TOWHATWATERPRICEDOCONSUMERSRESPOND?ASTUDYOFINCREASINGBLOCKRATESANDMANDATORYWATERRESTRICTIONSByAdamSolimanATHESISSubmittedtoMichiganStateUniversityinpartialfulÞllmentoftherequirementsforthedegreeofAgricultural,Food,andResourceEconomicsÐMasterofScience2016ABSTRACTTOWHATWATERPRICEDOCONSUMERSRESPOND?ASTUDYOFINCREASINGBLOCKRATESANDMANDATORYWATERRESTRICTIONSByAdamSolimanThewayconsumersreacttoblockpricinghasimportantwelfareimplicationsformanyeconomicpolicies.Standardeconomictheoryassumesthathouseholdsoptimizewithmarginalprice,yetthereisnoclearempiricalevidenceastowhatwaterpricetheyactuallyrespond.Ifhouseholdsarenotrespondingtomarginalprice,increasingblockratesforwatermaynotbecost-effectiveorevensuccessfulatachievingitspolicygoalsofconservationandequity.Usingadetailedhousehold-levelpaneldatasetfor16,277residentialcustomersinSouthernCalifornia,Ishedlightoncomplexpricingschedulesandanswerseveralquestionsaboutwaterconsumptionbehavior.IbeginbyexaminingahouseholdÕsperceivedpriceofwater,whereIamabletoexploitpricevariationfromseveralrateincreasesandaratestructurechangefromincreasingblockratestoÒwa-terbudgetsÓÑwaterbudgetsuseblocksizesthataredeterminedbyhouseholdandenvironmentalfactors.IÞndstrongevidencethatconsumersrespondtodifferentalternativeprices,ratherthanmarginalprice,dependingonwhichblockstructuretheyface.IalsoÞndthattheaverageconsumerisabletopredicttheirconsumptionwithastandarderrorof27%.Improvementsinpricesignalsandinformationprovisionmaylimitthistypeofsuboptimizingbehavioranduncertainty.Watersuppliersalsousemandatorywaterrestrictionstoinduceconservation,andIÞndthattheyreducedoverallconsumptionby5%Ñthiseffectwasstrongerforthosewithlargerlawns.Lastly,Icomparereduced-formandstructuralmethodsforestimatingpriceelasticitiesofdemand.Asconsumptionandpriceareinextricablylinked,Iconcludethatthemethodofinstrumentalvariablesmaybefundamentallyinappropriatefordemandestimationunderblockrates.Coveringmanyfacetsofwaterpricingandconsumptionbehavior,thispaperprovidesusefulinformationtosuppliersdecidinghowtobalancetheirbudgets,induceconservation,andprovidereliablesupply.CopyrightbyADAMSOLIMAN2016ThisthesisisdedicatedtoKarim,Hanaa,andRashaSoliman.ivACKNOWLEDGEMENTSIwouldliketothankDr.EricCrawfordforprovidingmewiththeopportunitytostudyatMichiganStateUniversityandfortheguidancehehasofferedthroughoutmygraduatestudies.IamalsogratefulforthecontinuedsupportofDr.KennethBaerenklau,andIamdeeplyindebtedtohimandtheMoultonNiguelWaterDistrictformakingthedataavailabletome.IwouldalsoliketothankDr.JosephHerriges,Dr.SorenAnderson,andDr.NicoleMasonfortheirtime,advice,andfeedback.vTABLEOFCONTENTSLISTOFTABLES.......................................viiLISTOFFIGURES.......................................viiiCHAPTER1INTRODUCTION...............................1CHAPTER2LITERATUREREVIEW...........................4CHAPTER3THEORETICALDISCUSSION........................8CHAPTER4CONTEXTANDDATA............................12CHAPTER5EMPIRICALANALYSISANDDISCUSSION................185.1PerceivedPrice....................................185.1.1BunchingAnalysis..............................185.1.2HowPredictableisConsumerUsageandMarginalPrice?..........215.1.3ShinÕsTestofPricePerception........................225.2MandatoryWaterRestrictions.............................245.2.1ImpactoftheMandate............................255.3Structuralvs.Reduced-FormEstimation.......................28CHAPTER6CONCLUSION................................32APPENDIX...........................................34BIBLIOGRAPHY........................................51viLISTOFTABLESTable2.1Summaryofselectedstudiesinresidentialwaterdemand.............6Table4.1HouseholdandcensusblockcharacteristicsofMNWD..............13Table4.2BlocksizesunderMNWDÕstworatestructures..................14Table4.3Summarystatisticsfortheentiresample......................15Table4.4Summarystatisticsunderincreasingblockratesbymarginalconsumptionblock.16Table4.5Summarystatisticsunderwaterbudgetsbymarginalconsumptionblock.....17Table5.1Estimatesofconsumeruncertainty.........................22Table5.2Estimatesoftheimpactofmandatorywaterrestrictions..............27Table5.3Pre-ratechangemodels...............................30Table5.4Post-ratechangemodels..............................31TableA.1ResidentialwaterratestructuredistributioninNorthAmericabywatersupplier.45TableA.2WaterpriceperCCFin2011............................45TableA.3Summarystatisticsunderwaterbudgetsbymarginalconsumptionblock.....45TableA.4Summarystatisticsofnon-priceconservationprograms..............46TableA.5EstimatesfromShinÕspartialadjustmentpriceperceptionmodel.........46TableA.6FirststageresultsforShinÕspartialadjustmentpriceperceptionmodel......47TableA.7Estimatesoftheimpactofmandatorywaterrestrictions..............48TableA.8EstimatesfromtheDCCmodel..........................49viiLISTOFFIGURESFigure1.1IncreasingblockratesfortheMoultonNiguelWaterDistrict(CA)in2011...2Figure3.1Utilitymaximizationunderatwo-tierincreasingblockratestructure......8Figure4.1MapofMoultonNiguelWaterDistrict......................12Figure5.1Consumptiondistributionunderincreasingblockratesbyyear.........19Figure5.2Consumptiondistributionunderwaterbudgetsbyyear..............20Figure5.3Averageconsumptionbylawnsizequintile....................25FigureA.1Typicalblockallocationbyhouseholdsize....................35FigureA.2Histogramofblocksizesunderwaterbudgetsin2012..............36FigureA.3Averageconsumptionbymonth..........................37FigureA.4Nominalratechanges...............................38FigureA.5Consumptiondistributionunderincreasingblockratesbymonth........39FigureA.6Consumptiondistributionunderwaterbudgetsbymonth.............40FigureA.7Consumptiondistributionunderwaterbudgetsbyhouseholdsize........41FigureA.8Scaledquantitiesunderincreasingblockrates..................42FigureA.9Scaledquantitiesunderwaterbudgets.......................42FigureA.10CostallocationsfortheMoultonNiguelWaterDistrict..............43FigureA.11MicrozonesintheMoultonNiguelWaterDistrict................44viiiCHAPTER1INTRODUCTIONMeetingresidential,industrial,andagriculturalwaterneedshaslongbeenanissueinmanypartsoftheworld.Anincreaseinthefrequencyofextremeweatherevents,areductioninthereliabilityofcurrentwatersupplies,andagrowingconcernabouttheenvironmentaleffectsofnewsupplyprojectshasincreasedtheneedtobetterunderstandbothwaterconsumptionandconservationbehavior.Forthesereasons,manyresidentialwatersuppliershavefocusedonimproveddemandmanagement.Whilenon-priceconservationprogramsandcommand-and-controlpoliciesarerelativelycom-monintheWesternUnitedStates,theprincipaltoolthatwatersuppliershavetoinduceconser-vationispricestructure.Tomanyeconomists,theidealwouldbetousemarginal-costpricingtoreßectthelong-runmarginalcost(LRMC).However,waterpricingisaimedatpursuingnotonlygreaterallocativeefÞciency,butalsoobjectivesofequity,publichealth,Þnancialstability,andpublicacceptability(Arbuesetal.2003).Waterpricesarethereforeadministrativelydetermined,andtheytypicallyliebelowLRMC.Thisisincontrasttomanynaturalresourcemarkets,suchasthoseforoilandcoal,wherepricesaredeterminedbyamarketequilibriumandreßectscarcity.Manyseeincreasingblockratesasasecond-bestattempttoreduceeconomicoveruse,andFigure1.1providesanexampleofa5-blockstructurefromthesupplierstudiedinthispaper.1ThenotionthattheyinduceconservationmaybethereasonfortheshiftawayfromdecreasingblockratesseeninTableA.1.Inordertoestimatepriceelasticitiesofdemandundertraditionalblockratesforwater,mostre-searchershaveusedeitherreduced-formorstructuralmethods,withtheassumptionthatconsumersoptimizewithmarginalprice.Thereis,however,agrowingbodyofevidenceintheresidentialelec-1Increasingblockrateschargehighermarginalpricesforhigherquantitiesconsumed.Undertheserates,watersupplierscanchargesomethingclosetoLRMCformarginaluses,whilemeetingzero-proÞtconstraintsthroughthemanipulationofblocksizesandlower-blockprices.Atthehouseholdlevel,consumerspaylowerratesfornecessitieslikeshoweringandcooking,andratesclosertomarginalcostforoutdoorirrigation.However,evenifthehighestblockpricereßectsLRMC,somewelfarelossesoccurduetothelowerpriceschargedonearlierunitsofwater.1Figure1.1IncreasingblockratesfortheMoultonNiguelWaterDistrict(CA)in2011tricityliteraturethatshowsthatconsumersrespondtoeitherexpectedmarginaloraveragepricewhenfacingblockrates.Giventhecomplexityofthewaterbudgetratestructure2andtheneces-sitytobetterunderstandconsumptionbehaviorinthefaceofclimatechange,amajorfocusofthispaperistoanalyzepriceperceptionandresponse.Sinceitisnotknownwhatwaterpriceconsumersactuallyrespondto,Iexaminethetopicwithauniquehousehold-levelpaneldatasetthatcontainssigniÞcantpricevariationanddetailedconsumptionrecordsfor16,277single-familycustomers.IbeginbyexaminingahouseholdÕsperceivedpriceofwaterusingbunchinganalysisandShinÕs(1985)dynamicadjustmentmodel.IÞndstrongevidencethatconsumersrespondtodifferentalternativeprices,ratherthanmarginalprice,dependingonwhichblockstructuretheyface.IalsoÞndthattheaverageconsumerisabletopredicttheirconsumptionwithastandarderrorofapproximately27%usingBorensteinÕs(2009)uncertaintymodel.Theseresultsimplythattheperfectly-optimizing,perfectly-informedconsumerisrare,andthatitisquitedifÞculttoinferpriceresponsivenessofdemandfromchangesaround2Thisratestructureutilizesblocksizesthatarebasedonhouseholdcharacteristics,environmentalconditions,andadecisionbythewatersupplierastowhatconstitutesefÞcientwaterusegiventhosecharacteristicsandconditions.Assuch,blocksizescandifferacrosshouseholdsatanygiventime,andovertimeforanygivenhousehold.Asof2013,3%ofCaliforniaÕsapproximately400urbanwatersuppliershadimplementedwaterbudgetsÑtheremainingsuppliersusetraditionalincreasingblockrates(65%),uniformrates(26%),seasonalorßatrates(5%),anddecreasingblockrates(1%)(AmericanWaterWorksAssociation,2013).SeeBeecher(2012)andBaerenklauetal.(2014)foranoverviewofthecostsandbeneÞtsofwaterbudgets,respectively.2discontinuitiesinmarginalprice.Manywatersuppliersalsousecommand-and-controlpoliciestoinduceconservation,andIexaminetheimpactofmandatoryoutdoorrestrictions.IÞndthattheydecreasedoverallconsump-tionbyapproximately5%andthattheeffectwasstrongerforthosewithlargerlawns.Lastly,reduced-formmethodswereutilizedtocomparepriceelasticitiesofdemandwithstructuralesti-matesgeneratedinapreviousstudy.Theresultswereverysensitivetothechoiceofinstrument,covariates,andspeciÞcation.Theseinstrumentalvariables(IV)approacheswerealsoseeminglyunabletoaddresstheendo-geneitypresentinincreasingblockrates.SinceIVmethodsdonotaccountforthediscretechoiceofblock,theseresultsmaybeduetothefactthathouseholdsswitchedtheirmarginalconsumptionblockfrequently.Morefundamentally,waterconsumptionandpriceareinextricablylinked,andIconcludethatreduced-formmethodsmaybeinappropriatefordemandestimationunderblockrates.Asthispaperaddressesseveraltopicsregardingwaterpricingandconsumerbehavior,itpro-videsusefulinformationtowatersupplierswhoaredecidinghowtobalancetheirbudgets,induceconservation,andprovidereliablesupply.Theremainderofthispaperproceedsasfollows.Chapter2brießysummarizesthewaterdemandliterature.Chapter3introducesthetheorybehindthestudyofkinkedbudgetconstraintsandpriceperception.Chapter4containsinformationaboutthestudyareaanddata.Chapter5providestheeconometricanalysisanddiscussion.Chapter6concludes.3CHAPTER2LITERATUREREVIEWTheliteratureonresidentialwaterdemandisextensive,andeconomistshavegenerallyagreedonthevariablestoincludeinwaterdemandfunctions.Sincewaterhasnoclosesubstitute,theonlypriceenteringthedemandfunctionshouldbethatofwater.Othervariablesthataffectwaterconsumptionareincome,householdcharacteristics,homefeatures,andweathervariables.Atthecoreofthisliterature,however,liesdifÞcultiesintheoreticallyandempiricallymodelingtheblockpricingusedbymanywatersuppliers(seeArbuesetal.2003foranoverview).ConsensushasbeendifÞculttoobtainonthebestwaytomodeldemandunderblockpric-ing,asthistypeofratestructureleadstoakinkedbudgetconstraint,andanonlinearandanon-differentiabledemandfunction.ResearchersalsodisagreeontheproperspeciÞcationofthepricevariable.Therefore,earlyworkexaminedwhetherthepricevariableshouldbetheaveragepriceorthemarginalprice,whichclearlydifferaftertheÞrstconsumptionblockinbothincreasinganddecreasingblockrates.FollowingtheworkofTaylor(1975)andNordin(1976)intheelectricityliterature,themarginalpricespeciÞcationwasmodiÞedtoincludetheÒdifferencevariableÓÑthisisdeÞnedasthediffer-encebetweenwhattheconsumeractuallypaidandwhattheywouldhavepaidifallconsumptionwaschargedatthemarginalprice.ThemotivationforthismodiÞcationwasthatitisdifÞculttoanalyzetheimpactofchangesinratesthatdonotcorrespondtothecurrentlevelofconsumption,whichareknownasintra-marginalrates.Giventhatachangeinintra-marginalratesdoesnotaffectthemarginalprice,theformerwillonlyaffectdemandthroughanincomeeffect.Atheoreticalar-gumentwasmadethatthedifferencevariableshouldbeofequalmagnitudetoincomebutoppositeineffectinthecaseofincreasingblockrates(Corraletal.1995).TheworkofTaylor(1975)andNordin(1976)gaverisetoanumberofpapersthattriedtoempiricallytestthisrelation,suchasBillingsandAgthe(1980),FosterandBeattie(1981),and4Howe(1982).ThissetofpapersusedIVtechniquestoattempttocorrectforthebiaspresentinordinaryleastsquares(OLS)estimationduetothesimultaneityorco-determinationofquantity,price,andthedifferencevariable.However,therehasbeenrelativelylittleempiricalsupportforthehypothesisthatthedifferencevariableisequalinmagnitudeandoppositeinsigntotheincomevariable.Ruijs(2009)suggeststhatthismaybeduetoconsumersÕlackofinformationabouttheratestructure,thedifferencevariablebeingsmallrelativetoincome,orestimationbiases.Ageneralshortcomingofthisliterature,andanotherpossibleexplanationforthelackofem-piricalsupport,hasbeentheuseofaggregateconsumptiondataandproxiesforhouseholdincome.Intheirreviewofthewaterdemandliterature,Arbuesetal.(2003)arguethattheuseofaggregatedatahasbeenthemajorsourceofincorrectspeciÞcation.Theirreasoningisthatresearchersareunabletodeterminethedistributionofwateruseacrosshouseholdsandhowitvariesasafunctionoftheratestructure.Others,suchasOpaluch(1982),ChicoineandRamamurthy(1986),andNieswiadomy(1992),havearguedthatthepricethatconsumersrespondtoisanempiricalquestionandiscontext-speciÞc.TheirworkshowsthatitcanbedifÞcultforconsumerstodeterminetruemarginalpricesbecausetheymaybeunawareoftheblocknatureofpriceormaynotreactuntiltheyreceivetheirbill.NieswiadomyandMolina(1991)andNieswiadomy(1992)useamodeldevelopedbyShin(1985)totestwhetherconsumersreacttoaverageprice,marginalprice,orafunctionofbothÑthismodelandothereconometrictechniqueswillbedescribedingreaterdetailinChapter5.Usingdecreasingblockdataforresidentialelectricity,Shin(1985)Þndsthatconsumersreacttoaverageprice.NieswiadomyandMolina(1991)andNieswiadomy(1992)Þndthatconsumersrespondtomarginalpricewhenfacedwithincreasingblockratesforwater.Amorerecentexami-nationbyIto(2014)Þndsthatresidentialelectricityconsumersrespondtoaverageprice.Becauseofanincreaseinaggregateconsumptioncomparedtouniformrates,heconcludesthatthisresponsemakesblockratesunsuccessfulinachievingtheirgoalofenergyconservation.Therehavebeenrelativelyfewattemptstoexplicitlymodelthedecisionprocessofaconsumerfacingblockratesforwater,speciÞcallythechoiceofwhichblocktolocateconsumption.When5waterissoldunderblockrates,aseriousissueformodelspeciÞcationandestimationistheafore-mentionedco-determinationofprice,quantity,andthedifferencevariable(Corraletal.1995;HewittandHanmann1995).NaugesandThomas(2000)arguethatthecorrectspeciÞcationinsuchcasesutilizesworkbyBurtlessandHausman(1978)fromthelaborsupplyliterature.Theseauthorsproposedatwo-stagemodelinwhichaconsumerÞrstselectstheblock(discretechoice),thenmaximizestheirutilitysubjecttoabudgetconstraint(continuouschoice).HewittandHanmann(1995),Pint(1999),Olmstead(2009),Baerenklauetal.(2014),andSz-abo(2015)areamongtheonlyauthorstousethiskindofstructuraltwo-stepordiscrete-continuouschoice(DCC)modelinthestudyofwaterdemand.However,duetothecomputationalintensityoftheDCCmodelandalackofmicro-data,manyresearchershavesimpliÞedthedemandfunctionbyonlyconsideringtheblockwheremostconsumersarelocated(selectionbias)orbyomittingthechoiceofblockbytheconsumer(simultaneitybias)(NaugesandThomas,2000).Despitethedifferencesamongeconometricmethodsandthedatautilized,economistsgenerallyagreethatresidentialwaterdemandisinelasticwithrespecttoprice,butnotperfectlyso.Thevastmajorityoftheliteraturehavefoundpriceelasticitiesintherangeof0and-1,andTable2.1presentsresultsfromsomeofthesestudies.AuthorsDataMethodPriceSpeciÞcationPriceElasticityHoweandLinaweaver(1967)CSOLSMP-0.21to-1.57FosterandBeattie(1979)CSOLSAP-0.27to-0.76BillingsandAgthe(1980)LDOLSNordin-0.27to-0.49Billings(1982)LDIVNordin-0.56to-0.66ChicoineandRamamurthy(1986)CSOLSMP-0.60to-0.61Moncur(1987)LDOLSMP-0.03to-0.68NieswiadomyandMolina(1989)LDIVNordin-0.09to-0.86Nieswiadomy(1992)CSIVMP,AP-0.22to-0.60HewittandHanemann(1995)LDIV,DCCNordin-1.57to-1.63Corraletal.(1995)LDDCCNordin-0.11to-0.17Pint(1999)LDDCCMP-0.04to-1.24Olmstead(2009)LDIV,DCCMP-0.28to-0.64Baerenklauetal.(2014)LDDCCMP-0.58to-0.76Notes:CSforcrosssectionaldata.LDforlongitudinaldata.NordinforMPplusdifferencevariable.Table2.1Summaryofselectedstudiesinresidentialwaterdemand6Borenstein(2009)argues,however,thatmuchofthisliteraturehasbeenbasedontheassump-tionthatconsumersareperfectlyinformedandconstantlyoptimizingonthemargin.Suchanassumptionisseeminglyatoddswiththewaythatalmosteveryonethinksabouttheirwatercon-sumption.HegoesontoexaminepriceresponseinmoredetailthanOpaluch(1982)andShin(1985),andÞndsthatresidentialelectricitycustomersinCaliforniarespondtoexpectedmarginalpriceinthepresenceofuncertaintyaboutconsumption.ConsumersmayalternativelyuseaveragepriceasanapproximationofmarginalpriceifthecognitivecostofunderstandingcomplexpriceschedulesissigniÞcant(Ito2014).Thissuboptimizationbehavior,whichhasitsfoundationsinearlierwork,isdescribedasÒschmedulingÓbyLiebmanandZeckhauser(2004).LiebmanandZeckhauser(2004)statethatutilitypricinghasseveralfeaturesthatmakeitdif-Þcultforconsumerstoknowtheirtruemarginalprice:(1)pricingschedulesaresometimesnotpublishedorpresentedclearlyonthebill;(2)consumersvarytheirconsumptionseasonally;(3)pricingschedulescanchangerelativelyfrequentlyorseasonally;(4)billsaggregatemanydis-parateindividualdecisionsandaretypicallypresentedinunitsthatarenotdirectlyobservabletotheconsumer;and(5)thelinkbetweenaconsumerÕschoicesandconsumptionisdifÞculttorec-oncile,suchashowmanygallonsareinashower.Thesefactors,Ò...anonstationaryeconomicenvironment,delayedpayoff,andbundledconsumption[,]combinetomakeitalmostimpossi-bletodetermineoneÕsmarginalpricebyobservinghowbillsvarywithbehaviorÓ(LiebmanandZeckhauser2004,p.11).Therehavebeenmanyimprovementstowaterdemandestimationunderblockrates.Theseincludethecorrectionfortheendogeneitybetweenpriceandquantity,theuseoftimeseriesdata,andtheutilizationofempiricaltechniquesthatareconsistentwithutilitytheory.However,theassumptionimplicitinmuchofthisliterature,thathouseholdsoptimizewithmarginalprice,isnowseenastoostrong.ThereisagrowingbodyofevidenceintheresidentialelectricityliteraturethatÞndssuboptimizingbehaviorandsigniÞcantuncertaintywithregardstoconsumption.Withrisingmarginalcostsofnewwatersuppliesandclimatechangeaddinguncertaintytoweatherpatterns,thereisaneedtobetterunderstandhowhouseholdsarerespondingtoprice.7CHAPTER3THEORETICALDISCUSSIONBlockratepricingpresentstheoreticalandempiricaldifÞcultiesinthemodelingandanalysisofresidentialwaterdemand.Incontrasttotraditionalconsumerdemandanalysis,thedemandfunc-tionforagoodfacingblockratesistypicallynonlinearandnon-differentiable.Standarddemandcurvescannotaccuratelyrepresentconsumerbehaviorwhenfacingakinkedbudgetconstraint.1Empiricalestimationcanalsobequitecomplexbecausepriceandquantityaresimultaneouslyde-termined.Moreover,thediscretechoiceofblockandthecontinuouschoiceofquantityshouldbothbemodeled.TheeconometricchallengesarediscussedingreaterdetailinChapter5.Figure3.1Utilitymaximizationunderatwo-tierincreasingblockratestructureHouseholdsareassumedtomaximizeutility,subjecttoabudgetconstraint,whichiskinkedunderblockratepricing.Anexampleofasimpletwo-tierincreasingblockratestructureisshowninFigure3.1,whereYisincome,!YisÒvirtualincomeÓ(deÞnedbelow),w1isthelevelofcon-sumptionatwhichthepricechanges(thekinkpoint),andp1andp2arethepricesofwaterin1SeeMofÞtt(1986)forageneralderivationofthedemandfunction,andHewittandHanemann(1995)foracarefulderivationofitinthecontextofwaterdemand.8block1andblock2,respectively.Insuchaframework,theconsumerthenfacesthreepossibleconsumptionchoices:consumeontheinteriorofsegmentone,ontheinteriorofsegmenttwo,oratthekinkpoint.ForhouseholdsconsuminganywhereonakinkedbudgetconstraintotherthanintheÞrstlinearsegment,themarginalpricevariesacrossunitsofconsumption.ThisproblemcanberesolvedintheexamplefromFigure3.1bydeÞningthebudgetconstraintasfollows:Y="##$##%p1w+x,ifw!w1p1w1+p2(w"w1)+x,ifw>w1orequivalently:Y=p1w+x,ifw!w1Y+(p2"p1)w1=p2w+x,ifw>w1,wherewisthequantityofwaterconsumedandxisacompositegoodwithpricenormalizedto1.Theterm!Y=Y+(p2"p1)w1isvirtualincome,whichdenotestheinterceptofthesecondsegmentonthebudgetconstraintextendedtotheverticalaxis,whereas!D=(p2"p1)w1isthedifferencevariable.Whilethedifferencevariablewascommonlyusedinearlierliterature,virtualincomeisnowmoreprevalent,asitprovidesaconvenientrepresentationofthesituationfacedbyconsumersinblocksbeyondtheÞrst.MorespeciÞcally,virtualincomerefundstheimplicitsubsidythatahouseholdreceivesfromtheblockratestructure(Olmstead2009).However,Borenstein(2009)statesthatthistraditionalviewofconsumptionbehaviorrequiresconsiderableeffortfromtheconsumerbecause:...intheDCCmodels,consumersareassumedtocalculatetheirpreferredconsumptioniftheyweretofaceeachofthepossiblemarginalpricesonthedifferentstepsandthenchooseonwhichofthestepstoconsume.Theseapproaches,however,relyondiscretepricechangesatidentiÞablepointsandontheassumptionthatconsumersrespondtothoseabruptpricechanges.Thatis,thesepapersassumethatconsumerschosetheirconsumptionquantitybasedonthemarginalpricethattheyareobservedtohavefaced.Someresearchrecognizesthatconsumers9donotexactlyhittheirconsumptiontargetineverybillingperiodduetovariationsindailyactivities,weather,andotherfactors.Thisoptimizationerrorisarguedtobepartoftheerrorterm.Inpractice,thisviewofconsumerbehaviorisquitedemanding.First,ithastheobviousinformationrequirementsthatthecustomerknowsthedatehiscurrentbillingperiodbeganandwillend,andthepricesandquantitybreakpointsintheincreasing-blockschedule.Moreimportantly,ifthereareanyexogenousshockstohisdemand,thisapproachrequiresthattheconsumerknows(or,atleastthinksheknows)thoseshockswithcertaintyfortheentirebillingperiodatthetimetheperiodbegins.Otherwise,whentheconsumerischoosingconsumptiononday1ofthebillingperiodhewillnotknowthemarginalpriceonwhichheshouldbasehisdecision(p.6).Therehasrecentlybeenmoreexaminationintowhatpriceconsumersactuallyrespondto,speciÞcallyinthecontextofelectricityconsumption.AnapproachbyIto(2014)extendsthediscussionbystatingthateconomictheorygivesthreepredictionsaboutconsumersÕperceivedpriceunderblockpricing.Tocharacterizethepredictions,considerapriceschedulep(w),wherethemarginalpriceofwequalsp1forw!w1andp2forw>w1.Thestandardmodelofkinkedbudgetconstraintsmentionedabovepredictsthatconsumersop-timizewbasedonthetruemarginalpriceschedulep(w),orputdifferently,thattheperceivedpriceisequaltop(w).Implicitinthisresponseistwoassumptions:(1)consumershavenouncertaintyaboutw;and(2)theyfullyunderstandthestructureoftheblockpriceschedule(Ito2014).Boren-stein(2009)andSaez(2010)relaxtheÞrstassumptionÑtheyarguethatitisunrealistictoassumethatconsumersbothknowwwithcertaintyandrespondtotheirtruemarginalpriceofw.Intheirmodels,consumersincorporateuncertaintyaboutwandrespondtotheirexpectedmarginalprice.Theymakedecisions(behavioralrules)andcancalculatetheirexpectedmarginalpricebasedonthedistributionofpredictedrandomshocksthatwilloccurduringabillingmonth;theydonotnecessarilyneedinformationabouttheirdailyconsumption(Borenstein2009;Ito2014).LiebmanandZeckhauser(2004)relaxthesecondassumptionbyallowinginattentiontothedetailsofcomplexpriceschedules.TheirmodelpredictsthatifthementalcostofunderstandingthepricescheduleissigniÞcant,consumersrespondtotheaveragepriceasanapproximationfortheirmarginalprice.Comparedtomarginalpriceorexpectedmarginalprice,lessinformationisrequiredtocalculateaverageprice.10Ito(2014)considersageneralformofperceivedpricethatencompassesallthreetheoreticalpredictions,andhiskinkpointanalysisismotivatedbythemodelpresentedinSaez(2010).Sev-eralofhisempiricaltechniquesrequiresigniÞcantexogenouspricevariationandawell-identiÞedcontrolgroup.Heisabletoexploitpricevariationatspatialdiscontinuitiesinelectricityserviceareas,wherehouseholdsinthesamecityexperiencevastlydifferentblockpriceschedules.Theserequirementsareunfortunatelynotmetinthedatausedforthispaper,butcomponentsofhissta-tisticalmethodsareutilizedinChapter5.TheexaminationthatfollowsutilizestheapproachesofShin(1985),LiebmanandZeckhauser(2004),Borenstein(2009),andIto(2014).Theseauthorscallintoquestionthevalidityofastan-dardeconomicassumption,andstudyingthepriceconsumersrespondtoiscurrentlyseenasanempiricalinvestigation.Therefore,theseauthorsÕmethodsaremorerelevantforthesubsequentanalysis.11CHAPTER4CONTEXTANDDATAThedataforthisstudycomesfromtheMoultonNiguelWaterDistrict(MNWD),locatedinOrangeCounty,California.MNWDprovideswater,recycledwater,andwastewaterservicetoapproxi-mately170,000peopleinitsservicearea,whichincludesthecitiesofAlisoViejo,LagunaNiguel,LagunaHills,MissionViejo,andDanaPoint.SeeFigure4.1foramapoftheirservicearea.Figure4.1MapofMoultonNiguelWaterDistrict12Approximately80%ofMNWDÕswaterispurchasedfromtheMunicipalWaterDistrictofOrangeCounty,whichpurchasesitswaterfromtheMetropolitanWaterDistrictofSouthernCal-ifornia,aregionalwaterwholesalerthatdeliverswaterfromtheColoradoRiverandNorthernCalifornia(MNWD,2015b).ThedemographicbreakdownoftheMNWDserviceareaisshowninTable4.1.Itshouldbenotedthatresidentsarewell-educatedandliveinrelativelynewandexpensivehomes.DataSourceVariableMeanStd.Dev.MNWDHouseholdsize4.050.76Irrigatedarea(feet2)34954654ACS5-Year,2009-2013Medianhousevalue#(2013,$1000)662.3191.1(allvaluesbycensusMedianyearstructurebuilt#1982.210.2blockgroup)Bachelorsdegree(%)32.98.8Professionaldegree(%)4.03.4Medianage#42.66.6Populationdensity(peoplepersquaremile)62863309Numberofhousingunits691291Note:Variableswitha(*)representthemedianvalueforacensusblockgroup.Table4.1HouseholdandcensusblockcharacteristicsofMNWDHouseholdsizeandirrigatedareaareconÞrmedonahouseholdbasisbyMNWD.Theyaretypicallyupdatedvoluntarilybycustomers,whocaneitherprovideinformationaboutchangesintheirhouseholdcompositionorsubmitapetitionforalargermonthlyblockallowance.1LargereportedhouseholdsizesnormallyrequireveriÞcation,andlargereportedirrigatedareaswouldtriggerafollow-up,sinceMNWDhasbaselinevaluesfromparcelmapsandassessordata.TheremainingvariablesinTable4.1weregatheredusingthe2009-2013AmericanCommunitySurvey(ACS)5-Yearcensusestimatesandarebycensusblockgroup.Otherthanadjustmentsforinßation,demographicvariablesaretime-invariant.2Thedatasetusedfortheanalysiscoverscontinuousmonthlyuserecordsof16,277single-familyhouseholdsfromOctober2007toMarch2015.Twomajorchangesoccurredduringthistimeperiod.First,MNWDimplementedmandatorywaterrestrictionsfromApril2009untilApril1Thesearetypicallygivenformedicalneed,livestock,orincreasesinirrigatedarea.2ThewatersuppliermergedthecensusdatawiththeconsumptionandpricingdataÑtheythenremovedallpotentiallyidentiÞableinformationpriortomyreceiptofthefulldataset.13BlockUnderIncreasingBlockRatesUnderWaterBudgetsBlock1Upto10CCFUptoindoorbudgetBlock210CCFupto20CCFUptooutdoorbudgetBlock320CCFupto30CCFTotalwaterbudgetupto125%oftotalbudgetBlock430CCFupto50CCF125%oftotalbudgetupto150%oftotalbudgetBlock5Over50CCFOver150%oftotalbudgetNote:1CCF=100cubicfeet=748gallonsTable4.2BlocksizesunderMNWDÕstworatestructures2011.Thislimitedoutdoorwaterusetothreedaysperweek,withadailymaximumof15minutes.Forthetimeperiodsbeforeandafterthemandate,therewerenorestrictionsonoutdooruse.Sec-ond,MNWDswitchedfromincreasingblockratestowaterbudgetsinJuly2011ÑseeTable4.2forthesizeofeachconsumptionblockunderthetworatestructures.Underwaterbudgets,resi-dentialcustomersaregivenanindoorandanoutdoorallocationbasedonhouseholdcharacteristicsandenvironmentalconditions,whichcanvarymonthly.FigureA.1showstheblocksizesfacedbytypicalhouseholdsinthesample,andFigureA.2providesahistogramofblocksizeallocationunderwaterbudgets.ForcustomerslocatedinMNWDÕsservicearea,indoorwaterbudgetsarecalculatedusingthreefactors:(1)60gallonsofwaterperpersonperday(deemedÒefÞcientÓbyMNWD);(2)thenumberofpeopleinthehousehold;and(3)thenumberofdaysinthebillingcycle.Outdoorwaterbudgetsarealsocalculatedusingthreefactors:(1)theamountofirrigatedarea;(2)actualdailyplantwaterloss,capturedbyevapotranspiration;and(3)aplantfactorthatreßectsthewaterneedsofnativeplants.AmoredetaileddescriptionoftheseoutdoorfactorscanbefoundinSectionA.3.SomesummarystatisticsareprovidedinTable4.3,andagraphofaveragemonthlywaterconsumptionforthesampleisincludedintheAppendix(FigureA.3).ThisÞgureshowsthatwhileseasonalshiftsinconsumptioncontinuetooccur,theyareonaveragelessextremeaftertheratestructurechange.MNWDincreasednominalvolumetricchargestwiceundertheirtraditionalincreasingblockratepricingschedule:onceinJuly2009andagaininJuly2010.WhenMNWDswitchedfromincreasingblockratestowaterbudgetsinJuly2011,whichresultedinanadditionalrateincrease,nominalpricesforeachblockremainedthesameuntiltheendofthestudyperiod.14Variable200720082009201020112012201320142015Consumption(CCF/month)16.3118.7716.9114.8214.9215.3416.0215.3612.68Evapotranspiration(inches/month)2.384.074.173.814.114.604.294.213.97Nominalprice($/CCF)0.860.860.941.091.281.381.381.381.38Block20.960.961.051.231.431.541.541.541.54Block31.161.161.271.482.212.752.752.752.75Block41.361.361.491.733.845.515.515.515.51Block51.461.461.601.866.9111.0211.0211.0211.02Nominalaveragepricepaid($/CCF)0.910.921.001.151.411.531.551.531.46Realprice(2013,$/CCF)0.950.921.031.171.311.391.381.371.39Block21.061.031.151.311.471.551.541.531.56Block31.281.251.391.582.272.772.752.732.78Block41.501.461.621.853.945.545.515.475.57Block51.611.571.751.987.0911.0911.0210.9411.14Realaveragepricepaid(2013,$/CCF)1.000.991.091.221.451.531.551.521.48Realbudget(2013,$/month)372.7372.2366.7363.2363.2368.6369.8376.5386.6Notes:ThestudyperiodisfromOctober2007toMarch2015.TheratestructurechangedinJuly2011.Consumptionisreportedinintegervalues.1CCF=100cubicfeet=748gallons.Table4.3SummarystatisticsfortheentiresampleItshouldbenotedthatwhentheratestructurechangedinJuly2011,therealpricepaidperCCF(100cubicfeet)ofwaterincreasedby25%andthehighest-blockpriceincreasedbyapproximately450%.FigureA.4showshownominalrateschangedovertime.Theincomevariable,whichisdeÞnedasÒrealbudgetÓinTable4.3,followsfromtherecom-mendationofStrongandSmith(2010)andBaerenklauetal.(2014).ItisbasedoncensusblockincomeandadjustedforthefractionofincometypicallyspentonthecensuscategoryofÒutilities,fuels,andpublicservicesÓ(proportionaltoincome).Thiswasthenadjustedfortemporalchangesinper-capitapersonalincomefortheLosAngeles-LongBeach-SantaAnametropolitanstatisticalareausingdatafromtheBureauofLaborStatisticsinordertocaptureßuctuationsaroundthetimeoftherecession.SummarystatisticsbymarginalconsumptionblockarefoundinTables4.4and4.5.Table4.4showsthatunderincreasingblockrates,marginalconsumptionwasinblock1orblock2for75%oftheobservations.Thoseconsuminginblocks3through5hadaboveaverageconsumption,realbudgets,evapotranspiration,householdsize,irrigatedarea,graduateeducation,medianhousevalue,andage,andlivedinlessdenseareasÑthesetrendsaregenerallymorepronouncedasoneincreasesmarginalconsumptionblock.15VariableFullSampleBlock1Block2Block3Block4Block5Fractionofobservations1.000.390.360.140.080.03Consumption(CCF/month)16.456.5614.8624.6837.7773.66Evapotranspiration(inches/month)3.923.493.964.434.604.79Householdsize4.053.784.154.294.394.49Irrigatedarea(feet2)3495192931434534703114725Realbudget(2013,$/month)367.3365.4365.8369.2375.6382.6Bachelorsdegree(%)32.933.932.531.532.134.7Mastersdegree(%)4.03.23.94.45.68.4Medianage42.641.042.643.945.648.5Medianhousevalue(2013,$1000)662.3603.1663.1702.6778.6945.8Populationdensity(peoplepersq.mile)628672336232544845322894Housingunitsincensusblock691712702664625576Note:RepresentsdatafromOctober2007untilJuly2011.Includes716,188observations.Table4.4SummarystatisticsunderincreasingblockratesbymarginalconsumptionblockUnderwaterbudgets,blocksizesvaryacrosshouseholdsatanygiventime,andovertimeforanygivenhousehold.Inordertofacilitatecomparisonsbetweenthemarginalconsumptionblocksofeachratestructure,theblocksinTableA.3weregeneratedusingpre-ratechangeblocksizes.However,blocksizesundertraditionalincreasingblockratesareoftendeterminedusingtheconceptofaÒtypicalÓhousehold.Forexample,ifthevastmajorityofcustomersinadistricthaveahouseholdsizeoffour,thesuppliercouldusethisinformationtodeterminethesizeoftheÒnecessitiesÓblock(block1).Assuch,thereismeritinlookingatsummarystatisticsbymarginalconsumptionblockunderwaterbudgetsusingtheactualblocksizecalculation.However,thatTables4.4and4.5shouldnotbecompareddirectly(onlyTables4.4andA.3).Table4.5(p.17)showsthat80%oftheobservationswerewithinahouseholdÕswaterbudget(block1orblock2).ConsumptioninBlocks2through5wereaboveaverage,aswashouseholdsize,irrigatedarea,masterÕsdegreeattainment,andmedianhousevalue.Thesesamehouseholdsliveinareasthatarelessdense.16VariableFullSampleBlock1Block2Block3Block4Block5Fractionofobservations1.000.440.360.120.050.03Consumption(CCF/month)15.426.9318.9124.0329.9340.62Evapotranspiration(inches/month)4.313.974.674.464.404.25Householdsize4.053.884.164.204.254.29Irrigatedarea(feet2)349519455274353137714174Realbudget(2013,$/month)371.5369.9370.3376.5378.0379.6Bachelorsdegree(%)32.933.831.333.834.134.1Mastersdegree(%)4.03.34.44.64.95.2Medianage42.641.144.042.943.243.6Medianhousevalue(2013,$1000)619.0568.3653.6656.8677.0696.8Populationdensity(peoplepersq.mile)628671645541581555575296Housingunitsincensusblock691714656707704700Note:RepresentsdatafromJuly2011untilMarch2015.Includes732,465observations.Table4.5SummarystatisticsunderwaterbudgetsbymarginalconsumptionblockSummarystatisticsfornon-priceconservationprogramscanbefoundintheAppendix(TableA.4).Thisinformationisnotincludedintheanalysisbecauseofverylowparticipationrates.17CHAPTER5EMPIRICALANALYSISANDDISCUSSIONInthischapter,Iexaminepriceresponseandtheimpactsofmandatorywaterrestrictionsonwaterconsumption.5.1PerceivedPriceEvidencefrommanyrecentstudiessuggeststhatconsumersmaynotrespondtoblockpricingasstandardeconomictheorywouldpredict(Ito2014).Apossibleexplanationisthatinformationregardingactualmarginalpriceiscostlytoobtain.Analternativehypothesisisthatrationalcon-sumerswillrespondtoaveragepriceifthenetbeneÞtofdeterminingmarginalpriceisnegative(Shin1985).Sinceitisnotknownwhatpriceconsumersactuallyrespondto,thisistreatedasanempiricalissuetobeinvestigatedwithMNWDdata.Ibeginwiththreeempiricaltestsadaptedfromthelaborsupplyandresidentialelectricityliterature.5.1.1BunchingAnalysisBunchingorclusteringatkinkpointsshouldbeobservedifconsumersareactuallyrespondingtomarginalprice(Ito2014).However,manyhouseholdscannotperfectlycontroltheirwaterconsumption,ortheymaynotbeawareoftheexactlocationofthekinkpoints.Theremayalsobemeasurementerrorintheconsumptiondata.Inthesecases,bunchingshouldbeexpectedaroundthekinksinsteadofexactlyatthekinks(Saez2010).Theamountofbunchingshouldbegreaterwhenthediscretejumpinmarginalpriceislarge,thepriceelasticityofdemandislarge,ortheabilitytopreciselycontrolconsumptionisstrong(Ito2014).Inordertoexaminethepresenceofbunching,Figures5.1and5.2presentyearlyhistogramsofconsumptionlevelsforthe16,277householdsinthesample.Eachbincorrespondstoa1CCF18Figure5.1Consumptiondistributionunderincreasingblockratesbyyearincrementinconsumption,asusageisbilledandreportedbyMNWDinintegervalues.ThekinkpointsintheincreasingblockratescheduleareindicatedbyverticalredlinesinFigure5.1ÑtheyarenotincludedinFigure5.2becausekinkpointsunderwaterbudgetsvarybyhouseholdduetoalargevariationinlawnandhouseholdsize.EvenwithsigniÞcantmarginalpriceincreasesbetweenblocks,whicharemorepronouncedunderwaterbudgets,allconsumptiondistributionsarequitesmoothÑtheÞguresshownoevidenceofbunchingundereitherpricingstructure.Similarly,histogramsofmonthlyconsumptiondonotshowanyevidenceofclusteringatkinkpoints(FiguresA.5andA.6intheAppendix).Thereisstillapossibilitythatbunchingisoccurringunderwaterbudgets,butitisbeingmaskedbythecontinuousnatureofirrigatedareaordifferenthouseholdsizesÑeithercouldsmoothoutbunchingintheaggregate.Therefore,thesamplewasbrokendownintothemostcommonhouse-holdsizesÑthemeanandmedianblocksizesthateachgroupwouldfacewerethencalculated.ThehistogramsbyhouseholdsizearepresentedinFigureA.7,andagainshownoevidenceofclustering.Approximately78%ofthesamplehaveahouseholdsizeoffour,followedby13%19Figure5.2Consumptiondistributionunderwaterbudgetsbyyearwithahouseholdsizeofthree,5%withahouseholdsizeofÞve,and3%withahouseholdsizeofsix.Thesmoothestdistributionsareforhouseholdsofsizethreeandfour,whichcanbeattributedtothefactthattheyhavethelargestshareofobservations.AÞnalbunchingexaminationinvolvedthescalingofquantitiesinordertohaveastandardmeasureacrosstimeandhouseholds.ThecalculationinvolveddividingblockusagebyblockallocationforthemarginalconsumptionblockinagivenmonthÑanintegerfactorwasthenadded:1ifmarginalconsumptionwasinblock2,2ifinblock3,andsoon.Forexample,ifahouseholdÕsmarginalconsumptionwasinblock4,andtheirusageandallocationwere3and12,respectively,theirscaledquantityforthatmonthwouldbe3.25.TheresultsforthisexercisecanbefoundinFiguresA.8andA.9.Theysuggestthatthereisbunchingunderwaterbudgets(FigureA.9),butonlyattheÞrstandsecondkinkpoints.Intuitively,itisunclearwhytherewouldbebunchingatthesekinkpoints,especiallysincethediscretejumpsinpricearenotverylarge.ApossibleexplanationforthebunchingfoundinFigureA.9isthatMNWDroundedmonthlyconsumptiontointegervaluesforbillingpurposesandsimplicity.Ifhouseholdsconsumeslightly20belowthekinkpointbutarethenroundedup,thebunchingisartiÞcial.Thissamepracticemaybeacontributingfactortothelackofbunchingfoundinpreviousexercises.Ignoringtheerrorsthatroundingcanproduceforamoment,thelackofacounterfactualorcontrolgroup,suchastheonecreatedbyItoÕs(2014)spatialdiscontinuityoraswitchfromuniformrates(nokinks)toblockrates,makesitquitedifÞculttofurtherexaminethepresenceofbunching.Nevertheless,thevastmajorityoftheevidencefromtheseexercisessuggeststhatthereisnobunchingundereitherincreasingblockratesorwaterbudgets.AccordingtoIto(2014),theab-senceofbunchingimpliestwopossibilities.First,consumersmayberespondingtomarginalpricewithclosetozeroelasticity.Second,consumersmayberespondingtoanalternativepriceÑthispossibilitywillbeexaminedinSection5.1.3.5.1.2HowPredictableisConsumerUsageandMarginalPrice?Thedegreetowhichthestandardestimationofresidentialwaterdemandcapturesconsumerbe-haviordependsinpartontheconsumerÕspredictabilityoftheirowndemand.Thisuncertaintycanalsoaffecthowaconstrained-optimizingconsumerwillrespondtoblockrates(Borenstein2009).Inordertoexaminethisuncertainty,Borensteinrecommendsthefollowingregressiontobeestimatedforeachhouseholdseparately:ln(Monthly_Use)t=12!j=1!jMonthj+"ln(Monthly_Use)t"1+#1t+#2t2+#3t3+$,(5.1)whereMonthjaretwelvemonth-of-yeardummyvariables.Therootmeansquarederror(RMSE)ofthisregressionisameasureofconsumerpricevariabilitybecausepriceandquantityaresi-multaneouslydetermined.Itisinturnacomponentofpredictiveability.TheÒRMSEcouldbeanupwardbiasedestimateofconsumeruncertaintyifconsumershavebetterinformationaboutthismonthÕsconsumptionthanisrevealedbytheirtypicalseasonalpattern,lastmonthÕsconsump-tion,andacubicfunctionintime.ItcouldbebiaseddownbecausesomeconsumerspayfarlessattentiontoconsumptionthanthisregressionsuggestsÓ(Borenstein2009,p.18).21TheresultsfromtheseregressionsareinTable5.1Ñforthesakeofcomparison,BorensteinÞndsameanRMSEof0.186andamedianof0.159forresidentialelectricityconsumersinCal-ifornia.ThemeanRMSEforthefullsamplesuggeststhattheaverageconsumerwillbeabletopredicttheirconsumptionwithastandarderrorofapproximately27%.ThiswouldimplythatitisquitedifÞculttoinferpriceresponsivenessofdemandfromchangesarounddiscontinuitiesinmarginalprice.Moreover,itshowsthatevenunderthemostvigilantoptimizingbehavior,house-holdswouldbeunabletochooseconsumptionbasedonexpostmarginalpricebecauseexogenousshockstodemandmakeitvirtuallyimpossibleforconsumerstoknowwhatmarginalpricetheywouldface.StatisticUnderIncreasingBlockRatesUnderWaterBudgetsFullSampleMeanRMSE0.26970.26280.2694(Std.Dev.)(0.0934)(0.0933)(0.0926)MedianRMSE0.25300.24630.2531Note:Therootmeansquarederror(RMSE)wasestimatedseparatelyforeachhousehold.Table5.1EstimatesofconsumeruncertaintyAnareaoffurtherresearchwillbetouncoverwhatattributesaredrivingthisuncertainty.Otherthanhouseholdsizeandirrigatedarea,thecovariatesinthisdatasetarebycensusblockgroupandarethereforenotspeciÞcenoughtodeterminewhattypesofhouseholdshavethelargeststandarderrororwhataffectspredictiveability.Thiswillbeexaminedthroughprimarydatacollectioninthiswaterdistrictorbyidentifyinganotherdatasetwithmoredetailedhouseholdcharacteristics.5.1.3ShinÕsTestofPricePerceptionOpaluch(1982)wastheÞrsttoprovideatesttodeterminewhetheramarginaloraveragepricemodelismoreappropriate.Shin(1985)arguedthattheassumptioninherentinpreviouswaterdemandliterature,thatconsumersarewell-informed,istoostrong.Heextendedtheexaminationtoincludeacomponentthatcapturesimperfectinformation,deÞnedasperceivedprice,whichisafunctionofbothaverageandmarginalprice.ThespeciÞcationofwateruseinthissection22followsfromtheconventionalwaterdemandanalysisandutilizesShinÕs(1985)perceivedpricemodiÞcation.Thisresultsin:w=f(p#,÷y,z),(5.2)wherethemonthlydemandforwater(w)dependsontheperceivedrealpriceofwater(p#),thehouseholdÕsbudgetforutilitiesandrelatedexpenditures(orvirtualincome,÷y),andhouseholdandenvironmentalcharacteristicsthatarethoughttoaffectwaterusage(z).Perceivedprice,p#it,forhousehold(i)inmonth(t)isconstructedasafunctionofmarginalprice,averageprice,andapriceperceptionparameter,k,suchthat:p#it=MPit(APi,t"1/MPit)k,(5.3)whereMPisthemarginalpriceofwaterperCCF,APistheaveragepriceperCCF,andkisaÞxedparameterdesignedtomeasurepriceperception.Iwilluseaveragepricefromthepreviousmonth,whichwillbeexplainedingreaterdetailbelow.Iftheconsumerrespondsonlytomarginalprice,thenk=0.Iftheconsumerrespondsonlytoaverageprice,thenk=1.IftheconsumerÕsperceivedpriceliesbetweenmarginalandaverageprice,whichmaybeduetothefactthattheconsumerstopssearchingforinformationwhenexpectedmarginalbeneÞtequalsexpectedmarginalcost,then0<k<1.NieswiadomyandMolina(1991)notethatunderincreasingblockrates,k>1impliesthatP#<AP<MPandk<0impliesthatP#>MP>AP.Whileitisexpectedthatkliesintheunitinterval,norestrictionswereplacedonitbecauseofhowthemodelisestimatedin(5.4).Iassumethatwaterconsumption(w)isadoublelogarithmicfunctionofexplanatoryvariablesforhousehold(i)inmonth(t),whichisthemostcommonformfoundintheliterature;thisisduetotheextremerightskewnessofwaterdemand.Whenestimatingthepriceperceptionparameter,Shin(1985)andNieswiadomyandMolina(1991)useapartialadjustmentmodel.InNieswiadomyandMolinaÕsmodel,thelaggedvaluesofaveragepriceandconsumptionfromthepreviousmonthareincludedasrighthandsidevariables.TheirargumentisthatthepreviousmonthÕsaverageprice23isembeddedintheperceivedpricethatconsumersarereactingtointhecurrentmonth.Therefore,theestimatingequationbecomes:ln(wit)=%1ln(MPit)+%1kln(APi,t"1/MPit)+%2ln(wi,t"1)+%3ln(÷yit)+&(seasonal)+'(timetrend)+(evapit+zi+)it(5.4)where(seasonal)arethreeseasondummyvariables,evapitistheweatherfacedbyhousehold(i)intime(t),zirepresentshouseholdÞxedeffects,and)itistheidiosyncraticerrorterm.Equation(5.4)isestimatedforeachratestructureseparatelywithÞxedeffectsandÞxedeffects-IVmodels.1Theprimaryvalueofinterestisthepriceperceptionparameter,k,andtheresultscanbefoundinTablesA.5andA.6.UsingonlytheÞxedeffects-IVmodels,kwasestimatedtobe0.10underincreasingblockratesand-0.29underwaterbudgets.2Theincreasingblockratekvalueimpliesthatconsumersperceivedpriceliesbetweenmarginalandaverageprice,whileunderwaterbudgets,itislargerthanbothmarginalandaverageprice.ThekestimatethatNieswiadomyandMolina(1991)obtainedforincreasingblockratesinDenton,Texaswas-0.43.Thistestwasneverperformedforhouseholdsfacingwaterbudgets,sothereisnobaselineestimatetocomparemyresultswith.However,bothestimatedkvaluesareconsistentwiththenotionthatundercomplexpricingstructures,householdsoftenrespondtoanalternativeprice.5.2MandatoryWaterRestrictionsMNWDimplementedmandatorywaterrestrictionsfromApril2009untilApril2011.Duringthistime,theylimitedoutdoorwateringtothreedaysperweek,withadailymaximumof15minutes.Inordertovisualizetheimpactoftheserestrictions(Figure5.3),householdsweregroupedby1AdaptedfromMcFaddenetal.(1977)andNieswiadomyandMolina(1991),theÞrststageinvolvesregressingobservedwaterdemandonthemarginalpricesatpresetquantities,andusingthepredictedconsumptiontocomputepredictedmarginalpriceandvirtualincome.Inthesecondstage,thesepredictedvaluesareusedasright-hand-sidevariablesinthedemandequation.295%CI[0.068,0.137]and[-0.296,-0.274]forkunderincreasingblockratesandwaterbudgets,respectively.24irrigatedareaquintiles.IntheMNWDservicearea,theprimaryuseofoutdoorwaterislawns,andthetablebelowprovidescontextforthedistributionoflawnsizes:MeanStd.Dev.Min10th25thMedian75th90thMaxIrrigatedArea(sq.ft.)3495465403009772500430010393156351Note:Irrigatedareaistime-invariant.Figure5.3Averageconsumptionbylawnsizequintile5.2.1ImpactoftheMandateTherewerenowaterrestrictionspriortothemandate,andthelimitationsonoutdoorwaterusagewereeasedafteratwoyearperiod.Inordertoexaminetheirimpactonwaterconsumption,Isplitthesampleintotwogroups:(1)householdswithlawns(theÒtreatmentÓgroup);and(2)those25withoutlawns(theÒcontrolÓgroup).3Inordertoseethedifferentialimpactbylawnsize,theÒtreatmentÓgroupwasagainsplitintoquintiles.ThefullspeciÞcationforthisestimationis:ln(wit)=!lawniq+"1restrictions+"2postrestrictions+#(lawniq#restrictions)+*(lawniq#postrestrictions)+(evapit+'(timetrend)+zi++it,(5.5)wherelawniqisthetreatmentdummyvariableequalto1ifhousehold(i)haslawnsizewithinquintile(q),restrictionsisadummyvariableequalto1duringtheperiodofmandatoryre-strictions(April2009toApril2011),postrestrictionsisadummyvariableequalto1fortheperiodaftertherestrictionswereeased(May2011toMarch2015),(lawniq#restrictions)and(lawniq#postrestrictions)aretheinteractionterms,zirepresentshouseholdÞxedeffects,and+itistheidiosyncraticerrortermÑ#and*aretheparametersofinterest.TheresultscanbefoundinTable5.2andtheysuggestthattherewasa5-6%reductioninoverallconsumptionfollowingthemandateÑthisisbasedonthemostbasicspeciÞcations(models1,2,5and6)whereahouseholdisclassiÞedaseitherhavingalawnornot.Models3,4,7,and8splitupthebasictreatmentgroup(lawn)intoquintiles.ThecoefÞcientsontheinteractiontermsofrestrictiondummyandlawnsizequintileshowthathouseholdsrespondeddifferentlytothemandate.Thosewithlargerlawnsreducedtheirconsumptionmoreduringtherestrictionsperiodrelativetothereferencegroupofquintileone.TheresultsfromadifferentgroupingoflawnsizecanbefoundinTableA.7,andtheyprovideforsimilarconclusions.Whenanalyzingtheseresults,itisimportanttorememberthatCaliforniaiscurrentlyinitsÞfthyearofaseveredrought.Duringthestudyperiod,severalstatewideinformationalcampaignsandnon-priceconservationprogramscouldhavealsoaffectedusage.MorespeciÞcallyintheMNWDservicearea,anewpricingstructure,theaforementionedwaterbudgets,wasimplemented3IÞrstseparatedevapotranspirationintoquintilesbyyear,ashottermonthsinducemore(outdoor)consumption.Ithenproducedscatterplotsofwaterdemand(y-axis)andirrigatedarea(x-axis)bytheevapotranspirationquintilesforthepre-mandate,mandate,andpost-mandateperiods.Iincludedahorizontallinetocaptureathresholdamountequivalenttowateringthreedaysperweek,15minuteseachday,foranentiremonth(severalthresholdswerecalculatedfordifferentspigot/sprinklerquantities).Themotivationforthisexerciseisthatthereshouldbeabindingamountofwaterinwhichcertainhouseholdswouldhavetochangetheirbehavior.Iexpectedtoseeaßatteningatthethresholdamountduringthemandateperiod,butunfortunately,thisexercisedidnotproduceanymeaningfulresults.26(1)(2)(3)(4)(5)(6)(7)(8)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)restrictions0.0319##-0.117###0.0229###-0.128###-0.0367##-0.0342##-0.0460###-0.0440###(0.0113)(0.0131)(0.00364)(0.00436)(0.0112)(0.0132)(0.00353)(0.00455)lawn*postrestrictions-0.0508###-0.0582###-0.0488###-0.0581###(0.0114)(0.0132)(0.0114)(0.0132)postrestrictions-0.207###-0.211###-0.00156-0.00179(0.0189)(0.00588)(0.0190)(0.00622)lawn*postrestrictions-0.0100-0.0128(0.0190)(0.0190)quint2*restrictions-0.0315###-0.0477###-0.0245###-0.0477###(0.00482)(0.00566)(0.00480)(0.00566)quint3*restrictions-0.0376###-0.0535###-0.0345###-0.0534###(0.00476)(0.00571)(0.00476)(0.00571)quint4*restrictions-0.0566###-0.0599###-0.0547###-0.0599###(0.00485)(0.00581)(0.00484)(0.00581)quint5*restrictions-0.0774###-0.0664###-0.0776###-0.0664###(0.00495)(0.00595)(0.00495)(0.00595)quint2*postrestrictions-0.0213##-0.0325###(0.00754)(0.00753)quint3*postrestrictions-0.0219##-0.0264###(0.00764)(0.00762)quint4*postrestrictions-0.00474-0.00729(0.00773)(0.00772)quint5*postrestrictions0.01470.0155#(0.00782)(0.00782)evapotranspiration0.137###0.148###0.137###0.148###0.146###0.146###0.146###0.146###(0.000700)(0.000710)(0.000701)(0.000711)(0.000708)(0.000709)(0.000708)(0.000709)ln(income)-0.233###-0.296###-0.224###-0.269###0.0845##0.0640#0.0980###0.107###(0.0314)(0.0281)(0.0316)(0.0285)(0.0281)(0.0294)(0.0282)(0.0298)timetrend-0.0440###-0.0417###-0.0440###-0.0421###(0.000443)(0.000640)(0.000443)(0.000639)_cons3.312###3.797###3.258###3.635###1.638###1.756###1.558###1.501###(0.186)(0.166)(0.187)(0.168)(0.166)(0.173)(0.166)(0.176)N14486531448653144865314486531448653144865314486531448653Notes:AllmodelsincludehouseholdÞxedeffects.Alllawndummyvariablesdroppedduetocollinearityandarenotreported.Quintile1(quint1)isreferencecategory.Standarderrorsareclusteredathouseholdlevelandinparentheses.#p<0.05,##p<0.01,###p<0.001Table5.2Estimatesoftheimpactofmandatorywaterrestrictionstwomonthsaftertherestrictionswereeased(inJuly2011).Thispotentiallycontaminatesthepostrestrictionresults,andthereforeitcannotbedeterminedwhetherhabitformationduetothemandateactuallyoccurred.InordertominimizethispotentialconfoundingandbemoreconÞdentintheresults,atimetrendtermwasaddedtomodels1through4(whichgenerated5through8).ThecoefÞcientonthistermshowsthatconsumptiondecreasedbyabout4%peryear.Theresultsfromthesetwosetsofmodelsarequitesimilar,whichsuggeststhatthemandateactuallychangedtheconsumptionbehaviorofhouseholdswithlargerlawnsmorethanthosewithsmallerlawns.275.3Structuralvs.Reduced-FormEstimationThepriceelasticityofdemandisakeyvariableofinterestinthewaterdemandliterature,aswatersuppliersusepricetoinduceconservationandgeneraterevenue.AsmentionedinChapter2,re-searchershaveutilizedDCCmodelsandIVtechniquestoaddresstheendogeneitypresentinblockpricing.Ingeneral,theDCCapproachisconsideredtobebetterthanIVmethodsbecauseoftheirlarge-samplepropertiesofconsistency,asymptoticnormality,andasymptoticefÞciency(MofÞtt1986).Theyarealsoabletomodelboththediscreteandcontinuouschoiceinherentinblockrates,andareconsistentwithutilitytheory.Additionally,IVmethodsdonotaccountforthepotentialbunchingaroundkinkpoints.However,Olmstead(2009)pointsoutthatÒcheaperÓmodels,suchasthesereduced-formmethods,maybeappropriateforcertainpurposes.Thedownsidetobothtechniquesisthattheyassumeconsumersknowandarerespondingtothemarginalpricesignals.StructuralestimationusingtheDCCmodelandthesamedatasethasbeenconductedbyKen-nethBaerenklauandKurtSchwabeforaninternalMNWDreport.TheirmaximumlikelihoodestimationresultscanbefoundinTableA.8.Becausestructuralestimationhasalreadybeencar-riedout,traditionalIVtechniquesareexploredinstead.Veryfewpreviousstudieshavehadtheopportunitytomakesuchamethodologicalcomparison,andtheDCCresultswillbeusedasbase-lineestimatesfortheexercisethatfollows.TheideabehindtheseIVmethodsistoinstrumentthemarginaloraveragepricewithvarioussummarystatisticsofthenonlinearpriceschedule.ÒThisamountstoapproximatingthenonlinearpriceschedulewithalinearfunctionofthemarginalprices.Thisprocedureisvalidtotheextentthatthislinearapproximationholds(sothattheobservedmarginalpricesarestronglycorrelatedwiththeinstruments)andtotheextentthattheerrortermisuncorrelatedwiththecharacteristicsofthetariffstructureusedasinstruments(sothattheexclusionrestrictionissatisÞed)Ó(Szabo2015,p.16).Fourinstrumentswereexamined,andtheyincludetwoofthemostcommonfoundintheliter-ature(1&2)andtwomorerecentones(3&4):28(1)WilderandWillenborg(1975):theÞrststageinvolvesregressingobservedmarginalpriceonthecharacteristicsofthepricestructure(Þxedchargesandthefullsetofmarginalprices),aswellasalloftheexogenouscovariates.Thepredictedvaluesofpriceandtheexogenouscovariatesareusedinthesecondstage.(2)McFadden,Puig,andKirschner(1977):theÞrststageinvolvesregressingobservedwaterdemandonthemarginalpricesatpresetquantities,andusingthepredictedconsumptiontocomputepredictedmarginalpriceandvirtualincome.Inthesecondstage,thesepredictedvaluesareusedasright-hand-sidevariablesinthedemandequation.(3)Olmstead(2009):theobservedmarginalpriceandvirtualincomeareinstrumentedbythemarginalpricesatpresetquantities(thekinkpoints).(4)Szabo(2015):theaveragepriceisinstrumentedbythemarginalpricesofconsumingatpresetquantities(themostcommonkinkpoints).Thebasicanalyticalmodelusedtodescribehouseholdwaterdemandinthissectionis:ln(wit)=!ln(pit)+"ln(÷yit)+zit#+$it(5.6)wherewitisthemonthlywateruseofhousehold(i),pitisthepriceofwaterfacedbythehousehold(eithermarginalortheinstrument),÷yitisvirtualincome,zitisavectorofhousehold,economicandenvironmentalcharacteristicsthatarethoughttoaffectusage,and$itistheidiosyncraticerrorterm.ForeaseofcomparisonwithTableA.8,thesameexogenousvariablesusedintheDCCmodelswereincludedintheIVmodels.BaerenklauandSchwabeconsideredadifferentapproachforeachratestructure:(1)thepre-ratechangemodelutilizedhouseholdÞxedeffects;and(2)thepost-ratechangemodelusedtime-invariantsocio-demographiccharacteristics.Thepre-andpost-ratechangeresultscanbefoundinTable5.3and5.4,respectively.4Theresultsarequitesensitivetothechoiceofinstrument,exogenousvariables,andspeciÞcation.WhatisimmediatelystartlingisthefactthatallsigniÞcantpriceparameterestimates,6ofthe8elasticities,arepositive.Moreover,underagivenpricestructure,themodelsproducerelativelysimilarestimatesforprice.Forthesakeofcomparison,theDCCmodelinTableA.8generatesapriceelasticityof-0.009underincreasingblockratesand-3.073underwaterbudgets.4TheÞrststageestimatesandresultsfromtestingforweakinstrumentsareavailableuponrequest.AllfourinstrumentsproducedF-statisticsgreaterthan10underbothratestructures.29(OLS)(SzaboIV)(OlmsteadIV)(McFaddenIV)(WilderIV)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)spring0.0653###0.140###0.114###0.0963###0.148###(0.00109)(0.00124)(0.00141)(0.00155)(0.00131)summer0.0139###0.236###0.191###0.163###0.260###(0.00146)(0.00171)(0.00208)(0.00197)(0.00169)fall-0.00473###0.236###0.204###0.191###0.257###(0.00139)(0.00159)(0.00189)(0.00153)(0.00157)restrictions-0.0713###0.0513###-0.0166###-0.0796###0.0724###(0.00119)(0.00139)(0.00151)(0.00172)(0.00146)evapotranspiration0.0954###0.127###0.140###0.161###0.113###(0.000519)(0.000568)(0.000666)(0.000666)(0.000702)timetrend-0.137###0.0451###-0.00593###-0.0528###0.0609###(0.00103)(0.00120)(0.00145)(0.000972)(0.00120)ln(income)7.165###18.88###9.101###20.95###(0.0663)(0.0828)(0.144)(0.0924)ln(predicted_income)-3.633(2.849)lnap0.543###(0.00860)ln(mp)1.896###0.287###(0.00747)(0.0100)ln(predicted_mpM)-0.599(0.412)ln(predicted_mpW)0.540###(0.0107)_cons-40.06###23.59-122.3###(0.394)(16.93)(0.548)N716188716188716188716188666864Note:AllmodelsincludehouseholdÞxedeffects.apisforaverageprice.mpisformarginalprice.MisforMcFadden.WisforWilder.Standarderrorsareclusteredatthehouseholdlevelandinparentheses.#p<0.05,##p<0.01,###p<0.001Table5.3Pre-ratechangemodelsOnerelativelysimpleexplanationforthisapparentcontradictionwitheconomictheoryandtheDCCmodelisthattheseinstrumentsmaynotbecorrectingfortheendogeneitypresentinincreas-ingblockrates.Amorefundamentalexplanationisthatthisisadifferenttypeofendogenetiythanthatfoundinsaytheeducationliterature.Waterusageandpriceareintrinsicallyconnectedvariables,andaninstrumentcorrelatedwithpriceisbynecessitycorrelatedwithusage.Therefore,IconcludethatIVtechniquesmaynotbeappropriateforwaterdemandestimationunderblockrates.30(OLS)(SzaboIV)(OlmsteadIV)(McFaddenIV)(WilderIV)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)spring0.0215###0.110###-0.0633###0.116###0.101###(0.00122)(0.00191)(0.0139)(0.00200)(0.00207)summer-0.148###0.178###0.0338##0.182###0.130###(0.00166)(0.00237)(0.0126)(0.00226)(0.00396)fall-0.198###0.188###0.284###0.189###0.126###(0.00175)(0.00194)(0.00610)(0.00158)(0.00465)restrictions-0.158###-0.0800###0.0593###-0.0745###-0.0987###(0.00110)(0.00167)(0.00560)(0.00179)(0.00218)evapotranspiration0.0663###0.158###0.217###0.153###0.134###(0.000621)(0.000905)(0.00593)(0.000982)(0.00188)timetrend-0.280###-0.0523###0.0538###-0.0540###-0.111###(0.00113)(0.00128)(0.00452)(0.000981)(0.00402)education0.215###0.580###-9.207###0.834###0.501###(0.0265)(0.0455)(0.478)(0.0436)(0.0467)householdsize0.0839###0.158###0.110###0.160###0.163###(0.00325)(0.00517)(0.0270)(0.00530)(0.00543)ln(lawn)0.135###0.334###-0.0819###0.345###0.289###(0.00272)(0.00389)(0.0247)(0.00387)(0.00493)ln(income)0.0621###0.536###21.01###0.360###(0.0160)(0.0286)(0.870)(0.0309)ln(predicted_income)2.478(2.904)ln(ap)0.0333##(0.0115)ln(mp)3.126###0.733###(0.0118)(0.0344)ln(predicted_mpM)0.158(0.419)ln(predicted_mpW)0.787###(0.0510)_cons0.949###-4.532###-119.5###-16.21-2.971###(0.0966)(0.166)(4.908)(17.26)(0.193)N701932701932701932701932653752Note:apisforaverageprice.mpisformarginalprice.MisforMcFadden.WisforWilder.Standarderrorsareclusteredatthehouseholdlevelandinparentheses.#p<0.05,##p<0.01,###p<0.001Table5.4Post-ratechangemodels31CHAPTER6CONCLUSIONOneoftheprincipaltoolsthatwatersuppliershavetoinduceconservationispricestructure.Withanincreaseinthefrequencyofextremeweatherevents,areductioninthereliabilityofcurrentwatersupplies,agrowingconcernabouttheenvironmentaleffectsofnewsupplyprojects,andlegalconstraintswithregardstopricing,thesesuppliersareturningtomorecomplexratestructuresandnon-priceconservationinitiativestoachievereductionsindemand,maintainÞscalstability,andpromoteequity.TheMoultonNiguelWaterDistrictutilizedbothofthesestrategies,implementingincreasingblockratewaterbudgetsandmandatoryoutdoorwaterrestrictionsbetween2007and2015.Inordertoexaminepriceresponsivenessunderblockrates,muchoftheresidentialwaterde-mandliteratureassumesthatconsumersareperfectlyinformedandperfectlyoptimizingonthemargin.However,thereisagrowingbodyofevidencethatÞndsthatconsumersoftendonotre-spondtotheirtruemarginalprice.Infact,manyconsumersareinattentivetothedetailsofagivenpricingscheduleandarequiteuncertainabouttheirconsumptionpatterns.Therearemanypossi-blereasonsforthistypeofbehavior,suchasalackofinformationaboutthepricingscheduleandthefactthatbillsaggregatemanydisparateindividualdecisionsyetrepresentasmallshareoftotalincome.Asmanyeconomicpoliciesutilizeblockrates,understandinghowconsumersactuallyrespondtothemiscritical.Tothebestofmyknowledge,thisisoneoftheonlypaperstoexaminepriceperceptionwhenfacingblockratesforwater,andIÞndstrongevidencethathouseholdsarenotrespondingtomarginalprice.Theseconsumersinsteadrespondtoafunctionofmarginalandaverageprice.Additionally,theaveragehouseholdinmysamplepredictstheirconsumptionwithastandarderrorofapproximately27%.ThisimpliesthatitisquitedifÞculttoinferpriceresponsivenessofdemandfromchangesarounddiscontinuitiesinmarginalprice.Giventhecostofimplementing32increasingblockrates,speciÞcallywaterbudgets,thissuboptimizationbehaviorsuggeststhattheremaybemorecost-effectivepricestructuresandwaystoinduceconservation.Onealternativethatseveralsuppliersuseiscommand-and-controlpolicies,whichcanstillintroducecostandefÞciencyconcerns.IÞndthatmandatoryoutdoorwaterrestrictionsdecreasedoverallconsumptioninthedistrictbyapproximately5%.Whenhouseholdswerethengroupedbylawnsize,thosewithlargerlawnsreducedtheirconsumptionmoreduringtherestrictionsperiod.ThelastexerciseconductedinthispaperwastheuseoftraditionalIVmethodstoaddresstheendogeneitypresentunderblockpricing.IÞndthattheparameterestimatesareverysensitivetothechoiceofinstrument,exogenousvariables,andspeciÞcation.Moreover,positiveelasticitieswereobtained.TwopossiblereasonsforthisapparentcontradictionwitheconomictheoryandtheDCCmodelisthateithertheinstrumentsdidnotcorrectfortheendogeneity,orthattheintrinsicconnectionbetweenwaterusageandpricemayimplythatIVtechniquesareinappropriateforwaterdemandestimationunderblockrates.Severalcomponentsofthispaperwillberesearchedfurtherinthenearfuture.Theyinclude:(1)determininghowandwhichtypesofconsumersareabletominimizetheerrorintheirpredictiveability;(2)examiningclusteringunderwaterbudgetswithalternativeapproaches;(3)investigatingtheeffectivenessofnon-priceconservationprograms,andhowknowledgeorinformationisspreadinparticipatingcommunities;(4)comparingstructuralandreduced-formapproachesinotherwaterdistricts;(5)studyingthenon-convexitiespresentinthewaterbudgetratestructure;(6)determin-ingifinformationprovisionhelpsconsumersrespondtomarginalprice;and(7)examiningvariousformulationsofanoptimalpricingproblem.33APPENDIX34APPENDIXAA.1FiguresNote:IBRrepresentsblocksizesunderincreasingblockrates,whichwerethesameforeveryhousehold,whileHHS_#isthetypicalwaterbudgetallocationforagivenhouseholdsizein2011.Underwaterbudgets,IcalculatedBlock1using30daysforabillingcycle;theBlock2calculationusedmeanirrigatedareaforeachhouseholdsizeandmeanevapotranspirationforthesample;Blocks3and4are125%and150%,respectively,ofthesumofBlocks1and2.FigureA.1Typicalblockallocationbyhouseholdsize35FigureA.2Histogramofblocksizesunderwaterbudgetsin201236FigureA.3Averageconsumptionbymonth37FigureA.4Nominalratechanges38FigureA.5Consumptiondistributionunderincreasingblockratesbymonth39FigureA.6Consumptiondistributionunderwaterbudgetsbymonth40Note:RecallfromChapter5thatonly5%and3%ofthesamplehaveahouseholdsizeof5and6,respectively.FigureA.7Consumptiondistributionunderwaterbudgetsbyhouseholdsize41FigureA.8ScaledquantitiesunderincreasingblockratesFigureA.9ScaledquantitiesunderwaterbudgetsNote:Verticalredlinesrepresentkinkpoints.Truncatedatscaledquantityof6(5.4is99thpercentile).Scaledquantity=((blockusage)/(blockallocation))+1forblock2;2forblock3;3forblock4;4forblock5.42Source:MoultonNiguelWaterDistrict,2015aFigureA.10CostallocationsfortheMoultonNiguelWaterDistrict43Source:MoultonNiguelWaterDistrict,2015bFigureA.11MicrozonesintheMoultonNiguelWaterDistrict44A.2TablesRate20002002200420062008201020122014Decreasingblock%3531252428191816Uniform%3637394032313030Increasingblock%2932363640495254Source:2014WaterandWastewaterRateSurvey,AmericanWaterWorksAssociation,2015TableA.1ResidentialwaterratestructuredistributioninNorthAmericabywatersupplierTraditionalIBR(May)WaterBudgets(July)BlockNominalRealNominalRealBlock11.161.181.381.42Block21.301.321.541.59Block31.571.602.752.84Block41.841.875.515.69AboveBlock41.972.0011.0211.38TableA.2WaterpriceperCCFin2011VariableFullSampleBlock1Block2Block3Block4Block5Fractionofobservations1.000.420.370.130.060.02Consumption(CCF/month)15.426.4914.7924.6037.7273.80Evapotranspiration(inches/month)4.313.934.384.815.005.14Householdsize4.053.784.174.324.454.53Irrigatedarea(feet2)3495185832324918791617050Realbudget(2013,$/month)371.5369.5371.7373.3376.8378.4Bachelorsdegree(%)32.933.932.331.432.235.0Mastersdegree(%)4.03.24.04.66.08.9Medianage42.641.042.644.246.249.1Medianhousevalue(2013,$1000)619.0563.3623.5666.5751.9914.4Populationdensity(peoplepersq.mile)628672376134530242752581Housingunitsincensusblock691711702657607568Note:RepresentsdatafromJuly2011untilMarch2015.Includes732,465observations.Blocksizeswerecalculatedusingpre-ratechangecutoffs.TableA.3Summarystatisticsunderwaterbudgetsbymarginalconsumptionblock45VariableMeanStd.Dev.HouseholdsHighefÞciencywashersrebated0.0970.3262053(12.6%)HighefÞciencytoiletsrebated0.0970.4651688(10.4%)HighefÞciencynozzlesreceived000Dripirrigationinstalled(linearfeet)0.46524.952142(0.87%)Turfgrassremoved&replacedwithnatives(sq.feet)2.03352.288149(0.92%)Turfgrassremoved&replacedwithsynthetic(sq.feet)2.97851.896202(1.2%)TableA.4Summarystatisticsofnon-priceconservationprogramsIncreasingBlockRatesWaterBudgets(OLS)(McFaddenIV)(OLS)(McFaddenIV)ln(usage)ln(usage)ln(usage)ln(usage)ln(mp)0.874###0.124###(0.00960)(0.00333)ln(lagap/mp)-1.391###-0.320###(0.00915)(0.00333)ln(pred_mp)0.605###1.029###(0.0283)(0.0119)ln(pred_lagap/mp)0.0621###-0.293###(0.00991)(0.00495)ln(lagusage)0.373###0.383###0.400###0.145###(0.00197)(0.00383)(0.00234)(0.00482)spring-0.0806###-0.0779###-0.0942###-0.0946###(0.00116)(0.00147)(0.00136)(0.00153)summer-0.100###-0.0846###-0.0502###-0.0525###(0.00140)(0.00190)(0.00139)(0.00155)fall-0.0361###0.0744###0.116###0.129###(0.00115)(0.00146)(0.00104)(0.00116)evapotranspiration0.0923###0.161###0.152###0.0728###(0.000498)(0.000877)(0.000525)(0.00111)timetrend-0.0758###-0.0197###0.0154###0.00602###(0.000953)(0.00107)(0.000436)(0.000506)restrictions-0.0969###-0.0694###(0.000840)(0.00111)_cons1.289###0.930###0.591###0.957###(0.00656)(0.00772)(0.00673)(0.00956)N699911699911716188716188k0.10-0.28Note:AllmodelsincludehouseholdÞxedeffects.mpformarginalprice.apforaverageprice.predforpredictedvalue.Standarderrorsareclusteredathouseholdlevelandinparentheses#p<0.05,##p<0.01,###p<0.001TableA.5EstimatesfromShinÕspartialadjustmentpriceperceptionmodel46IncreasingBlockRatesWaterBudgets(1)(2)(3)(4)usagempusagemplaggedusage0.710###0.606###(0.000749)(0.000738)block1p14687.6###6199.7###(384.0)(455.9)block2p-4264.0###9905.3###(188.7)(406.7)block3p5454.4###3929.4###(352.9)(347.8)Þxedsewer1618.6###-3106.2###(167.0)(176.8)irrigatedarea0.000468###0.000602###(0.00000231)(0.00000196)evapotranspiration2.048###1.742###(0.00718)(0.00533)income0.0157###0.0398###(0.000206)(0.000100)predicted_usage0.0113###0.0699###(0.0000181)(0.000162)_cons-15.43###1.031###-32.31###1.029###(0.546)(0.000372)(0.616)(0.00316)N699911699911716188716188Standarderrorsinparentheses#p<0.05,##p<0.01,###p<0.001TableA.6FirststageresultsforShinÕspartialadjustmentpriceperceptionmodel47(1)(2)(3)(4)(5)(6)(7)(8)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)ln(usage)restrictions0.0319##-0.117###0.0321##-0.117###-0.0367##-0.0342##-0.0365##-0.0326#(0.0113)(0.0131)(0.0113)(0.0131)(0.0112)(0.0132)(0.0112)(0.0132)lawn*restrictions-0.0508###-0.0582###-0.0488###-0.0581###(0.0114)(0.0132)(0.0114)(0.0132)postrestrictions-0.207###-0.207###-0.001560.000790(0.0189)(0.0189)(0.0190)(0.0190)lawn*postrestrictions-0.0100-0.0128(0.0190)(0.0190)verysmallinteraction-0.004850.00155-0.003750.00177(0.0139)(0.0165)(0.0139)(0.0165)smallinteraction-0.0149-0.0255-0.0143-0.0254(0.0119)(0.0138)(0.0118)(0.0138)mediuminteraction-0.0450###-0.0614###-0.0390###-0.0613###(0.0116)(0.0135)(0.0116)(0.0135)largeinteraction-0.0588###-0.0698###-0.0572###-0.0696###(0.0117)(0.0136)(0.0116)(0.0136)extrainteraction-0.0799###-0.0773###-0.0798###-0.0772###(0.0117)(0.0136)(0.0117)(0.0136)superinteraction-0.149###-0.0782##-0.154###-0.0782##(0.0214)(0.0248)(0.0214)(0.0248)verysmallpostinter0.009220.00766(0.0230)(0.0230)smallpostinter-0.0146-0.0154(0.0197)(0.0197)mediumpostinter-0.0217-0.0311(0.0193)(0.0194)largepostinter-0.0154-0.0172(0.0194)(0.0194)verylargepostinter0.003220.00360(0.0194)(0.0195)extremelypostinter0.0959##0.106##(0.0328)(0.0328)timetrend-0.0440###-0.0417###-0.0440###-0.0421###(0.000443)(0.000640)(0.000443)(0.000640)evapotranspiration0.137###0.148###0.137###0.148###0.146###0.146###0.146###0.146###(0.000700)(0.000710)(0.000701)(0.000711)(0.000708)(0.000709)(0.000708)(0.000709)ln(income)-0.233###-0.296###-0.221###-0.269###0.0845##0.0640#0.100###0.105###(0.0314)(0.0281)(0.0315)(0.0284)(0.0281)(0.0294)(0.0282)(0.0298)_cons3.312###3.797###3.242###3.636###1.638###1.756###1.545###1.512###(0.186)(0.166)(0.186)(0.168)(0.166)(0.173)(0.166)(0.176)N14486531448653144865314486531448653144865314486531448653Note:Lawnsizesbinnedbypercentiles.0<VerySmall<10th;10th!Small<25th;25th!Medium<50th;50th!Large<75th;75th!VeryLarge<99th;ExtremelyLarge$99th.AllmodelsincludehouseholdÞxedeffects.Alllawndummyvariablesdroppedduetocollinearityandarenotreported.nolawnisreferencecategory.Standarderrorsareclusteredathouseholdlevelandinparentheses.#p<0.05,##p<0.01,###p<0.001TableA.7Estimatesoftheimpactofmandatorywaterrestrictions48(Pre-RateChange)(Post-RateChange)ln(usage)ln(usage)spring0.0958###0.213(0.0021)(0.1721)summer0.1639###0.4518###(0.0021)(0.1118)fall0.1914###0.2505###(0.0011)(0.0217)restrictions-0.0821###(0.0009)evapotranspiration-0.0821###0.1433###(0.0004)(0.038)timetrend-0.052###-0.0104(0.0005)(0.0169)ln(mp)-0.009###-3.0732###(0.0009)(0.2183)ln(income)-0.0001-0.0765(0.0006)(0.1111)education0.2181(0.139)householdsize0.6258###(0.0411)lawnsize0.0812###(0.0017)_cons0.6858(0.6004)N716188716188Note:(Pre-RateChange)includeshouseholdÞxedeffects,while(Post-RateChange)onlyincludestime-invariantdemographicvariables.Standarderrorsinparentheses#p<0.05,##p<0.01,###p<0.001TableA.8EstimatesfromtheDCCmodel49A.3DescriptionofOutdoorFactorsforWaterBudgetsThesourceforthissectionisMNWD(2015a).(1)Irrigableareaistheamountoflandscapedareaonthepropertythatreceivesregularwater-ing,andthisincludespoolsandspas.GISandCountyAssessorparceldatawereusedtodeterminetheirrigableareaforeachhome.(2)Evapotranspiration(ET)istheamountofwaterlostduetoevaporationandplanttranspira-tion.Evaporationwillvaryduetofactorssuchaswind,humidity,andtemperature.Planttranspirationistheamountofwaterthatplantslosefromtheirleavesandplanttissues.TheETrateismeasureddailyby110virtualweatherstationsinMNWDÕsservicearea.Eachweatherstationisassociatedwithamicrozone(seeFigureA.11foramapofthemicro-zones),withtheactualETcorrespondingtoamicrozoneaddedupforeachdayinthebillingcycle.ThereishighermonthlyETduringsummermonths.(3)TheplantfactormeasuresthespeciÞcamountofirrigationwaterrequiredbyeachtypeofplant.Forexample,turfgrasshasaplantfactorbetween0.6and0.8,whilewater-efÞcientplantscanhaveaplantfactorofonly0.3.Residentialwaterbudgetsarecalculatedusingaplantfactorof0.7.50BIB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