PUBLIC GOODS AND CONTINGENT VALUATION ROBERT SUGDEN pot

Thus, when we specify the utility functions of a set ofindividuals, the level of provision of each public good is represented by asingle variable, which is an argument in each individual

5 Public Goods and Contingent

Valuation Public Goods and Contingent Valuation

5.1 PUBLIC GOODSMany applications of the contingent valuation (CV) method are concernedwith public goods This chapter considers some of the special problemsinvolved in eliciting preferences for such goods

In economic theory, the distinction between public and private goods isclear-cut What is now the standard deWnition of a public good derives from

a classic paper, only three pages long, by Paul Samuelson (1954); thisencapsulates some of the key elements of a tradition of public Wnancewhich can be traced back to Lindahl (1919/1958) and Wicksell (1896/1958).The deWning characteristic of a public good is that the same units of the goodare consumed by, or give utility to, more than one individual

For example, consider the beneWts that the residents of a suburban areaderive from an expanse of open-access woodland One way of modellingthese beneWts would be to deWne a good, `open-access woodland', measured

in hectares A typical resident, we may assume, prefers more of this good toless, just as she prefers to have more rather than less of private consumptiongoods, such as food and clothing But there is a crucial diVerence betweenfood and clothing on the one hand and the woodland on the other Inrelation to food and clothing, individual consumers are rivals: if any givenunit of one of these goods (say, a particular packet of frozen peas or aparticular coat) is consumed by one person then, necessarily, it is not con-sumed by another person In contrast, in the case of the woodland, there is

simultaneously Thus, when we specify the utility functions of a set ofindividuals, the level of provision of each public good is represented by asingle variable, which is an argument in each individuals' utility function,while the level of consumption of each private good is represented by aseparate variable for each individual

This chapter was written as part of a research project supported by the Economic and Social Research Council, through its Transport and the Environment Programme (Award No W 119

25 1014) Thanks go to Ian Bateman, Alistair Munro, and Chris Starmer for their help.

At Wrst sight, it may seem odd that the theoretical distinction betweenpublic and private goods should be so categorical Isn't there a continuumstretching from almost pure private goods (such as frozen peas) to almostpure public goods (such as national defence)? The answer is that Samuel-son's distinction between public and private goods is not so much a classiW-cation of goods as a classiWcation of ways of modelling them Indeed it isoften possible to choose whether to model a given source of beneWts as aprivate good or as a public one.

Take the case of the woodland In an informal sense, open-access land in a suburban area is not a `pure' public good Beyond a certain point,the more visitors there are to a wood, the poorer is each visitor's experience.Thus, one might say, visitors are rivals But this factor can be incorporatedwithin a model in which woodland is a public good in Samuelson's sense.The eVects of congestion come through as properties of individuals' valua-tions of the public good; one of the reasons why an increase in quantity (i.e

wood-an increase in the area of woodlwood-and) is valued is because this reducescongestion However, the same real-world state of aVairs could be modelled,with equal legitimacy, in private-good terms We could deWne `visits towoodland areas' as a good, measured in (say) numbers of visits per year.Visits to woodland are private goods, even if there is open access: each visit ismade by a particular person In this framework, an increase in the area ofwoodland would appear as an improvement in the quality of the good

`visits', and thus as an outward shift of the demand curve for that good.Whether a given source of beneWts should be analysed as a public good or

as a private good is a question of modelling strategy If we wish to elicitindividuals' valuations of some beneWt, we can often choose between alter-native ways of setting up the problem; some ways of setting it up call forvaluations of private goods, others for valuations of public goods In thecase of the woodland, for example, we might try to elicit valuations of theprivate good `visits', perhaps by asking people about their willingness to paydiVerent hypothetical entry charges, or (if they travel to the woodland bycar) diVerent charges for parking

The strategy of valuing visits has some obvious limitations: it fails to pick

up some of the ways in which individuals derive beneWts from woodland.Expanses of woodland make a suburban area look more attractive, and thiscan be a source of beneWt even to residents who never set foot in a wood Butthese beneWts, too, can be valued through private goods If what peoplevalue is the amenity beneWts of having trees near their homes, then it isequally true to say that they value homes that are near trees Here we cantry to Wnd out how much extra people are willing to pay to buy or renthouses in well-wooded areas This could be investigated either by using ahedonic pricing method (i.e identifying diVerences in market prices forhouses in diVerent areas) or by using a CV survey to elicit individuals'housing preferences

However, the more diVuse the nature of the beneWt, the more diYcult itbecomes to Wnd an appropriate private good An extreme case is the exist-

some-thing ± a wildlife habitat, a landscape, an historic monument ± exists One ofthe apparent strengths of the CV method is that it can be used to elicitpreferences both for private and for public goods This chapter will beconcerned with applications of the CV method to public goods

5.2 THE THEORY OF PUBLIC GOODSFor the purposes of exposition, it is convenient to start with a very simplemodel in which there are just two goods, one private and one public Thepublic good is supplied under conditions of constant costs; the cost ofsupplying each unit is p There are n individuals, labelled by iˆ 1; ; n,each of whom consumes the quantity yiof the private good The quantity ofthe public good is x; this quantity is consumed by, or is made available to,every individual Thus individuals' preferences can be represented by theutility functions:

Preferences over combinations of public and private consumption areassumed to have the conventional neo-classical properties; thus, each per-son's preferences can be represented by a family of smooth, strictly convex,downward-sloping indiVerence curves in (x; yi) space I shall also make thevery weak assumption that the private good is a normal good

For any individual i, we may deWne the marginal valuation of the publicgood as v…x; yi†, where

v…x; yi† ˆ ‰@ui= @xŠ = ‰@ui= @yiŠ i ˆ 1; ; n: …5:2†Thus, starting from any given bundle (x; yi), the value of v…x; yi† representsthe individual's valuation of a marginal increase in the quantity of the publicgood, expressed in units of the private good If the private good is treated asthe numeÂraire (i.e if quantities of the private good are measured in moneyunits), v…x; yi† can be interpreted as the individual's willingness to pay(WTP) for a marginal increase in the quantity of the public good Sincethe private good is normal, v…x; yi† is decreasing in x Since more of eachgood is preferred to less, v…x; yi† is strictly positive for all values of x and yi

It is easy to see that Pareto eYciency will be achieved if and only if

Xi

That is, the sum of all individuals' marginal valuations of the public goodmust be equal to the marginal cost of that good If the sum of marginal

valuations was greater than marginal cost, it would be possible to makeeveryone better oV by increasing the quantity of the public good and divid-ing the extra cost between individuals in proportion to their marginalvaluations Conversely, if the sum of marginal valuations was less thanmarginal cost, it would be possible to make everyone better oV by reducingthe quantity of the public good and distributing the cost saving betweenindividuals in proportion to marginal values.

Unfortunately, market economies contain no mechanisms which can berelied on to ensure that (5.3) is satisWed Under conditions of constant costs,competitive Wrms will supply a good at a price equal to its marginal cost;thus, p may be interpreted as the competitive market price of units of thepublic good In a market economy, the public good will be supplied only tothe extent that it is bought by individuals Thus, we need to ask how much of

it would be bought at the price p

One apparently natural assumption is that each person maximizes utility,taking as given both the price of the public good and the quantities bought

by all other individuals I shall call this assumption parametric instrumentalrationality `Instrumental' signiWes that the individual treats her choicesamong goods as means, her ends being given by her preferences over Wnaloutcomes `Parametric' signiWes that she treats other people's decisions asgiven, rather than seeing herself as engaged in strategic interaction withthose other people Consider the implications of this assumption

For each person i, let zibe the value of i's endowments, and let wibe thetotal quantity of the public good bought by people other than i (i.e.,

wiˆPj 6ˆi‰zjÿ yjŠ=p) Then i faces two budget constraints:

and

The market is in equilibrium (analogous with a market-clearing equilibrium

in a private-good economy) if x and y1; ; ynare such that, for each person

i, the combination…x; yi† maximizes i's utility subject to the constraints (5.4)and (5.5)

In such an equilibrium, the following must be true for each person i:

be achieved consistently with (5.6a) or (5.6b) being true for all persons i.Since v…x; yi† ˆ p for any person i who chooses to buy any of the publicgood, and since v…x; yi† > 0 for all i, the sum of v…x; yi† across all i must begreater than p; and this is incompatible with the Pareto-eYciency condition(5.3) If in equilibrium the public good is supplied at all, the sum of indivi-duals' marginal valuations of the public good will be greater than the good'smarginal cost.

Thus, the implication of this model is that if the supply of public goods isleft to the market, there will be undersupply Intuitively, the source of theproblem is easy to see: each individual buys the good (if at all) with a view tothe beneWts to herself; but each unit that any individual buys suppliesbeneWts to all individuals

5.3 INCENTIVE COMPATIBILITY: THE THEORETICAL PROBLEMWelfare economists have generally argued that public policy should aim atachieving Pareto eYciency in the supply of public goods The problem, then,

is to Wnd a procedure for discovering enough about individuals' preferences

to allow us to identify Pareto-eYcient levels of provision for public goods.Samuelson was pessimistic about the prospects; in a section of his classicpaper with the title `Impossibility of Decentralized Solution', he argued that

no decentralized pricing system could identify Pareto-eYcient solutionsbecause `it is in the selWsh interest of each person to give false signals, topretend to have less interest in a given collective consumption activity than

he really has' (1954: 338±9)

Subsequent theoretical work has shown that this problem is slightlyless intractable than Samuelson thought Clarke (1971), Groves (1973),and Groves and Ledyard (1977) have proposed a demand-revealing mechan-

preferences as reported by him The essential idea is that each person isinvited to `vote' by reporting his WTP for a public good; the supply ofthat good is then set at a Pareto-eYcient level, relative to the reportedpreferences of all voters; Wnally, each voter is required to pay a tax equal

to the marginal net cost that he has imposed on other individuals by votingrather than abstaining Under reasonable assumptions about preferences,this mechanism can be shown to be incentive-compatible ± that is, no indi-vidual can beneWt by misrepresenting his preferences if no one else ismisrepresenting theirs Unfortunately, however, the demand-revealingmechanism is very vulnerable to strategic behaviour by small coalitions ofvoters, and for this reason probably cannot be regarded as a practicalproposal

In any case, it is clear that Samuelson's claim about the `impossibility ofdecentralized solutions' applies to CV: if the CV method is used to elicit

individuals' preferences for a public good, and if the Wndings are then used todetermine the supply of that good, then each individual typically has a selWshinterest in giving a false signal To see why, consider a simple case in which acollective decision has to be made between two options ± either not to supply

a particular public good (option A) or to supply it (option B) If the good issupplied, it will be paid for from taxes; each individual's share of the increase

in tax will be independent of how he or she responds to the CV survey.Assume that each individual has preferences of the kind described in Section5.2 After taking account of taxes, each individual must either prefer A to B,

or prefer B to A, or be indiVerent between the two Now consider whatresponse it would be rational for a self-interested individual to make to a CVsurvey Subject to her response being credible, the larger the WTP a personreports, the more likely it is that B will be chosen Thus if she prefers B to A,her best strategy is to report the highest WTP that would be credible.Conversely, if she prefers A to B, her best strategy is to report the lowestWTP that would be credible

Some commentators have suggested that CV respondents believe that theresponses they make as individuals may determine the tax payments theymake as individuals, and that this discourages the overstating of WTP(Hoehn and Randall, 1987; Mitchell and Carson, 1989: 153±70) It is possi-ble that some respondents do believe this; but since the belief is false, itwould be unwise for CV researchers to count on it and unethical for them totry to induce respondents to hold it I know of no CV survey in whichindividual responses have been used to determine individual tax payments.Furthermore, it is standard practice in surveys to assure respondents that theinformation they give will be treated anonymously Any respondent whounderstands and believes this assurance must realize that she cannot betaxed according to her reported willingness to pay

It is sometimes implied that the CV method can be made compatible by using a referendum format, in which each respondent ispresented with just two options and asked to report which she prefers Forexample, the `Blue Ribbon' Panel on Contingent Valuation argues that thereferendum format is preferable to the use of open-ended WTP questions,because the latter encourage the overstatement of true valuations as `acostless way to make a point' (Arrow et al., 1993: 29; see also Mitchell andCarson, 1989: 148±9) The truth, however, is that any CV study which elicitspreferences for a public good oVers respondents a costless way to make apoint

incentive-It is important to distinguish between a real referendum and a CV surveywhich uses a referendum format It is easy to see that if there are only twooptions A and B, and if a collective decision is to be made between them bymajority voting, then no voter has any incentive to misrepresent her prefer-ences But such a referendum will not elicit the distribution of WTP in thepopulation, which is the whole point of the CV method A CV study which

uses a referendum format presents diVerent respondents with diVerent pairs

of options, and uses the resulting data to estimate the distribution of WTP inthe population Thus, a respondent who understands what is going on hasexactly the same incentive to misrepresent her preferences as if she hadanswered an open-ended question For example, if she really prefers B (thepublic good's being supplied at its true cost) to A (its not being supplied), sheshould `vote' for the public good in a CV survey, whatever hypothetical costshe is asked to consider

I can see no escape from the conclusion that, if survey respondents aremotivated solely by rational self-interest, the CV method is fatally Xawed.Like other forms of social-survey research, CV studies cannot work unlessthe vast majority of respondents can be relied on to give honest answers towell-formulated questions But whether surveys elicit honest responses orstrategic ones is ultimately an empirical question; it cannot be settled by apriorideduction from the axioms of rational choice theory

5.4 INCENTIVE COMPATIBILITY: IS IT A PROBLEM FOR SURVEY RESEARCH?The possibility that responses may be self-interested rather than honest isnot a problem that is peculiar to CV studies Almost all social surveys oVersome incentives for strategic behaviour Consider, for example, a survey ofvoting intentions before an election A respondent who was motivated solely

by rational self-interest might choose his answer by thinking about theeVects of the publication of the survey on other voters; thus, a supporter

of party X might pretend to be intending to vote for party Y so as to inducecomplacency among the supporters of Y Or consider a survey of the extent

of unreported crime If someone would like to see more public spending onthe police, it might be in her interest to pretend to have been the victim ofnon-existent crimes In these examples, of course, the self-interested beneWts

to be gained by answering dishonestly are tiny But the same is true of CVsurveys, provided the sample size is suYciently large

In many social surveys, self-interest provides no obvious incentive torespondents to answer in one way rather than another For example, this

is typically the case in the censuses and panel surveys on which tricians rely for their data If respondents are motivated solely by rationalself-interest, we have no reason to expect honest answers to such questions.Conversely, if there are forces at work which can generate systematic hon-esty in the absence of positive incentives to be honest, the same forces might

econome-be expected to have some inXuence even when there are weak incentives to econome-bedishonest For example, it might be hypothesized that, other things beingequal, honesty involves less cognitive strain than dishonesty, or that thesocial setting of interviewer and interviewee evokes norms of honesty.These hypotheses might explain honesty in the absence of incentives; but

they would also imply a tendency for respondents to give honest answersrather than strategic ones when the incentives for strategic behaviour aresuYciently weak.

Thus, when assessing the validity of the assumption that CV surveys elicithonest responses, it is legitimate to draw on evidence from social-surveyresearch in general Social psychologists have done a great deal of researchinto the relationships between attitudes (as reported in surveys) and actualbehaviour The balance of evidence, drawn from many studies, is thatbehaviour and attitudes are positively correlated (Schuman and Johnson,1976; Hill, 1981) Of course, the mere demonstration of such a correlation is

a relatively weak result, but attitudes are more remote from behaviour thanthe intentions into which CV surveys enquire For example, compare theattitude `I agree strongly that the Government should spend more money onnational parks' with the intention `If there were a referendum on the issue, Iwould vote for more spending on national parks.'

Experimental psychology and experimental economics oVer anothersource of evidence Many investigations of decision-making behaviourwere Wrst carried out by asking subjects to make hypothetical choices, andhave subsequently been replicated in settings with Wnancial incentives Inmost cases, the same patterns of behaviourÐoften patterns that are incon-sistent with received economic theoryÐare found in both types of experi-ment For example, this is the case for the preference-reversal experimentsdiscussed in Chapter 6 (Grether and Plott, 1979; Slovic and Lichtenstein,1983) Notice, however, that such similarities in patterns of behaviour acrossexperiments does not imply that incentives do not aVect behaviour at all Forexample, psychological eVects such as response compatibility and anchoringmight come into play irrespective of incentives, and these might generatepreference reversals (see Chapter 6), but subjects might still be more risk-averse in the presence of incentives

Further evidence comes from experiments which compare responses tohypothetical questions about willingness to trade with real trading behav-iour Bishop, Heberlein, and their associates have carried out a series ofinvestigations of individuals' valuations of hunting permits in cases in whichthese are strictly rationed (Bishop and Heberlein, 1979, 1986; Bishop et al.,1983; Heberlein and Bishop, 1986) A typical experiment is conducted withtwo random samples drawn from a population of applicants for huntingpermits Subjects in one sample are treated as in a normal CV survey: WTP

or willingness to accept (WTA) is elicited by using hypothetical questions.Subjects in the other sample are oVered genuine opportunities to buy or sellpermits The results are mixed, but the general picture seems to be thathypothetical responses overstate real WTP and WTA In one typical case,mean hypothetical WTA was $101 and mean real WTA was $63 (Bishop andHeberlein, 1979) In another, mean hypothetical WTP was $32 and meanreal WTP was $24 (Bishop and Heberlein, 1986)

Thus, it seems that there may be a systematic discrepancy betweenhypothetical responses and real behaviour If such a discrepancy exists, itundoubtedly poses a problem for CV research; but it need not be interpreted

as evidence that responses are casual or insincere People may be honestlyreporting their beliefs about how they would respond to trading opportun-ities, were these to arise; but those beliefs may be systematically biased (forexample, in a hypothetical context people may underestimate their aversion

to giving up money) I suggest that observed diVerences between tical responses and real behaviour are more plausibly explained by sucheVects than by assuming that survey respondents act strategically It seemsreasonable to proceed on the working assumption that respondents in CVsurveys make honest attempts to answer the questions they are confrontedwith

hypothe-5.5 THE LINK BETWEEN PREFERENCE AND CHOICE

Respondents in CV surveys are typically presented with hypothetical ios within which they are asked to make choices Even if we can assume thatresponses are honest, two diYculties must be overcome if we are to makeinferences about individuals' preferences from the data generated by CVsurveys (A further problem, that preferences with the properties postulated

scenar-by economic theory might not exist at all, will be considered in Chapter 6.)The Wrst diYculty is that the scenario has to represent a conceivablesituation in which the respondent chooses between alternative combinations

of money and the relevant good In the case of a private good, the scenariocan be based on the market For example, a respondent may be asked toimagine that hunting permits are on sale at a price of $30, and to say whether

or not he would buy one at that price Most people have a vast amount ofexperience of buying private goods, and at least some experience of sellingthem; thus, they will Wnd a market scenario quite familiar But the design ofscenarios for public goods is less straightforward The problem is to Wnd acontext in which people make decisions as individuals about the supply ofpublic goods There seem to be two obvious candidates: voluntary contribu-tions to public goods, and voting on issues concerned with the supply andWnance of such goods

The second diYculty is to Wnd a theory which connects preferences tochoices of the kind described by the scenario For private goods and marketsettings, economics oVers a simple theoryÐthat each individual maximizesutility, taking prices as given Using this theory, we can infer preferencesfrom choices made in markets, or from hypothetical choices made in marketscenarios If we are to elicit valuations of public goods, we need a corres-ponding theory of how individuals' decisions about voluntary contributions

to public goods, or about how to vote, connect with their preferences

5.6 VOLUNTARY CONTRIBUTIONS TO PUBLIC GOODS

Some signiWcant goods are Wnanced by the voluntary contributions of manyindividuals: think of the activities of humanitarian, educational, medical andenvironmental charities and pressure groups Donors to such organizationsmake decisions which involve giving up private consumption in order toincrease the supply of public goods Decision contexts of this kind mightseem to oVer suitable scenarios for eliciting preferences for public goods.However, it is surprisingly diYcult to explain such voluntary contributions

in terms of conventional economic theories of decision-making In thissection I shall examine these diYculties and the problems they create for

CV research

A number of economists have tried to explain voluntary contributions topublic goods by using variants of the model presented in Section 5.2 Eachindividual is assumed to have preferences over combinations of private andpublic goods; each individual chooses how much to contribute to publicgoods, maximizing her utility while taking prices and other individuals'contributions as given The equilibrium state of the model is taken to be arepresentation of the real world (e.g Schwartz, 1970; Becker, 1974; Arrow,1981)

More recent work, however, has shown that this type of theory yieldsimplications which are clearly inconsistent with the facts of voluntary giving.These implications are generated because, in the model, each individualregards other people's contributions to a public good as perfect substitutesfor her own Thus, each individual's contribution is highly sensitive tochanges in other people's contributions Under reasonable assumptionsabout preferences, we should expect to Wnd that each individual reducesher own contribution by almost one dollar for every extra dollar contributed

by others; but we do not Wnd anything like this degree of responsiveness inreality (Sugden, 1982; Warr, 1982; Roberts, 1984) If real people behavedlike the individuals of the model, virtually no one would contribute anything

to public goods in a large economy (Andreoni, 1988) And if individualsbecame aware of the extent to which their contributions were interdepend-ent, the prospects for the voluntary supply of public goods would be stillworse Since each would know that a reduction in her own contributionswould be almost wholly made up by increases in others' contributions,rational self-interest would lead each to try to take a free ride (Sugden,1985)

A further challenge to the conventional theory of public goods has comefrom experimental research In a classic series of experiments, Marwell andAmes (1979, 1980, 1981) investigated the extent to which individuals arewilling to contribute to public goods In a typical experiment, subjects wereassigned to groups, within which interaction was anonymous (groups didnot meet; all interactions were via the experimenters) Each subject was

endowed with tokens to be allocated between a private activity and acollective activity; the subject was given a money pay-oV which depended

on the amount that he had allocated to the private activity and on the totalamount that all group members had allocated to the public activity This set-

up corresponds very closely with the model described in Section 5.2, andthus provides a direct test of the conventional theory that individuals actaccording to parametric instrumental rationality The typical result was thatsubjects contributed less to the collective activity than would be necessaryfor Pareto eYciency, but much more than was implied by the conventionaltheory (an interesting exception occurred when the experiment was carriedout with economics graduate students: these subjects acted according to thedictates of rational self-interest)

Vernon Smith and his associates have carried out a diVerent kind ofinvestigation into the voluntary provision of public goods (e.g Smith,1980) Smith's concern is not to test any particular theory, but to try todesign a mechanism for decentralized decision-making about public goodswhich will be as eYcient as possible The mechanism which Smith hasdeveloped is a form of auction; as the auction proceeds, each individualreceives feedback about the bids made by others The basic set-up is similar

to that in Marwell and Ames's experiments, but instead of requiring eachindividual to make a unilateral decision about how much to contribute to thecollective activity, Smith runs an auction

In Smith's auction, each individual i makes a two-part bid: he statessome contribution bi which he is (provisionally) willing to make, and heproposes some amount ti to be the total of everyone's contributions Theauctioneer then calculates the mean of everyone's proposal for the total (i.e.,P

jtj=n, where n is the number of individuals) and reports this back toeveryone The auctioneer also calculates, for each person i, his proposedcontribution as a proportion of total proposed contributions (i.e., bi=P

jbj)and reports this back to that person New bids are invited, and the processcontinues until there is unanimous agreement (that is, everyone proposes thesame total ti, and this is equal to the sum of all biproposals) If no agreement

is reached after some predetermined number of rounds, the public good isnot supplied at all This mechanism turns out to be able to reach outcomeswhich are reasonably close to Pareto eYciency, at least for fairly smallgroups (up to nine individuals)

The puzzle is to explain why Smith's auction mechanism works so well Itseems to be in each individual's self-interest to act as if the public good is oflittle value to him, in the hope that it will be provided at other people'sexpense Of course, if everyone tries to take a free ride, the public good willnot be supplied at all, and everyone will be a loser But why should thisconsideration be relevant to rational individual decisions? We know from thePrisoner's Dilemma that individually rational actions can aggregate toPareto-ineYcient outcomes Smith's results, then, seem to provide further

evidence against theories that explain private contributions to public goods

in terms of rational self-interest

So how are we to explain private contributions to public goods? Twoalternative lines of approach seem particularly worth following Oneemphasizes the moral norms of fairness and reciprocity; the other empha-sizes the expressive or symbolic aspects of decisions

A number of economists have proposed theories of moral behaviourwhich can be characterized as broadly rule-utilitarian or Kantian in Xavour(e.g LaVont, 1975; Collard, 1978; Harsanyi, 1982) These theories modelpreferences in a conventional way, but do not make the usual assumptionthat individuals maximize utility: the connection between preference andchoice is more complex than this Roughly, the individual considers alter-native rules which could be followed by everyone, and which satisfy certaincriteria of anonymity or fairness The individual chooses the rule which, iffollowed by everyone, would lead to the outcome that she most prefers; thenshe follows that rule I have proposed a variant of the rule-utilitarianapproach, in which each individual accepts a moral obligation to act onher optimal rule only to the extent that other people follow that rule too; thisamounts to a norm of reciprocity which forbids free-riding but which doesnot require anyone to provide free rides for others (Sugden, 1984)

In these theories, private contributions to public goods are motivated bypeople's moral commitment to rules which they see as fair Thus, contribu-tions to public goods do not reveal the donors' preferences in the same directway that decisions to buy private goods do What is revealed is the combinedeVect of the donor's own preferences, her beliefs about fair rules for cost-sharing, and (in the version which emphasizes reciprocity) other people'scontributions

An alternative approach to explaining voluntary contributions to publicgoods is proposed by Andreoni (1990) Andreoni suggests that contributionsmay be motivated by the desire for the `warm glow' of believing that one hasdone a good deed (perhaps compounded by the belief that other peopleknow this too) He models this warm glow by making each person's utility afunction not only of the total quantity of each public good, but also of herown contribution to it Thus, private contributions to public goods becomeprivate goods in their own right

A theory of this kind has little content unless it can explain why some actsgenerate a warm glow while others do not If the answer is that the warmglow is associated with following moral norms of fairness or reciprocity,then we need to model those norms; and this takes us back to the Wrstapproach But there is an alternative way of developing the theory: actsmay generate a warm glow through their expressive content

Consumption goods are desired, not only for instrumental reasons, butalso as expressions of the consumer's sense of identity (Douglas and Isher-wood, 1979; Hargreaves Heap, 1989) The distinction between expressive

valueand instrumental value is imprecise, but nevertheless useful Consider asports car This has instrumental value as a means of transport But bybuying a sports car, a person can also expressÐor try to bolsterÐa self-image of being young, rich, and carefree: this is the expressive value of the car.Similarly, a bicycle has instrumental value as a means of transport and as away of getting exercise; it has expressive value by expressing or bolstering aself-image of being Wt and environmentally responsible In the context ofprivate goods, economic theory has no need to distinguish between expressiveand instrumental value; both are subsumed under the concept of preference(that is why, for an economist, the distinction seems to lack precision) But inthe context of public goods, this distinction is much more signiWcant.Contributions to public goods can have expressive value By sending adonation to Greenpeace, for example, a person can express a self-image ofbeing public-spirited, environmentally conscious, and mildly radical Theinstrumental value of the donation (that it allows Greenpeace to do margin-ally more campaigning) is non-rival, but its expressive value is private to thecontributor Thus, expressive value can be used to explain private contribu-tions to public goods (Kahneman and Knetsch, 1992) One implication ofthis explanation is that decisions about private contributions to public goodsmay reveal much more about the expressive value of contributions than they

do about the instrumental value of those goods

Whether voluntary contributions are motivated by norms of fairness or byexpressive value, we should not expect responses to questions about suchcontributions to reveal preferences in any straightforward way A telephonesurvey reported by Kahneman and Knetsch (1992) provides an illustration

In this survey, respondents were asked to think about the environmentalservices provided by federal and provincial governments in Canada Thenthey were asked questions such as the following: `If you could be sure thatextra money collected would lead to signiWcant improvements, what is themost you would be willing to pay each year through higher taxes, prices, oruser fees to go into a special fund to improve environmental services?' Noticethat there is no reference to any speciWc improvement in environmentalservices which respondents might try to evaluate Nor is the respondenttold how many other individuals will pay the `higher taxes, prices, or userfees' which he is being invited to consider He is being asked to decide howmuch to contribute to a special fund; the general purpose of the fund isknown, but how much it will be able to do will depend on its total income,which is not known; there is a suggestion that others will match his con-tributions in some way, but no details are given For most respondents, Iguess, such a scenario will evoke thoughts about voluntary contributions tocharitable funds Kahneman and Knetsch seem to think so too, suggestingthat responses to their questions `express a willingness to acquire a sense ofmoral satisfaction by a voluntary contribution to the provision of apublic good' (1992: 64)

In Kahneman and Knetsch's survey, diVerent respondents were askedabout diVerent classes of environmental services, some classes being subsets

of others For example, some respondents faced the question presented inthe previous paragraph, involving a special fund `to improve environmentalservices'; they were told that `environmental services' included `preservingwilderness areas, protecting wildlife, providing parks, preparing for disas-ters, controlling air pollution, insuring water quality, and routine treatmentand disposal of industrial wastes' Other respondents were asked a similarquestion, but in relation to `a special fund to improve preparedness fordisasters' In the Wrst case, the mean WTP was $136 and the median was

$50; in the second case, the mean was $152 and the median was again $50.Kahneman and Knetsch interpret this and other similar results as evidence

of an embedding eVect: reported WTP for a whole (environmental services) is

no greater than reported WTP for a small part of that whole (preparing fordisasters)

Such embedding eVects are not surprising if respondents are thinking interms of voluntary contributions In the case of voluntary contributions, thedistinction between superset and subset is far from clear Suppose, forexample, that I give £5 to the Woodland TrustÐa charity which maintainswoodlands throughout Britain Should I think of the eVect of this donation

as an inWnitesimal increase in the quality of thousands of acres of woodland,

or should I think of it as one new tree planted somewhere? Either tion seems legitimate, and there seems no obvious reason why I should givemore if I think in terms of the thousands of acres than if I think in terms ofthe single tree Most fund-raisers, incidentally, seem to expect the opposite,encouraging potential donors to think in terms of something speciWc thatcan be paid for from a small donation

interpreta-This irrelevance of scale can readily be understood if voluntary tions are motivated by expressive value As Kahneman and Knetsch (1992:64±5) argue, the expressive value of a contribution to an inclusive cause, andthe expressive value of a contribution to a representative subset of thatcause, are likely to be similar to one another Alternatively, the irrelevance

of scale can be understood as part of a theory in which voluntary tions are motivated by norms of fairness and reciprocity If there is a moralnorm that each person should contribute a certain amount to some inclusivepublic good, then it would seem that an individual can discharge thatobligation by contributing the required amount of money to any represent-ative component of that good For example, if everyone has an obligation tocontribute a certain amount towards tree-planting, and if this amount isequal to the cost of planting one tree, then a person who pays to plant aspeciWc tree has `done his bit'

contribu-So where does this leave us? Given the limitations of current knowledgeabout why individuals contribute to public goods, and the lack of consensus

on a theory linking contributions to preferences, scenarios involving

ary contributions to public goods seem unlikely to be useful as a means ofeliciting preferences Similarly, scenarios (like that of Kahneman andKnetsch's telephone survey) which prompt respondents to think in terms

of voluntary contributions should be avoided

5.7 VOTING

An alternative approach to eliciting preferences for public goods is to usescenarios based on decisions about how to vote The referendum format isoften recommended for CV surveys which involve public goods (Mitchelland Carson, 1989: 94±7, 148±9; Arrow et al., 1993: 18±25) In a survey withthis format, each respondent considers just two options, although diVerentrespondents may consider diVerent pairs of options The options in any pairdiVer in two respects: the level of provision of the relevant public good andthe level of taxation The respondent is asked to say which option he prefers.Notice that the options are descriptions of states of aVairs that, were they tocome about, would aVect everyone in the community, and not just theindividual respondent Ordinary people do not have experience of takingdecisions of this kind as individuals; but typically they have experience ofparticipating in collective decision-making about public aVairs Thus thequestion `Which option do you prefer?' can be construed as: `If a collectivechoice had to be made between these two options, which would you vote for?'

I have argued that we are entitled to assume, as a working rule, thatrespondents give honest answers to the questions they face (see Section5.4) So if we ask respondents to say how they think they would vote in areferendum between A and B, we should interpret their answers as honeststatements of their intentions or inclinations When a collective decision has

to be made between two options, there is nothing to be gained by strategicvoting (see Section 5.3) Thus, it might seem obvious that the referendumformat will elicit individuals' true preferences: a person who prefers A to Bwould vote for A rather than B in a real referendum, and so, if asked toimagine such a referendum, would say that he would vote for A rather than B.But to reach this conclusion, we need to make a particular assumptionabout how voting behaviour connects with preferences: we need to assumethat voters are instrumentally rational That is, we have to assume that thevoter thinks of the act of voting as a means of trying to bring about theoutcome that he prefers Unfortunately, as Brennan and Buchanan (1984)and Brennan and Lomasky (1985) have argued, this assumption is question-able

Many public-choice theorists have noticed that instrumentally rationalindividuals would not vote in elections with large electorates (see, e.g.,Mueller, 1989: 348±69) This is just another instance of the public goodsproblem For example, consider a presidential election with two candidates,

Xand Y, and an electorate of, say, 20 million If approximately 10 millionelectors prefer X to Y, then every vote cast for X is a public good for a group

of 10 million individuals For any individual who prefers X, the cost ofvoting (perhaps giving up half an hour in front of the television) is borne

by that individual privately, but the beneWt (a tiny increase in the probabilitythat X will be elected) is spread among 10 million people Although the value

to the individual of X's being elected rather than Y may be quite large, thishas to be discounted by the inWnitesimally small probability that an electioninvolving 20 million voters will be decided by the margin of a single vote.Thus, if the act of voting involves any signiWcant costs, an instrumentallyrational individual who expected many other people to vote would choosenot to vote himself Since we repeatedly observe elections in which largenumbers of people vote, the hypothesis that voters are instrumentallyrational must be rejected

It is natural to try to explain the act of voting in much the same way thatvoluntary contributions to public goods are explained: either in terms ofnorms or in terms of expressive value Public-choice theorists often invokenotions of civic duty for this purpose Civic duty might be construed as aprinciple of fairness, prescribing that everyone bears her share of the costs ofmaintaining an institutionÐdemocracyÐthat everyone values Or it might

be construed in more expressive terms: by voting, a person expresses a image of being concerned with public aVairs and proud to be a citizen of ademocratic country But if these are the sorts of motivations that get people

self-as far self-as the polling station, why should we self-assume (self-as public-choice ists usually do) that the same people become instrumentally rational whenchoosing how to cast their votes?

theor-First, consider the possibility that, as Brennan, Buchanan, and Lomaskysuggest, voting for one option rather than another has expressive content.For example, imagine two options A and B, where A is the status quo and B

is a policy of cleaning up a marine oil spill at the cost of an increase intaxation In a referendum between A and B, the act of voting for B may be away of expressing a self-image of being concerned about the environment.The same act has instrumental value in making it marginally more likelythat the oil spill will be cleaned up, and instrumental disvalue in making

it marginally more likely that taxes will be increased But because theexpressive value is private to the individual voter, while the instrumentalvalues and disvalues are public goods, we should expect voting behaviour toreveal more about expressive value than it does about instrumental value.Discussing the implications of this argument for CV surveys, Mitchell andCarson express unconcern In response to Brennan and Buchanan (1984),they say:

We regard their arguments as another way of saying that people may behave in amore public-spirited manner in political markets than they do in private goods

markets Brennan and Buchanan are disturbed by the implications of this type ofbehaviour for the use of voting outcomes to reveal economic preferences; we are not(1989: 149).

But Mitchell and Carson ought to be disturbed The whole CV methoddepends on the assumption that individuals have well-deWned preferenceswhich are independent of the context in which those individuals act It is thisassumption that allows us to use preferences elicited in one context (thehypothetical scenario of the CV survey) to guide decisions in another context(public policy-making) If Brennan, Buchanan, and Lomasky are right, then

CV surveys will elicit diVerent valuations of the same beneWt, depending onwhether they use a private-good format (e.g eliciting valuations for entrypermits) or a public-good referendum format

A further possibility, not considered explicitly by Brennan, Buchanan,and Lomasky, is that voters may be inXuenced by norms of fairness andreciprocity When people make voluntary contributions to public goods,they may be motivated by moral rules which prescribe, for each individual,

a fair share of the total cost of providing a public good (see Section 5.6).Thus, when comparing two alternative options A and B, where A is the

increased taxation, an individual might ask two distinct questions: `Do Iprefer B to A?' and `Is B a fair proposal?' The Wrst of these questions is theone that is relevant for a CV survey But it may not be the only one that isrelevant for a person who is deciding how to vote

To answer the Wrst question, the individual has to consider the beneWtsthat she would derive from the increased provision of the public good, andthen to compare these beneWts with the extra taxes that she would have topay; how much other people would have to pay is irrelevant To answer thesecond question, she has to make other comparisons too; in particular, sheneeds to compare the extra taxes that she would have to pay with the extrataxes that other people would have to pay It is quite possible that she wouldprefer B to A, and yet also believe that B imposed on her an unfairly largeshare of the costs If so, how would she vote in a referendum to decidebetween A and B?

An instrumentally rational voter would, of course, vote according to herpreference (provided she believed that A and B really were the only twooptions available) But we know that the instrumental beneWts of voting oneway rather than another are extremely small The kind of person who wassuYciently lacking in instrumental rationality to take the trouble to cast avote in the Wrst place might well use that vote as a means of expressing hersense of fairness

There is a body of experimental evidence which suggests that people areprepared to incur some costs rather than acquiesce in arrangements which,

in their view, treat them unfairly This evidence comes from studies of

ultimatum gamesÐa type of game Wrst analysed by GuÈth et al (1982) In theclassic ultimatum game, two players have to agree on how to divide a Wxedsum of money between them One player is assigned the role of `allocator',the other that of `recipient' The allocator proposes a division of the moneybetween the two players The recipient can either accept this proposal orreject it Either way, the game ends immediately If the recipient rejects theproposal, neither player gets anything An instrumentally rational recipientwould accept any proposal which gave her a positive amount of money.However, in experiments involving ultimatum games, allocations which givethe recipient a very small share are often rejected (GuÈth et al., 1982; Thaler,1988).

A related item of evidence comes from CV studies which have tried to elicitindividuals' willingness to accept money in return for giving up public goods

CV researchers often suggest that respondents Wnd questions about theirWTA for public goods morally objectionable For example, consider:

`Would you accept $100 as compensation for the destruction of wildlife bythis oil spill?' Such questions seem to presuppose that each respondent has aproperty right in the public good, which he is entitled to exchange for privateconsumption if he chooses; respondents may refuse to answer such questions,

or give extreme responses, as a way of signalling their rejection of thisconception of property rights (e.g Mitchell and Carson, 1989: 34) In suchcases, respondents are revealing their judgements about fairness, not theirpreferences (In contrast to the previous examples, however, the concern here

is with fairness tout court, rather than with fairness to the respondent herself.)Thus, it is not always clear how answers to questions about hypotheticalreferenda can be mapped on to the conventional model of preferences.Suppose a person is asked a question of the form `Would you vote for aproposal which supplied this public good and imposed $x extra taxes onyou?' An answer of `yes' might indicate the expressive value of the act ofvoting for that proposal; but the respondent who gives this answer might (inthe instrumental sense) prefer the status quo to the package of public goodplus $x tax bill Conversely, a respondent who answers `no' may be expres-sing the judgement that, given the likely cost of providing the good, it would

be unfair to call on him to pay as much as $xÐeven though he may preferthe package of public good plus tax bill to the status quo The referendumformat does not provide an easy solution to the problem of eliciting prefer-ences for public goods

5.8 CONCLUSIONThe main message of this chapter can be summed up in a sentence: Prefer-ences for public goods are much more diYcult to elicit than are preferencesfor private goods

Suppose we can assume that individuals have well-deWned preferencesover private goods, and that these preferences have the properties postulated

by economic theory (whether we can assume this is a big question, to beconsidered in Chapter 6) Then there is a straightforward and fairly uncon-troversial theory of the connection between preference and action in compe-titive markets: each individual maximizes her own utility, taking prices asgiven Using this theory, we can infer preferences from choices made inmarket settings Similarly, CV researchers can set up market scenarios inwhich respondents make hypothetical decisions, and then infer preferencesfrom those decisions

If, however, we are prepared to make the corresponding assumption thatindividuals have well-deWned preferences over public goods, and that thesepreferences have the properties postulated by economic theory, we Wnd that

we still need a theory of how preferences connect with actions A satisfactorymethod for eliciting preferences must be able, for some readily understand-able scenario, to isolate the eVects of preferences on choices But it seemsthat in order to explain individual behaviour in relation to public goodsÐwhether private contributions to public goods, or voting behaviourÐwehave to take account of factors other than preference In particular, wehave to take account of the expressive value of actions, and of the moralnorms to which individuals subscribe Thus, we need a theory of decision-making which can explain how these factors work together, and which canallow a CV researcher to disentangle them As yet, no theory of choice seemssuYciently well-developed to do this reliably Until these fundamental the-oretical problems have been solved, attempts to elicit preferences for publicgoods must be treated with caution

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An Introduction to Kantian Economics', Economica, 42: 430±7

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11 The Statistical Analysis of

Discrete-Response CV Data Statistical Analysis of Discrete-Response CV Data

MICHAEL HANEMANN BARBARA KANNINEN MICHAEL HANEMANN, BARBARA KANNINEN

11.1 INTRODUCTION AND OVERVIEW

In recent years, increasing attention has been given to the statistical aspects

of contingent valuation (CV) survey design and data analysis The mainreason for the growing interest in statistical issues is the shift in CV practicefrom using an open-ended question to ask about willingness to pay (WTP) tousing a closed-ended question The open-ended format confronts respond-ents with a question on the lines of `What is the most you would be willing topay for ?' The closed-ended format uses a question like `If it cost $x toobtain , would you be willing to pay that amount?' The closed-endedformat was introduced into CV by Bishop and Heberlein (1979) Since themid-1980s it has gained widespread acceptance as the preferred way to castthe valuation question, a position that was recently endorsed by NOAA'sBlue Ribbon Panel on CV (Arrow et al., 1993) For reasons mentioned inSection 11.4, we share this preference against the open-ended approach and

in favour of the closed-ended approach However, the closed-endedapproach creates a heavy demand for statistical technique Statistical issuesare not pressing with the open-ended format because the data essentiallyspeak for themselvesÐthe survey responses yield a direct measure of WTPwhich requires little or no further analysis With the closed-ended format, bycontrast, the CV responses are not dollar amounts but answers of `yes' or

`no', and one obtains a WTP value from these responses by introducing astatistical model that links them to the dollar amounts that people faced inthe survey

Since the CV responses are binary variables, one needs a statistical modelappropriate for a discrete dependent variable Such models have come toplay an important role in many areas of microeconomics since the 1970s A

We gratefully acknowledge helpful comments and suggestions from Anna Alberini, Ian man, Richard Carson, Anni Huhtala, and Kerry Smith, as well as excellent research assistance

Bate-by Craig Mohn We are deeply indebted to Ian Bateman for his editorial kindness and forbearance.

major reason for this was the growth in availability of disaggregated surveydata on speciWc choices by individual agentsÐwhen economic behaviour isobserved at that level, the outcomes often turn out to be discrete variables,

or mixed discrete/continuous variables, rather than purely continuous ables Some of the most important statistical models for discrete dependentvariables used in Weld like labour economics were Wrst developed in the Weld

vari-of biometricsÐlogit and probit are obvious examplesÐbut they found readyapplication to microeconomic data Discrete-response CV is no exceptionÐlogit and probit play a key role in the analysis of CV data Moreover, there is

a direct analogy between the response-generating mechanism in some metrics applications and that in a CV survey A common setting in bio-metrics is the dose±response study, where the stimulus is an administereddose of some substance and the outcome is a discrete measure of healthstatus (e.g alive or dead) The aim is to measure the probability distribution

bio-of susceptibility to the substance in question In a CV survey, the monetaryamount presented to subjects (the `bid') can be thought of as the dose, andthe yes/no reply as the response; the equivalent of susceptibility is the WTPamount

Another fruitful analogy is with reliability analysis and life testing inindustrial engineering, where equipment is stressed until it fails Sometimesone does not know when it failed, only that it failed after more than 7,000hours, say, or less than 10,000 hours The aim is to estimate a probabilitydistribution for the true life of the itemÐanalogous to the true WTP in a CVsettingÐusing information on upper or lower bounds Statistically, the datalook just like responses from a discrete-response CV survey In CV the bidsare subject to the control of the researcher, just as the dose or stress aresubject to control by the researcher in dose±response and life-testing experi-ments Thus, one can apply to the selection of CV bids statistical techniquesfor optimal experimental design that have been developed in biometrics andreliability analysis These analogies with other branches of applied statisticshave substantially transformed the statistical side of CV research in recentyears

In this chapter we survey the statistical issues associated with response CV Our aim is to make the reader aware of the recent develop-ments in the design and analysis of CV surveys A major theme is the closeinterplay between economics and statistics The CV responses are analysedusing statistical models But the models must make sense from the point ofview of economic theory This places signiWcant restrictions on the statisticalmodels that can be used These implications were Wrst developed by Hane-mann (1984a), but his analysis was incomplete and incorrect in some parti-culars Here we extend his analysis and correct the errors We show thatmany of the models in the current literature violate some of the restrictions

discrete-of economic theory Another major theme is the value discrete-of richness in thestatistical models in order to accommodate heterogeneity of preferences in

the population of interest and, also, heterogeneity of response behaviour in asurvey setting Richness typically requires introducing additional parametersinto the model; the question is how this should be done Again, there areinteresting interactions between the statistics and the economics Structuralmodels provide the most information from an economic point of view, butthey can be fragile if the structure is misspeciWed Non-parametric modelsare more robust and oVer greater Xexibility in the shape of the responsefunction, but they provide less economic information Moreover, whicheconomic welfare measure one wants to use can aVect the choice of statisticalmethodology; for example, non-parametric models generally have moretrouble providing an estimate of mean than median WTP.

This chapter consists of three main sections Section 11.2 presents theeconomic theory of responses to CV survey questions, set within the frame-work of a random utility maximization model, and shows how this generatesstatistical models for the survey responses Section 11.3 reviews the statisticalissues that arise in the estimation of economic welfare measures from data

on CV responses using the maximum likelihood method; it also describesprocedures for selecting the bids to be used in CV surveys and for interpret-ing the results after the data have been collected, based on the principles ofoptimal experimental design Section 11.4 considers some advanced topics inthe statistical design and analysis of discrete-response CV data that are both

of practical interest and on the current frontiers of research Section 11.5oVers some brief conclusions

11.2 ECONOMIC THEORY AND STATISTICAL MODELS

11.2.1 Types of discrete response format

We start by reviewing the diVerent types of closed-ended question that could

be used in a CV survey In what follows, we denote the object of thevaluation by q.1The CV study could involve just two levels of q or multiplelevels of q, depending on whether the goal is to value a single programme,

to value multiple programmes, or indeed to estimate an entire valuationfunction

When valuing a single programme, one asks people about their WTP toobtain a change from q0 (the status quo) to some particular alternative q1.With closed-ended questions, there are single-bounded and multiple-boundedways to do this The single-bounded approach is the original format ofBishop and Heberlein (1979), where respondents are presented with a spe-ciWc dollar cost to obtain the change and asked whether they would bewilling to pay this amount With a public programme, the question can beframed in terms of whether they would vote for or against the programme if

1 Depending on the circumstances, q could be a scalar or a vector.

304 M I C H A E L H A N E M A N N , B A R B A R A K A N N I N E N

it involved a specific increase in their taxes.2Their response provides tative information in the form of a bound on their WTP for the changeÐalower bound if they answer `yes', and an upper bound if they answer `no'.The double-bounded format, proposed by Hanemann (1985) and Carson(1985) and Wrst applied by Carson and Steinberg (1990) and Hanemann et al.(1991), follows up on the initial question with a second question, againinvolving a speciWc dollar cost to which they can respond with a `yes' or a

quali-`no' The amount presented in this second bid depends on the response to theWrst bid: if the respondents answered `no' to the Wrst bid, the second bid issome lower amount, while if they answered `yes' it is some higher amount.Consequently, if they answer `yes' to one of the questions and `no' to theother, this provides both upper and lower bounds on their WTP for thechange Similarly, the triple-bounded format has an additional follow-upquestion with a bid amount that depends on the responses to the Wrst twoquestions (Chapter 15 below; Cooper and Hanemann, 1995) The additionalbids can lead to sharper bounds on the estimate of WTP

Other formulations of the survey question also generate bounds on WTP.For example, subjects can be shown a payment card listing various dollaramounts and asked to circle the one that comes closest to their own value(Mitchell and Carson, 1981) The response can be interpreted not as an exactstatement of WTP but, rather, as an indication that the WTP lies somewherebetween the highest number below the amount circled and the smallestnumber above it (Cameron and James, 1987) Equivalently, they can beshown a list of dollar amounts and asked to mark oV the amounts they aresure they would be willing to pay and those they are sure they would not(Welsh and Bishop, 1993) Similarly, they can be presented with alternativedollar ranges and asked to identify the one that comes closest to their ownvalue These approaches all yield upper and lower bounds on WTP for thechange in q

When dealing with multiple programmes, one can proceed similarly, paring each programme q1, q2, q3, in turn with the baseline status quo, q0,using either a single- or multiple-bounded format This is like valuing a singleprogramme, but repeated many times over Alternatively, one can askrespondents to assess several programmes simultaneously With contingentranking, introduced by Beggs et al (1981) and Chapman and Staelin (1982),respondents are presented with a set of programmes each involving a speciWcaction and a speciWc cost, and asked to rank them.3For example, they might

com-be oVered programs to save 5,000 acres of wetlands at a cost of $30

2 Because of this, the close-ended format is sometimes called referendum CV Strand (1981) appears to have been the first CV study to use the frame of voting.

3 If q is a vector, one must ask about not only diVerent levels of q but also diVerent combinations of the elements of q, in order to span the full range covered by the multi-attribute valuation function When valuing a single programme, by contrast, it matters little whether q is

a scalar or a vector because one is simply asking for a global valuation of q 1 versus q 0

per taxpayer, 10,000 acres at a cost of $60 per taxpayer, and 15,000 acres at acost of $150 per taxpayer, and asked to rank these from most to leastpreferred.

In each case, whether it is yes/no or a ranking, the response to the CVquestion provides only qualitative information about WTP Thus, from theraw responses alone, one cannot obtain a quantitative measure of WTP Toobtain that, one must embed the data in a model relating the responses to themonetary stimuli that induced them How this is doneÐwhat models to use,and how then to derive quantitative measures of valueÐis the subject of thissection

11.2.2 The economic foundations of a statistical model

Statistically, the CV responses are discrete dependent variables since they aremeasured on a nominal or ordinal scale There is a variety of statisticalmodels for analysing such data.4While we consider speciWc models below,their common structure can be summarized as follows In the general case,the CV responses can assume a Wnite number of values, which we index

jˆ 1; ; M For the ith observed response, the probability that it takes aparticular value can be expressed as some function

where Aiis the bid on that occasion, Zirepresents other covariates ing the subject, the item being valued, or any other pertinent aspect of thesurvey, and

describ-order for the probabilities to be well deWned, the right-hand side (RHS) of(11.1) must return a value between zero and one, and it must sum to unityover all possible outcomes jˆ 1; ; M In binary response models wherethere are just two possible outcomes, `yes' and `no', (11.1) reduces to

306 M I C H A E L H A N E M A N N , B A R B A R A K A N N I N E N

where T…
† is some real-valued function of A and Z,  is some randomvariable with cumulative distribution function (c.d.f.) F

both coeYcients associated with T…
† and parameters of the cdf The position ensures that the RHS of (11.10) returns a value within the range[0, 1] As we show below, diVerent discrete-response models involve diVerentformulas on the RHS of (11.1) or (11.10)

com-This statistical perspective can be distinguished from what might be calledthe economic perspective, which requires that the survey responses be eco-nomically meaningful in the sense that they constitute a utility-maximizingresponse to the survey question To satisfy both perspectives, one wants toformulate a statistical model for the CV responses that is consistent with aneconomic model of utility maximization In this section, we sketch how that

is done

We assume an individual consumer with a utility function like thatconsidered in Chapter 3 above, which is deWned over both market com-modities, denoted x, and some non-market item which is to be valued,denoted by q The corresponding indirect utility function depends on theindividual's income, y, the non-market item q, and various other argumentsincluding the prices of the market goods, perhaps attributes of the marketgoods, and attributes of the individual that shift her preferences.5For now,however, we suppress all of these arguments except (q, y) The other keycomponent of the indirect utility function is a stochastic component repre-senting the notion of random utility maximization (RUM) It is the RUMconcept that provides the link between a statistical model of observed dataand an economic model of utility maximization In a RUM model it isassumed that, while the individual knows her preferences with certaintyand does not consider them stochastic, they contain some components thatare unobservable to the econometric investigator and are treated by theinvestigator as random (Hanemann, 1984b) These unobservables could becharacteristics of the individual and/or attributes of the item; they can standfor both variation in preferences among members of a population andmeasurement error For now, we represent the stochastic component ofpreferences by " without yet specifying whether it is a scalar or a vector,and we write the indirect utility function as v…q; y; "†

To Wx ideas, we focus on the valuation of a single programme using thesingle-bounded approach.6Thus, the individual is confronted with the pos-sibility of securing a change from q0to q1> q0 We assume she regards this

as an improvement, so that v…q1; y; "†5v…q0; y; "† She is told this change will

5 Following the suggestion in McFadden and Leonard (1993), the variable y could be numerary income that remains after allowing for committed expenditures on market or non- market goods; i.e., y  y ÿ , where y is full income and  is committed expenditure The parameter  could be known exogenously or it could, in principle, be estimated from the CV responses along with the other model parameters.

super-6 The double-bounded approach and the valuation of multiple items are taken up in Section 11.4.

cost $A, and she is then asked whether she would be in favour of it at thatprice By the logic of utility maximization, she answers `yes' only if

v…q1; yÿ A; "†5v…q0; y; "†, and `no' otherwise Hence,

Prfresponse is `yes'g ˆ Prfv…q1; yÿ A; "†5v…q0; y; "†g: …11:4†

An equivalent way to express this same outcome uses the compensatingvariation measure, which is the quantity C that satisWes

v…q1; yÿ C; "† ˆ v…q0; y; "†: …11:5†Thus, Cˆ C…q0; q1; y; "† is her maximum WTP for the change from q0to q1

It follows that she answers `yes' if the stated price is less than this WTP, and

`no' otherwise Hence, an equivalent condition to (11.4) is

Prfresponse is `yes'g ˆ PrfC…q0; q1; y; "†5Ag: …11:6a†

In a RUM model, C…q0; q1; y; "† itself is a random variableÐwhile therespondent's WTP for the change in q is something that she herself knows,

it is something that the investigator does not know but treats as a randomvariable Let Gc…
† be what the investigator assumes is the cdf of C, and gC…
†the corresponding density function (the investigator will estimate the para-meters from the CV data); then (11.6a) becomes7

Equations (11.4) and (11.6a, b) constitute not only an economic model ofrespondent behaviour but also a statistical model, since the RHS deWnes a

1ÿ GC…A† In eVect, this represents the integrability condition for thesingle-bounded case: the statistical model (11.1') is consistent with an eco-nomic model of maximizing behaviour if and only if the RHS of (11.1') can

be interpreted as the cdf of a random WTP function, C…q0; q1; y; "†

There are two ways to formulate a statistical model with this property.One approach, associated with Cameron (1988), is to directly specify aparticular cdf for the individual's random WTP Let EfCg ˆ  (in a regres-sion model one would have ˆ X ), let varfCg ˆ 2, and let G…
† be thec.d.f of the standardized variate zˆ …C ÿ †=; then

Prfresponse is `yes'g ˆ 1 ÿ GC…A† ˆ 1 ÿ G Aÿ 

while G…x† ˆ …1 ‡ eÿx†ÿ1, the standard logistic, yields a logit model

The model is completed by specifying a probability distribution for  Let

G…
† be this c.d.f; the response probability formulas for the models (11.10)±(11.13) are given by:11

8 The c.d.f of a logistic with scale parameter  > 0 and location parameter 

is F …x† ˆ …1 ‡ exp‰ÿ…x ÿ †=Š†ÿ1; this has a mean and median of , and a variance of

 2  2 =3 In the standard logistic,  ˆ 0 and  ˆ 1 In (11.9), G…
† is taken to be the c.d.f of

z ˆ …C ÿ †=.

9 Since y > 0, the problems raised by Burbidge et al (1988) with the Box±Cox tion do not arise.

transforma-10 Note that 1 and 0 are not separately identiWable here, only their diVerence Similarly,

in this model the cdfs of " 1 and " 0 are not separately identiWable, only the c.d.f of  Depending

on the model structure, there will generally be some identiWability restrictions such as these.

 > 1, positive when  < 1, and is approximately equal to…1 ÿ † Thoughmore Xexible than the linear and logarithmic models, the Box±Cox modelsprovide a relatively restricted shape for the graph of WTP against income;more Xexible functional forms (with additional parameters) may be needed.Nevertheless, for convenience we will frequently use (11.11) in this chapter toillustrate points of modelling methodology.

normal c.d.f, (11.12') becomes

which is a probit model that becomes identical to the model in (11.8) whenˆ = and ˆ 1= This can be veriWed by inspection of the formula forC: since has zero mean and unit variance, it follows directly from (11.12)that EfCg   ˆ …= † and varfCg  2ˆ 1= 2 Similarly, when G…
† isthe standard logistic c.d.f, (11.12') becomes

apply when the random term enters the utility model nonlinearly, as in (11.19) below.

12 In this case, since  has a variance of  2 =3, (12) implies that var fCg   2 ˆ varfg= 2

ˆ  2  2 =3.

13 The probit model arises if " 1 and " 0 are normally distributed; if they are i.i.d normal with mean zero and variance 0.5, their diVerence, , is standard normal Similarly, the logit model arises if the "'s are extreme value variates The cdf of an extreme value variate with location parameter  and scale parameter  > 0 is F …"† ˆ exp‰ÿexp…ÿ" ÿ †=†Š; the mean is  ‡ 0:5772

310 M I C H A E L H A N E M A N N , B A R B A R A K A N N I N E N

appropriate choice of distributions, the two alternative approaches to erating a statistical model for the CV responses yield the same formula Thisresult holds generally There is no essential diVerence between the twoapproaches because any formula for an indirect utility function, v…q; y; "†,implies a corresponding formula for WTP, C…q0; q1; y; "† The converse isalso true since, from (11.5), one has

gen-Cˆ y ÿ m‰q1; v…q0; y; "†; "Š

where m…q; u; "† is the expenditure function associated with v…q; y; "†, and

K…q0; q1; y; "† is the income-compensation function which, as Hurwicz andUzawa (1971) showed, provides a complete representation of consumerpreferences Thus, C…
† and v…
† are alternative representations of the samepreference ordering; any probability distribution of u implies a correspond-ing probability distribution of C, and conversely

There are two important implications First, just as economic theoryplaces certain restrictions on v…
†, it also places restrictions on C…
† Thesemust be reckoned with whatever the approach to model formulation Theexisting literatureÐour own work includedÐhas not always paid adequateattention to these restrictions We discuss them further in the next section.Second, an essential feature of RUM models is that the stochastic anddeterministic components are commingled In conventional economic ana-lysis, one generally formulates a deterministic economic model and thenadds a random term for the purpose of statistical estimation The randomterm is assumed to arise outside the economic model and it plays no role inthe economic analysis once the model has been estimated In a RUM model,

by contrast, the stochastic component is an essential part of the economicmodel and it plays a substantive role in the use of the model for bothprediction of behaviour and evaluation of welfare

We have already seen an example of this in connection with the varianceparameter 2 varfCg Assuming a regression setting where iˆ Xi forthe ith respondent, the response probability formula in (11.7) can be written

Prfith respondent says `yes'g ˆ 1 ÿ G AiÿXi

which implies that the term 1= serves as the `coeYcient' of the bid amount

in the statistical model of respondent behaviour Thus, what mighthave been thought a purely statistical parameter also has a behaviouralsigniWcance This is a general result, not limited to any particular RUMand the variance is  2  2 =6 In the standard extreme value,  ˆ 0 and  ˆ 1 If " 1 and " 0 are independent extreme value variates with separate location parameters  1 and  0 and a common scale parameter ;  ˆ " 1 ÿ " 0 has a logistic distribution with location parameter  ˆ  1 ÿ  0

and scale parameter  The standard logistic arises when  ˆ  and  ˆ 1.

speciWcation.14,15 Some insight into the reason for it can be obtained fromthe Box±Cox utility model; (11.10b) implies that varfCg is a function notonly of the stochastic terms in the utility function but also of the structuralparameters, such as; q, or Moreover, in (11.10), (11.11), and (11.13),varfCg is a function of income, y, so that C has a heteroscedastic distribu-tion It is inappropriate, therefore, to think of varfCg as merely a statisticalconstant Many other examples of the commingling of stochastic and deter-ministic components in RUM models will be encountered below.

In their original paper, Bishop and Heberlein (1979) used the followingmodel for the CV responses:

Like (11.15), this is a logit model where the response probability is dent of income; the diVerence is that (11.15) uses A, whereas (11.17) uses (lnA) Hanemann (1984a) asserted that (11.17) was not consistent with eco-nomic theory because it was not a valid RUM model As we now show, thatassertion was incorrect

indepen-The deWnition in (11.16) implies that C…q0; q1; y; "† is independent of y ifand only if mu…q1; u0; "† ˆ mu…q0; u0; "† As shown in Chapter 3, this comesabout if

for some increasing function T…
† The resulting formula for C is

Cˆ …q1; "† ÿ …q0; "†; …11:18b†which implies response probabilities of the form

Prfresponse is `yes'g ˆ PrfC5Ag ˆ Prf…q1; "† ÿ …q0; "†5Ag: …11:180†

14 Holding all else constant, changes in  aVect response behaviour since, from (11.7),

@Pr f`yes'g=@5…4†0 according as A i 5 …4† i Note that …11:7 0 † assumes a homoscedastic distribution of WTP where  is the same across all survey responses This is not a necessary feature of RUM models; one can formulate models where  varies as a function of attributes of the individuals, attributes of the item being valued, and/or attributes of the survey administra- tion Examples appear in several parts of this chapter.

15 Assuming a homoscedastic WTP distribution, Cameron (1988) points out that  can be identiWed from the CV responses only because there is variation in A i If the same bid were used for all respondents,  would be unidentiWed In that case, one could still identify the ratio = if

X i varied across respondents; but one needs variation in A i to obtain separate estimates of  and ... RUMand the variance is   =6 In the standard extreme value,  ˆ and  ˆ If " and " are independent extreme value variates with separate location parameters  and  and a common... obtain(11.17), Bishop and Heberlein used the logistic distribution for G"…
†, whichmakes and C log-logistic If " is standard normal,  and C are lognormal ,and? ?11:190†... log-logistic, lognormal, andWeibull versions (11.17), (11.20), and (11.21) respectively, appears fre-

Box-Cox model, (11.12), in its probit and logit versions (14) and (15) Theseparticular