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. Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 EconometricSocietyMonographs Editors: JeffreyEly,NorthwesternUniversity DonaldW.K.Andrews,YaleUniversity TheEconometricSocietyisaninternationalsocietyfortheadvancementofeconomictheoryin relationtostatisticsandmathematics.TheEconometricSocietyMonographseriesisdesigned topromotethepublicationoforiginalresearchcontributionsofhighqualityinmathematical economicsandtheoreticalandappliedeconometrics. Othertitlesintheseries: G.S.Maddala,Limiteddependentandqualitativevariablesineconometrics,9780521241434, 9780521338257 GerardDebreu,Mathematicaleconomics:TwentypapersofGerardDebreu,9780521237369, 9780521335614 Jean-MichelGrandmont,Moneyandvalue:Areconsiderationofclassicalandneoclassical monetaryeconomics,9780521251419,9780521313643 FranklinM.Fisher,Disequilibriumfoundationsofequilibriumeconomics,9780521378567 AndreuMas-Colell,Thetheoryofgeneralequilibrium:Adifferentiableapproach, 9780521265140,9780521388702 TrumanF.Bewley,Editor,Advancesineconometrics–FifthWorldCongress(VolumeI), 9780521467261 TrumanF.Bewley,Editor,Advancesineconometrics–FifthWorldCongress(VolumeII), 9780521467254 Herve´Moulin,Axiomsofcooperativedecisionmaking,9780521360555,9780521424585 L.G.Godfrey,Misspecificationtestsineconometrics:TheLagrangemultiplierprincipleand otherapproaches,9780521424592 TonyLancaster,Theeconometricanalysisoftransitiondata,9780521437899 AlvinE.RothandMarildaA.OlivieraSotomayor,Editors,Two-sidedmatching:Astudyin game-theoreticmodelingandanalysis,9780521437882 WolfgangHardle,Appliednonparametricregression,9780521429504 Jean-JacquesLaffont,Editor,Advancesineconomictheory–SixthWorldCongress(VolumeI), 9780521484596 Jean-JacquesLaffont,Editor,Advancesineconomictheory–SixthWorldCongress(VolumeII), 9780521484602 HalbertWhite,Estimation,inferenceandspecification,9780521252805,9780521574464 ChristopherSims,Editor,Advancesineconometrics–SixthWorldCongress(VolumeI), 9780521444590,9780521566100 ChristopherSims,Editor,Advancesineconometrics–SixthWorldCongress(VolumeII), 9780521444606,9780521566094 RogerGuesnerie,Acontributiontothepuretheoryoftaxation,9780521629560 DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics– SeventhWorldCongress(VolumeI),9780521589833 DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics– SeventhWorldCongress(VolumeII),9780521589826 DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics– SeventhWorldCongress(VolumeIII),9780521580137,9780521589819 DonaldP.Jacobs,EhudKalai,andMortonI.Kamien,Editors,Frontiersofresearchineconomic theory:TheNancyL.SchwartzMemorialLectures,1983–1997,9780521632225, 9780521635387 (continuedafterIndex) Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 Revealed Preference Theory Christopher P. Chambers DepartmentofEconomics, UniversityofCaliforniaSanDiego Federico Echenique DivisionoftheHumanitiesandSocialScience, CaliforniaInstituteofTechnology Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learningandresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781107087804 (cid:2)c ChristopherP.ChambersandFedericoEchenique2016 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. 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 LCrecordavailableathttp://lccn.loc.gov/2015040826 ISBN978-1-107-08780-4Hardback ISBN978-1-107-45811-6Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyInternetWebsitesreferredtointhispublication, anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain, accurateorappropriate. Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 ToEvan,HelenaandNatalia Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:42, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:42, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 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 Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:42, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293 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 Downloaded from https://www.cambridge.org/core. Universitaetsbibliothek Leipzig, on 22 Jan 2022 at 17:20:42, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316104293