Incomplete beliefs and nonmarket valuation

Resource and Energy Economics 20 Ž1998. 139–162

Incomplete beliefs and nonmarket valuation Thomas D. Crocker ) , Jason F. Shogren, Paul R. Turner Department of Economics and Finance, UniÕersity of Wyoming, Laramie, WY 82071-3985, USA Received 8 January 1996; accepted 17 December 1996

Abstract We explore implications of the failure of the individual to behave in accordance with the predictions of the utility maximization paradigm for the application of consumer sovereignty principles to the valuation of environmental goods. A subjective probability framework is used to develop an index of the completeness and the coherence of the individual’s risk-neutral beliefs and valuations. These beliefs and valuations are shown to be institutiondependent, and thus endogenous to the choices the individual makes about the medium in which to express herself. A variety of propositions about the influence of incomplete beliefs on value expressions is derived. q 1998 Elsevier Science B.V. JEL classification: Q28; D61 Keywords: Valuation of environmental goods; Consumer sovereignty; Utility maximization; Subjective probability

1. Introduction Readers of Braden and Kolstad Ž1991., Freeman Ž1993., and similar methodological overviews might readily conclude that the extension of the economic theory of choice to the valuation of nonmarketed environmental commodities is a resource economics ‘success story.’ The extension from marketed commodities is built upon parsimonious, solid axiomatic foundations; it represents significant breakthroughs in the analytics and empirical practice of assessing environmental

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Corresponding author. Fax: q1-307-766-5090; e-mail: [email protected]

0928-7655r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 9 2 8 - 7 6 5 5 Ž 9 7 . 0 0 0 3 3 - X

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values, and it stands ready to provide many of the theoretical underpinnings for coherent applications of economics and the natural sciences to environment and natural resource policy issues. However, although they do not yet loom large enough to discomfort those who built and continue to inhabit this intellectual edifice, the sensitive ear can detect audible, if faint, rumblings that might disturb the repose of its occupants. The expression of instantaneous dispositions through repeated give-and-take with others in the context of a coordinating exchange institution is the foundation of the economic theory of choice. This institution prescribes uniform incentives and articulates knowledge and beliefs about relevant laws of nature and of man. It relates the individual’s choices to the choices of others, and to the consequences the sum of these choices produce. Moreover, it conserves resources and goods by redistributing them in accordance with individuals’ desires. The exchange institution is therefore a collective habit. When it is absent, the individual must draw more intensely upon her personal resources. Exchange institutions often, even usually, do not exist for environmental assets. The individual can act as if her value expressions will not be contested; she is asocial, and therefore need not be accountable to others. Unless one makes the rather stilted presumption that she is a complete image of a nonstrategic, anonymous, competitive market that is very broad in scope, the individual may lack the incentives to act in accordance with the utility maximization paradigm and the economic theory of choice that follows from it. This paper explores some implications for efforts to assess the economic value of nonmarketed environmental goods of the failure of the individual to behave systematically in accordance with the predictions of the utility maximization paradigm. We are suggesting that a Coasean corollary exists for nonmarket valuation: if information processing costs are zero, the researcher will have enough understanding to provide identically perceived information, such that respondents’ beliefs will be complete and identical, and consequently elicited values will be identical to the market price, if it existed. But if information costs are really zero, respondents will endogenously generate their own information frames that will be identical to the exogenously provided information frames, i.e., elaborate information packages in survey research are redundant, as respondents would select the same frame endogenously. Information costs are not zero, obviously, thereby implying that the rules and exchange institutions implied by a researcher’s exogenous frame impact a respondent’s elicited value. Therefore, artificially restricting the range of rules and exchange institutions will result in revealed values that underestimate the true value of the resource. Expanding the endogenous choice of exchange institution in nonmarket valuation is needed to allow for incomplete beliefs to become more complete, as the respondent has the opportunity to participate in the selection of both what goods will be produced and how they will be provided. In addition, formal assessments of whether an individual’s beliefs are complete and coherent Ži.e., the no-arbitrage condition. should play a substantially larger role in nonmar-

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ket stated valuation exercises to improve understanding of the reliability of stated values.

2. Background Economic and psychological evidence is abundant that, without the disciplines and the protections that exchange institutions offer, individuals frequently do not act systematically according to the imperatives of utility maximization, the axiomatic foundation of the economic theory of choice. The utility maximization paradigm frequently fails to bridge the gap between our conjectures and our everyday observations. When no exchange institution provides the gravity to hold her rationality together, the unsocialized individual commonly engages in anomalous behaviors Žnaive expectations or sucker behaviors. inconsistent with the paradigm. Unsocialized individuals fail to exploit existing gains from trade and often engage in behaviors that allow others to exploit these gains. Thaler Ž1992. presented a lengthy catalogue of violations of the continuity, completeness, and transitivity axioms upon which the descriptive power of the paradigm rests. Included are endowment effects Žgoods in inventory are valued more highly than the same goods not in inventory., framing effects Žproblem context affects choices., preference reversal effects Žthe order in which people rank lotteries differs between when they do and do not have to pay for them., anchoring effects Žstatus quo points affect choices., opportunity cost effects Žout-of-pocket costs are accorded greater weight in choices than are opportunity costs. availability effects Žinformation irrelevant to the decision is employed because it is available., immediacy effects Žrecent events have greater weight in decisions than do distant events., control illusion effects Žchance events are treated as if skill can control them., representativeness Žcorrelation is taken to imply causation., and many others. Psychologists ŽHogarth, 1988. and occasional economists ŽSimon, 1973; Heiner, 1983. explain these unsocialized behaviors in terms of the cognitive limits of individual human beings. Problem-solving performance is said to depend upon the individual’s computational skills and upon the information processing demands of the problem at hand. Problems can be arrayed from the ill-structured to the well-structured. Well-structured problems are the norm for the Hicks–Slutsky individual who obeys the utility maximization paradigm. For every decision—taking a drink of water, walking two steps to obtain a better outdoor view—she impeccably acts as if she deduces first-order necessary and second-order sufficiency conditions with respect to the number of goods in her opportunity set and the sequential and stochastic properties of each of these goods, even if the deduction is once-in-a-lifetime. Her rationality seems unbounded. Real people use the Hicks–Slutsky algorithm to resolve well-structured problems, but ill-structured problems strain their abilities to comprehend complex

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structures, to process Hicks–Slutsky relevant information, and to coordinate activities Žsee also Mazzotta and Opaluch, 1995.. Real people must decide how to decide ill-structured decision problems. External conditions combined with only an objective function can no longer alone provide a choice imperative. With ill-structured problems the individual selects a frame from a set of competing frames Žcognitive representations or abstractions. to choose and to interpret data. The quality of the solutions achieved for these ill-structured decision problems and the efforts expended to resolve them are thus taken to depend upon the structure of the problem. Economists have adopted three modes of argument to contest the empirical evidence that individuals’ behaviors in complex, ill-structured environments frequently do not conform to the constrained utility maximization paradigm. One mode challenges the experimental procedures that psychologists use. The procedures are said to be poorly suited to ill-structured problems. In particular, objections are raised to one-shot experiments in which inexperienced subjects that do not have the opportunity to learn and to acquire feedback are asked to resolve these problems ŽGrether and Plott, 1979.. Moreover, objections are raised to the absence of decision aids that people would normally use to help solve a problem ŽEdwards and von Winterfeldt, 1986., and to the use of only weak, if any, incentives that match rewards to performance ŽGrether, 1980, 1994.. A second mode of defense willingly grants that many decision problems are ill-structured and that unconnected individuals often exhibit unsocialized behaviors when dealing with them. The task is then taken to be the identification of social processes that make the problems well-structured so that the individual will apply the Hicks–Slutsky algorithm ŽAlchian, 1950.. Camerer Ž1987. identifies several such processes, including the use of financial incentives and experience to avoid mistakes, the canceling out of presumed random individual biases, smart traders acting as arbitrageurs who make the marginal trades that determine prices, natural selection operating such that bankruptcy drives suckers from participation, and suckers learning from smart traders. In general, arguments are sought, such that the hive of trading activity in the exchange institution protects suckers from their own irrationality, or forces them to be rational. Unsocialized individuals are either drummed out of the exchange institution, or they learn not to be unsocialized. The third mode of defense was initiated by Becker Ž1962.. In effect, Becker demonstrated that exchange institutions may be well-structured even if individuals do not behave according to the utility maximization paradigm. He showed that the presence of binding constraints Že.g., a budget constraint. is sufficient to generate rational Žexhaustion of gains from trade. outcomes at the level of the exchange institution Žat the collective level., although each individual may be making her choices in a purely random manner: the utility maximization paradigm is not necessary to generate economically efficient collective outcomes. Human interventions such as bankruptcy and learning are redundant. There need be no direct connection between individual and collective rationality. The allocative efficiency

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of exchange institutions comes from their structure rather than from the learning or motivations of the participating individuals ŽWilson, 1987.. Thus, although standard economic practice commonly assumes a direct, causal relation between individual and collective behaviors ŽRussell and Thaler, 1985., one should draw this link only with great caution. Exchange institutions such as markets provide structure for individuals’ choices and will thus induce a collective behavior that differs notably from the behaviors of an arbitrary set of disjointed individuals. However, as Coleman Ž1986. remarked, we currently lack deep understanding of how exchange institutions transform what may be irrational individual behaviors into rational collective behaviors. Gode and Sunder Ž1993. provide empirical evidence on the relevance of exchange institution structure for rationality. They show that the irrationality of individuals cannot foolishly be extrapolated to collective behaviors. In their experiments, they had ‘zero intelligence’ ŽZI. computer program traders having neither knowledge, memory, learning, or motivation randomly submit bids and offers in a double auction setting. Bids and offers were subject to a binding budget constraint. The rationality of these double auction markets with ZI as well as with human traders was close to 100%. The human traders simply attained rationality more quickly than did the ZI traders. These results imply that at least the double auction structure demands that its participants possess only very low information processing capabilities to attain collective rationality. The findings of Gode and Sunder Ž1993. reinforce the results of Chu and Chu Ž1990., that motivations, prior knowledge, and information play minor roles at best in the use of exchange institutions to achieve collective rationality. The results of Chu and Chu Ž1990. supply experimental evidence with human subjects that extreme simplification of a complex lottery does little, if anything, to alter that form of individuals’ irrational behaviors known as preference reversals. However, the presence of arbitrage opportunities in both complex and simple lottery environments induces collective and individual rationality. Shogren Ž1997. also demonstrated that in an exchange institution with a nonlinearly increasing payoff scheme Ži.e., tournament., notions of altruism or ‘warm glows’ can be eliminated from exchange, replaced instead by the traditional presumption of rational self-interest. When the stakes of exchange increase at an increasing rate as one advances his or her relative ranking, charity to others dissipates. Because exchange institutions, especially markets, are thin or nonexistent for environmental commodities, individual irrationalities plausibly exercise great influence over the allocation of these commodities and thus the values derived from their presence and use. Delivery of a means to allocate these commodities rationally might be viewed as a major purpose of benefit–cost analysis, the kit of tools that economists use to infer the values individuals would attach to these commodities if market disciplines were in place. The delivery may be less than perfect, however, if only because applications of the kit usually require the introduction of strong auxiliary conditions linking the individual to the market.

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The auxiliary conditions can be used to make what appears to be an ill-structured problem even to the researcher appear as a well-structured problem to that same researcher. For example, with the increasingly popular contingent valuation method ŽHanemann, 1994., the isolated individual, in response to a researcher request to do so, is presumed to be able to imagine an exchange institution, visualize the details of her and others’ participation in it, and then to state her one-time willingness-to-pay or willingness-to-accept payment for a nonmarketed environmental commodity. The brief review in this section of the analytical foundations of and the empirical evidence for individual irrationality and collective rationality suggests that these auxiliaries may often only be devices that force worldly observations to fit the utility maximization paradigm at the level of the individual. In Sections 3–6, we take seriously the notion that the individual views most environmental problems as ill-structured. We also grant that costs of coordination and negotiation may prevent those exchange institutions which can provide structure from being formed. 1 Section 3 considers the implications for value measurement of varying degrees of exchange institution transformation of ill-structured environmental decision problems into well-structured problems. Section 4 evaluates the trade-offs between the benefits and costs of supplying these transformations. We conclude that value measurement tools that disregard irrationalities or unsocialized behaviors will misvalue environmental commodities. These misvaluations will be reinforced by the standard implicit assumption that only a single exchange institution, the Walrasian tatonnment process, is capable of excising ˆ irrationalities. Instead we accept the result of Smith Ž1962. that a variety of coordination and negotiation devices are capable of extracting potential economic surplus. We conclude that the total value of an environmental asset may be the sum of surpluses generated in multiple exchange institutions rather than the surplus generated in a single institution.

3. Value measurement Maximum extraction of potential surplus is performed at the level of the exchange institution rather than at the level of the individual ŽSmith, 1991.. By using the utility maximization parable to interpret value expressions for environmental assets, economists try to establish the individual preference expressions that would be revealed if the individual were not socially impoverished, i.e., if the arbitraging offered by exchange institutions that are nonstrategic, competitive, and 1

We thus presume that surplus maximizing exchange institutions could and would be formed in the absence of any costs of formation. This presumption sets aside issues of multiple equilibria ŽFriedman, 1991. and just-noticeable-differences ŽHeiner, 1986. that may inhibit exchange institution formation whatever its cost.

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very broad in scope were freely available to her. This section considers some of the implications for interpretations of these value expressions when these institutions are not freely available, or when the auxiliary conditions imposed by the researcher to make these institutions appear freely available lack credibility. 2 Because uncertainty is a common feature of nearly all environmental decision problems, we develop our analysis in terms of the subjective probability framework of de Finetti Ž1974.. Personal probabilities Žbeliefs. about events are defined by de Finetti in terms of the money prices of lottery tickets. He shows that such prices must coincide with a classical, finitely additive probability measure taken over states, given that the marginal utility of money is constant across states and linear for consequence quantities within states. Individuals’ ‘true’ or risk neutral probabilities and relative utilities then coincide and are revealed by their acceptances of money gambles. If, as follows from the axioms of Savage Ž1954., beliefs and preferences are completely ordered such that between any pair of gambles with weakly positive expected values, the individual can express a weak preference, then the distribution, p , across states of these risk-neutral probabilities must be unique. 3 That is, for every state there exists a single price above which the individual is willing to sell a lottery ticket on the state and below which she is willing to buy a ticket, i.e., the individual is indifferent between buying and selling the lottery. The distribution of these prices across states is then the individual’s unique risk-neutral probability distribution. 4 This risk-neutral price is the no-arbitrage price because, as de Finetti shows, no other individual could win a positive sum by either buying a lottery ticket from you or by selling a ticket to you. Just as the assumption of completeness in preferences has evoked broad skepticism about the universal applicability of the deterministic theory of choice, the assumption of completeness of beliefs and therefore preferences in the subjective probability approach to stochastic choice has frequently been said to be

2 The subsequent discussion builds upon a heuristic device originally used by Nau and McCradle Ž1991.. Spash and Hanley Ž1995. provide empirical evidence of incomplete preferences for an environmental good—biodiversity. 3 Savage characterizes the individual’s decision problem as a set of states of nature, S, a set of consequences, C, a set of acts, A, which map S into C, and a binary relation, G, on A. The choice objects of subjective probability are thus the acts or gambles that assign a consequence to each state of nature. Those axioms upon which the framework rests imply an additive subjective probability measure over states and a von Neuman–Morganstern utility function over consequences. Together, the probability measure and the utility function yield a preference ranking over all acts so that the set of acts is not some limited set framed for the decision problem but is instead completely ordered. See pp. 205–207 of Mas-Colell et al. Ž1995. for a succinct treatment of the underlying logic. 4 Kadane and Winkler Ž1988. show that differences in the marginal utility of money across states Žstate-dependent utility. cause probabilities and utilities to be nonseparable. Thus, the apparent probabilities that an individual’s acceptance of belief gambles reveals must now be interpreted as normalized products of her ‘true’ probabilities and her marginal utilities.

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incredible Že.g., Smith, 1961.. Consider, for example, the question of whether you believe that you will avoid an air pollution-induced illness at a specified date. You will be able to specify a value, p, such that odds less than this value are incredibly low and another, higher value, q, such that odds greater than this value are incredibly high, where 0 F p q q F 1. In between, over the w p,q x interval, you would prefer not to or are unable to discriminate. If you feel totally ignorant, your interval would presumedly span the w0,1x domain of risk-neutral subjective probabilities. When these probability intervals vary across states, you will have a set of such intervals, one set to a state. Thus, for any particular state, rather than having a single price for a lottery ticket, you will have a greatest buying price and a least selling price for the ticket. Then, again using the logic of de Finetti Ž1974., the greatest credible odds, p, correspond to your greatest buying price and the smallest credible odds, q, correspond to your smallest selling price. However, this incompleteness of your beliefs, thus your preferences, makes you susceptible to arbitrage. If an individual were to gamble at odds derived from incomplete beliefs and thus incomplete preferences and the side Žbuying or selling. of the bet and the size of the stake could be dictated by another bettor, the other bettor could win a positive sum come what may. This is sometimes called the Dutch Book argument. The other bettor would drain your potential surplus. These ideas are readily illustrated in a three-state space, a simplex ŽMarschak, 1950., which here represents the set of all risk-neutral distributions p s Žp 1 , p 2 , p 3 . satisfying p 1 q p 2 q p 3 s 1. The restriction that the set of risk-neutral beliefs must sum to unity corresponds to the notion of coherence of de Finetti Ž1974., i.e., Dutch book avoidance or no-arbitrage Žsee Nau, 1995.. If it is the case that p 1 q p 2 q p 3 / 1, another player can rebundle the lotteries to guarantee a net loss to the individual. The simplex has coordinates p 1 , p 2 , and p 3 s 1 y p 2 y p 1. Fig. 1a depicts the baseline case, the case in which the individual’s probability beliefs and thus her preferences over the lotteries, p i , i s 1,2, are complete such that for a lottery ticket paying US$1 if state i occurs, her greatest buying price, pi , and her least selling price, qi , coincide for each lottery. The set of all p satisfying p i s pi s qi is the set of all risk-neutral distributions satisfying the prices. Because her beliefs are complete, this set is the single point in the interior of the simplex. The individual is the perfect image of a nonstrategic, competitive market with zero costs of coordination. Her greatest willingness-to-pay and her least willingness-toaccept would coincide. Fig. 1b depicts the case in which the individual’s probability beliefs and thus her preferences over lottery tickets are incomplete. The set of all risk-neutral distributions satisfying w pi ,qi x is now that intersection of the bands satisfying pi - p i - qi for i s 1,2. By self-insuring, self-protecting, or by enhancing her human capital, the individual may be able to round the sharp edges of the intersection, or to reduce it to the dotted area within the larger circle. If human capital enhancement, etc., is more productive in one lottery than another, the circle may be an ellipse.

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Fig. 1. Risk neutral beliefs: complete and otherwise. Ža. Individual with complete beliefs; Žb. individual with incomplete beliefs; Žc. Marshall’s representative individual; Žd. three unsociable individuals; Že. three unsocialized individuals; Žf. learning.

Now presume that each lottery ticket is held by a distinct individual. Each individual has incomplete and dissimilar probability beliefs. Because probabilities are additive, some third individual, say individual C in Fig. 1c, can purchase a p 1 ticket at price pA from individual A, a p 2 ticket at price p B from individual B, bundle them to make a single ticket at price pA q p B on the union of p 1 and p 2 , and then sell the bundle to the fabled Marshallian ‘representative’ individual who issues from an exchange institution. 5 The set of acceptable gambles for this representative will be the sum of the acceptable gambles for the real individuals who have incomplete beliefs. This representative could follow an analogous 5

See Stokes Ž1993. for a review of the sufficient conditions for the existence of the representative individual. This literature assumes that preferences are complete. Because our representative individual is the image of interactions among heterogeneous individuals, the criticism of Kirman Ž1992. about the use of the representative individual to examine collective economic behaviors does not apply.

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procedure for the individuals’ least selling prices. The intersection of the sets of risk-neutral distributions of the real individuals will then be the representative’s set of risk-neutral distributions, the remaining set of arbitrage opportunities, or the surplus or slack that has not yet been drained that could be generated from exchange. Coordination costs or the costs of making and maintaining a market prevent full extraction of the surplus. Note in Fig. 1c that the discrepancy between the representative’s greatest buying prices, pi , and least selling prices, qi , is less than those for either of the real individuals, A and B. The representative or the exchange institution has reduced the impact of incomplete beliefs upon observed valuations. In addition, no matter how the risk neutral distributions of the real individuals are sketched, the representative’s least selling price for a lottery ticket on state i will be no greater than the smallest least selling price among the real individuals, and will generally be less than this price. Similarly, the representative’s greatest buying price will be no less than that of any real individual and will generally be greater than this price. The foregone opportunities for surplus extraction associated with incomplete beliefs imply that observed selling prices in the exchange institution are greater, and buying prices are less relative to those that would be observed in the presence of complete beliefs. Participation in exchange under incomplete beliefs will therefore be greater in selling activities and in buying activities than under complete beliefs. 6 As participation changes so do beliefs, because participation in the exchange institution encourages rationality. Fig. 1d depicts a case where individuals have incomplete probability beliefs, and where arbitrage opportunities are absent. An example might be those frequent instances in contingent valuation exercises in which the researcher poses an exchange institution, and the respondent refuses to participate in the valuation exercise. Alternatively, the respondent may state a bid that the researcher treats as an outlying or ‘protest’ bid. The researcher then removes this bid from the sample on the grounds that the bid would be unrealistic for the exchange institution that the researcher has posed. Given that the respondent is aware that no exchange institution exists relevant to her risk-neutral probability distribution, the removal of her bid may well be inappropriate. Fig. 1e provides an insight about the effects upon the accuracy of valuation exercises when there exist discrepancies between the scope of the exchange institution presumed in the valuation exercise and that found in reality. The discrepancy may arise due to the researcher’s imposition of auxiliary conditions, intended to make the analytical framework that she wishes to use to guide interpretation of the data to conform to a setting in which beliefs and preferences are complete, and markets are nonstrategic, competitive, and broad in scope. For example, coordination costs may cause the actual exchange institution to be one in

6

Kolstad and Guzman Ž1995. obtained a similar result while approaching the same problem with a different framework.

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which individuals are relatively unsocialized such that their least selling prices are q1B , q1A , and q1C in Fig. 1e. Considerable potential surplus remains, but coordination costs inhibit its capture. If the auxiliary conditions imposed imply an exchange institution with a scope that leaves only an unextracted surplus in the darkened area at the union of the risk-neutral distributions of individuals A, B, and C, the valuations inferred will be greater than those which the individuals are actually able to or expect to extract. In the extreme, coordination costs might be entirely removed by the auxiliary conditions. The inferred values would then mimic those obtained in Fig. 1a: the exchange institution would be an image of the individual with complete beliefs. Zero coordination costs assure, as Becker Ž1962. and others have shown Žsee Section 2., that the valuation results of incomplete beliefs, and thus incomplete preferences are consistent with a setting in which all potential surplus is realized. However, this neat piece of logic sidesteps the issue of exactly how valuation expressions set forth in a real-world setting of incomplete beliefs and preferences are to be transformed in a world of nonzero and often significant coordination costs into value expressions that result from complete beliefs. Standard procedures instead treat complete beliefs as a maintained hypothesis and inquire about the values the hypothetical holders of these beliefs would express in a zero coordination cost world. If this world is often but a fiction or a faint approximation of reality, and if real expressions of value are desired, then three options are available: Ža. make beliefs more complete; Žb. encourage the development of exchange institutions that make irrelevant the incompleteness of individuals’ beliefs; or Žc. acquire deeper insight into the value implications of incomplete beliefs. Otherwise, value expressions issued in a world of incomplete beliefs cannot, in the absence of a willingness to employ logically handy fictions, provide any obvious conclusions about what value expressions would be in a world of complete beliefs ŽCrocker, 1973.. The data that would be realized in a world of complete beliefs cannot be observed. Fig. 1e also illustrates that there is a fundamental divergence between the revealed prices and the stated values of a representative individual given incomplete beliefs. The representative individual’s revealed price is the market price, q1B —the lowest selling price. The representative individual’s stated price, however, is the average price, q, of the three respondents. Therefore, by definition, q1B / q. Fig. 1f pictures a setting in which learning makes beliefs more complete. In valuation exercises, the setting is probably most frequently seen in experimental markets in a laboratory venue. The vast majority of experimental markets use numerous trials. These trials allow the bidder to revise her bids as she gains experience with market procedures and signals. Coppinger et al. Ž1980., Kagel et al. Ž1987. and many others provide evidence that subjects take full advantage of these bid revision opportunities, often extracting all of the potential surplus that was left unrealized in the initial trial. For example, Shogren et al. Ž1994. observed that repeated trials were necessary before willingness-to-pay and willingness-to-

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accept measures of value for goods with numerous close substitutes would converge. Repeated experience and exchange was needed to discipline and to shape incomplete beliefs, thereby improving the correspondence between observed behavior and the predictions of the theory of choice under complete beliefs. In general, the available experimental evidence suggests that individuals’ beliefs evolve within an exchange institution: that is, individuals’ beliefs are institutiondependent Žsee for example Plott, 1996.. These beliefs become more complete or appear to be more complete with greater incentives to participate in the institution and with greater opportunities to practice within it. Section 4 elaborates upon this theme.

4. Value and exchange institutions We now construct a model in which a representative individual tries to form conjectures and accumulate experience about the effect that a well-specified and clearly communicated lottery on an environmental commodity has on her wellbeing. We presume that she has incomplete beliefs that can be made more complete Žor made to appear more complete. if she chooses to participate in one or more exchange institutions. These institutions pressure the individual to behave in accordance with institutional norms. However, the manner in which these pressures induce the individual to submit her beliefs and preferences may differ considerably across institutions, and the individual may well have preferences over the manner of submission. For example, public good clubs may compel her to reveal herself more than she would like in interminable meetings for which she does not care. She may instead prefer the anonymity of the nonstrategic, competitive market. The incompleteness of her risk-neutral beliefs about, and thus the value she attaches to a lottery for the environmental commodity will therefore differ with the exchange institutions in which she chooses to participate, and with the intensity of her participation. We assume that only after she selects her optimal mix of exchange institutions, does she use her own instincts to allocate her total wealth, M, among z commodities, x 1 , . . . , x z , subject to a wealth constraint, z Ý ks 1 p k x k s M, where price p k , and M are predetermined. More specifically, let u i j represent the capacity of the jth exchange institution, j s 1, . . . , m, in the ith state, i s 1, . . . , n, to capture all economic surplus from trade of a lottery on an environmental commodity in a world devoid of incomplete beliefs. 7 u i j is appropriately viewed as a measure of the inertia due to purely

7

As did Arrow and Debreu Ž1954. and as has nearly everybody since, we assume that this state space is exogenous, and common to all individuals.

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incentive compatibility and informational issues commonly associated with the individual’s initial property claims and access to public goods. Hypothetical contingent claims markets, Vickrey second-price auctions, the exchanges involved in travel outlays, property acquisitions, bargaining about job tenure and conditions, referenda and other public forums all qualify as alternative exchange institutions. Given an exchange institution and an environmental state, the representative individual maximizes the difference, W, between the surplus, K i , that would be generated in a world of nonstrategic, anonymous, competitive markets and a world of incomplete beliefs and exchange institutions that are costly to gain access to and to operate. W is the analog of the non-blackened area in Fig. 1c that arbitrage activities have removed. The representative individual is to maximize W s ÝÝ K i y Ž 1 y u i j . Di j Ž u i j . y Ci j Ž u i j . i

Ž 1.

j

where Di j Ž u i j . is the distribution of the risk-neutral individual’s incomplete beliefs defined in terms of the properties of the w pi , qi x spread, and Ci j Ž u i j . is the cost of making, gaining access to, and operating the jth exchange institution. Di j Ž u i j . is thus the cost of organizing exchange institutions to pressure the irrationalities that incomplete beliefs produce. The Ci j Ž u i j . are commonly known as transaction, coordination, or negotiation costs. Assume u i j is continuous and can thus be characterized as lying in the unit interval w0,1x where the upper bound implies that the exchange institution captures all economic surplus for the institution in question, and the lower bound implies that no surplus is captured. 8 Further assume DXi j ' d Di jrd u i j ) 0, CiX j ' dCi jrd u i j ) 0, DYi j - 0, and CiYj ) 0. These assumptions imply that the surplus exhaustion capacity of the exchange institution influences incomplete beliefs and the costs of organizing the institution in a well-behaved fashion. The first-order condition for Eq. Ž1. with respect to u i j is

w s ÝÝ Di j Ž u i j . y Ž 1 y u i j . DXi j y CiX j F 0 i

j

Ž 2.

u i j G 0, and u i j w s 0 The first two terms in the brackets of Eq. Ž2. are the indirect and the direct benefits of changing the surplus exhaustion capacity of the exchange institution.

8 Although we attempt to exploit it here, note that this property suggests that u i j will possess the properties of a cumulative probability distribution. If, in accordance with Becker and Murphy Ž1992., u i j is made a positive function of ‘general human capital,’ it will be monotonically increasing, approach a value of unity as human capital increases, and have a derivative with respect to human capital that will simply be the density of the distribution.

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For example, a fuller specification of the commodity in a contingent valuation exercise might increase this capacity. An increase in capacity increases the opportunity costs of incomplete beliefs. The last bracketed term is the marginal cost of organizing and exploiting this capacity. Eq. Ž2. therefore states that the direct and indirect benefits of organizing and exploiting an exchange institution to reduce incomplete beliefs must exceed the marginal costs of organization. The inequality implies that a given exchange institution will not be worth organizing in all states. Thus, an exchange institution that induces complete beliefs, and the value expressions associated with these beliefs in one state, may not alter beliefs at all in another state. The values expressed in the two states will then be incomparable unless the distributions of beliefs underlying these values can be adequately characterized. At least three interesting additional implications of Eq. Ž2. readily follow. First, the higher the expected costs for its potential participants of organizing and maintaining an institution, the greater the influence that incomplete beliefs will exercise over value expressions derived from that institution. Complete rationality will concede to organizational costs. Second, the more incomplete are beliefs, the greater the opportunity stakes from not organizing. Third, there will be states where the exchange institution is not worth organizing. Valuation techniques that use auxiliary restrictions to impose this exchange institution in these states will grant full exercise to the expression of incomplete beliefs. An obvious and significant extension of Eq. Ž1. involves consideration of multiple exchange institutions differing in their surplus exhaustion capacities and in their costs of organizing. To do so, again consider the unsocialized individual who is concerned only with a single period and who has incomplete beliefs. 9 Thus her expected utility is V s EU, where E is the expectations operator calculated with respect to the individual’s risk neutral distribution of utilities in this strictly self-provisioning mode. Now presume that this individual who labors under incomplete beliefs has a number of alternative exchange institutions available. She may therefore allocate her wealth among the goods across these exchange institutions. The specific values that solve her allocation problem for any single exchange institution could result in any one of a variety of realized utilities in different institutions. She learns something about her beliefs by participating in different institutions and is able to control what happens to her beliefs by her choice of exchange institutions. This anticipated learning enhances the surplus she expects that she will be able to extract from any particular allocation. Each exchange institution induces a distribu-

9

In a sequential, multiple period setting, incomplete beliefs imply myopia, a topic that, beginning with Strotz Ž1956., has garnered considerable attention in the time preference literature.

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tion of risk neutral beliefs, in accordance with the discussion in Section 3. This distribution will depend upon the surplus exhaustion capacity, u i j , of the institution. The individual now calculates the expected utility, W ) , associated with the distribution, for the allocation of goods for each exchange institution. Because u i j differs across institutions, alternative institutions differentially reduce incomplete beliefs, and thus generate different expected utility outcomes. Thus, the individual’s initial incomplete beliefs, along with the different exchange institutions that she can use, induce a set of belief distributions, each member of which has an associated expected utility, W ) . These expected utilities are distributed according to the probability function, V . By behaving as a Bayesian statistician, she can calculate the expected utility function W s Ew W < V x. She uses what she has learned in her self-provisioning activities, and then chooses another allocation across institutions for which the sum of V, from her self-provisioning, and W, from alternative institutions, is maximized. Thus, Eq. Ž1. is modified to

½

max V q W s ÝÝ K i y Ž 1 y u i j . Di j Ž u i j . y E Ž Di j Ž u i j . . y Ci j Ž u i j . i

j

5 Ž 3.

where EŽ Di j Ž u i j .. is the expected utility consequence of engaging the jth exchange institution in the ith state. Assuming an interior solution, the first-order necessary condition for Eq. Ž3. is

w 0 s ÝÝ Di j Ž u i j . y Ž 1 y u i j . DXi j Ž u i j . y CiX j Ž u i j . q Ž 1 y u i j . E Ž DXi j Ž u i j . . i

j

yE Ž Di j . s 0

Ž 4.

The first three terms in Eq. Ž4. are identical to the first three terms in Eq. Ž2.; the last two terms in Eq. Ž4. represent the indirect and the direct marginal impacts of u i j upon expected beliefs. To make her beliefs less incomplete and thus increase the surplus she can extract, the individual has to distribute her exchange activities across institutions such that she maximizes the surplus to be expected from what she learns. Eq. Ž4. thus implies that the representative individual will try to distribute her social activities across exchange institutions such that

ÝÝ i

Di j Ž u i j . y Ž 1 y u i j . DXi j Ž u i j .

j

s ÝÝ CiX j Ž u i j . q E Ž Di j . y Ž 1 y u i j . E Ž DXi j Ž u i j . . i

Ž 5.

j

where the left-hand-side represents the benefits of the reduction in incomplete beliefs in the jth institution and the right-hand-side is the direct cost, CiX j , and the

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change in opportunity costs of the incomplete beliefs in other institutions. Given that these gains and costs differ across institutions, and that the net gains in one institution do not dominate those of all other institutions, this implies that the representative individual will diversify her activities across institutions such that the marginal surpluses generated in each institution are equal. 10 It then follows that the total value of an environmental asset is the sum of the surpluses that exchange generates in multiple institutions rather than the surplus generated in any single institution. Simple Le Chatelier-type reasoning says that a singular focus on one institution like the nonstrategic, competitive market will cause the value of environmental improvements to be underestimated, and the harm from environmental degradation to be overestimated. Now consider the conditions under which individuals’ efforts to use markets and other exchange institutions will reinforce or discourage others’ efforts to organize and to participate in these institutions, thus to reduce incomplete beliefs. Consider a simple model where, with two individuals, A and B, we allow individual B’s organizing and participating efforts to affect those of A parametrically. One could view the model as if B selected his or her mix of institutions first, and then A selected hers. A’s surplus extraction problem while using the jth institution will then be max W A s ÝÝ K i y Ž 1 y u iAj . DiAj Ž u iAj , u iBj . y CiAj Ž u iAj , u iBj . i

Ž 6.

j

That is, B’s organizing and participation efforts in the institution influence both A’s incomplete beliefs and her costs of operating and participating. A’s first-order and second-order conditions for a given i and j are

ED A A

A

u : yŽ 1 y u .

A

Eu A

qD y

E CA Eu A

s0

Ž 7.

and

u Au A : y Ž 1 y u A .

E 2D A

Ž Eu A .

ED A 2

q

Eu A

E 2CA y

Ž Eu A .

2

-0

Ž 8.

Upon differentiating the first-order equilibrium conditions for A and B with respect to a parametric shift in B’s mix of exchange institutions, we get du A du B 10

u Au B sy

u Au A

Ž 9.

By now the reader will probably have remarked that we are in danger of being caught in a web of infinite regress in that we are treating complete beliefs as synonymous with rationality. However, we mean to apply the paradigm to the problem of establishing this degree only in the weaker sense of a purposeful, bounded rationality ŽSimon, 1973., which recognizes that consistent extraction of all potential surplus can require considerable effort while perhaps not producing much in the way of benefits.

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where

u Au B : y Ž 1 y u A .

E 2D A Eu AEu B

ED A q

Eu B

E 2CA y

Eu AEu B

Ž 10 .

Eq. Ž9. will be negative or positive according to whether E 2D A rŽEu A . 2 and E 2DrŽEu A Eu B . are positive or negative, given that organizing and participation costs increase at an increasing rate for A and B individually and jointly, i.e., E 2 C A rŽEu A . 2 and E 2 CrŽEu A Eu B . are positive. The principles of diminishing marginal productivity and increasing marginal costs imply negative signs for E 2D A rŽEu A . 2 and a positive sign for E 2 C A rŽEu A . 2 . By definition, E D A rEu A and E D A rEu B are strictly negative. The sign of Eq. Ž9. will therefore depend upon the signs and the relative magnitudes of the two cross-partial derivatives in Eq. Ž10.. Theses two cross-partials can be viewed as ‘market discipline’ variables in the sense that Becker Ž1962. and others have used the term. If their net effects cause Eq. Ž10. to be negative, then Eq. Ž9. will also be negative implying that B’s organizing and participation efforts will reduce those of A. With this complementary, A will not to have to reduce her incomplete beliefs as much as otherwise to extract a given potential surplus. Examples of this complementary in environmental settings are easily identified. The existence of people who are knowledgeable about the attributes of a recreation site allows unknowledgeable individuals to observe the choices of the knowledgeable and thereby enhance the surplus that the unknowledgeable can extract from the area. Alternatively, if the net effects of the cross-partial in Eq. Ž10. cause Eq. Ž9. to be positive, A will have to increase her efforts to overcome her incomplete beliefs whenever B organizes or participates in the exchange institution. In order to maintain her initial utility position, A will have to make her beliefs more complete. Increased efforts by B will result in reduced surplus extraction by A. Tournaments and zero-sum-like settings would qualify. In environmental settings, a situation in which A was seeking wilderness solitude when B enters the same area on a poorly muffled dirt bike might be a worthy example. One simple extension to this model would be to allow A and B to select strategically their optimal mix of exchange institutions simultaneously and noncooperatively. Comparing the noncooperative Nash equilibrium, provided one exists, to the cooperative solution would yield the results that overprovision of an exchange institution would be selected if the individual efforts are substitutable, while underprovision would exist if efforts are complementary.

5. Institutional choice, completeness, and coherence in nonmarket valuation The impact of incomplete beliefs on nonmarket valuation in survey settings can be better understood if: Ža. the individual is allowed to choose the exchange institution; and Žb. the researcher can measure whether the individual’s stated

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value is based on a complete and coherent set of beliefs. As discussed in Section 3, completeness implies that an individual’s selling price equals her buying price, and both equal the market price, if it exists. Coherence or the no-arbitrage condition implies that the individual does not accept a strictly negative gamble, i.e., a sure loss or Dutch book Žde Finetti, 1974; Smith and Nau, 1995.. Implementing the choice of an exchange institution or some mix of institutions is relatively straightforward—use a two-step procedure in which the individual first selects the institution that she would want to participate in, and then elicit her willingness to pay for the good in question. For example, Shogren and Crocker Ž1994. allow for the choice of exchange institution in risk valuation by allowing individuals to choose between private or collective self-protection or self-insurance. The values revealed in their lab experimentation suggested that private reduction was preferred to collective reduction, and that therefore, an exclusive focus on collective action would undervalue risk reduction. Kask and Shogren Ž1995. also allow survey respondents the choice of private or collective risk reduction from dioxin exposure, and observe significant differences in values. Allowing for the choice of multiple exchange institutions does complicate the individual’s decision problem, but there is a fundamental tradeoff between efficient but biased estimates of simplistic scenarios and inefficient, unbiased estimates of more realistic choices. Incorporation of an index of individual completeness and coherence in a survey

Fig. 2. Decision tree example for risk reduction.

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setting is more difficult, but not impossible. Using the idea of risk-neutral beliefs discussed in Section 3, a measure of complete and coherent decisions, the C and C index, can be integrated into a contingent valuation survey. To do so requires the introduction of a series of small ‘belief’ gambles conditional on decisions Žsee Nau, 1995.. To better understand how these belief gambles can be used, consider the decision tree in Fig. 2. The decision tree captures a simple example of a

Fig. 3. Risk-neutral beliefs: Coherence and completeness. Ža. Categories of beliefs; Žb. complete and coherent; Žc. incomplete and coherent; Žd. complete and incoherent; Že. incomplete and incoherent.

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valuation problem where an individual selects whether she prefers to reduce, privately or collectively, the risk from some environmental hazard. For simplicity, assume the private risk reduction strategy will reduce her risk by 10, 30 or 40%, while due to numerous uncertainties associated with collective action Že.g., rent seeking, free riding, corruption., she believes that one of three states Ž s1 , s2 , s3 . will occur—either a 5, 10 or 20% risk reduction will be achieved. In our simple binary case, the individual is first given the choice of employing either the private or collective strategy, and is then asked her willingness to pay for the level of risk reduction given the desired exchange institution. To determine whether the individual’s valuation was based on complete and coherent beliefs, the individual is also asked to answer a series of belief gambles conditional on the choice of risk reduction strategy. She is first asked to suppose that private risk reduction has been selected, and then is asked to state the set of de Finetti prices at which she would both buy, pi , and sell, qi , lottery tickets paying US$1 in the event that states s1 , s2 , or s3 occur. These stated buying and selling prices represent the distribution of risk-neutral beliefs given that private protection was selected. For each exchange institution, these prices Ža. must be equal, pi s qi for complete beliefs to obtain, and Žb. sum to unity, Ý pi s 1 and Ýqi s 1, for coherent beliefs. Fig. 3 illustrates the four potential categories an individual could fall in for each institution, and the corresponding implications for beliefs in the unit simplex as discussed in Section 3. In our example, suppose the individual reveals that her set of de Finetti buying and selling prices for private reduction are respectively p s Ž0.2, 0.3, 0.5. and q s Ž0.2, 0.3, 0.5.. Since these prices are equal and sum to unity, the individual’s beliefs are both complete and coherent ŽFig. 3b.. For the collective case, say the revealed prices are p s Ž0.1, 0.2, 0.4. and q s Ž0.2, 0.4, 0.5., implying that the individual’s beliefs are incomplete and incoherent ŽFig. 3e.. Three fundamental questions are raised by the ability to measure the completeness and coherence of each respondent’s beliefs. First, to what degree should the willingness to pay or accept revealed by individuals with incomplete and incoherent beliefs matter in benefit–cost analysis? Second, what percentage of individuals with incomplete and incoherent beliefs is needed before consumer sovereignty is replaced by expert judgement? Third, given that belief completeness and coherence are endogenous to institutions, to what extent should policymakers exercise discretion over institutional choice? 11 We do not propose to answer these questions here, rather we ask then in the spirit of stimulating further thought on the appropriate role of consumer sovereignty in environmental policy.

11

The evaluating circularity that this question introduces has been recognized at least since Scitovsky Ž1941..

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6. Conclusion This paper views the individual as having incomplete beliefs that impose upon her an opportunity cost of foregone surplus. Only by incurring the costs of making and participating in exchange institutions can she extract some portion of that surplus over and above that which she can extract as an unsocialized individual. 12 The exchange institution provides the gravity to pull together her rationality. This gravitational pull keeps the individual tightly focused on the economic decision at hand, and on the consequences of deviations from rational, self-interested behavior. Because the most visible and well-understood exchange institution, the competitive market, has relatively little role in arbitraging environmental assets, incomplete beliefs perhaps have a more prominent role in individuals’ value expressions for environmental assets than for most other goods. Alternatively, in the absence of the market, individuals may seek out a variety of distinctive institutional arbitrage devices such as public dialogue and other ‘nonmarket’ forms of social activity that reconcile different value perceptions. In either case, a public policy focus for environmental assets upon the findings of benefit–cost analysis narrowly interpreted in terms of the real individual’s hypothetical, impeccable utility maximization is highly problematic and plausibly self-defeating. It likely neglects many economically efficient avenues through which values are expressed and arbitraged, and therefore made observable. Constraining people to be anonymous price takers when they prefer to express their values via other avenues causes the value of environmental improvements to be underestimated. Public policymakers who disregard the values expressed in these alternative avenues of exchange and who fail to alert people to opportunities for their formation likely forego social surplus. Recognition of the opportunities that exchange institutions in addition to the competitive market provide for exchange and rational, critical value articulation obviates the demand to invent and accept value schemes built upon incommensurability ŽAnderson, 1990. and ‘objective’ phenomena ŽGeorgescu-Roegan, 1979.. Such recognition has the potential to devolve environmental decision-making from would-be cultural elites or centralized bureaucracies peopled by benefit–cost technocrats to gatherings of ordinary people who have been encouraged to engage in exchange. Under the perfect competition whose complete belief data benefit–cost analysis tries to emulate, there is no room for bargaining, negotiation, remonstration, or mutual adjustment. The various individuals that contract together need not enter into continuing or recurrent relationships with one another. Yet solutions to

12

Grossman and Stiglitz Ž1980. identified plausible cases where the presence of these complementarities induces free-riding on the efforts of others to make markets and other exchange institutions that encourage rationality. Thus, rationality may be underprovided, implying the desirability of public interventions that encourage the formation and operation of exchange institutions.

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the consumption indivisibility and open access properties that are the root causes of environmental problems require the ‘ voice’ strategies rather than the ‘exit’ strategies that dominate market exchange ŽHirschman, 1970.. The exit strategy is arguably less capable of reducing incomplete beliefs for environmental assets than is a broad collection of voice strategies. Because of coordination costs, the exit strategy may do less ‘‘ . . . to induce that ‘wonderful concentration of the mind’ akin to the one Samuel Johnson attributed to the prospect of being hanged’’ Žp. 21 of Hirschman, 1970.. If so, it follows that greater insight will be acquired into the magnitude of the potential surpluses from environmental commodities by developing tools to infer values from voice strategies rather than always presuming that the exit strategy that rules the competitive market is consistently the most revealing belief revelation strategy. Nevertheless, tradition and habit may cause a singular focus on the exit strategy to persist in nonmarket good valuation exercises. If so, by communicating explicit measures of the belief completeness and coherence of the human subjects of the exercise, practitioners can provide the decision makers who will use the reported valuation results a further basis for judging their reliability.

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