Mad cows, terrorism and junk food: Should public policy reflect

15 Pages·2008·0.16 MB·English

Available online at www.sciencedirect.com
JournalofHealthEconomics27(2008)234–248
Mad cows, terrorism and junk food: Should public
policy reflect perceived or objective risks?
∗
Olof Johansson-Stenman
DepartmentofEconomics,SchoolofBusiness,EconomicsandLaw,Go¨teborgUniversity,
Vasagatan1,Box640,SE-40530Go¨teborg,Sweden
Received5June2006;receivedinrevisedform26March2007;accepted30April2007
Availableonline4January2008
Abstract
Empiricalevidencesuggeststhatpeople’srisk-perceptionsareoftensystematicallybiased.Thispaperdevelopsasimpleframe-
worktoanalysepublicpolicywhenthisisthecase.Expectedutility(well-being)isshowntodependonbothobjectiveandperceived
risks(beliefs).Thelatterareimportantbecauseofthefearassociatedwiththeriskandasabasisforcorrectivetaxationandsecond-
bestadjustments.Optimalityrulesforpublicprovisionofrisk-reducinginvestments,“internality-correcting”taxation(e.g.fattaxes)
andprovisionofcostlyinformationtoreducepeople’srisk-perceptionbiasarepresented.
©2007ElsevierB.V.Allrightsreserved.
JELclassification: D81;H4;I1
Keywords: Riskregulation;Riskperceptionbias;Internalities;Cost-benefitanalysis;Paternalism
1. Introduction
Virtuallyallpublicpolicyareasinamodernsocietyhavetodealwithrisks.Forexample,howshouldwedealwith
possiblenegativesideeffectsofmedicine,naturalcatastrophes,geneticallyengineeredfood,terrorism,airplanesafety,
gun control and toxic substances in food? And similarly, how should we deal with uncertain positive impacts from
sportactivitiesandhealthyfoods?Whileriskhasbeenincorporatedintomainstreameconomictheoryforalongtime,
therearemanyproblemswithapplyingtheconventionalapproachinpractice.Thispaperfocusesontheobservedfact
thatthegeneralpublic’sriskperceptionisoftenverydifferentfromthatoftheexperts,contrarytotheassumptionin
conventionaltheory.Shouldpublicpolicyinsuchsituationsbebasedonthegeneralpublic’sriskperceptionsorthat
oftheexperts?Ifneither,whatothercriteriashouldbeemployed?
Themainpurposeofthispaperistwofold:(1)toprovideasimplifiedbutgeneralandpracticallyusefulframework
forpolicyanalysiswhenpeoplehavebiasedriskperceptions,and(2)toderiveexplicitnormativepolicyconclusions
basedonthisframework,wherethepolicyinstrumentsanalysedincludedirectpublicinvestmentstoreducetherisk,
correctivetaxationtocounteractpeople’smisperceptions,aswellas(costly)informationprovisiontoreducepeople’s
risk-perceptionbiases.
∗ Tel.:[phone];fax:[phone].
E-mailaddress:[email protected].
0167-6296/$–seefrontmatter©2007ElsevierB.V.Allrightsreserved.
doi:10.1016/j.jhealeco.2007.04.004
O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248 235
Examples of risk perception biases have been identified in many areas including health care, air pollution, food,
smokingandterrorism.Itisforexampletypicallyfoundthatpeopleseverelyoverestimaterisksassociatedwithoutdoor
air pollution compared to indoor pollution (Breyer, 1993; Margolis, 1996). Many European smokers were recently
foundtobemuchmoreafraidofeatingbeefduetotheBovineSpongiformEncephalopathy(BSE),knownasthe‘mad
cowdisease’crisis,thantheywereofsmoking,eventhoughvirtuallyallexpertsconsideredtheindividualriskofBSE
negligiblewhencomparedwithsmoking;cf.Penningsetal.(2002)andSetbonetal.(2005).Similarly,mostpeople
(includingtheauthor)seemtofeelsaferwhentravellingbycarratherthanbyusingacommercialairline(cf.Carlsson
etal.,2004).Otherobviousexamplesincludethefearofeatinggeneticallymodifiedfood,despitethefactthatmost
expertsappeartoagreethattheobjectiveriskisverysmallcomparedwithforexampleadietthatistoohighincalories
(seee.g.Noussairetal.,2004),andpeople’sperceivedriskofterroristattacks,despitethefactthatalmosteverywhere
thisriskismuchsmallerthantheriskofexperiencingaserioustrafficaccident(e.g.Sunstein,2003,2005).1
Although there are large bodies of literature on both risk perception (see e.g. Slovic, 2000) and risk regulation
(Hahn, 1996; Viscusi, 1992a, 1998), systematic analysis based on the combination of the two has not attracted
much attention, which is surprising given its obvious policy relevance.2 For example, should the government apply
a higher value of a statistical life for outdoor air pollution compared with indoor air pollution, for consumption
of meat or genetically modified food compared with fatty foods, and for air transport (and terrorist attacks) com-
pared with other transport modes?3 Or should the same valuation per safety unit be used, irrespective of risk
beliefs?
Section2presentsthebasicmodelwheretheobjectiveriskcanbereducedbypublicsafetyinvestments.Section
3 presents a more general model that includes fear from risk beliefs and where people can consume both risky and
risk-free goods. The policy instruments, in addition to safety investments, include information provision in order to
reducetheriskmisperceptionaswellasdifferentiatedcommoditytaxation.Section4analysesasecond-bestmodel
similartotheoneinSection3,butwherenodifferentiatedcommoditytaxationispossible.Section5summarisesand
concludesthepaper.
2. Thebasicmodel:levelsversusmarginalriskchanges
The issue of whose risk perceptions should ultimately count in public policy is not new; see e.g. Portney (1992)
andPollak(1998)forpreviousdiscussions.Whilebothappeartobequiteundecidedonthisissue,accordingtoPollak
(1998),mostanalystswouldagreewithBreyer(1993)thatsuchdiscrepanciesdonotreflectdifferencesinvaluesbutin
theunderstandingoftherisk-relatedfacts,andthatpublicpolicyshouldbebasedonthesefactsratherthanonpeople’s
(mis)perceptions.Forexample,Viscusi(2000)stronglyarguesinfavourofusingtheobjectiverisks,accordingtothe
bestavailablescientificevidence,ratherthanusingpeople’sbiasedriskperceptions.Accordingtohim,tospendscarce
resourcesonreducingillusoryfearsratherthanrealrisks“isaformofstatisticalmurderinwhichlivesaresacrificed”
(p. 867). Harsanyi (1995, 1997) similarly argues that what should matter in social decision making is informed or
truepreferences,i.e.thepreferencesarationalindividualequippedwithperfectinformationwouldhave.Itisdifficult
to argue against this standpoint when it is obvious that people simply make mistakes due to limited information or
cognitivecapacity.Indeed,peopleknowthattheymakemistakesforvariousreasonsandtheyoftenvoteforsystems
whereexpertsmakemanychoicesforthem.Therefore,followinge.g.Broome(1999),Ng(1999),Johansson-Stenman
(2002)andO’DonoghueandRabin(2006),weassumethroughoutthispaperthatwhatmattersintrinsicallyiswell-being
ratherthanchoice.Or,usingtheterminologyofKahnemanetal.(1997),weareintrinsicallyinterestedinexperienced
utility rather than decision utility. This implies that the model allows for paternalism following a small but rapidly
1 Whyandhowriskmisperceptionsareformedandprevailisbeyondthescopeofthispaper.Themediaattentiongiventocertainspectacularrisks
appearstobeanimportantreason(Slovic,1986;Pidgeonetal.,2003).Moreover,researchinpsychologyindicatesthatpeoplehavelargedifficulties
dealingwithprobabilitieswhenstrongfeelingsareinvolved(e.g.Lowensteinetal.,2001).
2 Salanie and Treich (2005) constitutes an important exception, where a regulator can either be paternalistic or populistic in the sense that
preferencesbasedonerroneousbeliefsarerespectedaswell.OthernotableexceptionsareHammond(1981)andSandmo(1983),whoanalysed
riskmisperceptionsintheframeworkofex-anteversusex-postwelfareeconomics.SmithandDesvousges(1987)andGegaxetal.(1991)measure
people’swillingnesstopayforreductionsoftheperceived,ratherthanthereal,risk.
3 Inconventionalmodelswithnoriskmisperception,wheretheaimistomaximisethesafetybenefitsintermsofsavedlivesforagivenbudget,
itisofcourseoptimaltoapplythesamevaluepersavedlifeacrosscontexts.
236 O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248
growingliteraturethattakespeople’sdocumentedirrationality(notablytimeinconsistency)intoaccount(e.g.Camerer
etal.,2003;GruberandKo¨szegi,2002,2004;O’DonoghueandRabin,2003,2006;ThalerandSunstein,2003).4
Assumethatarepresentativeconsumer’sstrictlyquasi-concaveexpectedutilityfunction,whichreflectsexpected
well-being,isgivenby
U =u(x,r), (1)
wherexisnetprivateincomeandristheobjectiverisk(probability)ofanaccident,andwhereu >0,u <0(subscripts
x r
denotepartialderivatives).TheriskcanbereducedbyapublicinvestmentG,sothatr=r(G),wherer <0andr >0.
G GG
The objective for the government is to maximise (1), which is assumed as known to the government. Thus, the
modelimpliesthattheexpertsandpolicy-makers(whohaveaccesstotheexpertviews)arerightandcorrespondingly
thatthegeneralpubliciswrongwhentheriskperceptionsdiffer.Thisisofcoursenotastrictlyaccurateassumption.
Therealriskisoftendifficulttoestimateevenforexperts,andbothexpertsandpolicy-makersarealsotosomeextent
affectedbyperceptionbiases(Viscusi,1995;ViscusiandHamilton,1999).Nevertheless,theassumptionmadehere
constitutesanaturalandimportantbenchmarkcase.
2.1. Efficientpublicsafetyinvestments
Maximising(1)subjecttoabudgetrestrictionM=x+pGG,wherepGistheper-unitpriceofGintermsofxandM
istheavailablepublicbudget,impliesthestandardconditionforaParetoefficientinvestmentinGasfollows:
WTPirnformed(−rG)=pG, (2)
where WTPirnformed =−(uuxr)(x,r) reflects an informed individual’s marginal willingness to pay (WTP) for a risk
reduction(i.e.withoutanyriskperceptionbias),5andwhere−r istheriskreductioncausedperunitofG.Eq.(2)then
G
simplyreflectstheconventionalefficiencyrulewherethelefthandsideconsistsofthemarginalbenefitassociatedwith
theriskreductionofincreasedG,whereastherighthandsidereflectsthecorrespondingmarginalcost.Inthispaper
wewillnotgofurtherintothetechnicalrelationshipbetweenGandr;wewillinsteadfocusexclusivelyonpeople’s
perceptionoftheriskrandthecorrespondingWTPtoreducethisrisk.
2.2. Efficiencywithbiasedrisk-perceptions
Oneofthemostconsistentandwell-researchedconclusionsinthepsychologicalliteratureoneconomicdecision-
makingisthatpeople’sresponsestorisktendtodeviatesystematicallyfromwhatispredictedbyconventionaleconomic
theory(Kahnemanetal.,1982;KahnemanandTversky,2000;Gilovichetal.,2002).6
In order to formally handle systematic risk misperceptions, let s denote beliefs about the objective risk (i.e. the
perceived or the subjective risk), which may deviate from the objective risk r. We assume that s depends on r, i.e.
s=s(r),wheres >0.Forexample,peopleknowthattravellingbycarisrisky,butnothowriskyitis.Iftheobjectiverisk
r
increases,e.g.throughaspeedincrease,theirriskbeliefwillalsoincrease,andviceversa.Assumethatthegovernment
uses some method (e.g. a stated-preference method) to elicit individual preferences for a small risk-reduction. The
observedindividualmarginalwillingnesstopayforareductionintheriskr,attheperceivedrisklevels,isthengiven
4 Onecanofcoursearguethatindividualchoicesshouldbegivenmoralsignificanceperseindependentofpeople’swell-being;seee.g.Sugden
(2004).Still,itisnotdifficulttomodifythestandardwelfaristicapproachadoptedherebyassumingthatpeoplegetincreasedwell-beingfrom
choosingforthemselves.
5 Possiblebiasesrelatedtotheelicitationmethodpersearedisregardedthroughoutthepaper,althoughtheywillbetoucheduponintheconcluding
section.
6 Itissometimesarguedthattheobserveddifferencesinriskperceptionsmaynot,atleastnotsolely,reflectriskmisperceptionsbythepublic.
Instead,theymayreflectdifferencesinvaluesandprioritiesbetweenexpertsandpeopleingeneral(e.g.Krupnicketal.,1993;Morgan,1992).
Sunstein(2002),inacarefulassessmentofthisclaim,nonethelessconcludesthatdifferentprioritiesandvaluescanonlyexplainasmallextentof
thelargediscrepanciestypicallyobtained,andthatpeople’sriskmisperceptionsarethemainreasonsbehindthem.SeealsoHammitt(2000)fora
balanceddiscussionontheseissues.
O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248 237
Fig.1. Possiblerelationsbetweenthesubjectiveandtheobjectiverisk.
by
(cid:2) (cid:3)
WTPorbserved =sr −uur(x,s) = WTPΩirnformed, (3)
x
where the correction factor Ω= WTPirnformed = 1 ur/ux(x,r). By combining (2) and (3) we can write the efficiency
WTPorbserved sr ur/ux(x,s)
conditionintermsofobservedWTP:
−rGWTPorbservedΩ=pG. (4)
Consequently,Gshouldbeover-providedcomparedwiththeefficiencyruleintermsofobservedindividualWTPif
Ω>1,i.e.WTPorbserved <WTPirnformed,andviceversa.Tobeabletosaymoreabouttheconditionsforwhenthisisthe
case,letuslookcloserattherelationshipbetweentheperceivedandtheobjectiverisk.ConsiderFig.1.
IncaseA,theriskbeliefrisksissimplyaproportionalamplificationoftheactualriskr,clearlyimplyingthats >1
r
sothatachangeintherealriskimpliesalargerperceivedriskchange.Similarly,wehavethats <1incaseBwhere
r
peoplealwaysunderestimatetherisk.However,thereismuchevidencethatpeoplesystematicallyoverestimatesmall
risksandunderestimatelargeonesasincaseC(e.g.Viscusi,1992a,p.117),sothats <1generally.Thenanobjective
r
riskincrease(ordecrease)willalwaysimplyasmallerperceivedriskincrease(ordecrease),irrespectiveofthelevel
oftheriskmisperception.Thus,people’sriskbeliefmaybemuchlargerthantheactualrisk,butatthesametimethey
perceivethesizeoftheriskchangetobesmallerthanthetrueriskchange.
However,itissometimesarguedthatarelationshipasincaseDismorerealistic;seee.g.TverskyandKahneman
(1992)orGonzalezandWu(1999),andBleichrodtandPinto(2000)forahealthapplication.Inthiscasewehavethat
s >1forsufficientlysmallrisklevelsandthats <1forlargerones.Takentogether,wecanobservethatthefollowing
r r
patternholdseverywhereforeachofthefourdiagrams:
Assumption1. s ≤0,s(r=0)≥0.
rr
Thisimpliesasingle-crossingpropertysuchthatifs<rthens <1,whereastheoppositedoesnothold,i.e.s>rdoes
r
notimplythats >1.7 Inotherwords,ifpeopleunderestimatetherisk,theywillalsounderestimatetheriskchange,
r
butiftheyoverestimatetherisktheywillnotnecessarilyoverestimatetheriskchange.
7 Cumulativeprospecttheoryimpliesaninverses-shapedcurvewheresr>1holdsforasufficientlylarger(closeto1).Thisintervalisignored
herebecauseriskregulationstypicallydealwithmuchsmallerrisks.Moreover,thevaluefunctioninprospecttheoryneednotbebasedoncognitive
riskmisperceptions;itissufficientthatpeoplebehaveasiftheyhaveriskmisperceptions.Thesameapplieshere.Itisthussufficientthatpeople
behaveasiftheyhaveriskmisperceptions.
238 O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248
ConsidernowtheotherfactorofΩ:Strictquasi-concavityofuimpliesthattheWTPincreasesintheinitialbaseline
risklevel,8implyingthat−ur(x,s)>−ur(x,r)fors>randviceversa.Combiningthiswiththeassumedpatternfor
ux ux
sr we have that if s<r then WTPorbserved <WTPirnformed, but we cannot say whether the observed WTP exceeds the
informedoneifs>r.Combiningthiswith(4),wehave:
Proposition1. Ifpeopleunderestimatetherisk(s<r),thentheoptimalprovisionofGexceedsthebasicefficiency
rule in terms of observed WTP for a risk decrease. However, if people overestimate the risk (s>r), it is ambiguous
whetherornottheoptimalprovisionofGexceedsthelevelobtainedbythebasicefficiencyrule.
3. Decentralisation,fear,pricingandinformationprovision
Intherealworld,mostriskydecisionsaremadebypeoplethemselves(suchaswhattoeat,drink,howtotravel,
whether or not to smoke and if so what to smoke, etc.). Therefore, in this section we model a decentralised market
economywherepeoplechoosethemselveshowmuchtobuyofariskyandanon-riskygood,respectively.Wealsoallow
forthepossibilityofusingdifferentiatedconsumptiontaxes,wheretherevenuesaredistributedbackinalump-sum
manner.
Following Akerlof and Dickens (1982), Akerlof (1989) and Becker and Rubinstein (2004), we include the fear
associatedwithriskdirectlyintheutilityfunction.9Obviousexamplesincludefearrelatedtoaperceivedriskofflying,
health-riskanxietyduetotheuseofcertainchemicalsinfood,andterrorism,eventhoughtheactualrisksmightbe
fairlylow.Giventhatwecareintrinsicallyaboutpeople’swell-beingratherthantheirchoices,itishardtoseewhysuch
fear,oranxietyormentalsufferingmoregenerally,shouldcountlessthanotherdeterminantsofindividualwell-being.
However, one may argue that when the discrepancy between objective and perceived risk is due to imperfect
information,theappropriatetaskforthegovernmentistoprovideinformationinordertoeliminate,oratleastreduce,
thisdiscrepancy,ratherthantotrytocorrectforpossiblemisperceptions.Althoughthisargumentmayseemconvincing,
ithasoftenbeenfoundthatlargedifferencespersistevenafterintensivepublicinformationcampaigns;seee.g.Pidgeon
etal.(2003).Anoveltyinthemodelhereisthatinformationprovisioniscostly,andishencenofreelunch.Thefollowing
modelisgeneralisedtoencompasstheseaspects.Expectedutilityfortherepresentativeconsumeristhengivenby
U =u(x,y,r,m(s)), (5)
where x is a composite risk-free good, y a risky good, r the objective risk, and m is the fear (or mental suffering)
associatedwiththeriskbeliefs.Assumefurtherthatuisstrictlyquasi-concaveinitsarguments(toensureaunique
perceivedoptimumfortheconsumersandanactualexpectedutilityoptimum),ux>0,uy>0,uz<0,um<0,ms>0,
mss>0and∂(um/ux)/∂m<0.Thus,foragivenobjectiverisk,expectedutilitydecreaseswiththeriskbeliefandthe
marginalWTPtoreducefearincreaseswiththeamountoffear.Foranalyticalconvenience,wealsomakethefollowing
assumption:
Assumption 2. It is possible to write the utility function as weakly separable in the objective risk, as follows:
U =v(f(x,y,m),r(·)).
Thisimpliesthatthemarginalratesofsubstitutionbetweenx,yandm,respectively,areindependentoftheobjective
riskrperse.10Thisassumptiondoesnotseemoverlyrestrictiveand,althoughitisnotessentialforthemainconclusions,
itsimplifiesthesubsequentanalysisandtheoptimalityexpressions.Theobjectiveriskrisnowafunctionbothofthe
consumptionoftheriskygoodyandofpublicinvestmentstoreducetheriskG:
r =r(y,G), (6)
8 Althoughstrictquasi-concavityisnotself-evident,theimplicationthatWTPforagivenriskreductionincreasesintheinitialrisklevelisoften
assumed;seee.g.Jones-Lee(1974)andPrattandZeckhauser(1996).
9 Otherpapershavemodelledutilityasdependingonwheninformationisupdated,includingKrepsandPorteus(1978)andCaplinandLeahy
(2001,2004);forhealthapplicationsseeKo¨szegi(2003)andHoeletal.(2006).
10 Thatis,foraconstantperceivedrisk.Thefearinitselfisafunctionoftheperceivedrisk,whichinturndependsontheobjectiverisk.Moreover,
becauserdependsony,theconsumerchoicebetweenxandywillthereforestillbeaffectedbyexogenouschangesinr.
O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248 239
wherer >0,r <0,r <0andr >0.Theriskbeliefisafunctionofboththeobjectiveriskandofpubliclyprovided
y yy G GG
informationI,aimedatreducingthediscrepancybetweentheperceivedandobjectiverisks.Thus,wehave:
s=s(r(y,G),I), (7)
wheres >0andwheres <0,s >0fors>r,ands >0,s <0fors<r.Thus,itisassumedthattheriskmisperception
r I II I II
decreasesmonotonicallyinI,andalsothatitdecreasesatadecreasingrate.Moreover,wealsosimilarlyassumethatthe
marginalriskperceptionbiasdecreasesatadecreasingratewiththeinformationprovided,i.e.∂s /∂I<0,∂2s /∂I2>0
r r
fors >1,and∂s /∂I>0,∂2s /∂I2<0fors <1.Letusforsimplicityalsoassumealinearbudgetrestrictionsuchthat
r r r r
M =x+y+pGG+pII, (8)
wherepI istheper-unitpriceofpublicinformationI,andwherethepricesofxandywithoutlossofgeneralityare
normalisedtoone.Substituting(6)–(8)into(5)wecanwriteindividualexpectedutilityas
U =u(M−pyy−pGG−pII,y,r(y,G),m(s(r(y,G),I))). (9)
3.1. Optimalsafetyinvestments
Thefirstorderoptimumconditionisobtainedbydifferentiating(9)withrespecttothepublicsafetyinvestmentG:
WTPirnformed(−rG)+WTPmmssr(−rG)=pG, (10)
whereWTPm=−um/ux isthemarginalwillingnesstopayperunitoffearreductionintermsofx.Notethatbecause
weareinafirst-bestworld,thisexpressionwouldbeidenticalinthecasewithnoriskmisperceptions.Thetermson
theleft-handsidereflectcomponentsofthemarginalbenefitsofG,whichisbasedontheobjectiverisk,whereasthe
termontheright-handsidereflectsthemarginalcost(theperunitprice)ofGintermsofthenumerairegoodx.The
firsttermontheleft-handsideisidenticaltotheoneinSection2,andhasthesamestraightforwardinterpretation.The
second term reflects the WTP for the correspondingly decreased fear from a slight increase in the safety-enhancing
investmentG(andhenceadecreaseinrands).
TheWTPfortheriskdecreaseassociatedwithanincrementalincreaseinGforanindividualwithriskmisperception
isinsteadgivenbyWTPorbserved(−rG)+WTPmmssr(−rG).Thus,theconditionforwhentheoptimalprovisionofG
exceedsthelevelobtainedbytheconventionalefficiencyruleisthesameasintheprevioussection,anddependson
whetherWTPorbserved >WTPirnformed.Consequently,wehave:
Corollary1. If,inthegivenframework,peopleunderestimatetherisk(s<r),thentheoptimalprovisionofGexceeds
thebasicefficiencyruleintermsofobservedWTPforariskdecrease.However,ifpeopleoverestimatetherisk(s>r),
itisambiguouswhetherornottheoptimalprovisionofGexceedsthelevelobtainedbythebasicefficiencyrule.
Theintuitivereasonbehindthefactthatfeardoesnotaffectthisconditionisthatthereisnodiscrepancybetween
theeffectsondecisionutilityandexperiencedutilityhere.Peoplesimplyfeelwhattheyfeel,andafeelingisfroma
hedonicperspectiveequallyimportantwhenitisbasedonanillusoryrisk.
3.2. Optimalpricing
Wenowturntothepricingissue.Theoptimaltaxtontheriskygoodyisobtainedbycomparingthesocialoptimum
condition with respect to y with the corresponding private optimum condition, where a consumer faces the budget
constraint
M+τ =x+y(1+t), (11)
whereτ isalump-sumtransferfromthegovernment.Itcanbeshown(seeAppendixA)thatanoptimaltaxtonthe
riskygoodcanthenbewrittenasthefollowingstraightforwardexpression:
t =ry(WTPirnformed−WTPorbserved). (12)
Thus,thetaxequalsthedifferencebetweenwhataninformedindividualonthemarginwouldhavebeenwillingtopay
perunitofyifshehadperceivedtheriskaccurately,andheractualwillingnesstopay.Intheabsenceofanyperception
240 O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248
bias,i.e.whens=r,theoptimaltaxtisclearlyzero,whichsimplyreflectsthefirsttheoremofwelfareeconomics,i.e.
thatanundistortedmarketequilibriumisParetoefficient.
Suppose that people underestimate the risk of eating potato chips by 50% at the margin. This implies that their
WTPtoavoidtheriskofanadditionalpotatochip(holdingthefearoftheriskconstant)isreducedbymorethan50%
if the WTP increases with the perceived initial risk. Suppose it is reduced by 60%. Denote the first term of (12) by
α,implyingthatthesecondtermisequalto(1−0.6)αor0.4α.Thus,theoptimaltaxwouldbe60%oftheWTPthat
theywouldhavebeenwillingtopayforthisriskreductionwithoutriskmisperceptions,or,expressedalternatively,1.5
timestheWTPtheyactuallyhavefortheriskreduction(onceagainholdingfearconstant).
Now consider the case where we know that people misperceive the overall risk of consuming y, and know the
direction of this risk perception, but where we have no direct information regarding the perception of a marginal
change.Becausewehaveasbeforethatwhens<ritfollowsthatWTPorbserved <WTPirnformed,butnotviceversa,we
have,analogoustoProposition1:
Proposition2. Ifpeopleunderestimatetheriskassociatedwithconsumingthegood(s<r),thenafirst-bestoptimaltax
ontheriskygoodyisstrictlypositive.However,ifpeopleoverestimatetherisk(s>r),thesignofthetaxisambiguous.
Notethatthebasisforthiscorrectivetaxationisnotexternalities,i.e.costsimposedonothers,butwhatHerrnstein
etal.(1993)denoteinternalities,whereindividualshurtthemselvesbymakingbaddecisions.11
3.3. Optimalinformationprovision
Letusfirstassumeaninteriorsolutionwithrespecttotheoptimalamountofprovidedinformation,andthenbriefly
discussthepossibilityofalowercornersolutionwithnoinformationprovision.Thesocialoptimumconditionisthen
obtainedbydifferentiating(9)byI:
WTPmms(−sI)=pI. (13)
Thus, the marginal benefit should at optimum equal the per-unit cost of increased information. Note that there is
no benefit from improved consumer choices due to more information in the optimum condition. This is because
the regulator can always obtain efficient consumer choices by adjusting the relative prices (welfare effects of better
consumerchoicesareanalysedinthenextsection).Theexistenceofaninteriorsolutionisthereforefarfromobvious
here.Noteinparticularthatwhens<rthebenefittermisactuallynegative,implyingthatitisneveroptimaltoprovide
moreinformationinthiscase.Thisreflectsthatinafirst-bestworldwhentheconsumptionofxandyisoptimal,the
onlywelfaredifferencethatbetterinformationaboutthetruehigherriskwouldmakeistoincreasethefearassociated
withtheriskbelief.
Whetherinformationprovisionwouldbepartoftheoptimumconditionwhens>risnotobviouseither,butdepends
onwhetherthebenefitofprovidingasmallamountofinformationreducestheriskmisperception(andhencethefear)
sufficientlytowarrantthecostsinasituationwhereoptimalsafetyinvestmentsandrelativepriceadjustmentsaremade
anyway.Formally,itisoptimaltoprovideanon-zeroamountofinformationif,andonlyif,12thenetmarginalbenefit
ispositivewhennoinformationisprovided:
(WTPmms(−sI))I=0 >pI. (14)
Thuswehave:
Proposition 3. If people underestimate the risk (s<r) in a first-best economy, it is never optimal to provide the
consumers with costly information. However, if people overestimate the risk (s>r), it is optimal to provide costly
informationprovidedthattheper-unitpriceofinformationissufficientlylow.
11 Thereareofcourseothersourcesforinternalitiesbesidesriskmisperceptions.Forexample,O’DonoghueandRabin(2006)andGruberand
Ko¨szegi(2002,2004)argueinfavourofhighertaxesonunhealthyfoodandcigarettes,respectively,basedonselfcontrolproblems.Thetaxderived
hereisthensimilarinthatitismotivatedbyinternalities,eventhoughtheunderlyingreasonsdiffer.
12 The“if”partisobviousandthe“onlyif”partfollowsbecausethebenefittermincreasesatadecreasingrateinI,whichinturnfollowsbecause
themarginalWTPtoreducefearincreaseswiththeamountoffear,togetherwiththeassumedcurvatureofmands(insandI,respectively).
O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248 241
4. Whendifferentiatedtaxesarenotpossible:asecond-bestmodel
In Section 3 it was assumed that the government could use differentiated consumption taxes in order to correct
for people’s risk misperceptions. Even if these results are important as benchmark cases, one can question whether
suchtaxesarefeasibleinreality,e.g.duetoadministrativeandlegalreasons.13 Morefundamentally,manyimportant
activitiesfromahealthperspective,suchassexualbehaviour(andtheimplicationsforHIV/AIDS),drugcompliance,
andhospitalavoidanceduetofearofMRSA(methicillin-resistantStaphylococcusaureus),arenotmarkettransactions
at all, and where there is no tax levels that can be varied. The same applies to sports and other healthy activities.
Another natural benchmark case is therefore to assume that no differentiated taxes are possible. In such a situation
it is in general not possible to obtain a first-best solution, implying that our objective here is to derive second-best
optimalityrules.
ConsideramodelsimilartotheoneinSection3withtheonlydifferencebeingthatwecannotusedifferentiated
taxation,implyingthatwecannotaffecttherelativeprices.14 Expectedutilityisthus,asbefore,givenbythestrictly
quasi-concavefunctionU=u(x,y,r,m(s)),whichfulfilstheweakseparabilitypropertyinr(Assumption2),andwhere
r=r(y,G)ands=s(r(y,G),I).Inordertobeabletointerprettheresultsalsofornon-marketgoodsandactivitiessuchas
sexualactivity,thebudgetrestriction(8)mayalternativelybeinterpretedmorebroadlye.g.intermsofthealternative
costoftime.
4.1. Second-bestsafetyinvestments
Due to the impossibility of adjusting relative prices, the consumer choice between x and y will in general not
be optimal anymore. The only way the government can affect this choice is through its choice of G and I. It is
straightforwardtoshow(seeAppendixA)thattheoptimalprovisionofGisgivenasfollows:
WTPirnformed(−rG)+WTPmmssr(−rG)+(WTPorbserved−WTPirnformed)ryyG =pG. (15)
Thetermsontheleft-handsidereflectcomponentsofthemarginalbenefits,andthetermontheright-handsidereflects
themarginalcostsofGintermsofthenumerairex,asbefore.Thefirsttwotermsontheleft-handsideareidenticalto
theonesinafirst-bestworld,asshowninSection3,Eq.(10),andtheyhavethesamestraightforwardinterpretation,
whereas the third term reflects second-best welfare effects. The interpretation of this term is also straightforward:
Assumethatpeopleunderestimateamarginalriskchange,sothatWTPorbserved <WTPirnformed.Thenpeoplewillon
themarginconsumetoomuchofy,implyingthatitisbeneficialiftheconsumptionofyisreduced.Thesizeofthis
benefitisexactlyequaltothedifferencebetweentheperceivedandtheinformedvalueoftheriskchange,timeshow
muchtheriskisreducedonthemargin(throughreducedconsumptiony)perunitofG.
Theconsumers’perceivedoptimumconditionisgivenby
WTPorbserved(−rG)+WTPmmssr(−rG)=pG. (16)
Consequently, combining (15) and (16) we find that G should be over-provided compared with the conventional
efficiencyruleif(WTPirnformed−WTPorbserved)((−rG)−ryyG)>0,andviceversa.
Inordertodeterminethesignofthisexpression,letusstartwiththesignofy .Thereisampleevidencethatpublic
G
safety investments are partly crowded out by people making more risky individual choices. For example, Peltzman
(1975)inaclassicstudyshowedthatmandatoryseat-beltlawsimpliedmoreriskydrivingbehaviour;seeKeeler(1994),
Petersonetal.(1995)andMerrelletal.(1999)foradditionalevidence.However,fromthisliteratureitisalsotypically
foundthatpeopledonotover-compensate.Thisimpliesthatthereisindeedapositiveneteffectofthesafetymeasure
taken,albeitasmalleronethanwithoutcompensatorybehaviour.Followingthisempiricalevidence,wehave:
Assumption3. y >0;−r >r y .
G G y G
13 Moreover,inrealitypeopleareofcourseheterogeneouswithvaryingriskmisperceptions,sowewouldneedpersonalisedtaxestoobtain
efficiency;suchtaxesareclearlyunfeasibleinpractice.
14 Itisstraightforwardtogeneralisethemodelinmanywayssuchastoincreasethenumberofgoodsandallowforprivaterisk-reducinginvestments.
242 O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248
Considernowthecasewheres<r,implyingfromSection2thatsr<1andthatWTPirnformed >WTPorbserved.From
Assumption3weclearlyhavethat−r −r y >0.Hence,s<rimpliesthatGshouldbeover-providedcomparedto
G y G
thebasicefficiencyrule.Ontheotherhand,whens>rwehavethesameambiguityaspreviously,becausewecannot
saywhetherWTPirnformed >WTPorbservedornot.Then,conditionalonAssumption3,wehave:
Corollary2. If,inthegivenframework,peopleunderestimatetherisk(s<r),thentheoptimalprovisionofGexceeds
thebasicefficiencyruleintermsofobservedWTPforariskdecrease.However,ifpeopleoverestimatetherisk(s>r),
itisambiguouswhetherornottheoptimalprovisionofGexceedsthelevelobtainedbythebasicefficiencyrule.
Inordertoillustratethesesecond-bestresults,considertherecentEuropeanexperiencewheremanypeoplewere
afraidtoeatbeefduetothemadcowdisease,despitethefactthatmostleadingmedicalexpertsconsideredtheriskstobe
negligiblecomparedwithmanyotherrisks.Applyingtheriskbeliefwouldthenimplyfar-reachingimportrestrictions
onbeef,whereasapplyingtheobjectiveriskwouldnot(giventhattheexpertswereright).15Theresultsfromthispaper
suggestthatnorestrictionsshouldhavebeenimposedunlessonewouldhaveexpectedlargefeareffectsfromtherisk,
orunlesspeoplewouldhaveadjustedtheirbehaviourtoalargeextent.Inreality,weknowthatmanypeoplewereindeed
veryscared,andthattherewerelargefear-inducedconsumptionchanges.Therefore,theimportrestrictionsactually
undertaken may have been well motivated after all. Similar arguments can be made regarding the US investments
in safety after 9 November 2001, where presumably many more lives could have been saved if instead some of the
money would have been spent on, say, improved road safety; cf. Sandler (2004). On the other hand, without these
largeinvestmentsperhapspeoplewouldhavemadeevenmoreirrationaldecisions,suchasreplacingairtravelwith
moredangerouscartraveltoanevenlargerdegree(cf.Blalocketal.,inpress);seeFreyetal.(2007)forasurveyof
theoveralleconomicconsequencesofterrorism.Therearealsoimportanthealtheconomicexamples,includingsome
people’sexcessivefearofMRSAthatmaymakethemhesitatevisitingthehospitalwhentheyareill.Suchindirect
healtheffectsmayinfactbelargerthanthedirectones,whichhighlightstheimportanceofincludingindirecteffects
incostbenefitanalysisofMRSApreventingmeasures.
4.2. Second-bestinformationprovision
Theroleforinformationprovisionappearsmoreobviousinthissecond-bestworld,whereincreasedinformation
canhelppeoplemakebetterdecisions.Assumingtheexistenceofaninterioroptimum,wecanwrite(seeAppendix
A)theoptimalinformationprovisionconditionasfollows:
WTPmms(−sI)+ryyI(WTPorbserved−WTPirnformed)=pI. (17)
Thefirsttermof(17)isidenticaltothefirst-bestmodel,Eq.(13),andhasthesamestraightforwardinterpretation,i.e.
theWTPthattheindividualwouldhaveforthedecreasedfearassociatedwithaunitincreaseinpublicinformation
I.However,fromapolicyperspectivethemostimportantmotiveforprovidingbetterinformationispresumablythat
consumerswouldbeabletomakebetter-informeddecisionsregardingtheriskyactivities;sucheffectsarereflectedin
thesecondterm.Thistermcanbeinterpretedastheadditional(expected)welfare,inmonetaryterms,thatoneunitof
Icausesthroughbetterconsumerchoices.Forexample,studieshaveshownthatamajorityofwomenwithafamily
historyofbreastcancerhaveexaggeratedperceptionsoftheirownriskofthisdiseaseandexperienceexcessiveanxiety,
andthattheirriskmisperceptionandanxietycanbereducedwithbetterinformation(Lermanetal.,1995).Inorderto
determinethesignofthesecondterm,letusfirstmakethefollowingreasonableassumptions:
Assumption4. (i)Theconsumptionoftheriskygoodsdecreaseswiththeperceivedriskofconsumingonemoreunit
ofthegood,i.e.∂y/∂(s r )<0.(ii)Theconsumptionoftheriskygoodsdecreaseswiththeperceivedabsolutemagnitude
r y
oftherisk,i.e.∂y/∂s<0.
15 ItisimplicitlyassumedthathigherperceivedriskalsoincreasestheWTPforariskchange,whichseemsreasonableherebecausetheobjective
riskisclosetozero.Notealsothatweonlydiscussimportrestrictionsonbeef;therewasamuchstrongercaseforstringentimportrestrictionson
cattle.
O.Johansson-Stenman/JournalofHealthEconomics27(2008)234–248 243
Thenitfollowsthatwhenpeopleunderestimatetherisk,sothats<rands <1,wehavethaty <0,meaningthat
r I
moreinformationinducespeopletoconsumelessoftheriskygood.Moreover,becauseWTPorbserved <WTPirnformed,
weclearlyfindthatthesignofthesecondtermof(17)ispositive,whichfollowsintuition.Ontheotherhand,when
s>r,thenAssumption4isnotsufficienttosaythatthesignispositive,andwehaveinstead:
Proposition4. Thesecond-bestwelfareeffectsduetochangedconsumerchoicesfrommoreinformation(thesecond
termofEq.(17))arenegativewhens>rands <1,andthefollowingconditionholds:If ∂y∂|s−r| <(>) ∂y ∂|sr−1|
r ∂s ∂I ∂(srry) ∂I
thenWTPorbserved <(>)WTPirnformed.Forallothercases,thesewelfareeffectsarenon-negative.
Forproof,seeAppendixA.Intuitively,onemayexpectthatconsumerswithbiasedriskperceptionswouldmake
betterchoicesbetweenriskyandnon-riskygoodswithmoreinformation,becauseitisassumedthatboththeirabsolute
andmarginaldegreesofriskmisperceptiondecreasewiththeamountofpublicinformationprovided.Inmostcases
thisisalsothecase,butwhenpeoplesimultaneouslyoverestimatetheoverallriskandunderestimateariskchange,it
isambiguouswhethermoreinformationwillinducemoreorlessriskybehaviour,andthenwhetherthewelfareeffects
arepositiveornegative.
Consideranexamplewithtobaccosmoking,andassumethatanindividualoverestimatestheoverallriskofsmoking
(seeViscusi,1992b)andthathesimultaneouslyunderestimatesthemarginalriskassociatedwithsmokingoneadditional
cigarette(seeHammarandJohansson-Stenman,2004).Alsoassumethattheneteffectinthiscaseisthathesmokes
too much for his own interest, in terms of expected experienced utility. More publicly provided information about
thetrueriskofsmokingwillinthiscasehavetwoeffects:(1)Therisk-perceptionbiasintermsofabsoluterisklevel
will decrease. This effect will induce the individual to smoke more. (2) The marginal risk-perception bias will also
decrease.Thiseffectwillinducetheindividualtosmokeless.Thus,ifthefirsteffectdominatesthelatter,thenmore
informationwillhurttheindividualbymakinghimmakeevenworsechoices(inthiscasesmokemore)thanbefore
theadditionalinformation.16
However,evenwhenthesecondtermof(17)ispositive,itdoesnotfollowthatitisoptimaltoprovideanyinformation
atall.Inthefirstcase,wherepeopleunderestimatetheoverallrisk,thereisanincreasedfearcomponentfromproviding
moreinformationthatoneshouldtakeintoaccount,andinbothcasesthemarginalbenefitofmoreinformationmust
ofcourseoutweighthemarginalcost,ortheperunitprice,ofprovidingtheinformation.
Clearly,asufficientcondition17 forpositiveinformationprovisionisthatthelefthandtermsof(17)exceedpI,at
zeroamountofprovidedinformation,i.e.
(WTPmms(−sI)+ryyI(WTPorbserved−WTPirnformed))I=0 >pI. (18)
Thuswehave:
Proposition 5. If people underestimate the risk (s<r) in the second-best economy, it is optimal to provide costly
informationifthesecond-bestwelfareeffectsfromchangedchoicesaresufficientlylargecomparedtotheincreased
feareffectandtheper-unitpriceofinformation.Ifpeopleoverestimatetherisk(s>r),itisoptimaltoprovidecostly
information if the per-unit price of information is sufficiently low compared to the decreased fear and second-best
effects(whosesignisundecided).
5. Summaryandconclusion
Thispaperhasanalysednormativeimplicationsforoptimalpublicsafetyinvestments,internalitycorrectingtaxation
andcostlyinformationprovisionasaresultofbiasedriskperceptions,forwhichthereisampleempiricalevidence.
Forexample,itwasshownthattheoptimallevelofpublicsafetyinvestmentsquitegenerallyexceedsthelevelimplied
bytheconventionalefficiencyrule,intermsofindividualWTP,whenpeopleunderestimatetherisk,whereastheresult
isambiguouswhenpeopleoverestimatetherisk;seeTable1forasummaryofthemainresults.
16 ThisisincontrasttoCarboneetal.(2005),wheremoreinformationalwaysreducessmoking.However,thatpaperprovidesotherinteresting
insightsregardingthetimingofsmokingreduction.
17 Thisisalsoanecessaryconditionifthelefthandsideof(18)isneverlargerthanatI=0.Theconditionsforthis,inturn,arehoweverquite
complex.