelationsovertimeforarangeofcountries.WeassumethatthetruevaluesforMalaysiawillbesomewhereinthisrangeofempiricalcorrelations.Ourproposition,then,isthatabootstrapsampleoftheseempiricalincomecorrelations,coupledwiththeassumptionthatresidualsfollowabivariatenormaldistribution,yieldsameaningfulpointestimatefortransitionquantities,andplausiblestandarddeviations.Obviously,wedonotknowwhattheactualMalaysiancorrelationsareineachinterval,sothatwewillfocusonthebandwidtharoundthepointestimate,ratherthantheactualestimateitself.

OurpointestimatesarebasedonthemethodputforwardbyDangetal.(2014),thesamepaperthatintroducedboundestimates.Precisioncomesatthecostofintroducingadditionalassumptions,however.Notably,weassumethattheerrorsofourincomemodel,εi1andεi2,followabivariatenormaldistributioncharacterizedbythecorrelationcoefficientp.Wederivehypothesizedvaluesforthecorrelationoftheerrorterms(p)bydrawingonincomecorrelationcoefficients(py1y2)fromactualpaneldatainothercountries.DangandLanjouw(2023)providethefollowingpropositionfordoingso:

Theequationcombinesmeasuresofthevariationinourdatawithahypotheticalincomecorrelationtoarriveatanestimateofp.OursampleoftheincomecorrelationshasbeenobtainedfromColgan(2023,2024)andDangandLanjouw(2023),whoprovideactualpanelcorrelationsforfourteencountriesintheEU-SILCdatabaseandtheUnitedStates.

Westandardizetheseempiricalcorrelationstoatwo-yearreferenceinterval,sincethecorrelationsreportedcoveredintervalsofdifferentduration.Subsequently,wedrawabootstrap

6Dang&Lanjouw(2023)alsopresentamethodtoobtainpointestimates,whichdependsoncohort-levelincomecorrelationstoinferhousehold-levelcorrelation.However,therobustnessofthismethodisnotgenerallyaccepted.Instead,wemakeuseofdocumentedempiricalmeasurementsofhousehold-levelcorrelationinothercountries.

5

sampleofsize100fromthesestandardizedcorrelations.

7

Foreachdraw,weestimatetransitionprobabilitiesforallintervalsofadjacentsurveyroundsinourdata.Byinterval,wefirstcomputetheresultingerrorcorrelation,andthenemploythebivariatestandardnormalcumulativedistributionfunctionΦ2(.)toobtainestimatesforallpovertytransitionprobabilities,e.g.asfollowsforthepoortopoortransition

8

:

Foreachdraw,householdlevelresultsareaggregateduptopopulationandsubgrouplevel.Then,averagingoverall100drawsyieldsthebootstrapmeanprobabilities,ourpointestimates,andallowsustocomputestandarddeviationsoverthe100draws.

2.3.Vulnerability

Weanalyzevulnerabilityandtheachievementofeconomicsecurityintwoseparateways.OneapproachisbasedonthedefinitionofavulnerabilitylineasintroducedbyDangandLanjouw(2017).Below,wesummarizethisapproachandexplainhowittiesinwiththesyntheticpanelmethod.Ourgoalistoestimate3x3transitionmatricesfortheincomecategoriespoor,vulnerableandeconomicallysecure.

9

Thisapproachfocusesonthelowerpartoftheincomedistribution,whichisreflectedinourchoiceofincomecategories.Wenotethatonceanindividualreachesthesecurecategory,thereisnofurtherscopeformobilityinthisset-up.Furtherdown,weoutlinetwootherscenariosthatareabletoshedlightonmobilityhigheruptheincomedistribution.

Westartbydefiningthecategory‘vulnerable’asthosenon-poorinperiod1whofaceacertain

probabilityPvorhigheroffallingintopovertyinperiod2.Thisconditionalprobabilitycanbedenotedas:

7Wealsousedmaximumlikelihoodestimationtofitbetaandnormaldistributionstotheempiricaldata,fromwhichwethenwouldhavebeenabletodrawasampleofcoefficients.However,thefitofthesetheoreticaldistributionswasnotcompletelysatisfactory,suchthatwepreferredtostickwiththeempiricaldistribution.

8WerefertoEquations20-23inDangetal.(2014)foralltransitionformulae.

9Therearenogenerallyagreeduponnamesforthesecategories.Insomeapplications,thenon-poorwhoarenotconsideredvulnerablehavebeenlabelled‘middleclass’.Weoptforthemoreneutral‘economicallysecure’.Onereasonisthatsomeofthesehouseholdswillbequiterich,sothatmiddleclasswouldbeamisnomerforthem.

6

wherev1standsforthevulnerabilityline.ThelatterisderivedempiricallyatpopulationlevelaftersettingthevulnerabilityindexPv,thehighestprobabilityoffallingintopovertythatwearewillingtoacceptbeforewenolongerconsiderahouseholdtobeeconomicallysecure.Forexample,wemightsettheindexPvatavalueof20percent.Ifahouseholdfacedaprobabilityoffallingintopovertygreaterthan20percent,wewouldconsiderthishouseholdtobevulnerable.Formally,thevulnerabilitylineisthenderivedfromthisindexasfollows

10

:

max{v1|P(y2≤z2|z1<y1≤v1)≥Pv}

Thisapproachcontrastswithotherapproachesinthesensethatthevulnerabilitylineisnotsetarbitrarily,forexampleat1.5timesthepovertyline,butderivedempiricallyfromthevulnerabilityindex.Inpractice,thisrequiresarecursivealgorithmthatgoesoverthesyntheticpaneldatatoarriveatthevulnerabilitylinethatyieldsthedesiredvulnerabilityindex.Weacknowledgethatsettingthevulnerabilityindexisstillanarbitrarydecision,butitisbasedonatransparentweighingofrisksthatevokestheinsecuritythatisinherenttovulnerability.

Wemostlypresentresultsforpovertyandvulnerabilitydynamicsinfiguresthatdonotindicatethelevelofprecisionoftheestimates.Themainreasonforthisisthattheresultsalreadyconsistofboundsthatincorporateuncertaintyabouttheerrorsinourincomemodel.Theboundsarehighlylikelytocontainthetruevalueoftheprobabilityestimates,aswasconfirmedinothersettingsbyDangetal.(2014)andHéraultandJenkins(2019).Inaddition,samplesizesforeachroundarelarge,sothatthestandarderrorsofourestimatorsaregenerallysmall.

ThesecondapproachisbasedonamethodforanalyzingvulnerabilityintroducedbyChaudhuri(Chaudhurietal.(2002);Chaudhuri(2003)).

11

Here,weagainconceiveofvulnerabilityasacertainprobabilityoffuturepoverty,withtheimportantfeaturethatahouseholdthatiscurrentlypoormaynotnecessarilybevulnerable:itscharacteristicscouldmakethelikelihoodofpovertyinthenextperiodlow,butitcouldhaveanincomebelowthepovertylinethisperiodduetosomeshock.Ahousehold’sprobabilityoffuturepoverty,i.e.itsChaudhurivulnerability,isestimatedasfollows:

whereitisassumedthattheerrortermoftheregressionfollowsanormaldistribution.Theprobabilitythathouseholdincomeyℎwillbebelowthepovertylinez,givenhouseholdcharacteristicsXℎ,isthen

10Recallthatweareassumingapositivecorrelationbetweentheerrorsinourincomemodel,whichensuresthatP(y2≤z2|z1<y1≤v1)isdecreasinginv1.

11OnereasonforincludingthisapproachisthattheWorldBankusesitacrosstheEastAsiaPacificregiontodefinevulnerabilitylinesbasedonaconsistentmethodology,seeKrahetal.(forthcoming).

7

derivedfromthestandardnormalcumulativedensityfunctionΦ(.),withestimatedexpectationand

^^

varianceofxhβandxhθrespectively.

Weapplythismethodprimarilytoderiveaggregateincomethresholdsthatseparatethefollowingthreegroups:thepoorandvulnerable,theaspiringmiddleclass,andthemiddleandupperclass.

12

Notethatthegroupinginthisscenariodiffersconsiderablyfromtheclassificationinthepreviousscenario.LetuscallthethresholdbetweenthefirsttwogroupsinthisscenariotheChaudhurivulnerabilityline,andthelinedividingthelasttwogroupsthemiddleclassline.TheChaudhurivulnerabilitylineistheaveragepredictedpercapitaincomeofthegroupofhouseholdsthathaveacertainprobabilityofbeingpoorinthefuture,10percentinourapplication.Buildingonthis,themiddleclasslineistheaveragepredictedincomeofhouseholdswithacertainprobabilityofbeingvulnerable,again10percentinourapplication.Householdsarethenclassifiedintothethreegroupsaccordingtothesetwolines.

2.4.Relativemobility

Sofarwehavedetailedhowweanalyzemovementspastcertainfixedmonetarygoalposts.Alimitationofsuchabsolutemobilityanalysisisthatwhathappensoncehouseholdsmovecomfortablybeyondsuchthresholdsisoutofouranalyticalscope.Analyzingrelativemobilityacrossthefivequintilesoftheincomedistributionenablesustotakeabroaderviewandtoconsidermovementsalongtheentireincomespectrum.Quintilethresholdsaredeterminedbasedonthecross-sectionalincomedistributioninagivenyear,sotheydifferfromyeartoyear.Thesyntheticpanelisthenemployedtoestimatetheprobabilitythatahouseholdhasmadeaparticulartransitionfromonequintiletoanotheroveradjacentsurveyrounds.Weobtaina5x5transitionmatrixonceestimatesareaggregated.

Forthepointestimatesofrelativemobility,weapplythemethodasdescribedabove,substitutingthequintilethresholdsforthepovertylinesinthebivariatestandardnormalcumulativedistributionfunctionabove.Forthebounds,wetakeadifferentapproachfromtheonedescribedinsection2.1.Becausewewanttoestimatetheprobabilitiesoftwenty-fivetransitionsweneedhigherprecision:thestandardboundsapproachwouldlikelyresultinuninformativeestimates.Hence,wetakethesmallestandlargestcorrelationvaluesinoursampleofincomecorrelationstoestimateourrelativemobilitybounds.

12WeusethisterminologyinlinewiththeumbrellastudyoninequalityinMalaysiatowhichthispapercontributed.

8

Thelowestcorrelationcoefficientinoursampleis0.53forGreece,whilethehighestis0.89forCzechia.

13

Theserepresentrespectivelythehighandlowmobilityscenario,asthecloserthecoefficientistoone,thestickierincomesare.AfurtherassumptionthenisthattheseimportedcoefficientsaresufficientlyextremetoformupperandlowerboundsinthecaseofMalaysia.Giventhevarietyofcountriesincluded,atvariouslevelsofeconomicdevelopment,wesuggestthatthisassumptionisnotunreasonable.

TherelevanttransitionprobabilitiescanthenbeestimatedbydrawingonthebivariatestandardnormalcumulativedistributionfunctionΦ2(.),asbefore.Forexample,theprobabilityofbeinginthebottomquintiletwosurveysinarowisestimatedasfollows:

whereprepresentsthe20thpercentileofthedistributioninyearjandtheothersymbolsareas

definedinsection

2.1.

2.5.Data

Thisstudyanalyzeseightroundsofcross-sectionaldatafromtheHouseholdIncomeSurvey(HIS)collectedbytheDepartmentofStatisticsMalaysia.Thedataarefortheyears2004,2007,2009,2012,2014,2016,2019and2022;weconsiderallpairsofadjacentsurveyrounds.

14

Onerequirementforanalyzingwelfarechangesovertimeisthatthemeasureofwelfare,incomeinourcase,ismeasuredinaconsistentandcomparablemanner.TheMalaysiandataareofhighqualityandsatisfythisrequirement.Inaddition,thesamplesizesofthesurveysarelarge,rangingfrom36,000toover80,000household-levelobservationspersurveyyear.

Thedependentvariableinouranalysisisthenaturallogarithmofmonthlyhouseholdpre-taxincomepercapita,whichisevaluatedagainstourpovertylinetodeterminethepovertystatusofahousehold.Wedidnotusepost-taxincomebecausefewMalaysiansaresubjecttopersonalincometax;itisthusunlikelytoaffectpovertyorvulnerabilitystatus.Householdsreportincomeoverthetwelvemonthsprecedingtheinterview.Notably,thismeansthathouseholdsinterviewedin2022alsoreportoverpartof2021.

13InthecaseofGreece,thisisthecorrelationofdisposablehouseholdincomebetween2001-2004;forCzechia,itisthe2014-2015correlationofdisposableincomes.

14Surveysmayextendintothesubsequentyear.Whenwe