Revealed Preference Theory

239 Pages·2016·5.029 MB·English

by  Christopher P. Chambers, Federico Echenique

RevealedPreferenceTheory
PioneeredbyAmericaneconomistPaulSamuelson,revealedpreferencetheory
is based on the idea that the preferences of consumers are revealed in
their purchasing behavior. Researchers in this field have developed complex
and sophisticated mathematical models to capture the preferences that are
“revealed”throughconsumerchoicebehavior.Thisstudyofconsumerdemand
and behavior is closely tied up with econometrics (especially nonparametric
econometrics), where testing the validity of different theoretical models is an
important aspect of research. The theory of revealed preference has a very
longanddistinguishedtraditionineconomics,butuntilnowtherehasbeenno
systematicpresentationofthetheory.Thisbookdealswithbasicquestionsin
economictheory,suchastherelationbetweentheoryanddata,andstudiesthe
situations in which empirical observations are consistent or inconsistent with
someofthebest-knowntheoriesineconomics.
Christopher P. Chambers is an associate professor of economics at the
Department of Economics, University of California, San Diego. He has pub-
lished articles in the American Economic Review, Econometrica, Games and
EconomicBehavior,JournalofEconomicTheory,andTheoreticalEconomics.
He is an associate editor of the Journal of Economic Theory, Journal of
MathematicalEconomics,andSocialChoiceandWelfare.Heisalsoco-editor
ofMathematicalSocialSciences.
FedericoEcheniqueisaprofessorofeconomicsattheDivisionoftheHuman-
ities andSocialScience,California Institute ofTechnology.He haspublished
articlesintheAmericanEconomicReview,Econometrica,JournalofPolitical
Economy, Games and Economic Behavior, Journal of Economic Theory, and
Theoretical Economics. He is an associate editor of the Journal of Economic
Theory, Economic Journal, Economic Theory, andACM Transactions on
EconomicsandComputation.
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EconometricSocietyMonographs
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ChristopherSims,Editor,Advancesineconometrics–SixthWorldCongress(VolumeI),
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ChristopherSims,Editor,Advancesineconometrics–SixthWorldCongress(VolumeII),
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DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics–
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DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics–
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DonaldP.Jacobs,EhudKalai,andMortonI.Kamien,Editors,Frontiersofresearchineconomic
theory:TheNancyL.SchwartzMemorialLectures,1983–1997,9780521632225,
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(continuedafterIndex)
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Revealed Preference Theory
Christopher P. Chambers
DepartmentofEconomics,
UniversityofCaliforniaSanDiego
Federico Echenique
DivisionoftheHumanitiesandSocialScience,
CaliforniaInstituteofTechnology
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(cid:2)c ChristopherP.ChambersandFedericoEchenique2016
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Firstpublished2016
PrintedintheUnitedStatesofAmericabySheridanBooks,Inc.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloguinginPublicationdata
Names:Chambers,ChristopherP.,1975–author.|Echenique,Federico,author.
Title:Revealedpreferencetheory/ChristopherP.Chambers,FedericoEchenique.
Description:NewYork:CambridgeUniversityPress,[2016]|
Series:Econometricsocietymonographs|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2015040826|ISBN9781107087804(hardback)|
ISBN9781107458116(pbk.)
Subjects:LCSH:Revealedpreferencetheory.|Consumption(Economics)|
Consumers’preferences–Econometricmodels.
Classification:LCCHB801.C39452016|DDC339.4/7–dc23
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ToEvan,HelenaandNatalia
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Contents
Preface pagexiii
1 MathematicalPreliminaries 1
1.1 Basicdefinitionsandnotationalconventions 1
1.1.1 Relations 1
1.1.2 Partiallyorderedsets 2
1.1.3 Euclideanspaces 2
1.2 Preferenceandutility 3
1.2.1 Propertiesofpreferences 3
1.2.2 Utility 4
1.3 Orderpairs,acyclicity,andextensiontheorems 5
1.4 Cyclicmonotonicity 9
1.5 TheoremoftheAlternative 12
1.6 Chapterreferences 13
2 ClassicalAbstractChoiceTheory 15
2.1 Strongrationalization 16
2.1.1 Weakaxiomofrevealedpreference 19
2.1.2 Maximalrationalizability 22
2.1.3 Quasitransitivity 22
2.2 Satisficing 23
2.3 Weakrationalization 24
2.4 Subrationalizability 28
2.5 Experimentalelicitationofchoice 31
2.6 Chapterreferences 32
3 RationalDemand 34
3.1 Weakrationalization 34
3.1.1 ProofofAfriat’sTheorem 42
3.1.2 ConstructiveproofofAfriat’sTheorem 44
3.1.3 Generalbudgetsets 46
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x Contents
3.2 Strongrationalization 47
3.2.1 Smoothutility 50
3.2.2 Generalbudgetsets 50
3.2.3 Partiallyobservedpricesandconsumption 51
3.3 Revealedpreferencegraphs 53
3.4 Chapterreferences 54
4 TopicsinRationalDemand 57
4.1 Discretegoods:Supermodularandsubmodularrationalizations 57
4.2 Divisiblegoods 60
4.2.1 Homotheticity 60
4.2.2 Separability 63
4.2.3 Quasilinearutility 65
4.2.4 Grosscomplementsandsubstitutes 66
4.3 Chapterreferences 69
5 PracticalIssuesinRevealedPreferenceAnalysis 71
5.1 MeasuresoftheseverityofaviolationofGARP 72
5.1.1 Afriat’sefficiencyindex 72
5.1.2 Varian’sversionofAEI 73
5.1.3 TheMoneyPumpIndex 73
5.2 PoweroftestingGARP 74
5.2.1 Bronars’index 75
5.2.2 Engelcurvecorrection 76
5.3 Anoverviewofempiricalstudies 77
5.3.1 Paneldata 77
5.3.2 Cross-sectionaldata 78
5.3.3 Time-seriesdata 78
5.3.4 Experimentaldata 79
5.4 Chapterreferences 80
6 Production 83
6.1 Costminimization 83
6.2 Profitmaximization 87
6.2.1 Unobservedfactorsofproduction 91
6.2.2 Measuringviolationsfromrationalizability 93
6.3 Chapterreferences 93
7 StochasticChoice 95
7.1 Stochasticrationality 95
7.1.1 ProofofTheorem7.2 98
7.2 Luce’smodel 103
7.2.1 ProofofTheorem7.6 105
7.2.2 Luce’smodelandthelogitmodel 106
7.3 Randomexpectedutility 109
7.4 Chapterreferences 112
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