Analyzing Multidimensional Well-Being: A Quantitative Approach

329 Pages·2018·3.02 MB·English

by  Satya R. Chakravarty

(cid:2)
AnalyzingMultidimensionalWell-Being
(cid:2) (cid:2)
(cid:2)
(cid:2)
Analyzing Multidimensional Well-Being
AQuantitativeApproach
SatyaR.Chakravarty
(cid:2) (cid:2)
(cid:2)
(cid:2)
Thiseditionfirstpublished2018
©2018JohnWiley&Sons,Inc.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or
transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingor
otherwise,exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfrom
thistitleisavailableathttp://www.wiley.com/go/permissions.
TherightofSatyaR.Chakravartytobeidentifiedastheauthorofthisworkhasbeenassertedin
accordancewithlaw.
RegisteredOffices
JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,USA
EditorialOffice
111RiverStreet,Hoboken,NJ07030,USA
Fordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWiley
productsvisitusatwww.wiley.com.
Wileyalsopublishesitsbooksinavarietyofelectronicformatsandbyprint-on-demand.Some
contentthatappearsinstandardprintversionsofthisbookmaynotbeavailableinotherformats.
LimitofLiability/DisclaimerofWarranty
Thepublisherandtheauthorsmakenorepresentationsorwarrantieswithrespecttotheaccuracy
orcompletenessofthecontentsofthisworkandspecificallydisclaimallwarranties;including
withoutlimitationanyimpliedwarrantiesoffitnessforaparticularpurpose.Thisworkissold
withtheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservices.The
adviceandstrategiescontainedhereinmaynotbesuitableforeverysituation.Inviewofon-going
research,equipmentmodifications,changesingovernmentalregulations,andtheconstantflow
ofinformationrelatingtotheuseofexperimentalreagents,equipment,anddevices,thereaderis
(cid:2) urgedtoreviewandevaluatetheinformationprovidedinthepackageinsertorinstructionsfor (cid:2)
eachchemical,pieceofequipment,reagent,ordevicefor,amongotherthings,anychangesinthe
instructionsorindicationofusageandforaddedwarningsandprecautions.Thefactthatan
organizationorwebsiteisreferredtointhisworkasacitationand/orpotentialsourceoffurther
informationdoesnotmeanthattheauthororthepublisherendorsestheinformationthe
organizationorwebsitemayprovideorrecommendationsitmaymake.Further,readersshould
beawarethatwebsiteslistedinthisworkmayhavechangedordisappearedbetweenwhenthis
workswaswrittenandwhenitisread.Nowarrantymaybecreatedorextendedbyany
promotionalstatementsforthiswork.Neitherthepublishernortheauthorshallbeliableforany
damagesarisingherefrom.
LibraryofCongressCataloging-in-PublicationData
Names:Chakravarty,SatyaR.,author.
Title:Analyzingmultidimensionalwell-being:aquantitativeapproach/by
SatyaR.Chakravarty.
Description:Hoboken,NJ:JohnWiley&Sons,Inc.,2018.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2017033909(print)|LCCN2017019107(ebook)|ISBN
9781119256908(cloth)|ISBN9781119256946(pdf)|ISBN9781119256953
(epub)
Subjects:LCSH:Socialindicators.|Economicindicators.|Qualityof
life–Statisticalmethods.|Well-being–Statisticalmethods.
Classification:LCCHN25.C4492017(ebook)|LCCHN25(print)|DDC306–dc23LCrecord
availableathttps://lccn.loc.gov/2017033909
CoverdesignbyWiley
Coverimage:©Wasant/Shutterstock
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
(cid:2)
(cid:2)
InlovingmemoryofmyeldestbrotherDr.KeshabR.Chakravarty,
whosehonestyanddedicationtowardsprofessionhavealwaysbeenan
inspirationtome.
(cid:2) (cid:2)
(cid:2)
(cid:2)
vii
Contents
Preface xi
Endorsements xv
1 Well-BeingasaMultidimensionalPhenomenon 1
1.1 Introduction 1
1.2 IncomeasaDimensionofWell-BeingandSomeRelated
Aggregations 4
1.3 ScalesofMeasurement:ABriefExposition 10
(cid:2) (cid:2)
1.4 PreliminariesforMultidimensionalWelfareAnalysis 11
1.5 TheDashboardApproachandWeightsonDimensionalMetricsina
CompositeIndex 14
1.6 MultidimensionalWelfareFunctionAxioms 17
1.6.1 InvarianceAxioms 17
1.6.2 DistributionalAxioms 19
1.7 MultidimensionalWelfareFunctions 27
1.8 ConcludingRemarks 37
References 38
2 AnOverviewofMultidimensionalEconomicInequality 49
2.1 Introduction 49
2.2 AReviewofOne-DimensionalMeasurement 51
2.2.1 NormativeOne-DimensionalInequalityIndices 51
2.2.2 Subgroup-DecomposableIndicesofInequality 53
2.3 MultidimensionalInequalityIndices 56
2.3.1 TheDirectApproach 56
2.3.1.1 AxiomsforaMultidimensionalInequalityIndex 56
2.3.1.2 ExamplesofIndices 60
2.3.2 TheInclusiveMeasureofWell-beingApproach 69
2.4 ConcludingRemarks 77
References 78
(cid:2)
(cid:2)
viii Contents
3 ASynthesisofMultidimensionalPoverty 85
3.1 Introduction 85
3.2 ABriefReviewofOne-DimensionalAnalysis 89
3.3 PreliminariesforMultidimensionalPovertyAnalysis 93
3.4 IdentificationofthePoorandDeprivationCounting 95
3.5 AxiomsforaMultidimensionalPovertyMetric 99
3.5.1 InvarianceAxioms 100
3.5.2 DistributionalAxioms 103
3.5.3 DecomposabilityAxioms 108
3.5.4 ThresholdLimitSensitivityAxiom 111
3.5.5 TechnicalAxioms 112
3.6 MultidimensionalPovertyMeasurement 113
3.6.1 TheDashboardApproach 113
3.6.2 TheDirectApproach 117
3.6.3 TheInclusiveMeasureofWell-beingApproach 123
3.7 MultidimensionalPovertyOrderings 125
3.7.1 ABriefOutlineofOne-DimensionalOrderings 126
3.7.2 MultidimensionalOrderings 129
3.8 DimensionsofWell-BeingwithOrdinalSignificanceand
MultidimensionalPoverty 131
(cid:2) 3.9 OrderingsBasedonDeprivationsCounts 134 (cid:2)
3.10 MultidimensionalMaterialDeprivation 138
3.11 ConcludingRemarks 142
References 143
4 FuzzySetApproachestotheMeasurementof
MultidimensionalPoverty 163
4.1 Introduction 163
4.2 FuzzyMembershipFunction 165
4.3 AxiomsforaFuzzyMultidimensionalPovertyIndex 173
4.3.1 InvarianceAxioms 175
4.3.1.1 FuzzyStrongRatio-ScaleInvariance 175
4.3.1.2 FuzzyStrongTranslation-ScaleInvariance 177
4.3.1.3 FuzzyWeakFocus 177
4.3.1.4 FuzzyStrongFocus 178
4.3.1.5 FuzzySymmetry 178
4.3.1.6 FuzzyPopulationReplicationInvariance 179
4.3.2 DistributionalAxioms 179
4.3.2.1 FuzzyMonotonicity 179
4.3.2.2 FuzzyMonotonicitySensitivity 180
4.3.2.3 FuzzyDimensionalMonotonicity 181
4.3.2.4 FuzzyTransfer 182
(cid:2)
(cid:2)
Contents ix
4.3.2.5 IncreasingFuzzyPovertyunderCorrelation-Increasing
Switch 184
4.3.3 DecomposabilityAxioms 185
4.3.3.1 FuzzySubgroupDecomposability 185
4.3.3.2 FuzzyFactorDecomposability 185
4.3.4 FuzzySensitivityAxiom 186
4.3.4.1 IncreasingFuzzyPovertyforIncreasedMembership
Function 186
4.3.5 TechnicalAxioms 187
4.3.5.1 FuzzyBoundedness 187
4.3.5.2 FuzzyContinuity 187
4.4 FuzzyMultidimensionalPovertyIndices 187
4.5 FuzzyPovertyOrderings 191
4.6 ConcludingRemarks 195
References 195
5 PovertyandTime:AMultidimensionalAppraisal 201
5.1 Introduction 201
5.2 Preliminaries 207
5.3 TheBlockApproach 208
(cid:2) 5.3.1 IndividualMultidimensionalIntertemporalPovertyIndex 208 (cid:2)
5.3.2 AggregateMultidimensionalIntertemporalPovertyIndex 218
5.3.3 AReviewofSomeRelatedOne-DimensionalProposals 220
5.4 AnExplorationoftheCountingApproachestoMultidimensional
IntertemporalDeprivations 226
5.5 TheMultidimensionalDurationApproach 229
5.5.1 AReviewofOne-DimensionalDuration-ReliantOffers 229
5.5.2 AxiomsforaChronicMultidimensionalPovertyQuantifier 231
5.5.3 TheBourguignon–ChakravartyApproachtoChronic
MultidimensionalPovertyMeasurement 240
5.6 IntertemporalPovertyOrderings 243
5.7 ConcludingRemarks 245
References 246
6 VulnerabilitytoPoverty:AMultidimensional
Evaluation 251
6.1 Introduction 251
6.2 AReviewofOne-DimensionalMeasurement 254
6.3 MultidimensionalRepresentationofVulnerabilitytoPoverty:An
AxiomaticInvestigation 262
6.4 ConcludingRemarks 269
References 271
(cid:2)
(cid:2)
x Contents
7 AnExplorationofSomeCompositeandIndividualistic
Indices 277
7.1 Introduction 277
7.2 HumanDevelopmentIndex 278
7.3 HumanPovertyIndex 284
7.4 GenderInequalityIndex 286
7.5 BetterLifeIndex 288
7.6 ActiveCitizenshipCompositeIndex 291
7.7 MeasuringHumanOpportunity:ACountingApproach 293
7.8 AssessmentofProgresstowardAchievementsinMillennium
DevelopmentGoals 295
7.9 AirQualityIndex 301
7.10 ConcludingRemarks 303
References 304
Index 311
(cid:2) (cid:2)
(cid:2)
(cid:2)
xi
Preface
Since often an income distribution of a society fails to include heterogeneity
in the distributions of one or more other dimensions of well-being of a pop-
ulation such as health, education, and housing etc.; income’s unsuitability as
thesolitaryattributeofwell-beingisclearlyunderstandable.Infact,ithasnow
becomewell-recognizedthathumanprosperityshouldbetreatedasamultidi-
mensionalaspect.Consequently,therehasbeenaspuramongresearchersto
workonmultidimensionaleconomicwell-being.
Therehasbeensignificantdevelopmentintheareasofmultivariatewelfare,
(cid:2) inequality,andpovertyintherecentpast,andhence,Ifelttheneedtotakethe (cid:2)
opportunitytodelvedeeperintothecorevaluesofthestatedconcepts.Whatis
presentedinthisbookisatheoryofmultidimensionalwelfare,inequality,and
povertyinanaxiomaticarchitecture.Theaimistoclarifyhowwecanproceed
to the evaluation of the three issues and address the questions of enhancing
welfareandreducinginequalityandpoverty.
Themonographcastsamplelightontheconcepts,andIbelievesuchanelu-
sivediscussionwillintriguestudents,teachers,researchers,andpractitionersin
thearea.Substantivecoverageofongoingandadvancedtopicsandtheirinquis-
itive,eloquent,accuratebestowalmakethetreatisetheoreticallyandmethod-
ologically quite concurrent and comprehensive and highly susceptible to the
practicalproblemsofrecentconcern.
Since the use of simple one-dimensional indices for reckoning welfare and
inequalityofapopulationorthecomparisonofsimilarmeasurementspertain-
ingtoanotherpopulationisanimproperanalysis,Chapter1lookstoassesshow
welloffasocietycanbeintermsofindividualachievementsindifferentdimen-
sions.ThepurposeofChapter2istoreviewthealternativeapproachestothe
evaluationofmultidimensionalinequality.Pickingupfromthenotethatwel-
fareofapopulationneedsanappraisalfromamultivariateperspective,poverty
canberegardedasademonstrationofinadequacyofachievementsindifferent
dimensionsofwellbeing.Hence,Chapters3attemptstopresentananalytical
discussionontheaxiomaticapproachtothemeasurementofmultidimensional
poverty.
(cid:2)