production using revealed preferences andhousehold Is the environment a luxury? An empiricalinvestigation Resource and Energy Economics

ContentslistsavailableatScienceDirect

Resource and Energy Economics

jo u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / r e e

Is the environment a luxury? An empirical investigation using revealed preferences and household production

Chiara Martini

, Silvia Tiezzi

aDepartmentofEconomics,UniversityofRome–RomaTre,viaSilvioD’Amico77,00145Roma,Italy

bDepartmentofEconomicsandStatistics,UniversityofSiena,PiazzaSanFrancesco7,53100Siena,Italy

a r t i c l e i n f o

Articlehistory:

Received3September2012

Receivedinrevisedform8November2013 Accepted25November2013

Availableonline4December2013

JELclassification:

H22 H23 D63

Keywords:

Incomeelasticityofwillingnesstopay Householdproduction

Mixeddemandsystems Integrability

a b s t ra c t

Thispapercombinesdemandanalysiswithhouseholdproduction toestimatethemarginalwillingnesstopayforimprovementsinair qualityinItalyandthecorrespondingincomeelasticityofwilling- nesstopay.WeusechoicebaseddataonItalianhouseholds’current consumptionexpendituresfromJanuary1999toDecember2006 mergedwithanairqualityindex.Weconsistentlyfindthatthe incomeelasticityofwillingnesstopayforenvironmentalquality isveryclosetooneacrossincomegroups.Besidescontributingto astrandofliteraturewherethereisscantempiricalevidence,we providethefirstattemptatimplementingthetheoreticalapproach suggestedbyEbert(2007),whichderiveswillingnesstopayandits incomeelasticityusingrevealedpreferencescombinedwithhouse- holdproduction.

©2013ElsevierB.V.Allrightsreserved.

1. Introduction

Theobjectiveofthispaperistoestimatethewillingnesstopay(WTP)andtheincomeelasticity ofWTPforimprovementsinairqualityinItalyusinganewmethodologicalapproach,proposedby Ebert(2007),andanewdataset.

∗ Correspondingauthor.Tel.:+393337611200.

E-mailaddresses:cmartini@uniroma3.it,martinichi@gmail.com(C.Martini),silvia.tiezzi@unisi.it(S.Tiezzi).

1 Authorsorderisalphabetical.

0928-7655/$–seefrontmatter©2013ElsevierB.V.Allrightsreserved.

http://dx.doi.org/10.1016/j.reseneeco.2013.11.014

Themethodologyappliedinthispaper(Ebert,2007)isbasedonthefollowingassumptions:(i)a complete(conditional)demandsystemformarketgoods,whichmaydependonenvironmentalgoods, canbeobserved;(ii)ahouseholdproductionfunction,combiningmarketandenvironmentalgoods accordingtoagiventechnology,isknown;(iii)theenvironmentalgoodsconsidereddonotenterthe utilityfunctiondirectly.Usingtheseassumptions,Ebertshowsthatonecanderivethemarginalwill- ingnesstopayfunctionsforthenonmarketgoodswhichaugmenttheconditionaldemandsystem.

Thenonehastoinvestigatetheintegrabilityofthemixeddemandsystemconsistingofthedemand functionsformarketgoodsandtheinversedemandfunctionsforthenonmarketgoods.Iftheintegra- bilityconditionsaresatisfied,auniquepreferenceorderingcanberecoveredwiththepossibilityof performingwelfareanalysisandofestimatingimportantderivedparameters,liketheincomeelasticity ofwillingnesstopay.

Toimplementthisapproachweconsiderhouseholdproductionoftheinternallevelofairquality chosenbythehouseholdsandassumethattheycombineamarketgood,airconditioning,withanon marketgood,thelevelofexternalairquality,accordingtoagiventechnologytoproducethedesired levelofinternalairquality.Sincethehouseholdproductionfunctionimplicitlydescribesthemarginal rateofsubstitutionbetweenairqualityandairconditioning,wecancomputethemarginalwillingness topayformarginalimprovementsinairquality.Wethusestimateacompleteconditionaldemand systemformarketgoodsaugmentedbytheWTPfunctionforimprovementsinairquality.Thedata setweuseisobtainedbymergingdataonItalianhouseholdsmonthlycurrentexpenditureandunique informationonabundleofairpollutantsconcentrations.Weshowthattheresulting(mixed)demand systemisintegrableandwecomputethemarginalwillingnesstopayforamarginalincreaseinthe indexofairqualityandthecorrespondingincomeelasticityofWTP.Besidescontributingtoastrandof literaturewherethereissurprisinglylittleempiricalevidence,thisisthefirstattemptatimplementing theapproachdevelopedbyEbert(2007),usingdemandanalysiscombinedwithhouseholdproduction toestimateWTPforanonmarketgood.

WefindanincomeelasticityofWTPnotsignificantlydifferentfromoneacrossincomegroups.Our findingshaverelevantpolicyimplications.Growthinincomeandinenvironmentalqualitycouldbe decoupledashigherincomegroupswouldnotshowstrongerpreferencesforenvironmentalquality thanlowerincomegroupsdo.TheincomeelasticityofWTPisalsolikelytoinfluencecost-benefit analyses,becauseignoringtherealincidenceofsocialprojectsmayproducedecisionsthatare“biased”

againstthepoor.¹Moreover,theincomeelasticityofWTPforenvironmentalbenefitsisimportantfor shapingefficientenvironmentalpolicies.ChichilniskyandHeal(1994)showthat,ininternational agreementsforcurbingcarbon-dioxideemissions,poorercountriesshouldbeallocatedlargershares ofthetotalnumberofemissions’rightsatanefficientallocation,iftheincomeelasticityofWTPis betweenzeroandone.Finally,thepoliticalappealofenvironmentalpolicieswouldbeincreasedrather thanlimited,sinceincomegroupswouldbenefitfromenvironmentalimprovementsinaproportional way.

Theremainderofthepaperisstructuredasfollows.Section2reviewstheliteratureonthemethods forestimatingthedemandfornonmarketgoodsandonthemeasuresofincidenceofenvironmental benefits.Section3introducesthemethodologybasedonrevealedpreferencesandhouseholdproduc- tion.Thespecificationofthedemandsystem,theestimationstrategy,thedata,andtheresultsare presentedinSections4and5.Section6concludes.

2. Demandfornonmarketgoodsandmeasuresofbenefitsincidence

Researchersfacetwomainproblemswhentryingtoevaluateenvironmentalgoods:firstthese goodsarenottradedinmarkets,thereforeitisnotpossibletoobserveprices.Second,eventhough priceswereobservable,theymightnotreflecttheconsumer’smarginalwillingnesstopaybecause

1GiventheuseoftheHicks-Kaldorcompensationcriterion,aprojectresultinginaregressivedistributionofenvironmental benefitsislesslikelytopassthanaprojectthatwouldprimarilybenefithighincomegroups.Thisisbecausethesocialprofitability oftheprojectisdecidedbythesumofWTPsandrichpeoplehaveahigherWTPthanpoorpeople(HökbyandSöderqvist,2003).

Therefore,thefindingthatenvironmentalbenefitsareregressivelydistributedsuggeststheneedtouseappropriateweights takingintoaccountthedistributionofcostsandbenefitsofprojects.

thequantityofanenvironmentalgoodistypicallyrationedandcannotbemodifiedbyconsumers,at leastintheshortrun.Becauseofthepublicgoodnatureofenvironmentalcommodities,therelevant incidencemeasureisnottheincomeelasticityofdemand,buttheincomeelasticityofwillingnessto pay(KriströmandRiera,1996).Inthissectionwereviewbothissues:howtoestimateWTPandhow tomeasurebenefitsincidence.

Sincetheearlyseventiesdifferentapproacheshavebeenadoptedtoestimatethedemandforpublic goods.Thefirstwasacollectivechoiceapproachbasedonthemedianvotertheorem(Boercherding andDeacon,1972;BergstromandGoodman,1973).Theassumptionisthatpoliticaldecisionsaboutthe levelofexpendituresonpublicgoodswillbeidenticaltothequantitydemandedbythemedianvoter.

Theexpenditureofanymunicipalityonapublicgoodisassumedtobeanobservationonthedemand curvefortheconsumercharacterizedbythemedianincomeofthatmunicipality.Thisapproachhas beenpartiallyoutdatedinrecentyears.Champetal.(2003),Freeman(2003),andMälerandVincent (2005)provideusefulandbroadoverviews.

Thehedonicandlocationchoiceapproacheshavebeenwidelyused,sincetheseminalpaperby Rosen(1974),formeasuringthevalueofpublicgoods,includingcleanair,especiallyintheUnited States.Theappealofthisapproachisgivenbytheuseofobservedbehaviorinthehousingandlabor marketstoinferthevalueofnon-marketgoods.Themarginalwillingnesstopayforpublicgoods ismeasured,inthiscase,bytheirimplicitpricesasreflectedinhousingpricesandwages.Recent methodologicalinnovationscanbefoundinBajariandBenkard(2005),Ekelandetal.(2004),and Bayeretal.(2009).Inparticular,Bayeretal.(2009)showhowmigrationcostscanbeincorporated intoahedonicanalysis,includingmigrationintothecanonicalwage-hedonicmodel(Roback,1982).

AnotherimportantsurveybasedapproachwasintroducedbyBergstrometal.(1982)whofitted demandequationsforlocalpublicservicesondatafromahouseholdsurveyondemandsforpublic spendingsuppliedbytheUniversityofMichigan.Thiswasfollowedbytheflourishingofcontingent valuation(CV)studiesusingstatedpreferencestoestimateWTPforpublicgoods,suchasKriström andRiera(1996),Alberinietal.(1997),HökbyandSöderqvist(2003),Schläpfer(2006)tociteafew.

Finally,theavertingbehaviorapproachemploysthedemandformarketgoodsasaproxyforenvi- ronmentalgoodsorservices(Costa,1997;PereyraandRossi,1999;Ghalwash,2006).Severalstudies –suchasBergeretal.(1987),DickieandGerking(1991),Bresnahanetal.(1997)andMansfieldetal.

(2006)amongothers–usedavertingbehaviortoobtainWTPvaluesforareductioninexposuretoair pollutantsorinthesymptomsthatresultfromit.DickieandGerking(1991),forexample,presentan applicationofthehouseholdproductionapproachtovaluingpublicgoods.Technicalrelationshipsare estimatedbetweenhealthattributes,privategoodsthataffecthealth,andairquality.Resultsshow thatindividualsequatemarginalratesoftechnicalsubstitutioninhouseholdproductionwithrelevant priceratios.Differently,Mansfieldetal.(2006)combinestatedpreferenceandavertingbehaviordata toestimateparents’WTPforadecreaseinchildrenexposuretoozonepollution.Bergeretal.(1987) developamodeltoevaluatechangesinriskstohumanhealthandderivewillingnesstopayusing bothcostofillnessandavertingexpendituresincludingairconditioners.

Clearly,eachoftheapproachesoutlinedherehasitsadvantagesanddisadvantages,theanalysisof whichwouldbeoutofthescopeofthispaper.Itisimportanttohighlightthatthetheoreticalapproach developedbyEbert(2007)isanalternativemethodforestimatingWTP,whichwillbediscussedin thefollowingsections.

OnceanestimateoftheWTPfunctionforimprovementsinoneenvironmentalgoodisavailable,the incomeelasticityofWTPcanbecalculated.Correctlymeasuringtheincidenceofenvironmentalpoli- ciesiscrucialforassessingtheirdistributionaleffectsandhasveryimportanteconomicandpolitical consequences.Forexample,howthenetbenefitsofenvironmentalimprovementswillbedistributed byincomelevelsisveryimportantwhenevaluatingreforms,liketheKyotoprotocol,thatwillaffect othercountriesorgenerationsordifferentgroupsofcitizenswithinacountry.Dependinguponthe distributionofcostsandbenefits,environmentalpoliciesmaybepro-richorpro-poor.Environmental benefits,expressedasafractionofincome,areprogressivelydistributedwhentheyrisewithincome.

Inthiscasethecorrespondingenvironmentalpolicyispro-rich.Environmentalbenefitsare,instead, regressivelydistributed,andenvironmentalpoliciesarepro-poor,whentheyfallwithincome.²

Thedegreeofprogressivenessmaylimitapolicy’spoliticalappeal.Ifenvironmentalbenefitsare progressivelydistributed,forexample,opponentsofenvironmentalpolicies(thinkoftheU.S.refusalto ratifytheKyotoprotocol)couldgroundtheirargumentsondistributionalissuesbecause“...excessive concernwiththeenvironmentisbasicallymiddleclass”(Beckerman,1974,p.49).Paradoxically,itcould bearguedthatfurtherimplementationofenvironmentalpolicieswouldresultinaredistribution againstlowerincomegroups.

Sincethequantityofmostenvironmentalgoodsisrationed,theincomeelasticityofWTPfora fixedquantityofthepublicgoodratherthantheincomeelasticityofdemandistherelevantparam- eterformeasuringbenefitincidence.Themainproblemisthatwecannotdirectlyobserveindividual demandandpricesforapublicgood.Differentapproacheshavebeenadoptedintheliterature.The mainoneusesstatedpreferencedatabasedoncontingentvaluationsurveys(KriströmandRiera, 1996;HökbyandSöderqvist,2003;Schläpfer,2006).Studiesbasedonthisapproachconsistentlyfind averylowincomeelasticityofwillingnesstopayintherange0.1–0.5.McFaddenandLeonard(1993) andMcFadden(1994)arguedthatincomeelasticitiesinCVsurveysaretoolowaccordingtoeconomic intuition.Schläpfer(2006,p.16)emphasizesthatincomeelasticitiesofWTPbasedonCVstudiesmay bebiasedby“apeculiarcombinationofrandombidlevelsandwell-specified,realisticsurveyscenarios inCVsurveys”.Moreover,theseelasticitiescontrastinmagnitudewiththosecalculatedfromcollec- tivechoice-basedstudiesforvariouspublicgoods(BoercherdingandDeacon,1972;Bergstromand Goodman,1973)whereelasticitiesaregreaterthanone;andfromavertingbehaviorapproachesusing thedemandformarketgoodsasaproxyforenvironmentalgoodsorservices(Costa,1997;Pereyraand Rossi,1999;Ghalwash,2006).Boththecollectivechoiceapproachandtheavertingbehaviorapproach haveweaknessesthough.Asemphasizedearlier,socialchoiceprocessesaredifficulttolinktoindi- vidualpreferences.Avertingbehaviorapproaches,ontheotherhand,onlyallowforthecalculationof theincomeelasticityofdemandandnotoftheincomeelasticityofWTP.FloresandCarson(1997,p.

294)explainthatthetwomaywelldivergeandthat“discussingtheissueintermsoftheincomeclas- sificationofdemandsmayhavelittle,ifany,relevancewhenquantityrationingapplies”.Sotheincome elasticityofWTPforapublicgoodremainsanunresolvedissueeventhoughthedistributionofbene- fitsbyincomeisclearlyimportantforpolicydesign.FloresandCarson(1997)andEbert(2003)usea standardrationedmodelofconsumption(DeatonandMuellbauer,1980a)toderivetheincomeelas- ticityofWTP.Hereconsumerswiththesamepreferenceorderinghaveconvexpreferencesovern marketgoods,denotedbythevectorxandkpublicgoods,denotedbythevectorq.Consumersmay freelychoosethelevelsofx,butfacequantityrationingoverq.Virtualprices,p^v,aredefined(Flores andCarson,1997)asthosethatwouldinducechoosingthesamelevelsofxandqasthoseresulting underrationingofq.Thus,avirtualpriceisaninversedemandfunctionthatdependsonthelevelsof p,qandontheutilitylevelu,whenutilityisheldconstantandonp,qandincomey,whenincomeis heldconstant.

Ifweareinterestedinthedegreetowhichthesevirtualpriceschangewhenincomevaries,the incomeelasticityofthevirtualpricecanbecalculatedas³:

^v_i= ∂p^v_i(p,q,y)

∂y y

p^v_i (1)

whereastheincomeelasticityofdemandis⁴:

^d_i = ∂q^m_i (p,p^v,e^v)

∂y e^v

q^m_i (2)

2Turningtoenvironmentalcosts,ratherthanbenefits,theywillbeprogressively(pro-poor)distributedwhentheyrisewith incomeandregressively(pro-rich)distributedwhentheyfallwithincome.

3Whenq^m_i,theMarshalliandemandofgoodi,varies,totalvirtualexpendituree^vvariesaswell,thisiswhythederivativeof q^m_i wrtincomeismultipliedbytheratiobetweene^vandq^m_i.

4Thecaseofmorethanonepublicgoodismorecomplexandthecorrespondingmeasuresofbenefitsincidencearederived byFloresandCarson(1997)andEbert(2003).

whereiisthegoodinvolved,q^m_i is theuncompensateddemandforgoodi,and e^vis totalvirtual expenditure.Totalvirtualexpenditureisdefinedasthelevelofexpenditureresultingfromchoosing thequantitiesxandqatthevirtualprices.Therelationshipbetweenthesetwoelasticitiesisnot determinate.Whenmorethanonepublicgoodisinvolveditmaywellbethatagoodwithanincome elasticityofdemandgreaterthanone(aluxury)hasanincomeelasticityofWTPsubstantiallyless thanone(FloresandCarson,1997).Whenonlyonepublicgoodisinvolved,Ebert(2003)provedthe followingrelationshipbetweentheincomeelasticityofthevirtualprice,^v₁,andtheincomeelasticity ofdemand,^d₁,(seeEbert,2003,equationR6candHanemann,1991,equation16^):

^v₁=−^d₁

₁₁^d y

e^v (3)

where^d₁₁istheowncompensatedpriceelasticityofdemandforgood1.Thisincomeelasticitydepends on^d₁₁andontheincomeelasticityofdemand,^d₁.Sincetheownpricesubstitutioneffectisalways negative,thesignofthisincomeelasticityisgivenbythesignoftheincomeelasticityofdemand.

FloresandCarson(1997)furthershowthattheincomeelasticityofwillingnesstopay,definedas

^WTP=(∂WTP/∂y)(y/WTP),liesbetweentheminimumandthemaximumvirtualpriceincomeelas- ticity.Ingeneral,^WTPexpresseshowmuchincomehouseholdsarerelativelywillingtopayforan increasedprovisionofanenvironmentalgood.^WTPcanbeusedtoidentifythedistributionalpattern ofWTP,i.e.whichgroupsinsocietybenefitthemostfromenvironmentalimprovements.Environmen- talbenefitsaresaidtoberegressivelydistributedif^WTP<1,proportionallydistributedif^WTP=1and progressivelydistributedif^WTP>1.

3. Householdproductionanddemandanalysis

Householdproduction⁵impliesthataspecificmarketgood,m,iscombinedwithanonmarketgood q⁶toproduceacommodityZ.Wethushaveamodelofavertingbehavior(Bartik,1988;Courantand Porter,1981;Harford,1984)wheremisthequantityofavertingordefensivegood.⁷Whilethevector ofmarketgoodsxconsumedbythehouseholdyieldsutilitydirectly,qyieldsutilityonlyindirectly throughthecommodityZ.Inourapplication,qisthelevelofairpollution,misairconditioning,and Zisthehousehold’spersonallevelofairquality.Thetechnologyisdescribedbyatwicecontinuously differentiableproductionfunctionZ=F(m,q)strictlyincreasingandconcaveinmandq.Households preferencesformarketgoodsxandforthecommodityZarerepresentedbyatwicecontinuously differentiabledirectutilityfunction,U,whichismaximizedsubjecttoabudgetpxx+pmm=yandwithq fixed.Assumingaweaklyseparableutilityfunction,agivenspecificationforthehouseholdproduction functionF(m,q),andassumingthatUdoesnotdependonqdirectly,theWTPforimprovementsinair quality,wq,canbeobtaineduniquelybytheconditionalsystemofdemandfunctions:

x=x(p,q,y) (4)

and

m=m(p,q,y) (5)

wherep=(px,pm)andbythehouseholdproductionfunctionF(m,q).Becauseofweakseparabilityof theutilityfunction,themarginalrateofsubstitutionbetweenqandmissimply:

MRSqm(m,q)= ∂F/∂q

∂F/∂m= F_q(m,q)

Fm(m,q) (6)

5ThissectionreliesonEbert(1998,2007).

6Weassume,forsimplicity,thatthereisonlyonenonmarketgoodqwhichisthelevelofoutdoorairquality.

7Inthismodel,followingEbert(2003),itisassumedthatpeopletaketheenvironmentalgood(i.e.airquality)asanexogenous factor.Inotherwords,thedecisionabouthousinglocationisexogenous,anditcanbeconsideredashavingalreadybeentaken inapreviousstage.Thisisnotthecaseintheliteratureonsortingequilibriumandhedonicmodels.

whereF_qandF_mdenotepartialderivatives.Themarginalwillingnesstopayforimprovementsinair quality,wq,isimplicitlydefinedbyMRSqm=wq/pmfromwhichweobtain:

wq=p^v=pmMRSqm=pm

Fq(m,q)

Fm(m,q) (7)

Thedualminimizationproblemofchoosingbothqandxsoastominimizetotalexpendituresub- jecttopricespandp^vandtotheutilitylevelUwouldalsoproducetheconditionalmixeddemand systemdefined byEqs.(4), (5)and (7)by applicationof Shepard’sLemma sothatwecan write wq=−Cq(pm,q,F(m(p,q,y),q))whereCq=−pmFq/Fm.ThemarginalWTPfunctioncanthereforebe determinedfromtheobserveddemandfunctionsformarketgoodsx,fromthehouseholdproduction function,andfromthemaintainedhypotheses.

Inpracticewehaveaconditionaldemandsystemforx,tobeestimated,augmentedbytheWTP function(7).Wedonotknow,atthisstage,whethertheconditionaldemandsystem(4)and(5)sup- plementedby(7)isconsistentwithutilitymaximization.Stateddifferently,wedonotknowwhether thereisaquasi-concaveutilityfunctionfromwhichthemixeddemandsystem(4),(5)and(7)canbe derived.Ebert(2007,p.283)setsoutthenecessaryandsufficientconditionsforintegrabilityofthis conditionaldemandsystemsupplementedbyaWTPfunction.Thefirstthreeconditionsaresymmetry conditionsoftheSlutskymatrixfortheaugmenteddemandsystem:

sxm= ıx ıpm+mıx

ıy= ım ıpx+xım

ıy =smx (8)

sxq= ıx ıq−wq

ıx ıy=−



ıp_x +xıwq

ıy



=−sqx (9)

smq=ım

ıq −wqım ıy =−



ıpm+mıwq

ıy



=−sqm (10)

wheresxmaretheconventionalSlutzkysubstitutioneffectsformarketgoodsxandm,i.e.theymeasure thechangeinthequantitydemandedofeachelementinvectorxfollowingachangeinthepriceof goodm,whereassxqisthechangeinthequantitydemandedofeachelementinxfollowingachange intheprice(WTP)ofq.Condition(8)issatisfiedbyassumption,becausexandmformaconditional demandsystem,butconditions(9)and(10)havetobechecked.Inaddition,theSlutskymatrixof substitutioneffectsforthemarketgoodsxandmmustbenegativesemidefinite.Finally,thechange inthequantitydemandedofgoodqfollowingachangeinitsprice(WTP)mustbenegative:

sqq=ıwq

ıq −wq

ıwq

ıy <0 (11)

Whenconditions(8)–(11)aresatisfied,themixeddemandsystemwithhouseholdproductiondefined by(4),(5)and(7)isintegrable.

Thisapproachdoesnotrequirefurtherassumptionsanditprovidesausefulandoperationalbasis forrecoveringpreferences.Itsstartingpointsarethe“observed”demandfunctionsforthemarket goodsandthehouseholdproductionfunction.Conditionslikeweakcomplementarityortheessen- tialityofinputsarenotrequired,norisrequiredtheimpositionoftheWilligconditiontoderiveexact welfaremeasures(seeEbert,2007,p.278foradiscussionofthispoint).

4. Specificationandestimationofaconditionaldemandsystemwithhouseholdproduction

4.1. AConditionalCensoredAlmostIdealDemand(CCAID)System

Conditionaldemandfunctionscanbeusedtodealwithnonmarketgoods,suchasenvironmental goodsorbads.Thelevelof,forexample,airqualityprovidedwithoutchargetotheusermayaffect theindividual’sconsumptionofgoodsavailableinthemarket.Sinceconsumptionofairqualityis fixed,itistheconditionaldemandfunctionswhichareappropriatefortheanalysisofanindividual demandforgoodsandservicesintheshortrun(Pollack,1969).Thefunctionalformchosentospecify

ourmodelistheAlmostIdealDemandSystem(AIDS,DeatonandMuellbauer,1980b).Toobtainthe systemofconditionaluncompensatedsharesequationsweusealogarithmicconditionalcostfunction, forhouseholdh,whichimpliesPIGLOGpreferences(PollackandWales,1992):

lnC(u,p,d^h,q)=lna(p,d^h,q)+ub(p) (12)

wherea(p,d^h,q)andb(p)arefunctionsofthemarketpricevectorp,lnindicatesthenaturallogarithm, d^haredemographicvariablesandqisthefixedquantityofthenonmarketgood,airqualityinthiscase.

a(p,d^h,q)isincreasingandhomogenousofdegreeoneinpandb(p)isincreasingandhomogenous ofdegreezeroinp.C(u,p,d^h,q)istheconditionalcostfunction,i.e.theminimumcostnecessaryto achieveutilitylevelu,giventhepricevectorp,givendemographicsd^handwhenthequantityqofthe nonmarketgoodisfixed.ThecorrespondingsystemofconditionalMarshalliandemandfunctionsfor householdhandgoodsi=1,...,nexpressedasexpendituresharesisgivenby:

w^h_i =˛_i+



j

c_ij lnp_j+b_iln





+



i

(˛_i+˛_ikd^h_k+g_iq)lnp_i (13)

wherey^histotalexpenditureofhouseholdh;theparametersc_ijaredefinedasc_ij=(1/2)(c_ij^∗+c^∗_ji)=c_ji;

˛_ikarethecoefficientsofthetranslatinginterceptsd^h=d^h₁...d^h_kwhichinthismodelincludehouse- holds’types,households’locationandanannualtimetrendandP^hisaTranslogpriceindexspecified as:

P^h=˛₀+



i

(˛_i+g_iq+˛_ikd^h_k)lnp_i+1 2



i



j

c^∗_ij lnp_ilnp_j (14)

Demandfunctions(13)satisfyintegrability,i.e.areconsistentwithutilitymaximization,whenthefol- lowingparametricrestrictionshold:



i˛_i=1,



ib_i=



jc_ij^∗=0,



i˛_ik=0∀^k(Adding-up);



jc_ij=0 (Homogeneity);c_ij=c_jiforalli,j(Symmetry).

Thepresenceofzerosinthedependentvariablesisquiteimportantforourspecificsample.To dealwiththisproblemweusethetwo-stepestimatorproposedbyShonkwilerandYen(1999)which involvesprobitestimationinthefirststepandaselectivity-augmentedequationsysteminthesecond step.⁸Thesystemofequations(13)isthusestimatedinthefollowingform:

s_i=˚(z_i^_i)w_i(p,y;)+ı_i(z_i^_i)+_i (15) wheres_iistheobservedexpenditureshareforgoodi;z_iisavectorofexogenousvariables;_iisa parametervector;isavectorcontainingallparameters(˛_i,˛_ik,b_i,g_iandc_ij)inthedemandsys- tem,_i=s_i−E(s_i)and where(·) and˚(·)arethe standardnormal probabilitydensity (pdf)and distribution(cdf)functions,respectively.Thesystemofequations(15)isestimatedintwo-steps:

(i)weobtainMaximumLikelihood(ML)probitestimates ˆ_iof _iusingthebinaryoutcomes_i=0 ands_i>0;(ii)wecalculate˚(z_i^, ˆ_i),(z^_iˆ_i)foralliandestimate,ı1,ı2,...,ınintheaugmented system(15)byML.Suchtwo-stepestimatorisconsistent,buttheerrortermsareheteroscedastic, thustheestimatedelementsofthesecond-stepconventionalcovariancematrixareinefficient.For simplicity,weempiricallycalculatethestandarderrorsofWTPandelasticitiesusingbootstrapping andrunning500replications.Thisensuresthatthestandarderrorsofthesederivedparametersare correct.⁹

Thedependentvariableinthefirst-stepprobitestimatesisthebinaryoutcomedefinedbythe expenditureineachgood.TheproportionofconsuminghouseholdsforFood,HousingandCommuni- cationallexceed95%,whichpreventsreliableprobitestimates.Thus,probitisestimatedonlyforthe

8ShonkwilerandYen(1999);Yenetal.(2003)andYenandLin(2006)provideusefulliteraturereviewonestimation proceduresforcensoreddemandsystems.

9DifferentiationofEq.(15)givesdemandelasticitiesforthefirstn−1goods.Elasticitiesforthenthgoodareobtained exploitingtheCournotandEngelrestrictions(DeatonandMuellbauer,1980a,p.16).DenotingtheMarshallian,Hicksianand expenditureelasticitiesforgoodias^h_ij,^∗h_ij and_i^h,respectively,then_nj^h,^∗h_nj and_n^hcanbecalculatedusingtheCournot restriction



i=1w^h_i^h_ij+w^h_j=0andtheEngelrestriction



j=1^h_ij+^h_i =0.

remainingcommodities,forwhichthepredictedpdfandcdfareincludedinthesecondstepofthe procedure(seeYenetal.,2003,p.464).Exogenousvariablesusedinthefirst-stepprobitestimatesare:

totalexpenditure,anannualtimetrendinlogarithmsandasetofdummyvariablestocapturespatial effectsinexpenditures:householdlocation,whetherthehouseholdresidesinabigtown,seasonality.

Inallestimatesweimposehomogeneityandsymmetry.Economictheoryalsorequiresthematrix ofthesubstitutioneffectstobenegativesemi-definite.Sucharequirementissatisfiedbyadopting aCholeskydecompositionprocedureofthepricecoefficients.Finally,wedropthe“othergoodsand services”equationtoaccommodateaddingup.

4.2. HouseholdproductionandWTPforairqualityimprovements

TospecifytheWTPfunctionforimprovementsinairqualitywechoosetheclassofhousehold productionfunctions:

Z=Fε(m,q)=(m^1/2+1)q^ε (16)

forε∈(0,1/2]proposedbyEbert(2007,p.285)wheremistheimplicitquantityofairconditioning usedasaninputintothehouseholdproductionofZ,theinternallevelofairqualitychosenbythe household,andqisourindexofairquality.Inthishouseholdproductionfunctionmisanonessential good,thatistosaymisnotnecessarilyrequiredtoproduceZgivenq.¹⁰Thisisoneofthedesiderable propertiesofthechosenclassofproductionfunctions:wecanhaveaWTPdifferentfromzeroeven whentheexpenditureonairconditioningequalszero.Moreover,thisclassofproductionfunctions hasdecreasingreturnsofscaleinairconditioningexpenditure,namelywhenthelatterincreases, WTPincreaseslessthanproportionally.Thisisarealisticrepresentationoftheuseoftheconditioning technology.Theparameterεcanbeconsideredameasureofthedegreetowhichthelevelofexternal airqualityinfluencestheinternallevelofairqualitychosenbythehousehold.Thehigherisε,the higheristheimpactofexternalairqualityonthehouseholdproductionfunction.Finally,badair qualityconditionsareverylikelytobecorrelatedwithairconditioningexpenditures,whicharean inputinproducingthelevelofairqualitypreferredbythehousehold.Consequently,intheproduction functiontheexternallevelofairquality,q,isincludedasaninputbesidesm.Theexternaltemperature levelisnotincludedasaninput,eventhoughitcouldalsoberelevantininfluencingairconditioning’

demand.Itcanbeassumedthatahighconcentrationofthesepollutantsismainlyassociatedwitha demandforventilationandinternalairquality.Thisisbecausethebundleofairpollutantsconsidered inourairqualityindexisknowntohavestronghealtheffectsintermsofrespiratorydiseases(WHO, 2005)buthigherconcentrationsarenotcorrelatedwithhighertemperaturelevelsanddiscomfort fromheat.¹¹Moreover,withtheexceptionofozone¹²(IPCC,2007), theotherpollutantsincluded intheairqualityindexarenotgreenhousegases,thereforetheyarenotassociatedwithlongterm temperatureeffects.

Thisclassofhouseholdproductionfunctionsimpliesthecostfunctions¹³:

Cε(pm,q,z)=

⎧ ⎨

⎩

0forZ≤q^ε p_m

q^ε−1

forZ>q^ε

(17)

AccordingtoEq.(7),thecorrespondingWTPfunctionis:

wq(p,q,y)=2εpm(m^1/2+1)m^1/2/q (18)

10SeeEbert(2007),footnote11,foraninterpretationofthisproperty.

11Thecorrelationcoefficientbetweentheindexofairqualityandmaximumandminimumaverageannualtemperatures(in Celsiusdegrees)intheeightregionsunderconsiderationis0.327and0.325,respectively.

12SeeSection4.3foradetaileddescriptionoftheairqualityindex.

13ForeachhouseholdthetotalcostofproducingZisgivenbyCε(pm,q,Z)=pm(m)andtheclassofcostfunctionsinEq.(17)is obtainedbysolvingthehousehold’stotalcostminimizationproblem.WhenZ≤q^εthequantityofinputmisnegativeandthis isnotafeasiblelevel,thisiswhythecostfunctionequalszero.

Weconsiderthreevaluesofε:ε=0.1,ε=0.35andε=0.5andwetestwhethertheWTPfunction(18) isintegrablebycheckingwhetherconditions(8)–(11)aresatisfied.

4.3. Data

Weusemonthlycross-sections,fromJanuary2002toDecember2006,ofindividualItalianhouse- holds’currentexpenditurescollectedbytheIstitutoNazionalediStatistica(ISTAT)throughaspecific androutinelyrepeatedsurvey.¹⁴Currentexpendituresareclassifiedinabouttwohundredelementary goodsandservices,withtheexactnumberchangingfromyeartoyearduetominoradjustmentsin theitem’slist.¹⁵Thesurveyalsoincludesdetailedinformationonthehouseholdstructure,sothatrel- evantdataondemographiccharacteristics(suchaslocationonaregionalbasis,numberofhousehold members,ownershipofairconditioners)areavailable.Allannualsamplesareindependentlydrawn accordingtoatwo-stagedesign.¹⁶

Asub-sampleof10,671observationshasbeenselectedconsideringonlyhouseholdsowningair conditioners,usingadichotomicvariableincludedinthesurveywhichcontrolsforownership.There- fore,ourresultsarevalidforthespecificfamilytypesweconsideronlyandarenotrepresentativeof theentireItalianpopulationofhouseholds.

Airconditioningexpendituresaremainlycurrentexpenditures,soobservingazerovalueimplies thatduringthespecificmonththehouseholddidnotuseit.Thisisconsistentwithconditionersbeinga nonessentialinputinthehouseholdproductionfunction.¹⁷Thehouseholdsincludedinthesamplelive ineightregionsofItaly:Friuli-VeneziaGiulia,TrentinoAltoAdige,Liguria,Lombardia,Toscana,Lazio, SardegnaandSiciliarepresentingfourmacro-regions:Northeast(NE),Northwest(NW),Centre(CE), SouthandtheIslands(SI).Weestimateatencommoditiesdemandsystem:(1)Foodandbeverages;

(2)Housingexcludingrent¹⁸;(3)AirConditioners;(4)Clothing;(5)HealthCare;(6)Transports;(7) Communication;(8)Recreation;(9)AlcoholandTobacco;(10)Othergoodsandservices.¹⁹

Thesecommoditiesarechosenaccordingtomonthlyandregionalconsumptionpriceindicesavail- ablealsosuppliedbyISTAT,whichareincludedinthedataset.Thesepriceshavebeenextracted fromtheConsumerPriceIndex(1998=100),alsopublishedbyISTAT.SpecificallyweusetheCon- sumerPriceIndexforthewholenation(NIC)whichmonitorssalespriceseverymonthinallItalian provinces.NICisdividedinto12expenditurecategoriesenteringthenationalindexwithaspecific weightreflectingtherelativeimportanceoftheconcernedgoodontotalconsumption.Manyofthese categoriescoincidewiththecommoditiesinourdemandsystem.Someofthemhavebeenaggregated tocorrespondtotheremaininggoodsinourdemandsystem.Inaddition,weconsiderexpenditures onairconditioningandthecorrespondingelementarypriceindexalsosuppliedbyISTAT.Wehave identifiedtheexpenditureonconditionersasthebestproxyofdefensiveexpenditureagainstairpol- lutionandclimatechangewecouldfindintheSurveyonHouseholdsExpenditures.ISTATrecords expenditureonairconditionersbyItalianhouseholdsonamonthlybasis.Weselectonlyhousehold owningairconditionersfortworeasons:first,thisallowsustoestimatethehouseholdproduction function(forwhichotherwisearelevantinputwouldhavebeenequaltozero);second,byassum- ingthathouseholdspurchasedairconditionerspreviously,theexpenditurerecordedbyISTATcanbe

14Adifferentsampleofhouseholdsisinterviewedduringeachmonth;theitemlistincludesalsononcurrentexpenditures, withatotalnumberofabout280goodsandservices.

15Weimplicitlyassumestrongseparabilityinconsumers’preferencesbetweencurrentandotherexpenditures.

16DetailsonthesamplingprocedureusedtocollectthesedatacanbefoundinISTAT,IndaginesuiConsumidelleFamiglie.File standard.Manualed’uso.Anni1997–2006.

17SeeSection4.2foradescriptionofthehouseholdproductionfunction.

18Therationaleforchoosingtoincludehomerelatedexpenditures(compositecommodity(3))isthatasubstitutionrelation- shipislikelytoexistbetweenairconditioningandothergoodsandservicespurchasedbythehousehold(bywayofexample, theneedofairconditioningislikelytodiminishinbetterinsulatedhouses).

19Eachcommodityhasbeenobtainedasanaggregateofdetailedcurrentexpendituresonmorethantwohundredelementary goodsandservices.Aggregationispossibleassuming,asitisusuallydone,thatgoodswithineachgroupareconsistentwith theHicksandLeontiefCompositeCommodityTheorem(DeatonandMuellbauer,1980a,pp.120–121).

consideredasbeingcurrentasitisgivenbyoperatingandmaintenancecostsonly.²⁰TheNorthwest (NW)regionhasthehighestexpenditureshareonairconditioners(seeAppendixTableA1),followed bytheSouth(SI),theNortheastand theCentre(CE).Thusa markedgeographical trenddoesnot exist:livingintheNWproducesapositiveeffectonconditionersexpenditureshare,butthisisalso trueintheSouth.Airconditioners’demanddependsonhouseholdlocationanditdoesnotincrease proportionallywithtotalexpenditure.Thesepatternssuggesttheimportanceofincludingdummy variablesrelatedtotheregionandlocationwherethehouseholdliveswhenanalysingWTPforair quality.

Tosummarize,thesampleusedinourestimationsconsistsof10,671householdobservationscol- lectedfor8regionsover12monthsfor5years.Usingrtoindicatetheregion,mthemonthandy theyear,thedatahavebeenorganizedbyliningupmonthlydata(m=1−12)oneachmacro-region (r=1−4)foreachyear(y=1−5)inavectorof10,671observations.Asetofdummyvariablesisincluded toaccountforthemacro-areainwhichthehouseholdlives(NW,NE,CE,SI)inordertomodeldiffer- encesinpurchasingpatterns,inparticularwithrespecttotheexpenditureonairconditioners.Inorder totakeintoaccounttherelevantroleplayedbyexternaltemperature–andthenthelikelyseasonality inairconditioningexpenditure–weincludeadummyvariable(SEASON)equalto1forthewarmest monthsoftheyear:June,July,AugustandSeptember.Ourhypothesishereisthattheeffectofair pollutionmaybeworsenedinthewarmestmonthsoftheyear.Forthisreason,itseemsappropriate tocontrolfortheseasonalityeffectofexternaltemperaturesininfluencingtheexpendituresrelated totheuseofairconditioners.Theseasonalityeffectsassociatedwithtemperatureareinsteadashort termphenomenaandassuchseemedworthtobetakenintoaccountbyusingadichotomicvariable.

Wealsoaddacategoricvariable(LOC)forwhetherthehouseholdlivesinatownwithmorethan 50,000inhabitants(1),lessthan50,000inhabitants(2)orinasmallvillage(3)inordertomodel spatialeffects,andalogarithmicannualtimetrend.

Wecombinethesedatawithinformationonairconcentrationsofthreepollutants:Ozone(O₃), Particulate(PM₁₀)andNitrogenDioxide(NO₂).Thesehavebeenusedtocomputeacategoricallycon- tinuousindexofairquality(IQA),astandardizedindicatorofairqualityinagivenlocation.Following thedefinitiongivenbytheNationalAgencyfortheProtectionoftheEnvironment(APAT)according toguidelinesfromtheEnvironmentalProtectionAgency(EPA),theindexisconstructedasaweighted averageofdataonhourlyconcentrationsofthreeairpollutantssuppliedbyAPAT.²¹Theweightswere providedbyeachoftheagenciesinchargeofcalculatingairqualityindicesonaregionalbasis.

DataonhourlyconcentrationsofOzone(O₃),Particulate(PM₁₀)andNitrogenDioxide(NO₂)were availablefromJanuaryfirst2002toDecember31st2006.ForeachItalianregionhourlypollutants concentrationshavebeencollectedfromaverylargenumberofstationslocatedinaTraffic,Industrial orBackgroundarea.WeconsiderconcentrationsfromTrafficandBackgroundstationsonlyinorder tomergethemwithconsumptionexpendituresofhouseholdsinUrbanorBackgroundareas.Dueto missingdataovertheinvestigationperiod,onlyeightItalianregionshavebeenconsidered:Lombardia, Liguria,FriuliVeneziaGiulia,TrentinoAltoAdige,Lazio,Toscana,SiciliaandSardegna.

Startingfromatotalof1,596,938hourlyobservations,adailyregionalIQA_dhasbeenobtainedas:

IQA_d=(I1+I2)/2wherethesubscriptdindicatestheday;I1=(PM10/PM10)×100isasub-indexwhere PM₁₀isthemeandailyparticulateconcentrationandPM₁₀isthethresholdvalueforparticulatecon- centrationsadmittedbytheItalianlaw²²(50␮g/m³).Thesecondsub-index,I₂,issimplythehighest betweenNitrogenDioxideandOzoneconcentrations:I2=max(NO2,O3).ThresholdvaluesforNO2and O₃concentrationsare,respectively,200␮g/m³and120␮g/m³.

DailyIQAshavebeenaveragedovereachmonthtoobtainmonthlyindices.Asaresult,ourregional IQAisgivenbyasampleof960observations(12months×5years×16areas).Fromthesemonthly

20Itisimportanttonotethattheexpenditureonconditionersisnotrelatedtotheelectricitybill,sincehouseholdswouldnot beabletodisentangletheshareofelectricityconsumptionrelatedtoconditioners.Theexpenditureonelectricityiscollected inaspecificcategoryincludedintheSurveyonHoseholdExpenditure.

21Dataonairpollutantsconcentrationsarefreelydownloadableatwww.apat.it.ThesamedataareavailablefromtheEuropean AirQualityDatabaseoftheEuropeanEnvironmentalAgency.

22D.M.60/02.

Table1 Thedata.

No.ofhouseholds:10,671

Currentexpenditures(Euro/month) Mean Std.dev. Min Max

Totalexpenditure 1784.705 1063.757 250.019 6958.370

Foodfromstores 485.747 283.304 0.000 2374.739

Alcoholandtobacco 44.466 58.495 0.000 551.480

Clothing 190.509 285.023 0.000 4387.530

Householdoperation 210.760 154.237 0.000 3501.580

Airconditioners 12.315 82.999 0.000 1028.930

Health 112.068 278.392 0.000 5228.750

Transports 162.021 129.441 0.000 1042.620

Communication 64.838 50.950 0.000 652.949

Recreation 52.934 85.197 0.000 1597.560

Othergoodsandservices 458.282 530.354 0.000 5228.920

Priceindices(1998=1)

Foodfromstores 1.135 0.034 0.826 1.337

Alcoholandtobacco 1.247 0.115 0.826 1.436

Clothing 1.127 0.040 0.824 1.364

Housing 1.145 0.053 0.821 1.365

Airconditioners 0.964 0.040 0.869 1.074

Health 1.095 0.034 0.816 1.365

Transports 1.190 0.068 0.815 1.392

Communication 0.842 0.083 0.701 1.393

Recreation 1.101 0.030 0.813 1.393

Othergoodsandservices 1.185 0.052 0.809 1.393

Otherexogenousvariables

IQA 5.630 1.232 1.000 7.000

NW 0.279 0.448 0.000 1.000

NE 0.108 0.311 0.000 1.000

CE 0.219 0.414 0.000 1.000

SI 0.393 0.488 0.000 1.000

LOC 1.158 0.446 1.000 3.000

SEASON 0.346 0.476 0.000 1.000

Annualtimetrend 3.183 1.378 1.000 5.000

indices,theIQAisconstructedasacategoricalvariable(LQ)varyingbetween1(Veryunhealthy)and 7(Excellent).²³SummarystatisticsofthedataareshowninTable1.

4.4. Results

TableA2intheappendixshowsfirst-stepprobitestimatesalongwiththeirasymptoticstandard errors.Thedependentvariablesaretheexpendituresharesforthe9commoditiesinoursystemof demands,listedinthefirstrowofthetable.Manyofthevariablesincludedaresignificantatthe5%level ineachexpenditureshareequation.Incomeplaysapositiveroleinexplainingthebudgetshareofall goods.Seasonalityandtheannualtimetrendalsoplayasignificantroleintheprobabilityofconsuming manyofthecommodities.Theindexofairquality(LQvariable)isalsosignificantinexplainingthe expendituresonairconditionersandhastheexpectednegativesign,²⁴namelybadairqualitylevels areassociatedwithhigherexpenditures.Goingfromabigtoasmalltown(LOCvariable)hasanegative roleindeterminingairconditioners’purchase,probablybecausebigcitiesaremorepolluted.Going froma bigtoa smalltownalsoplaysapositive andsignificantroleinexplainingTransportsand Alcohol/Tobaccochoices,buthasanegativeandsignificantrole,asexpected,inexplainingrecreation

23Wetreateachchangeincategoryashavingthesameeffectonairquality.WefollowtheRegionalAgenciesfortheProtec- tionoftheEnvironment(APATs)thatconstructregionalairqualityindicesaccordingtotheguidelinesoftheEnvironmental ProtectionAgencyascategorical/ordinalvariables(ARPAPiemonte,2007).

24WeexpectanegativesignsincetheIQAiscomputedinsuchawaythathighervaluesareassociatedwithbetterairquality conditions.

Table2

Integrabilityconditions(samplemean).

Conditions Estimate

Sx₁,q+Sq,x₁=0 0.000529

Sx₂,q+Sq,x₂=0 −0.024384

Sx3,q+Sq,x3=0 0.369060

Sx4,q+Sq,x4=0 −0.121260

Sx5,q+Sq,x5=0 −0.036447

Sx₆,q+Sq,x₆=0 −0.036262

Sx₇,q+Sq,x₇=0 −0.024694

Sx₈,q+Sq,x₈=0 −0.036455

Sx₉,q+Sq,x₉=0 −0.036107

Sq,q<0 −0.259180

choices.TableA3showssecond-stepestimatesoftheCCAIDsystem.²⁵ Standarderrorshavebeen computedfromaheteroscedastic-consistentmatrixusingtheWhitecorrection.

Hicksian(compensated)elasticities,basedonparametersofthesecond-step,arecomputedatthe samplemeanas:^∗h_ij =^h_ij+^h_iw^h_j where^h_ij is theuncompensatedpriceelasticityofgoodiwith respecttopricejand_i^histheexpenditureelasticityofgoodi.TheseelasticitiesareshowninTableA4 alongwithexpenditureelasticitiesforallgoodsandtheestimatedbudgetshares.Allexpenditure elasticitiesaresignificantlydifferentfromzero.Airconditioningappearstobealuxurygood,withan incomeelasticityequalto1.30.²⁶Astothebudgetshares,Food,Housing,TransportsandClothingare theconsumptioncategoriesonwhichthelargestpartofthemonthlyexpenditureisallocated.Thisisin linewithsimilarworksonItalianhouseholdconsumption(MoschiniandRizzi,1997;BalliandTiezzi, 2010).Allthecompensatedownpriceelasticities,calculatedatthesamplemeansofvariables,have thecorrectsignandarestatisticallysignificant.Airconditioningdisplaysaveryhighandsignificant compensatedownpriceelasticity(1.80),butnoneofthecross-priceelasticitiesaresignificant.Some oftheothercompensatedownpriceelasticitiesaregreaterthanone:Food,Clothing,Health,Transport andCommunication.

Theconditionaldemandsystem(13)andtheWTPfunction(18)areintegrableifandonlyifcondi- tions(8)–(11)aresatisfied.Theseintegrabilityconditionshavebeencheckedatthesamplemeanand theresultsforε=0.5areshowninTable2.Theconditionsareallsatisfied,thereforethemixeddemand systemwithhouseholdproductionisintegrable.WTPformarginalimprovementsinairqualityand itsincomeelasticitycalculatedatthesamplemeanofexogenousvariables,alongwiththeirstandard errors,areshowninTables3and4.

HouseholdmarginalWTPforimprovementsinairqualityinEuro/monthforfiveincomegroupsare showninTable3forthreevaluesofε.WTPissmallerthan10eurosformosthouseholds,inparticular avaluearound3euroshasaveryhighfrequency. TheWTPispositivelycorrelatedtohousehold incomerevealingthatrichhouseholdsvalueairqualityimprovementsmorehighlythanpoorones.

NeverthelesswhenexpressedasafractionofhouseholdincomeWTPincreasesonlyslightlywith incomeforanyvalueofε.ForhigherincomelevelsWTPasafractionofincomedecreasesfrom0.25%

fory≤6000to0.13%fory>6000.Thefactthathouseholdsinlowerincomegroupshavearelatively higherWTPforairqualityimprovementsisconsistentwithfindingsbyKriströmandRiera(1996) andHökbyandSöderqvist(2003).Thismaybebecausehigherincomehouseholdsliveonaveragein areaswithrelativelylowlevelsofairpollutionandtheythereforeexperiencealessrelevantphysical improvement(e.g.airqualitychangesfromgoodtoverygood)inair qualityin comparisonwith

25Wereplicatedfirst(Probit)andsecond-stepestimatesaddingaverageregionalmaxtemperaturesamongtheexplanatory variablesoftheshareequations.IntheProbitequations,thecoefficientofmaxtemperaturesissignificantforthe“Clothing”

equationonly.Wedidnotdetectanyremarkablechangeintheestimatedparametersofthedemandsystem.

26Itisworthmentioningthattheincomeelasticityassociatedtoairconditioning,aswellasthepriceelasticities,areallshort termelasticities.Sincethestockofairconditionersisbuiltupovertime,andsuchaprocessislikelytobeincompleteinsome regions,theincomeelasticityofWTPisalsotobeinterpretedasvalidintheshortterm.

Table3

WTPforairqualityimprovements(Euro/month).

Incomelevel ε=0.15 ε=0.35 ε=0.5

Overallsamplemean 0.687 1.602 2.290

(10,671) 0.025 0.062 0.087

y≤800 0.141 0.329 0.470

(1016) 0.018 0.044 0.062

y≤2000 0.475 1.108 1.582

(4993) 0.022 0.049 0.070

y≤4000 1.476 3.444 4.920

(2808) 0.059 0.140 0.194

y≤6000 2.260 6.207 8.867

(401) 0.253 0.587 0.870

y>6000 2.296 5.357 7.652

(72) 0.484 1.071 1.568

Note:StandardErrorsinItalicsbelowcoefficients.BoldentriescorrespondtorejectionofH0:e=0atthe5%significancelevel foratwotailedtest.

y=householddisposableincomeproxiedbytotalcurrentexpenditure.

Table4

IncomeelasticityofWTPforairqualityimprovements.

Incomelevel ^WTP

Overallsamplemean 1.164

(10,671) 0.245

y≤800 1.234

(1016) 0.311

y≤2000 1.165

(4993) 0.266

y≤4000 1.128

(2808) 0.178

y≤6000 1.174

(401) 0.155

y>6000 1.345

(72) 0.258

Note:StandardErrorsinItalicsbelowcoefficients.BoldentriescorrespondtorejectionofH0:e=0atthe5%significancelevel foratwotailedtest.

y=householddisposableincomeproxiedbytotalcurrentexpenditure.

lowincomehouseholds.AlowerWTPforricherhouseholdsmayalsobeexplainedbyalargersetof substitutionpossibilities.

5. IncomeelasticitiesofWTPforairqualityimprovements

Wecalculate^WTP=(∂WTP/∂y)(y/WTP)fortheentiresampleandforfiveincomegroups.Theoverall samplemeanelasticityisequalto1.164,thusaonepercentincomeincreasewouldimplyanincrease inWTPofslightlymorethanonepercent.Therefore,WTPisbasicallyincome-neutralandanincome variationismorethancompletelytransferredtoWTP.Thisresultisconsistentwithotherstudiesfind- ingaWTPforenvironmentalgoodsbeinganincreasingfunctionofincome(HarrisonandRubinfeld, 1978;KriströmandRiera,1996;HökbyandSöderqvist,2003).

AnincreasingpatternoftheabsolutelevelofWTPwithrespecttohouseholdincomesignalsthat thedemandfunctionsforcleanairhavepositiveincomeelasticities.Weconsistentlyfindapositive incomeelasticityofWTP.Thusthericheracountry,thelargeristheabsolutelevelofWTPforair qualityincomparisonwithapoorercountry.Thismightbeimportantforenvironmentalplanswith longtimehorizons,asitsuggeststhat,associetiesgetricher,theytendtovalueenvironmentalquality morehighly.

Sincetheincomeelasticityofhigherincomegroupsmaybedifferentfromthatoflowerincome groups,wehavecomputedthiselasticityfordifferentincomeclasses(Table4).TheelasticityofWTP