THE COASE THEOREM
Steven G. Medema
Associate Professor of Economics, University of Colorado at Denver
Richard O. Zerbe, Jr.
University of Washington - Graduate School of Public Affairs
© Copyright 1998 Steven G. Medema and Richard O. Zerbe Jr.
The Coase theorem has evolved from an illustrative argument in Ronald Coase's"The Problem of Social Cost" to a centerpiece of the modern law and economicsmovement. Along the way, the theorem has generated an enormous amount ofcontroversy and discussion, including numerous theoretical attempts at proofand disproof and empirical and experimental analyses of the theorem'sapplicability. This essay surveys the literature surrounding the Coase theoremand presents an outline of the major issues within the Coase theorem debate. Indoing so, it attempts to assess the validity of the various challenges to thetheorem's correctness and the implications of those challenges for the theorem'sapplicability, which is a separate issue. The analysis presented here illustratesthe importance of transaction costs and property rights within the Coaseanbargaining process and the need for further research along these lines to fleshout their implications law and economics.
JEL classification: K00
Keywords: Efficiency, Externalities, Invariance, Property Rights
Ronald Coase's seminal essay, 'The Problem of Social Cost' (1960) , is one ofthe most cited articles in the economics and legal literatures, and much of thisattention is owed to a proposition that has come to be known as the CoaseTheorem. While the Coase Theorem is by no means the only idea containedwithin that essay, it has captured the attention and interest of economists andlegal scholars as have few other ideas. (For useful treatments of 'The Problemof Social Cost' as a whole, see Zerbe (1976) , Schlag (1986) , and Medema(1996a) ; for context, see Coase (1937 , 1959) .) Coase argued that, from aneconomic perspective, the goal of the legal system should be to establish apattern of rights such that economic efficiency is attained. The legal systemaffects transactions costs and the goal of such a system is to minimize harm orcosts, broadly conceived ( Coase, 1960, p. 2 ). With this in mind Coase (1960,pp. 2-15) demonstrates the importance of transaction costs by considering thenature of bargaining or of contracts that could be stuck by using an example ofcrop damage caused by straying cattle. He noted that negotiations amongaffected parties would result in an efficient and invariant outcome under thestandard assumptions of competitive markets (especially, that the costs oftransacting are zero), as long as rights are well-defined. Specifically, it isnecessary to know whether the damaging business is liable or not for damagecaused since without the establishment of this initial delimitation of rights therecan be no market transactions to transfer and recombine them. But the ultimateresult (which maximises the value of production) is independent of the legalposition if the pricing system is assumed to work without cost ( Coase, 1960, p.8 ).
This is as close as Coase comes in his essay to stating what has come to beknown as the Coase Theorem.
Although Coase had set forth this idea already in 'The Federal CommunicationsCommission' ( Coase, 1959, p. 27 ), the first formal statement of the CoaseTheorem did not come until 1966, when George Stigler (1966, p. 113) offeredthat 'The Coase theorem ... asserts that under perfect competition private andsocial costs will be equal'. Subsequently, the Theorem has been stated innumerous ways, including:
... if one assumes rationality, no transaction costs, and no legalimpediments to bargaining, all misallocations of resources would befully cured in the market by bargains ( Calabresi, 1968, p. 68, emphasisin original ).
... in a world of perfect competition, perfect information, and zerotransaction costs, the allocation of resources in the economy will beefficient and will be unaffected by legal rules regarding the initial impactof costs resulting from externalities ( Regan, 1972, p. 427 ).
If transaction costs are zero the structure of the law does not matter becauseefficiency will result in any case ( Polinsky, 1974, p. 1665 ).
... if there were (a) no wealth effects on demand, (b) no transaction costsand (c) rights to pollute or control pollution, the allocative solutionwould be invariant and optimal, regardless of the initial assignment ofrights ( Frech, 1979, p. 254 ).
In a world of zero transaction costs, the allocation of resources will be efficient,and invariant with respect to legal rules of liability, income effects aside ( Zerbe,1980, p. 84 ).
... a change in a liability rule will leave the agents' production andconsumption decisions both unchanged and economically efficientwithin the following (implicit) framework: (a) two agents to eachexternality bargain, (b) perfect knowledge of one another's (convex)production and profit or utility functions, (c) competitive markets, (d)zero transactions costs, (e) costless court system, (f) profit-maximizingproducers and expected utility maximizing consumers, (g) no wealtheffects, (h) agents will strike mutually advantageous bargains in theabsence of transactions costs ( Hoffman and Spitzer, 1982, p. 73 ).
... when parties can bargain together and settle their disagreements bycooperation, their behavior will be efficient regardless of the underlyingrule of law ( Cooter and Ulen, 1988, p. 105 ).
... a change in [law] affects neither the efficiency of contracts nor thedistribution of wealth between the parties ( Schwab, 1988, p. 242 ).
While in many ways similar to one another, these statements of the Theoremcontain important differences, many of which are at the heart of the theoreticaldebates over the Theorem.
Nonetheless, a casual reading of these statements reveals two general claimsabout the outcomes. The first is that, regardless of how rights are initiallyassigned, the resulting allocation of resources will be efficient. This proposition-- the 'efficiency hypothesis' -- is reflected in all statements of the Theorem.The second claim, which is not reflected in all statements of the Theorem, is thatthe final allocation of resources will be invariant under alternative assignmentsof rights. This is the so-called 'invariance hypothesis'. The debates over thecorrectness of the Coase Theorem, and/or its proper form, have turned on bothof these hypotheses, and this struggle has been manifest in the current tendencyto appeal to two different versions of the Theorem -- the 'strong' version, whichencompasses both the efficiency and the invariance propositions (reflected inthe statements of the Theorem by Regan, Frech, Zerbe, and Hoffman andSpitzer, quoted above), and the 'weak' version, which encompasses theefficiency proposition alone (reflected in the statements of the Theorem byCalabresi, Polinsky, and Cooter and Ulen, quoted above).
For economists -- Coase's target audience ( Coase, 1988 , 1993 ) -- theimplication of the Theorem is that if remedies are considered in the unrealisticworld in which competitive markets are normally considered, a world of zerotransactions costs, the Pigouvian remedies said to be necessary for an efficientresolution of externality problems are not, in fact, necessary. All that is neededis a common law or statutory rule which assigns rights over the externality toone party or another. The market/pricing mechanism will then function in thesame way as it does for ordinary goods and services over which rights areclearly defined. Furthermore, if rights are well-defined, the observed situationwill be efficient (the parties having taken all Pareto-improving steps) and anyfurther intervention (e.g., Pigouvian remedies) will make matters worse ratherthan better.
If the implications for the economics of externalities are heretical, those forlaw are downright perverse, for the Theorem tells us that the form of legal rulesdoes not matter -- only their presence or absence. Thus, we will have the sameamount of pollution (and thus clean air or water) and of outputs associated withthe generation of pollution regardless of whether polluters or the victims ofpollution are made liable for pollution damage. The same amount of effort willbe devoted to precaution against causing torteous injury regardless of whetherinjurers or victims are liable for harm caused. The structure of law pertainingto breach of contract will have no impact on the allocation of resources throughthe contracting process. Attempts by judges to engage in social engineeringfrom the bench will be fruitless, apart from distributional (as opposed toallocational) effects. Assuming that rights are alienable, the allocation ofresources will be the same regardless of the rule of the law, and that allocationwill be efficient. More generally, it is a matter of indifference whether courtsimpose property rules or liability rules ( Calabresi and Melamed, 1972 ), and theentire issue of adherence to precedent becomes a moot point in terms of itseffect on the allocation of resources.
The Theorem has never been formally proved. Arguments regarding itscorrectness or incorrectness generally consist of attempts to demonstrate that itdoes or does not hold in a particular context or under a certain set ofassumptions. Of particular import here is the framework within which thereallocations of rights contemplated by the Theorem are assumed to take place.Two basic frameworks can be identified: the 'quasi-competitive' framework,within which all relevant markets are assumed to be perfectly competitive andagents operate more or less along competitive lines in externality negotiations,and the 'game-theoretic' framework, within which there exists the potential forstrategic behavior among affected parties. We examine each of these in turn.
Most of the analysis of the Theorem has taken place within thequasi-competitive framework, under which are two different types of treatment.First, there are discussions of small numbers externality negotiations within amore broad competitive context of full information, no strategic behavior,agents operating within competitive markets, etc., with the result that partiesstrike mutually-beneficial bargains when they are available. This is analogousto the standard Edgeworth box analysis and is the environment contemplated byCoase in 'The Problem of Social Cost'. The second type of treatment actuallyassumes competitive markets in externality rights and analyzes the Theorem onthat basis. In the latter case, the first optimality theorem of welfare economicssuggests that the Coase Theorem is correct ( Arrow, 1969 ).
One of the earliest but merely technical arguments raised against the Theoremis that it cannot hold under perfectly competitive conditions in the long runbecause it pre-supposes rents that may not exist. To consider the objectionsuppose that both the polluter and the victim are in a zero-profit, long-runequilibrium position. (For expositional simplicity, in the following discussionwe will refer to the parties as 'polluters' and 'victims'. The analysis, of course,generalizes to all manner of externalities.) Then, the assignment of liability tothe polluter will force the polluter to cease operations, since it lacks theresources with which to make liability payments to the victim. Similarly, if thevictim is made liable, it will exit the market because it lacks the resources tobribe the polluter to reduce its harmful activity. Thus, it is argued, the CoaseTheorem will only hold in the presence of 'non-transferable resources givingrise to Ricardian rents' ( Wellisz, 1964, p. 351 ). It has been further argued thateven the prior existence of rents would not ensure the validity of the CoaseTheorem: the rents must be sufficient to support the externality -- that is,sufficient to allow the polluter to pay damages (if he is liable) or the victim topay the bribe (if the victim is liable); otherwise, a change in the direction ofliability will cause the party bearing the cost of the externality to exit theindustry ( Tybout, 1972 ; Shapiro, 1974 ). Let us analyze these claims.
Suppose that the polluter is not earning rents and that he is liable for damagecaused. Then, the polluter will be forced to go out of business in the long run,as he does not have the resources necessary to pay damages. This result isefficient since the externality existed inefficiently in the first place: the polluterwas able to inflict damages on the victim only because he did not bear the fullsocial cost of his actions. If the polluter is not liable for damages, the victimswould be willing to offer a bribe up to the amount of damage to induce thepolluter to cease operations, a bribe which the polluter would be willing toaccept since it was not earning any rents in the first place. Thus, whether thepolluter or the victim is earning no rents, we get the same, efficient, resultregardless of the assignment of rights.
If neither party is earning rents sufficient to support the externality, theexternality would not exist in the first place; the appearance of the externalitywould immediately drive the victim out of business and the externality wouldcease to exist. (See Wellisz (1964, p. 350) , Crain, Saurman, and Tollison(1978) , and Zerbe (1980, pp. 89-90; 99 at note 4) .) Thus rents must exist fornegotiation over rights to even be in the realm of possibility; that is, they areprior to the Coase Theorem analysis. But once they are satisfied, an efficientand invariant result will obtain.
The one case in which rents are not necessary is for externalities that areindustry-wide in their emission and public bads in their effects (so that all firmsin an industry are affected). Here, assuming that all firms are harmed equally (interms of the effect on marginal and average costs), the externality acts in amanner analogous to an increase in input prices, causing an increase in marginaland average cost, a reduction in supply, and an increase in market price. Theresult will be invariant under alternative rules of liability.
One of the most discussed challenges to the Theorem concerns the effect ofliability or bribe payments on entry into markets. If polluters are made liable fordamages, the flow of liability payments into the victim industry will increase therate of return in that industry. If one assumes that firms entering the market arealso eligible for compensation, then entry will occur in the long run, leading toan increase in the output of the victim industry. When victims are liable, incontrast, the flow of bribe payments from victims to polluters raises the rate ofreturn in the polluting industry, leading to entry into that industry and acorresponding increase in output. The arguments here are two: first, that theinvariance proposition fails to hold because of the disparate entry effects ofalternative legal rules; second, the efficiency proposition fails to hold becausewhen polluters are liable the bribe-induced entry will result in too much victimoutput, relative to what is optimal, while when victims are liable thebribe-induced entry will result in too much polluter output, relative to what isoptimal. (See Calabresi (1965) , Bramhall and Mills (1966) , Tybout (1972) , Baumol (1972) , Schultze and d'Arge (1974) , and Frech (1979) .)
The inefficiency issue is easily disposed of. First, if transaction costs arezero, agents are rational, and there are no legal impediments to bargaining, thenthe long-run inefficiency will be cured through the same type of bargainingtransactions that were employed to resolve the short-run inefficiencies causedby the externality ( Calabresi, 1968, p. 67 ). That is, available gains fromexchange will be exploited in the long run just as they are in the short run.Second, following Nutter (1968) , any long-run misallocation will be cured bya single owner who will enter the market in order to exploit the potential forgain. Third, the above argument assumes the existence of a single efficientlong-run equilibrium point (and thus that efficiency implies invariance), when,in fact, such need not exist. Here, the long-run equilibria are both efficient, andthus the subsequent corrective negotiations or entrepreneurial actions areunnecessary. That is, long-run entry effects do not invalidate the efficiencyargument.
The more difficult issue is that of invariance. While the above argumentagainst invariance would appear to be straightforward, consider the followingcounter-argument. Suppose that ranchers are liable for damage done by theircattle. The flow of liability payments will then be capitalized into the value offarmland that adjoins ranching property and there will be no incentive for entryinto farming in order to secure the bribe. In analogous fashion, any bribes thatresult from farmer liability will be capitalized into the value of ranchland thatadjoins farms, and there will be no incentive to enter ranching. Given this, thelong-run entry effects that are said to invalidate the invariance proposition willnot occur ( Demsetz, 1972a ; Frech, 1979 ).
The key to distinguishing between these competing claims regardinginvariance has been provided by Holderness (1989) , who pointed out thatinvariance turns on the issue of whether rights are assigned to open or closedclasses of individuals or entities. An open class is defined as one into whichentry is unrestricted, while a closed class is one which can be entered only if theright is purchased from a current class member (see also Demsetz, 1972b,229-231 ). Consider first the assignment of rights within closed classes.Landowners constitute a closed class since one can become a landowner onlyby purchasing the land and the attendant bundle of rights from a currentlandowner. The assignment of rights to one class of owners creates at once awindfall gain for those having the right and a windfall loss for those not havingit. However, in a competitive system these windfall gains and losses areimmediately capitalized into the value of the land so that both types of land yielda normal rate of return. Since the rate of return for each of these types of landis unaffected by the assignment of rights, there are no incentives for entry orexit. Thus, the invariance proposition holds for closed classes ( Holderness,1989, pp. 183-184 ).
The invariance claim does not hold for open classes, however. Holdnerness'separation of open from closed classes calls attention since to a broad categoryof spurious objections all based on incomplete property right specification.Here, those who are not parties to the lawsuit through which the initialassignment of rights is generated can acquire that right costlessly merely byentering, and this valuable right will not be capitalized into the price of anyresource. Entry will indeed result ( Holderness, 1989, p. 185 ). Similarly, theabsence of a right reduces the returns to that activity, thereby inducing exit. Theasymmetric entry/exit effects across alternative assignments of rights will thusresult in different long-run outputs under alternative assignments of rights,thereby negating the invariance proposition.
This distinction illuminates the divergent results obtained by many of thoseoffering support for or claiming to refute the invariance proposition. Those whohave found the invariance proposition to be valid in this (the entry issue) contexthave either explicitly or implicitly assumed or worked with examplesconstituting closed classes. On the other hand, those finding against invariancehave analyzed the problem in open-class contexts -- primarily situations withtwo industries where entry is possible. The invariance proposition is applicableto closed class situations, such as externalities affecting land values, but isinapplicable to tort situations, such as accident law, where there is free entryinto one or both classes and to assignments of rights which cover all (currentand future) entrants into an industry.
The open class case, however, would seem to violate an underlyingassumption of the Coase Theorem -- fully-specified property rights. That is,rights in open classes are not delimited to the extent necessary to make markettransactions possible; potential entrants are able to secure a valuable rightwithout paying for it. This is consistent with Barzel's (1989, p. 2) definition ofproperty rights as 'the powers to consume, obtain income from, and alienate ...assets', and Allen's (1995, p. 2) definition of an 'economic property right' as' one's ability, without penalty, to exercise a choice over a good, service, orperson ' (emphasis in original). In fact, the assumption of zero transaction costsis said by some to mean that rights are fully specified (see Cheung (1992) , Allen(1991 , 1995) , and the discussion in section 6 , below). As such, the issue ofincompletely specified rights, or open classes, goes to the issue of relevancerather than correctness.
Another class of interesting objections is based on a failure to consider fullycontract or merger possibilities. It has been argued, for example, that the validityof the efficiency (and invariance) proposition will turn on (in addition to otherpreviously-recognized problems) the form of the cost function of the victimfirm. It is well established that, if the victim's cost function is additivelyseparable (that is, if C B = C(q A , q B ) = C(q A ) + C(q B )), then the Coase Theoremholds -- the outcome is both efficient and invariant under alternativeassignments of rights (see Marchand and Russell (1973) ; Gifford and Stone(1973) ). Suppose instead, however, that the victim's (B's) costs of productionare dependent upon both its own output and the output of the polluting firm (A),so that C B = C(q A , q B ), where the pollution damage owing to firm A's outputincreases the costs of firm B.
With a non-separable cost function there is neither efficiency nor invariance.With a non-separable cost function, the level of pollution damage to B is afunction not just of A's output, but of B's output as well, and thus a given levelof output by A causes B more harm (i.e., causes a greater increase in B's costs)the more output B produces. In such a situation, the victim can and doescontribute to its own damage without having to bear the cost, since it is fullycompensated for all damage. As a result, the victim has no incentive to mitigatedamages and produces an inefficiently high level of output. Moreover, thedamage liability associated with this imposes a higher than optimal cost on thepolluter, causing it to restrict its output below the optimal level ( Marchand andRussell, pp. 613-615 ).
However, if both activities are controlled by a single owner, the result willbe efficient and invariant regardless of the initial assignment of rights andirrespective of whether the victim's cost function is separable or non-separable( Marchand and Russell, 1973, pp. 614-616 ). Moreover, one can imagine acontract between owners that mimics the effect of single ownership assumingcosts of monitoring and negotiation are zero. This demonstration is sufficientto negate the nonseparability critique, since the inefficiency contemplated willbe exploited through merger, which can be achieved costlessly, or by anentrepreneur (see, for example, Nutter (1968) , Coelho (1975) , and Zerbe (1980,pp. 87-88) ). Marchand and Russell (1975) have responded to this criticism byinvoking difficulties in carrying out a merger -- that is, by introducingtransaction costs. But introducing transaction costs is no argument against thecorrectness of the Coase theorem. A further argument that can be raised againstthe nonseparabilities critique is that it violates the assumption of fully-specifiedproperty rights (at least in the sense of Allen (1991 ; 1995) ), since the victim isable to procure revenues from the polluter without giving up anything in return.
Perhaps the one seemingly insurmountable criticism of the invarianceproposition comes from the recognition by Starrett (1972) that externalities willcause nonconvexities to exist in the production sets of victim firms. (See also Shapiro (1974 , 1978) , Editorial Addendum (1977) , and Vogel (1987) .) Theargument applies equally to consumption sets, and thus to externalities to whichconsumers are party.) This objection is similar to that of non-separable costfunctions in calling attention to a contacting problem. This is an interestingobjection because it points to the importance of information costs. In graphicalterms, rather than generating a convex production set, such as in Panel (a) ofFigure 1, below, the externality causes nonconvexities of the form illustrated in(b).
Here, q B is the output of firm B, the victim, and Z is the level of theexternality. The analysis turns on the effect of increasing pollution damage onthe victim's output. Panel (b) illustrates a situation of increasing marginaldamage from pollution (given by the reduction in the victim's output due to theexternality) with the recognition that, beyond some point (Z 0 ), marginal damagewill be zero ( Starrett, 1972, pp. 189-190 ).
The import of this for the Coase Theorem is as follows. Suppose that thepolluter's (A's) profit-maximizing level of pollution in the absence of the legalrule is some level Z 1 > Z 0 . With this level of pollution, B will produce no output.If the A has the right to pollute, the point Z = Z 1 , q B = 0 is the starting point fornegotiation over the level of pollution. The minimum payment that the polluteris willing to accept to reduce pollution is the reduction in profits that wouldaccompany the reduction in pollution. However, at (and around) Z 1 , there is nobenefit to the victim from a one unit reduction in pollution; the victim's output(q B ) would remain at zero with this one unit reduction in pollution. Thus, thevictim would not be willing to offer a bribe payment to induce the polluter toreduce its pollution by one unit (to Z 1 - 1 units) -- it is a cost with no attendingbenefit. Thus, the equilibrium when the polluter has the right to pollute will beat a pollution level Z = Z 1 and an output level for the victim of q B = 0, a resultwhich is due to the nonconvexity.
On the other hand, if the victim has the right to be free from pollution, thebaseline from which negotiation begins is Z = 0. The victim will be willing toaccept any bribe to allow positive levels of the pollution if the bribe is in excessof the lost profits due to pollution damage (or reduction in q B ). Thus, the partieswill be able to negotiate to an efficient result along standard Coasean lines, butthe final result will not (except by accident) be Z = Z 1 and q B = 0. Thus, theinvariance proposition does not hold in the presence of nonconvexities if thestarting point for negotiation when the polluter has the right to pollute fallswithin the non-convex region of the victim's production set. However, if theinitial level of pollution is some level Z < Z 0 , the invariance proposition holds.(See Cooter (1980) for a discussion of how legal rules can be specified tocircumvent the nonconvexity problem).
The force of this critique is sufficiently powerful that the editors of the Journal of Economic Theory said that Starrett's demonstration thatnonconvexities are inherent in externality problems 'destroy[s] the validity ofthe Coase Theorem' (Editorial Addendum, 1977, p. 222) . However, thisjudgment fails to understand the true nature of a fully transaction costs world.There is a Pareto-better point available, but the nonconvexity means that theparties will fail to reach it because the immediate marginal adjustments are notPareto-better. Essentially, the point is that the victim will not be able to spend15 dollars for a change that will make it 20 dollars better off because the firststep along this path would involve spending a dollar to get a zero improvementin welfare, and the victim, not being willing to take this first step, will neverknow that better things are on the horizon. The problem here is one ofinformation: it is certainly the case that the victim would take this first,welfare-reducing step if it was certain that, in the end, it would be better off. Ifboth victim and polluter knew of the existence of a superior position they couldalso merge to achieve it. Thus, the nonconvexities argument introducesimperfect information into the model. If, as most have maintained, informationcosts violate the zero transaction costs assumption of the Coase Theorem,fundamental non-convexities do not produce inefficiency. The non-convexitycritique of the Theorem points to the importance of information costs, but, ifthese are considered as part of transactions costs, it does not point to theincorrectness of the Theorem itself.
An additional complication B first hinted at by Buchanan and Stubblebine(1962) and Turvey (1963) and later more explicitly elaborated by Dolbear(1967) and Mishan (1965 , 1967 , 1971) within the economics literature and by Kelman (1979) within the legal literature B is introduced when one or bothparties to the externality are consumers, for, at this point, we are forced to takeaccount effects on demands that attend alternative assignments of rights. Theseeffects arise, first, from differences in tastes between parties, and, second, fromdifferences between the willingness to pay (WTP) and willingness to accept(WTA).
Differences in Tastes . If tastes are different, (that is, as long as indifferencecurves are not homothethic) a change in the income distribution will affect thepattern of demand and therefore the pattern of resource allocation, though notits efficiency. That is, alternative assignments of rights can have differentialeffects on the structure of demands for consumer goods. Since differentassignments of rights result in different distributions of income, the compositionof demands -- and hence equilibrium prices and quantities across markets -- willvary with alternative assignments of rights. For example, suppose that aneconomy produces only beef and fish, and that fertilizer runoff used to producegrass, an input into beef production, reduces fish production. Those thatproduce beef prefer to eat beef and those that produce fish prefer fish. A changein the liability rule from one in which beef producers are liable to one in whichthey are not will increase incomes of beef producers and reduce incomes of fishproducers. This will then increase the demand for beef and reduce the demandfor fish; thus, the relative production of beef and fish will not be invariant to theliability rule. This objection to the strong version of the Theorem is wellrecognized. But, we shall see that even this objection pre-supposes incompleteproperty rights.
Differences Between WTP and WTA . A change in the law can change the senseof ownership and thus change the measure of value from the WTP to WTA orvice versa. Following Willig (1976) , economists have tended to assume that anydifferences between willingness to accept (WTA) and willingness to pay (WTP)owing to a price change are small. This is now recognized as untrue in importantcases. For environmental goods, researchers have demonstrated repeatedly thatWTA questionnaires generate values from two to nineteen times greater thanthose elicited by WTP questions ( Levy and Friedman, 1994, p. 495 at n. 6 ; Hoffman and Spitzer, 1993, pp. 69-85 ). There are three reasons for thedifference: income effects, substitution possibilities, and loss aversion.( Hoffman and Spitzer (1993) present an excellent survey of the WTA v. WTPissue, much of the evidence regarding which comes from the experimentalliterature. The present discussion touches on what we believe to be the mostsignificant of these arguments.)
Let us first consider the implications of income effects. If most peopleexperience diminishing marginal utility of income, the utility loss resulting froma reduction in income of a certain amount is greater than the utility gainassociated with an increase in income of the same amount. Thus, if individualsbargain over utility, rather than over wealth per se , we would expect to seedifferences between WTA and WTP, and thus negotiated solutions that varywith the initial assignment of rights ( Hovenkamp, 1990 ). This is an incomeeffect. For example (and assuming that A, the polluter, is a firm, so that wealtheffects are irrelevant for it), if B (an individual) has the right to be free frompollution, then the amount of pollution generated will be a function of thepayment that he is willing to accept to avoid pollution. If B does not have theright to be free from pollution (i.e., A has the right to pollute), then the amountof pollution generated will be a function of the amount that B is willing to payto avoid pollution. Since the maximum amount a person is willing to pay toavoid damages is a function of his budget constraint, while there is no suchconstraint on the amount that the individual is willing to accept, we will see (aslong clean air is a normal good) a difference in the amount of pollution, and thusin pollution-related output, depending on the initial assignment of rights( Mishan, 1971, p. 19 ). Thus, the invariance proposition will hold only whenincome effects are not present or when all relevant income elasticities ofdemand are zero.
The force of the income effects critique has been reflected in one of the fewmajor modifications of the standard structure of the Coase Theorem: theaddition of the assumption of no income effects or the qualifier 'income effectsaside', as reflected in several of the statements of the Coase Theorem set outabove. The use by some of the weak rather than the strong version of theTheorem is also attributable largely to the role that income effects play innegating invariance.
Consider next the issue of substitution possibilities. Recently, Hanneman(1991) showed that the poorer the substitutes for the good, the greater thedivergence between the WTP and the WTA. Put another way, the divergencewill be greater the more unique the good. The substantial divergence betweenWTP and WTA for unique goods arises in part from the fact that many of thesegoods have no close substitutes. Thus, for most people, the WTA to allowdegradation of the Grand Canyon will be much greater than the WTP to preventdegradation for most people. A change in the law that results in a change froma WTP to a WTA criteria will have dramatic effects in the measure of value forthe good. Zerbe (1998a) and Cohen and Knetsch (1992) have argued that thecorrect measure of damages as between the WTP and WTA is, however, afunction of the psychological reference point which may not correspond withthe legal reference point. For example, Ellickson (1986) study of the responseto differing range laws shows such a difference. In one half of Shasta County,California, open range was the legal rule, and in the other half closed range wasthe rule. Yet in both parts of the County, in spite of opposite assignments ofliability, people expected and provided similar remedies. Cattle owners tookresponsibility for the damages in all cases, and this responsibility existed formany years and was enforced through social norms. The reference state was oneof crops not being damaged by straying cattle.
A further argument against the invariance proposition comes from theinfluence that alternative assignments of rights may have on WTA v. WTPthrough effects on consumer tastes and preferences. Here, the assertion is theconsumer tastes and preferences are not wholly exogenous to the structure oflegal rules but are influenced by them ( Zerbe, 1996 ). Prospect theory posits thatindividuals have a value (rather than utility) function which is convex for gainsand concave for losses and that the degree of concavity is greater than thedegree of convexity, so that losses of a given size are felt more acutely thangains of that same size ( Kahneman and Tversky, 1979 ). The link between thisidea and the WTA v. WTP argument is that the offer of money to relinquish aright would be treated as a loss, whereas the purchase of a right would beregarded as a gain. Since losses count more than gains, the minimum amountthat an individual would be willing to accept to relinquish a right will exceed theamount that he is willing to pay to acquire it ( Kahneman, Knetsch, and Thaler,1990 ). One reason for this loss aversion is suggested by what Thaler (1980) hascalled an 'endowment effect', owing to the fact that people value 'receivedincome' more highly than 'opportunity income'. Because of this, people will bewilling to forego more opportunity income to retain a right than they wouldspend in received income to acquire it and thus WTA will exceed WTP ( Thaler,1980 ; Kelman, 1979 ). Kelman attempts to apply this argument to the producerside as well, arguing that producers may value realized and opportunity incomedifferently. However, doing so would contradict the assumption of profitmaximization. Moreover, as Spitzer and Hoffman (1980, p. 1210) point out, aprofit-maximizing entrepreneur could (and, following Nutter (1968) , would)arbitrage this difference, thus generating the outcome implied by the Coasetheorem.
How important these forces are in creating a wedge between the WTP andthe WTA is as yet uncertain. At this point, however, it seems reasonable to saythat income and substitution effects and loss aversion are sufficient to invalidatethe invariance, although not the efficiency, claim of the theorem.
The above possible exceptions to the Coase Theorem represent importantcases, but do they really represent exceptions to the Coase Theorem? All of theobjections to the Coase Theorem that rest on consumer preferences rest on achange in the distribution of wealth. Yet, these arguments at base reflectproperty rights that are not fully specified or are inefficiently specified. Theseconditions then violate the Coase Theorem assumptions that property rights arefully specified.
Consider first a change in the rule of liability. If property rights are fullydefined (in the sense of complete ownership), this alteration of liability cannottake place without compensation; if it does, the right was not fully defined in thefirst place, in violation of the Theorem's assumptions. Thus, owing to thecompensation, the distribution of wealth will be unaffected ( Allen, 1995, p. 10 ).Allen's argument applies even to the income effects qualification. Of course,this rebuttal does not go to the case where non-existent rights are subsequentlydefined. However, in a world of zero transaction costs the definition of rightswould be perfectly anticipated and thus reflected in resource values ( Allen,1995, pp. 10-11 ). In sum, when alternative assignments of rights influence thedistribution of income and wealth, it must be the case that rights are less thanfully defined and/or that transaction costs are positive. Indeed, Allen (1991 ; 1995) has argued that fully-defined rights and zero transaction costs are reallythe same thing (see the discussion in section 6 , below).
Perhaps the most intriguing case is one suggested by the recent literature inwhich legal ownership is different from psychological ownership ( Zerbe, 1998a , 1998b ). Evidence suggests that a sense of ownership attends certainenvironmental goods even if there is no individual ownership. A decision to cutdown the last remaining stand of privately owned redwood trees, the HeadwaterGrove, may create a sense of loss among some that are non-owners of the grove.This loss is correctly measured by the WTA. If, however, a decision to measurethe value of the grove is based on legal ownership the value to the public willbe based on the WTP for preservation. Since for a normal good the WTP willbe less than the WTA, the grove may be cut when it should not. Property rightsare fully specified in this example so that it would appear to violate the strongversion of the Theorem.
However, Zerbe (1998a , 1998b) has noted that, although property rights inthis case are fully specified, they are inefficiently specified. He argues that' efficiency requires that the legal measure of property and damage correspondto psychological reference points '. Posner's (1992, p. 52) rule for the allocationof rights is a subsidiary of this theorem. This rule is that where one class ofclaimants values the right more than other classes, efficiency requires that theright should go to the claimants that value it the most.) If there is not acorrespondence between psychological and legal property rights, the use ofWTP and WTA based on legal criteria can impose net losses. Imagine that aparty, George, believes he owns a right or a property M, and that another party,Ronald, also believes that George owns property M. They discover that the law,however, holds that party George, not Ronald, owns M. Ronald suffers a lossof M psychologically and therefore economically, while George gains M. Sincelosses are, on the average, worth more than equivalent gains (due to income,substitution effects, and loss aversion), on the average George will gain lessthan what Ronald loses. This is perfectly general, so that the application of lawto affect a legal ownership different from psychological ownership must, onaverage, impose net losses (as long as Ronald and George may be regarded asequivalent in the sense that on average one does not have a greater income thanthe other or does not differ in some other relevant characteristic. Underlying thisproof is the notion that we cannot speak of it being efficient to changepreferences to be in accord with the law since this violates the proper contextfor benefit cost analysisYwhich requires that preferences be taken as theylieYand the very concept of efficiency. In any event benefit cost can notevaluate the advantages of a change in preferences since this does not takepreferences as they lie.) Similarly, if one class of claimant psychologicallypossesses property so that its removal is felt as a psychological loss, ascompared with a rival claimant who has a lesser psychological claim or noclaim, efficiency requires that the law grant the right to the psychologicalpossessor. But, in a zero transactions cost world this sort of inefficiency wouldnot arise since the law would be made to correspond with the psychologicalsense of ownership.
While the vast majority of the literature debating the validity of the CoaseTheorem employs the quasi-competitive framework, a number of commentatorshave addressed the Theorem from a game-theoretic bargaining perspective,arguing that that the quasi-competitive framework is not appropriate or relevantfor Coase Theorem-like bargains over rights owing to the small number ofparties contemplated and the potential for strategic behavior. (See, for example, Davis and Whinston (1962) , Samuelson (1966, p. 1141) , Shoup (1971, p. 310) , Regan (1972, p. 428) , and Cooter (1982, pp. 16-17) .) By placing the Theoremin a small numbers context but yet ignoring the potential for strategic behavior,it is presumed that the contemplated agreements 'can and will be reachedbecause it is in the joint interest of the parties to do so' ( Samuelson, 1985, p.322 ). Yet, this fails to consider the possibility that what is rational for the groupmay not be rational for the individual and constitutes, in essence, an ' a priori argument' for the Theorem ( Regan, 1972, pp. 429-431 ).
Several commentators (for example, Davis and Whinston (1965) , Arrow(1979) , Aivazian and Callen (1981) , Samuelson (1985) , and Aivazian, Callen,and Lipnowski (1987) ) have suggested that the Coase Theorem, as envisionedby its proponents at least, lends itself quite naturally to the theory of cooperativegames. It can be demonstrated that the Coase Theorem will always hold in atwo-person cooperative game. However, this result is not particularlycomforting since, by setting the problem in the context of a two-personcooperative game, efficiency is assured by definition (although there is noguarantee of invariance), making this more along the lines of an illustration ofthe Coase Theorem rather than a proof ( Schweizer, 1988, pp. 246, 254 ). In fact,much of the quasi-competitive literature (especially the two-person analysis)can, without too much injustice, be described as cooperative game analysis. Thesituation is complicated when the cooperative game involves more than twoplayers. While it has been suggested that the Theorem may not hold in such acontext ( Aivazian and Callen, 1981 ), this claim has been shown to be incorrect( Coase, 1981 ; De Bornier, 1986 ).
However, the most interesting, and potentially most damaging, game-theoreticanalysis of the Theorem has involved the use of noncooperative game theory.If parties have full information about each other's utility (or profit or productionand cost) functions, the Coase Theorem will hold in a noncooperative setting.The initial assignment of rights establishes the utility level of each player in theabsence of further reallocations of resources, and there are assumed to existreallocations of resources which are efficiency enhancing, in the sense that theutility of one player can be increased without reducing the utility of the otherplayer. However, neither party will agree to an alteration in the allocation ofresources unless that reallocation increases its utility. The question, from theperspective of the noncooperative game, is whether there exists a sequence ofpermitted moves which will generate an efficient (Nash) equilibrium. Supposethat A is given the right to pollute. Then the victim, B, has an incentive to offeran alternative allocation of resources (e.g., a combination of a bribe paid fromB to A and a reduced level of pollution by A) to A, but B knows that A willaccept this offer only if A's utility is increased under the new allocation. SinceB knows A's utility function, he can determine the range of allocationssufficient to garner A's acceptance. And, since B's utility is higher withreallocation than without, he will not offer an allocation that A would reject,choosing instead that allocation from the group A will accept which maximizeshis own utility. The resulting equilibrium is Pareto efficient, since, given theutility level of one player, the other player's utility is maximized. (As Arrow(1979, p. 29) points out, however, this is not the competitive equilibrium.) Thesame reasoning applies to the situation where the victim is given the right to befree from pollution ( Arrow, 1979, pp. 27-29 ; Schweizer, 1988 ). In fact, it is notnecessary for each party to enter the bargaining process with full information,only that each party perceives that there are net gains to it from providing fullinformation during the negotiation process and thus will reveal such informationduring that process ( Saraydar, 1983, p. 603 at note 12 ).
The problem, numerous commentators have pointed out, is that it is unlikelythat the players will know each others' respective utility (or profit, productionor cost) functions. This has a number of implications.
a. Implication One: The Baseline Problem
When victims are liable, the firm can influence the level of the bribe that itreceives by making an upward adjustment in pollution emission at the time thatthe baseline level of pollution (against which subsidized/bribe-induced pollutionreductions will be measured) is set or by choosing not to take cost-justifiedprecautions. That is, the level of pollution on which the bribe is based maydiffer from the level of pollution that would have been emitted if the polluterwas liable. The source of this incentive is the inability of the victim to ascertainwith certainty the true baseline level of pollution. Moreover, disagreements overthe baseline level of pollution may result in the failure to consummate bargainswhen the victim is liable. Conversely, if polluters are known to be liable fordamages, then, in the absence of full information about actual damages andmeasures taken by the victim to mitigate damages, the victim's moral hazard willresult in too few resources being devoted to precaution/mitigation by the victimand too many resources being devoted to abatement by the polluter ( Kamien,Schwartz, and Dolbear, 1966 ; Tybout, 1972 ; Harris, 1990 ). With endogenousliability assignment, however, the moral hazard problems disappear, since aparty does not know with certainty whether or not it will be forced to bear thecosts of the externality. Thus each party will act efficiently to minimizeexpected costs by engaging in the appropriate level of precaution/preventiveactivity ( Harris, 1990, pp. 701-702 ).
b. Implication Two: Extortion
Imperfect information raises the problem of extortion, which can arise in anumber of forms. First, and related to (1), above, polluters may threaten to emithigher levels of pollution in order to secure a larger bribe ( Mumey, 1971 ).Second, as Shoup (1971, pp. 310-312) has pointed out, potential entrants mayuse extortion: if externality generators are not liable, 'entrepreneurs' maythreaten to emit an externality in order to secure a bribe, or, symmetrically, ifexternality generators are liable, potential victims may threaten to 'come to theharm' in order to secure a bribe. If these threats necessitate the use of resourcesto establish credibility, the result will be inefficient. However, investingresources to establish credibility violates the zero transaction cost assumptionof the Theorem. Jaffe (1975, p. 661) offers a further counter to Mumey's result.The polluter will not wish to invest resources in making a threat which will notbe carried out, and the mere potential that it can carry out a threat will induce amore generous bribe. Moreover, this extortion argument implicitly assumes bothsufficient rents and an open class situation, and, on the latter ground, is subjectto the rebuttal noted above. Demsetz (1972a, p. 23) has also countered thiscriticism with the argument that competition for these gains will drive the priceof extortion to zero, so that extortion is not a barrier to the attainment of theefficient equilibrium. It should also be noted that Coase (1959, p. 27 at note 54) recognized that the employment of resources 'solely to establish a claim' couldpreclude the attainment of the efficient result.
Third, since there are multiple ways to divide the gains from a bargain andeach individual is interested in both achieving the benefits from cooperation andgetting as large a share of the benefits as possible for himself, there will bethreats of noncooperation in order to increase one's share of the gains. For thesethreats to be credible, however, they must occasionally be carried out, and, whenthis is done, the result will be sub-optimal ( Regan, 1972, p. 429 ). One can seeillustrations of what Regan (1972) has called the ' a priori argument' for theTheorem in the challenges to the extortion argument. For example, it is arguedthat the limits of extortion are set by the size of the available rents: if one partytries to extort from the other an amount greater than this, the other party couldsimply transfer its resources into their next-best use. The extorting agent, beingunwilling to forego the potential gain, will thus agree to a solution whichgarners for it an amount not in excess of the other party's rents. Thus, the onlydifferential impact of alternative legal rules will be on the distribution of rents;the final allocation of resources will be unaffected ( Boyd and Mohring, 1971 ; Demsetz, 1972a ; Feldman, 1974 ).
c. Implication Three: Private Information
While Davis and Whinston (1965, p. 118) argued early on that informationwould be revealed through the bargaining process, the application of morecomplex strategic thinking suggests that private information, if revealed, maybe used against one's self and thus adversely affect one's payoff. Given this,agents have an incentive to conceal information (through silence or lies) and toexpend resources both to protect the value of their own private information andto acquire information from/about others. These costs, and resultant delaysand/or failures to consummate mutually-beneficial bargains are likely topreclude the attainment of efficient negotiated solutions where information isasymmetrically distributed ( Cooter, 1982 ; Sutton, 1986 ; Farrell, 1987 ). Cooter(1982, pp. 17-18) even goes so far as to argue that an equally strong case can bemade that parties will never agree on the distribution of the surplus, even whentransaction costs are zero, a proposition that he labels the 'Hobbes Theorem'.However, he maintains that the ever-present strategic element is not as'insurmountable' as the Hobbes Theorem implies, nor as 'inconsequential' asthe Coase Theorem implies; in fact, he argues, 'gains from trade in bargainingsituations are realized more often than not' ( Cooter, 1982, p. 19 ). CentoVeljanovski (1982, p. 60) offers a theorem similar to Cooter's Hobbes Theorem-- the 'Johansen theorem', which holds that '[d]irect bargaining has an inherenttendency to dissipate the gains-from-trade through strategic behaviour'. (See Johansen (1979, pp. 515-520) ). Unlike Cooter, however, Veljanovski maintainsthat in a world of zero transaction costs the dissipation of gains is likely to bethe more common outcome.
A number of commentators have demonstrated the potential for bothagreement and non-agreement when information is imperfect. If neither party'sutility function is a function of the other's private information, then an efficientresult will be reached. However, if either party's utility function is a function ofthe other's private information, then there is no guarantee that an efficient resultwill be reached ( Schweizer, 1988, pp. 259-263 ). (See also Arrow (1979, pp.29-31) , Cooter (1982, pp. 20-24) , Samuelson (1985) , and Illing (1992) ). Ourdiscussion here will draw primarily from Cooter's analysis. Arrow andSamuelson reach conclusions very similar to Cooter, using the assumption thatthe parties are uncertain about each others' utility functions.) For example, Cooter (1982, pp. 20-24) points out that uncertainty regarding the opponent'sresponse causes each player to form a rational expectation of this response inthe sense of formulating a subjective probability distribution over hisopponent's moves. Given this rational expectation regarding his opponent'sstrategy, each player chooses for himself the strategy that maximizes hisexpected utility based on a comparison of the greater share of the gains fromtaking a harder line in bargaining with the higher probability that this harder linewill prevent an agreement from being reached. The problem is that, while eachplayer will be playing the strategy that is optimal against the distribution of itsopponent's possible strategies, this strategy is not necessarily optimal againstthe particular strategy played by the opponent. The outcome will be inefficientwhen players err in their predictions of the moves made by their opponents( Cooter, 1982, pp. 20, 23 ; Arrow, 1979, p. 31 ). In fact, Cooter contends thatzero transaction (communication) costs actually decreases the possibility ofreaching an agreement, in that it facilitates the transmission of threats and otherstrategic communications ( Cooter, 1982, pp. 23 ), although, as Arrow (1979) hasdemonstrated, it is possible to design a collective decision rule that will inducea truthful revelation of preferences.
If the situation involves large bargaining groups, two more potentialdifficulties arise. First, individuals will have an incentive to free ride and thusthe ability of the group to pay a bribe sufficient to induce the socially optimallevel of output/pollution will be greatly reduced. Second, if there are differentialdamage effects across victims, we may observe the rise of coalitions within thevictim group (e.g., by level of damage), each applying pressure to encourage theresult that best suits its interests. The greater is the number of coalitions, thesmaller is the likelihood that the optimal solution will be reached ( Wellisz,1964, p. 354 ). However, as the number of parties approaches infinity (with largenumbers of right-holders and large numbers of rights-seekers), the bargainingsolution here will approach the efficient result of competitive equilibrium( Samuelson, 1985, p. 338 ).
In sum, the likelihood of incomplete information gives us little reason tobelieve that the Coase Theorem is correct when specified in a noncooperativebargaining context. But while the game-theoretic critiques of the CoaseTheorem are suggestive of its demise, they have not gone unchallenged, largelyon the grounds that it is incorrect to place the Theorem in such a context. Atissue is what is meant by a world of zero transaction costs, to which we nowturn.
Perhaps the most sticky issue in the debate over the Coase Theorem is themeaning given to the assumption of zero transaction costs. Indeed, the veryconcept of transaction costs has been so vague and ill-defined that StanleyFischer (1977, p. 322 at note 5) was once led to remark that 'almost anythingcan be rationalized by invoking suitably specified transaction costs'. Coase's(1960, p. 15) definition of transaction costs encompasses those costs associatedwith search, negotiation, monitoring, and enforcement, which, as Dahlman(1979, p. 148) has noted, basically reduces to 'resource losses incurred due toimperfect information'. A bit more specificity (although even greater breadth)is found in more recent definitions within the property rights literature such as Barzel's (1989, p. 2) contention that transaction costs are the costs associatedwith the transfer, capture, and protection of rights', and Allen's (1991, p. 3) statement that they encompass 'the resources used to establish and maintainproperty rights'. Under these latter definitions, zero transaction costs impliescomplete property rights ( Allen, 1991 , 1995 ; Cheung, 1992 ). (See also Schlag,1989 ).
If we take the Barzel/Allen definition as the basis upon which to evaluate theCoase Theorem, three implications immediately follow. First, there is anunspecified property right that lies at the heart of the private informationexamples. For example, Farrell (1987) constructs a problem in which parties Aand B care about a time that is set. He notes that King Solomon would havelittle trouble finding the optimum value since he charges each party an amountequal to their effect on each other, and that a 'bumbling bureaucrat' can undersome circumstances find a superior (second best) result to that achieved underzero cost negotiations. The showing that a centralized authority can achieve anoptimum is, however, equivalent to showing that there is an unspecifiedproperty right. When A is allowed to set the time (about which both A and Bcare), B will prefer to not participate in bargaining since his gain is greater whenA just sets the time unilaterally, and B pays nothing. The advantage thatSolomon has is that he can force A and B to participate. Yet, in this example,B gets to use the time that A sets. For example, the time may represent the timefor beginning a race. Farrell's example assumes that B is nevertheless allowedto participate in the race. But, if the race is owned the owner will in fact chargeboth A and B, yielding the Solomon solution. Another analogy can be made toownership of a lake. The owner will charge each user at least the cost theyimpose on other users. Farrell implicitly assumes that government is the onlyowner of the lake. It is true that we can consider other examples in which theownership of the resource seems more foreign to our usual thinking, as when thetime represents a curfew or a time after which noise must be reduced--but thereis a lack of ownership none the less. These are simply examples in which theabsolute advantage of government with respect to certain sorts of enforcementcosts may support government ownership, but enforcement costs are alsotransaction costs.
Second, nearly all of the challenges to the Theorem's correctness areinvalidated under this conception of transaction costs, including entry,nonseparabilities, nonconvexities, and even wealth effects, as noted above.(This definition of transaction costs also invalidates other challenges to theTheorem which were not discussed in the preceding sections -- those based onrent seeking ( Jung et al ., 1995 ; see Medema, 1996b ) and the presence of risk( Posin (1990) ; see Medema (1995a) , and Posin's (1995) response). Of particularimport here is the implication of the Barzel/Allen definition (and evenDahlman's definition) for the game-theoretic challenges, which rely on theexistence of imperfect information. By any of these definitions, the presence ofimperfect information has the effect of introducing transaction costs into theanalysis through the behavior it induces, and the game-theoretic challenges arecorrespondingly invalidated. (On this point see also Allen (1995, pp. 12-13) , Dahlman (1979, pp. 158-159 at note 26) , Hovenkamp (1990, p. 787) , Illing(1992) , Samuelson (1985, p. 323) , and Zerbe (1980, pp. 85-86) ). Indeed, Saraydar (1983) , acknowledges that the imperfect information resulting fromstrategic behavior violates the assumption of zero transaction costs, but arguesthat such costs are virtually inevitable within a small numbers bargainingsituation due to the incentive to distort information. Further evidence for thisline of reasoning may be found within Coase (1960, pp. 31-33) , who discussesthe problem of moral hazard (along the lines of Harris, 1990 ) in the context of positive transaction costs.
Against these claims, defenders of the game-theoretic approach point outthat giving this type of content to the idea of zero transaction costs basicallyrenders the idea of bargaining meaningless and detaches the Theorem almostcompletely from reality, making it, in the words of one commentator 'more incommon with astrology than with market analysis' ( Veljanovski, 1982, p. 60 ).(See also Regan (1972, pp. 429-430) , Shoup (1971, p. 310) , and Cooter (1982,p. 17) .) In the end, then, whether the game-theoretic and other challenges to theCoase Theorem go to its correctness or its relevance comes down to 'how oneinterprets the almost mystical world of zero transactions costs' ( Zerbe, 1980, p.85 ).
This takes us directly to the third implication of the Barzel/Allen definition-- that '[t]ransaction costs are ubiquitous' ( Allen, 1991, p. 4 ). The effect of thisis to make the Theorem per se completely devoid of applicability to the realworld. Coase (1981, p. 187) has made this point a bit more graphically,contending that the analysis of a world of zero transaction costs is akin to'divining the future by the minute inspection of the entrails of a goose'. Indeed,by this definition the Theorem's efficiency proposition must hold, since anyviolation of it reflects a '[cost] associated with the transfer, capture, orprotection of property rights'. It may be argued with some justice that all of thisreduces the Coase Theorem to a mere tautology ( Regan, 1972, pp.429-30 ; Cooter, 1989, p. 67 ). So be it. Coase (1960, p. 15) never claimed that it wasrealistic, just that it follows logically from the same basic assumptionsunderlying Pigouvian theory circa 1960. And indeed, based on the foregoinganalysis the correctness of the Theorem remains untouched, apart from thepotential for taste and preference-induced divergences between WTA and WTPthat may impact the invariance claim. The issue of relevance is a different matteraltogether, and one to which we now turn.
A further facet of the extensive debate over the Coase Theorem has been theattempt to verify its predictions experimentally and empirically. Hovenkamp(1990, p. 794) has recently pointed out that '[c]onducting empirical tests of theCoase theorem is like conducting empirical tests of the Pythagorean theorem.Given the theorem's assumptions, the results flow out as a matter of logicalnecessity'. This is true; as such, and given the impossibility of satisfying thezero transaction costs assumption in the world in which we live, theexperimental and empirical tests go to the issues of relevance and applicability,rather than to the Theorem's correctness. In doing so, they begin to address thepotential difficulties for the Theorem that are raised by the challenges discussedabove, such as the effects of imperfect information, the potential for strategicbehavior, nonconvexities, and the presence of income or taste and preferenceeffects.
The experimental tests of the Coase Theorem are among the most interesting ofthe various tests, since they offer the potential to mimic as closely as possiblethe conditions of zero transaction costs. At the same time, they can begin tocapture the effects of factors such as imperfect information and isolate theimport of these effects vis-B-vis . situations in which they are absent.
The most extensive experimental tests of the Theorem are those undertaken byHoffman and Spitzer (at times with others B see Hoffman and Spitzer (1982 , 1985 , 1986) , Coursey, Hoffman, and Spitzer (1987) , and Harrison, Hoffman,Rustrom, and Spitzer (1987) ). The experiments undertaken by Hoffman andSpitzer all involve the same basic experimental framework. There is a range ofpossible outcomes, each with a different associated payoff. One party (the'controller') is given the 'property right' and thus can determine the outcomeunilaterally. Consider the following set of possible dollar payoffs (P A , P B ) in thespirit of Hoffman and Spitzer: (5,0), (4,4), and (0,5). If A is the controller, hewill chose (5,0) unless B induces him to choose a different outcome. The CoaseTheorem predicts that (4,4) will be chosen, with the actual distribution of thejoint payoff ($8) being a function of the negotiation process. And of course itis in B's interest to offer A up to $4 to choose (4,4) and in A's interest to acceptany payment greater than $1 to do so.
In well over 500 experiments with various sizes of bargaining groups(including 1x1, 1x3, 2x2, 5x5, 1x9, and 1x19) conducted within this framework,the results were quite favorable. In all, the parties bargained to the efficientresult 92 percent of the time, including 94 percent of the time under conditionsof full information and 90 percent of the time under imperfect information.Moreover, the support for the Theorem's prediction was actually greatest in the10 and 20 person situations -- 98 percent, including 100 percent in 20 personnegotiations, where the 19 people devised their own informal institutionalarrangements (choosing representatives from the group as bargaining agents) toovercome the large numbers problems. Given how little the student subjectshave at stake in these experiments, even those conducted under conditions ofimperfect information suggest very low transaction costs. While this may seemquite unrealistic, these experiments do offer some fairly substantial support forthe applicability of the Theorem when transaction costs are low.
One of the interesting issues raised by the early experiments came from thenearly equal division of the payoffs ( + 1 dollar) in the vast majority of the cases.Individual rationality suggests, with respect to the above example, that thecontroller would not settle for less than $5 and could potentially induce theother party to agree to a $7.99 - $.01 split of the $8 payoff, as in, for example,a one-shot game. The fact that so many controllers settle for less than whatshould be their reservation price suggests either altruism -- which contradictsentirely the theory of externalities, Coase Theorem or otherwise, since, if agentsare altruistic, the individually rational behavior that is said to generate theexternality in the first place would not occur ( Harrison and McKee, 1985, p.655 ) -- or a potential problem with the experimental environment.
One hypothesis offered to explain this result is that participants in theseexperiments did not understand the full meaning and import of having aunilateral property right as controllers ( Harrison and McKee, 1985 ). Another isthat they did not feel a morally justified right to be the controller, since thatposition was determined on the basis of a coin flip rather than being, in some(e.g., Lockean) sense, earned ( Hoffman and Spitzer, 1985 ). Once measures wereimplemented to control for this -- 'educating' subjects or having subjects 'earn'the position of controller by winning a preliminary game -- the extent ofindividually rational behavior increased dramatically, and without a significantdrop-off in the rate at which efficient bargains were made -- approximately 90percent ( Harrison and McKee, 1985 ; Hoffman and Spitzer, 1985 , 1986 ). Eventhen, however, 20-30 percent of the experiments generated less thanindividually-rational outcomes, suggesting that the subjects behave more likeLockeans than like utilitarians or egalitarians. Rather than taking this asevidence against the Coase Theorem, Hoffman and Spitzer (1986, pp. 159-160) suggest that it speaks to the robustness of the Theorem across alternativehypotheses regarding individual behavior.
One of the criticisms of these early experiments was that they did not accountfor the possibility of 'affronts to dignity' and other such factors to which peoplewould refuse to assign a monetary value or over which people would refuse tobargain ( Kelman, 1985, pp. 1038-1039 ). In an attempt to deal with the 'affrontto dignity' issue, Coursey, Hoffman, and Spitzer (1987) conducted experimentsthat introduced a discomforting externality. This was accomplished byintroducing the possibility that the 'victim' would have to hold one ounce of anunpleasant-tasting liquid in his or her mouth for twenty seconds. Theseexperiments had two possible payoffs: (i) the 'polluter' gets $0, and the victimgets $10 and does not have to taste the liquid; (ii) the 'polluter' gets $20, and thevictim gets $10 and does have to taste the liquid. The latter outcome, where thevictim is exposed to the externality, is, of course, the efficient one. Out of 40experiments, the efficient outcome was chosen 38 times -- 22 out of 22 timeswhen the polluter was the controller and 16 out of 18 times when the victim wasthe controller. The results with the polluter as the controller may not besurprising: when the 'polluter' has the right to pollute, polluting is efficient, andthere are substantial gains to the polluter from polluting, the polluter would beexpected to pollute.
What may be a bit surprising, however, is the propensity for victims to selltheir right to be free from the harm -- here, for a 90 percent increase in payoff(from $10 -- the payoff to the victim without tasting -- to $19.06 -- the averagepayoff to the victim when agreeing to taste), or roughly half of the gains to thepolluter. In spite of the authors' claim to the contrary, these results further callinto question the assumption of individual rationality (or the inducement thereofwithin the experimental environment), since, in half of the experiments, the'polluters' paid the victims to taste the liquid even when the polluters had aunilateral right to force them to do so. And while the authors do not jump froma willingness to sell the right to avoid tasting bitter liquid to, say, thelegalization of prostitution or pornography (although they do not entirely closethe door on such matters, choosing instead to 'express no opinion' as to whethersuch activities should be allowed), they do suggest a presumption in favor ofallowing individuals to transfer moderate amounts of dignity and/or moderateamounts of danger.
Based on their various findings, Hoffman and Spitzer (1986, p. 162,emphasis added) assert that their results ' produce a presumption in favor of theCoase Theorem ', by which they mean that 'a judge or a legislator should starthis analysis by presuming that the parties can and will, in general, exhaust thegains from trade available through private bargaining', and that those whowould argue against this 'must bear the burden of the proof'. Furthermore, theyargue, the strength of the evidence for the optimality of the bargaining outcomesestablishes a presumption in favor of injunctive over damages remedies becauseof the high probability that the parties will bargain to the efficient result( Hoffman and Spitzer, 1986, pp. 163-168 ). (See Calabresi and Melamed (1972) .For discussions of the relative efficacy of property rules and liability rules whentransaction costs are positive, see also Polinsky (1979; 1980) , Ayres and Talley(1995a , 1995b) , and Kaplow and Shavell (1995 ,1996) .)
In making these claims, Hoffman and Spitzer clearly go too far. It is onething to show that the Coase Theorem is largely confirmed in a laboratorysetting that attempts more or less to mimic the zero transaction costs world, butit is quite another to say that the results thus generated establish 'a presumptionin favor of the Coase Theorem' for efficiently resolving real-world externalityproblems with twenty or fewer parties. (It should be noted that the parties willalways reach an efficient point, in the Pareto sense. That is, even if transactioncosts are so large as to preclude rights transfers, that result is Pareto efficient,given transaction costs. See, for example, Samuels (1974) , Buchanan (1983) ,and Calabresi (1991) . However, the efficient result to which Hoffman andSpitzer's 'presumption' refers is the Pigouvian social optimum, which isequivalent to the Pareto optimal outcome when transaction costs are zero.) Whatmay be established is that up to twenty-party externalities will be resolvedefficiently through negotiations in many, and perhaps even most instances wheretransaction costs are very low and the stakes are very small. But transactioncosts consist of far more than factors introduced by a twenty-second-tasting ofa foul liquid or adding parties to a bargain, particularly when the group consistsof more-or-less homogeneous college students. The emphysema-ridden residentsof the neighborhood are likely to have a far different view of pollutionexternalities than would others who are not so affected; the light sleepers arelikely to look far differently at the neighborhood kennel than are the deepsleepers, and so on. And how many groups are absent one or two members whoare likely to impede any negotiated settlement? All of this is to say nothing ofthe information and coordination problems that may attend complicatedreal-world bargains. In sum, Hoffman and Spitzer develop some very niceresults offering rather strong support for the Theorem when the conditions itassumes are nearly met. However, to move from this to claims of wide-spreadapplicability and presumptions in favor of the Theorem in real-world cases is asomewhat different matter, one requiring far more caution and future study thanis implied by the authors.
Apart from transaction-cost-related issues of applicability, these experimentsalso fail to get at the invariance proposition per se . For example, might effectssuch as the normative sanction for rights, an affront to dignity, or wealth effectscause a divergence between WTA and WTP? These issues are side-steppedwithin the Hoffman and Spitzer experimental design that makes efficiency andinvariance go hand-in-hand. While the evidence regarding the existence of adivergence between WTA and WTP is not uniform (see the survey by Hoffmanand Spitzer (1993) and the references cited therein), it seems to weigh in favorof the existence of a non-trivial divergence, one that is too large to be explainedsolely in terms of wealth effects. Attempts to measure the relationship betweenWTA and WTP have been done through surveys and through experiments. Thesurvey evidence shows a substantial difference between WTA and WTP,although economists have been rather suspicious of these results because oftheir several potential biases. However, as we have noted, recent experimentaltreatments of this issue support the contention that WTA may be substantiallygreater than WTP, often more than twice as great ( Levy and Friedman, 1994 ; Hoffman and Spitzer, 1993, pp. 69-85 ). While this literature is too vast tosurvey here, one set of experiments, undertaken by Kahneman, Knetsch, andThaler (1990) , probes this issue in the context of the Coase Theorem and, in anumber of different types of experiments, finds significant endowment effects.Using items such as mugs, pens, binoculars, and chocolate bars, they find thatindividuals, when given the opportunity to exchange these items for cash,exhibit a strong reluctance to part with entitlements and thus that, contrary tostandard assumption of economic theory, preferences are apparently notindependent of entitlements ( Kahneman, Knetsch, and Thaler, 1990, p. 1339 ).The value that the subjects place on these objects 'appears to increasesubstantially as soon as the individual is given the object' ( Kahneman, Knetsch,and Thaler, 1990, p. 1342 ), and the resulting disparity between WTA and WTPdoes not dissipate in repeated trials (i.e., with market experience). They suggestthat this endowment effect is most likely to occur for items that are not easilyreplaceable, which makes the endowment effect particularly important for theCoase Theorem, since things like a nice view, or clean air or water, are noteasily replaced, and it thus can be expected that people will refuse to sell suchgoods even at prices somewhat greater than their reservation price for buyingthem.
Two implications of these WTA versus WTP experiments are particularlyimportant. The most obvious is that the results provide strong evidence againstinvariance in the outcomes of bargains even when transaction costs are zero.Second, endowment effects reduce the gains from trade as compared with aworld in which preferences are independent of endowments. Since fewermutually advantageous exchanges are possible, the volume of trade is lowerthan it otherwise would be ( Kahneman, Knetsch, and Thaler, 1990, p. 1344 ).Given the size of the potential disparity between WTA and WTP, one canconceive of situations where each party's WTA is greater than the other party'sWTP, so that no trade would occur, whereas if WTA were equal to WTP, wewould see bargains consummated. Experiments run to test this implication in aCoase Theorem context revealed substantial under-trading relative to theTheorem's predictions ( Kahneman, Knetsch, and Thaler, 1990, pp. 1339-1341 ).Even when transaction costs are negligible, then, there does not seem to bemuch room for confidence in the generation of an invariant outcome whenconsumers are party to an externality.
Even less favorable to the Theorem's applicability are the results of anexperiment by Stewart Schwab (1988) , who looked at the Theorem in thecontext of labor law and labor-management negotiations. The graduate studentsubjects in Schwab's experiments were asked to negotiate a union contract overwages, vacation time, and -- the crucial aspect of the experiment -- whether ornot the company had the right to transfer work to its nonunion plant over thecourse of the three-year contract. The implications for the Coase Theorem layin the contract presumption that was said to govern labor relations in theabsence of a specific contract provision: in one group of experiments, subjectswere told that the legal presumption was that the company must continue to useunion workers unless the contract explicitly states otherwise (i.e., includes a 'goclause'), while the other group was told that the presumption was that thecompany could transfer work to the nonunion plant during the course of thecontract unless the contract explicitly stated otherwise (i.e., includes a 'stayclause'). (These contract presumptions have actual counterparts in labor law Bthe Milwaukee Spring cases.)
Analysis of the results of these experiments shows that only about 20percent of the contracts were fully efficient when wage levels, vacation time,and the stay or go clause are accounted for, a vast difference from the roughly90 percent efficiency of the Hoffman and Spitzer and the Harrison and McKeeexperiments. Out of 108 contracts, all but two had efficient wage levels, butonly 31 percent had efficient vacation levels and only about 65 percent had astay clause where it was efficient or a go clause where it was efficient. Schwabcontends that three factors may account for these differences. First, parties inthese experiments were bargaining over multiple contractual terms under abinding time constraint, and thus may have found it difficult to make efficientchoices on all items. Second, unlike many of the other experiments, subjectshere were not given full and perfect information. This meant both thatinformation had to be communicated during the negotiation process and thatsignaling and bluffing could occur, leading to inefficient agreements. Finally,the subjects did not know what the 'best' outcome was from the beginning, andthus had to find their way to it and do so over a rather large bargaining range,which, of course, could easily result in inefficient outcomes ( Schwab, 1988, pp.251-252 ).
Given these factors, the rather high rate of failure to reach efficient bargainsis not particularly surprising. The environment of these experiments correspondsmuch more closely to a natural setting than do many of the other experimentaltreatments, and the factors that exist in these natural settings are such as toweigh heavily against the attainment of efficient results. By the same token,however, these experiments go much more to the application of the insights ofthe Coase Theorem than to the testing of the Theorem per se , in that theyintroduce a variety of factors that are assumed away by the Theorem'sassumption of zero transaction costs. Thus, earlier work, such as that byHoffman and Spitzer, speaks favorably to the Coase Theorem on its own terms,while Schwab's results are rather pessimistic about the ability of parties tobargain to efficient results in more natural settings. However, Schwab's resultstake on a better cast when evaluated in light of what he calls the 'weakefficiency hypothesis', which says that the law will not affect the rate at whichefficient bargains are consummated. (This is not to be confused with the 'weak'version of the Coase Theorem, noted above, which asserts efficiency but notinvariance.) The form of the contract presumption does not have a significanteffect on the inclusion of stay clauses or go clauses, nor on the efficiency of thecontracts ( Schwab, 1988, pp. 252-253 ).
There have been three studies that more or less take Coase's farmer-rancherexample into the real world to look at the ability of parties to negotiate efficientsolutions to animal trespass problems.
Kenneth Vogel (1987) examines the response of farmers and ranchers tochanges in California animal trespass laws between 1850 and 1890. At the timewhen, in 1850, California joined the Union, its principal industries were miningand cattle raising, and, reflecting the importance of the cattle industry to thestate, California had what was, in essence, strict nonliability for cattle trespass.This rule clearly favored the ranchers, and the evidence strongly suggests thatthe rule was designed with that in mind. At the same time, however, it playeda major role in hindering the development of agriculture in the state ( Vogel,1987, pp. 163, 167 ).
However, between 1851 and 1890 there were no less than 150 different lawsenacted by the California legislature altering the rules that governed cattletrespass in ways that benefited farmers ( Vogel, 1987, pp. 163-164 ). The CoaseTheorem predicts that these alterations in the law will have no effect on theallocation of resources; that is, ceteris paribus , these changes in the law shouldhave no effect on the level of resources devoted to ranching and farming, or onranching and farming outputs. And, according to Vogel, this situation isparticularly well-suited to testing the applicability of the Theorem to the realworld since 'the externality is visible, the parties are, at least post hoc, easilyidentifiable, and it is easy to measure, or use proxies to estimate, the damages'( Vogel, 1987, p. 181 ).
Contrary to the Theorem's prediction, however, the enactment of the variousestray laws beginning in the 1860s was accompanied by an enormous increasein farm output, particularly for wheat farming, which became common in thevalleys, while cattle were moved up into the foothills. Econometric analysisundertaken by Vogel shows that a number of variables attempting to capture theeffects of legal change on crop outputs are significant, and that these areuniformly positive in sign, which supports the claim that these legal changes didindeed influence the growth of agriculture ( Vogel, 1987, p. 184 ).
Given the strength of the evidence, it remains to explain why the CoaseTheorem fails here. Vogel suggests two reasons. First, transaction costs may besignificant, and, furthermore, are asymmetric across alternative assignments ofrights; specifically, they are lower when ranchers are liable ( Vogel, 1987, pp.176, 187 ). When ranchers are not liable for the damage done by their cattle, thefarmer wishing to keep the cattle off his land will have to negotiate with eachrancher whose cattle might potentially stray onto his land in order to accomplishthis. On the other hand, when farmers have the right to compensation fordamages, the onus is on the ranchers to initiate negotiations, and the rancherneed only bargain with those farmers on whose land his cattle may be expectedto stray. Second, there are nonconvexities as a result of the externality. Ifranchers are not liable for trespass damages, the fact that each farmer has tonegotiate with all ranchers whose cattle might stray onto his land in order toprevent damage means that '[i]f a farmer fails to contract with the rancherwhose cattle actually use his land, all payments made to the other ranchers areuseless' ( Vogel, 1987, p. 176 ). The farmer will thus have little incentive toinitiate such negotiations, with the result that efficiency will obtain only if it isefficient for cattle to be allowed to roam freely. This nonconvexity is not presentwhen farmers are given the right ( Vogel, 1987, pp. 174-176, 187 ). Takentogether, these two factors can explain why output was lower when the rancherswere not liable.
In contrast to Hoffman and Spitzer, who use their experimental results toclaim a presumption in favor of the Coase Theorem, Vogel (1987, pp. 186-187) argues that his results refute the general applicability of the Theorem. Yet,Vogel has not refuted the Theorem but rather has shown the importance for thecase of straying cattle of transactions costs and pointed out the importance ofassigning the legal rule to minimize transactions costs as both Coase (1960, p.19) and Posner (1983, p. 71) suggest should be done. Given the enormousvolume of legal change at the time, the nonconvexities present, and thedifficulty of ascertaining the source of the damage, Vogel's broad conclusionmay be premature. Some degree of support for a more moderate view can befound in the study of contemporary trespass disputes undertaken by RobertEllickson.
Ellickson (1986 , 1991) examines, among other things, the effects of open-versus closed-range laws on cattle trespass disputes in Shasta County,California. Under open-range laws, cattlemen are not usually responsible foraccidental trespass damage, whereas they are strictly liable under closed rangelaws. Ellickson finds that cattlemen and their neighbors do in fact behave in amanner suggested by the Coase Theorem, cooperating to resolve their disputesregardless of who is liable. However, the evidence also suggests that it is notCoase-Theorem-type mechanisms at work here; rather, individuals seem to relyon community norms to determine their behavior. For example, while theTheorem predicts that the cattleman would install a fence if he were liable(closed range), and that the neighboring farmer would do so if he were liable(open range), it is almost always the cattleman who installs the fence becauseboth cattlemen and their neighbors believe that the cattleman is morallyobligated to do so, since his cattle cause the damage. Moreover, the citizensseem to be very ignorant of the relevant law and ignore those aspects of the lawthat conflict with their view of the world. As such, they do not bargain 'in theshadow of the law' (see Mnookin and Kornhauser (1979) and Cooter, Marks,and Mnookin (1982) ), but beyond it; community norms seem to have muchmore force than the legal rule in place. Ellickson suggests that this may be dueto the fact that relations among the neighbors are both complex and continuing,because of which the transaction costs associated with acquiring informationand litigating disputes are high, and reliance on norms offers a lower-cost wayof resolving these disputes. Ellickson (1989 , 1991) also suggests that thisnorm-based behavior points to the need to revise certain of the behavioralconcepts underlying law and economics.
In a study that has interesting commonalties with that of Ellickson, Nick Hanleyand Charles Sumner (1995) examine an externality situation owing to theroaming of red deer in the Scottish Highlands which cause damage to growingtrees and, in the process, impose substantial costs on the owners of these forests,the value of the timber from which is diminished. In addition, the wanderingdeer may destroy growing crops on farmland, and, when they stray onto sheepgrazing land, reduce the forage for sheep, thus imposing costs on both farmersand sheep ranchers. The beneficiaries of the red deer population are estateowners, who derive substantial income and estate value from the presence of reddeer on their estates ( Hanley and Sumner, 1995, pp. 88-91 ).
Given the level of damage, the small number of parties, the ease ofquantifying damage to forests, and the relative ease with which estate ownerscould reduce the size of their herds, the situation seems to reflect aninefficiently-high deer population and a fertile ground for the working ofCoase-Theorem-type mechanisms. Even so, an extensive study by Sumner(1993) failed to turn up any instances of Coasean bargaining between ownersof deer estates and neighboring landowners. What one does observe, however,are Deer Management Groups which neighboring landowners have established'to coordinate deer management across neighboring estates ... andforest/farmland, in order to reduce the level of the externality'. The advantageof such groups is that they 'effectively [internalize] the externality acrossmembers of the group', thereby avoiding the third-party effects that can resultwith bilateral bargaining ( Hanley and Sumner, 1995, p. 93 ). It is interesting tonote the parallel between the rise of the cooperative Deer Management Groupsand the behavior of neighbors revealed in Ellickson's study of cattle ranchingin Shasta County. While the law offers a low-cost option (free governmentculling) for dealing with red deer damage, groups of neighboring landownersin essence ignore the law and work out a solution amongst themselves, perhapspresumably because it is the case that the transaction costs associated with thecooperative efforts of the Deer Management Groups are lower than those thatwould attend bilateral negotiations of the Coasean variety ( Hanley and Sumner,1995, p. 93 ).
The Coase Theorem has implications for all manner of legal rules, including, as Peters (1986 , 1992) points out, the rules governing divorce. Since 1970, therehas been a progressive movement in the U.S. from divorce by mutual consent(requiring the agreement of both parties), to unilateral divorce, where themarriage can be terminated at the demand of either party. Intuitively, the rulesgoverning divorce function to establish property rights with respect todissolution of the marriage. Under unilateral divorce law, the spouse seekingdivorce has property rights with respect to dissolution while, under mutualconsent, the right rests with the spouse who does not wish to see a divorce occur( Peters, 1992, p. 690 ). The conventional wisdom was that unilateral divorcelaws would make divorce easier (in economic terms, reduce transaction costs),thus increasing the divorce rates in states that adopted such laws. The CoaseTheorem predicts that if bargaining costs are minimal and information issymmetric across parties, divorces will only be undertaken when they areefficient (that is, joint benefits exceed joint costs), regardless of the lawgoverning divorce, and that the legal rule will have no impact on the divorcerate.
Peters (1986) tests a model corresponding to the Coase Theoremenvironment against one that posits asymmetric information and thus predictsthat divorce rates will differ across alternative legal rules and finds that the datasupport the predictions of the Theorem against the conventional wisdom: Themove to a unilateral divorce rule does not affect the probability that a womanbecomes divorced ( Peters, 1986, pp. 446-448 ). Moreover, the level of alimonyand child-support payments are 'significantly lower' in states with unilateraldivorce rules ( Peters, 1986, p. 449 ), and the labor force participation rates ofmarried women in such states are higher, which, she argues, may represent anattempt by married women to self-insure against the possibility of becomingdivorced without compensation ( Peters, 1986, pp. 448-449, 451-452 ). Thus,both the divorce rates and the distribution of compensation are consistent withthe Coase Theorem. However, a number of subsequent studies find that theevidence tends to support the conclusion that divorce rates are in fact higher inunilateral-divorce states than in mutual-consent states. (See, for example, Allen(1992) , Zelder (1993a , 1993b) , Friedberg (1995) , and Brinig and Buckley(1995) , which also contain numerous citations to literature on both sides of theargument.) Within this debate, each side claims that the other's empirical workcontains errors or biases that influence the results (see, for example, Peters(1986 , 1992) and Allen (1992) ).
Even if one is willing to accept the result that divorce rates are not impactedby the legal rules governing divorce, it remains to ascertain whether these resultsactually reflect the working of Coase-Theorem-type mechanisms. There isplenty of reason to suggest that the answer is 'no', or at least 'not necessarily'.First, there is no evidence to suggest that 'unilateral' divorces are undertakenonly when they are efficient. Rather, Peters infers that the efficiency propositionholds based on a questionable claim that transaction costs are low and the factthat the data confirm the model's invariance and distribution predictions. (Forcontrasting views on the potential magnitude of transaction costs here, see Peters (1992, p. 690) and Allen (1992, p. 684) . Allen (1992 , 1995) goes so faras to argue that, by working an uncompensated transfer of wealth from wivesto husbands, the move to no-fault divorce violates the zero transactioncosts/fully-specified rights condition assumed by the Theorem and thus that therise in the divorce rate does not constitute a legitimate argument against theTheorem.) Furthermore, Peters fails to account for the fact that the Theorempredicts not just an invariant divorce rate, but an invariant allocation ofhousehold resources as well -- just as the farmer-rancher example predicts aninvariant allocation of resources devoted to farming and ranching. The fact thatfemale labor force participation is higher in states with unilateral divorce rulesthus speaks loudly against the claim of invariance.
A similar problem attends the claim that the high rate at which suits are settledprior to trial supports the Coase Theorem ( Hoffman and Spitzer, 1986, pp.168-169 ). Glanter (1983, pp. 28-30) finds that roughly 90 percent of all lawsuitsare settled before they go to trial, and that, when they do not settle, it tends tobe due to (i) cases that require a judicial decree to be settled; (ii) cases that arenot costly to litigate, which reduces the incentive to settle; (iii) the placing byone or more parties of special value on having a judicial decree for reasonsincluding, inter alia , precedent and reputation; (iv) cases that involve an issuethat is not easily negotiated over, such as a 'fundamental value'; and (v) the hightransaction costs associated with settlement as compared to going to trial --factors that lie outside of the bounds of the Coase Theorem. However, the highproportion of settlements does not imply that the parties have bargained to thePareto optimal result contemplated by the Coase Theorem. There is no way toinfer from the settlement data whether the parties have bargained to the sociallyoptimal result contemplated within a zero transaction costs world, or if theysimply have realized some of the potential gains from negotiation but hit a pointwhere the transaction costs from further negotiation exceed the expected gains,and choose to settle at a 'sub-optimal' outcome because this settlement,although not optimal, is still better than going to trial.
Perhaps the most unique empirical test of the Coase Theorem is Donohue's(1989a) analysis of the Illinois employment experiment ( Spiegelman andWoodbury, 1987 ), which attempted to determine whether the payment ofbonuses to unemployed workers for securing employment, or to employers forhiring unemployed workers, would reduce the duration of unemployment andthe costs associated with the unemployment compensation system. While theexperiment was conducted to ascertain how such bonuses might affect theduration of unemployment, its application to the Coase Theorem isstraight-forward. The efficiency hypothesis predicts that mutually advantageousbargains will be struck under either scheme, and all workers and employers whosatisfy the eligibility requirements will collect bonuses. The allocativeinvariance proposition suggests that members of the worker-payment-group(WPG) will find jobs and collect bonuses at the same rate as members of theemployer-payment-group (EPG). The invariant distribution hypothesis predictsthat members of the WPG and EPG groups will have the same aggregatecompensation (wages plus bonus). The WPG workers would be expected tohave lower wages than EPG workers, reflecting a bargaining away of a share oftheir bonus, as compared to EPG workers' higher wages as employers bargainedaway a share of their bonus.
Donohue's inquiry into the results of the Illinois experiment reveals that theycontradict the predictions of the Coase Theorem on all counts. To begin with,the number of bonuses paid to WPG workers was about 5 times that paid toEPG employers. Furthermore, many workers and employers who met therequirements for bonuses failed to submit a voucher to receive their bonus --particularly employers. Given this, says Donohue, '[t]he conclusion that anumber of individuals and employers acted inefficiently is hard to rebut'( Donohue, 1989a, p. 573 ). The experimental results also revealed that membersof the WPG had a significantly greater improvement in obtaining employment,relative to the control group, than did members of the EPG, which, along withthe differential bonus collection rates among the groups violates the allocativeinvariance prediction of the Theorem ( Donohue, 1989a, pp. 569-577 ). Finally,there was no significant difference in wages across the WPG and EPG hirees,so that aggregate (wages plus bonus) compensation was higher for WPGworkers than for EPG workers, in violation of the invariant distributionprediction of the Theorem. That is, it appears that workers did not bargain withemployers over the wage or the bonus as a result of this program ( Donohue,1989a, pp. 586-590 ).
Donohue (1989a, pp. 591-601) asserts that transaction costs are extremelylow here, and thus that the Theorem fails in a case most favorable to its success.He offers two possible explanations for why the experiment failed to satisfy thepredictions of the Coase Theorem, each of which goes to the issue of individualbehavior/decision making in the context of such bargains. One possibility, towhich Donohue lends a great deal of support, is ignorance on the part ofworkers, who seemed not even to realize that bargaining was possible and maynot have understood that the bonuses could aid them in gaining employment.Moreover, there may have been an authoritarian effect which caused theworkers to believe that the bonus was in effect inalienable -- that the partydesignated to receive the bonus was in fact entitled to its full value, an effectthat would also discourage the type of bargains envisioned by the Theorem( Donohue, 1989a, pp. 600-602 ).
Donohue's conclusions regarding the implications of the Illinois experimentfor the Coase Theorem's applicability have been challenged by Ellickson (1989) and Lindgren (1990) , both of whom contend that Donohue greatlyunderestimates the effect of transaction costs within this experiment. Acquiringthis so-called 'free' money actually involves a substantial number of steps (andeven more for employers than for workers), the aggregate effect of which is tomake the process rather costly, relative to the size of the bonus . Lindgren (1990,pp. 581-582, 585) , for example, lists the steps that participants in the WPG andEPG programs must go through in order to collect bonuses, and offers severalreasons why one would not anticipate an invariant distribution of income, orbargaining over the bonuses. In fact, Lindgren (1990, p. 583) suggests that theresults do in fact match the predictions of the Coase Theorem (see also Ellickson, 1989, p. 625 ).
First, because costs are high relative to the bonuses, the insights underlyingthe Coase Theorem would lead one to predict that many workers or employerswho are eligible for bonuses would not collect them. The Illinois studyconfirmed this prediction. Second, because costs are higher for employers thanfor workers, the insights of the Coase Theorem would lead one to predict thatmore workers in the worker-bonus group would be influenced to participate inthe program, obtain work quickly, and collect the bonuses. Again, the Illinoisstudy confirmed these predictions ( Lindgren, 1990, p. 583 ).
Indeed, if transaction costs were zero, the entire premise of the experimentwould disappear, since job search is a positive transaction cost phenomenon( Lindgren, 1990, p. 578 ). Finally, the presence of stigma and institutionalrigidity effects would lead one to predict minimal bargaining over wages andbonuses (in an amount different from the control group), a result againsupported by the Illinois experiment. In fact, Ellickson finds the results of theIllinois experiment very consistent with his own study of Shasta County -- thatpeople often tend to rely on norms rather than 'legal rules' to govern theirbehavior, particularly when the stakes are low and there is an expectation of acontinuing relationship, as among neighbors in Shasta County and betweenemployers and employees in the Illinois experiment ( Ellickson, 1989, pp.627-628 ).
The two earliest attempts to empirically validate the working ofCoase-Theorem-type mechanisms in real-world environments were undertakenby Steven N.S. Cheung (1969a , 1973) , who examined two of the classicillustrations of market failure caused by externalities -- share tenancyarrangements in agriculture and the relationship between beekeepers and appleorchard owners. These studies undertake to examine the 'Stigleresque' versionof the Theorem, which asserts the efficient internalization of externalities underconditions of perfect competition.
The standard view in the economics and tenancy literatures has long beenthat share tenancy leads to an inefficient allocation of resources, owing to (i) theshort duration of the leases; (ii) the discouragement of effort on the part of thetenant, since a portion of each unit of output must be paid to the landowner asrent; and (iii) the disincentive for either party to make investments in the landthat will maximize the land's productivity (see Cheung, 1969a, pp. 3-4, 7-8 , andthe references cited therein). As a result, one would expect to observe lowercrop yields under share tenancy than under alternative cultivation arrangements.However, the Coase Theorem predicts that, if transaction costs are zero andthere are well-defined and freely alienable private property rights in land, theallocation of resources will be 'the same whether the landowner cultivates theland himself, hires farm hands to do the tilling, leases his holdings on a fixedrent basis, or shares the actual yield with his tenant. In other words, different[observed] contractual arrangements do not imply different efficiencies ofresource use Y' ( Cheung, 1969a, p. 4 ).
An examination of share tenancy in China and Taiwan prior to the landreforms of 1949 shows that there was a well-developed system of privateproperty rights in land in China and Taiwan at this time and that the market byand large comported with the dictates of competition. Furthermore, Cheung did not observe lower ratios of labor and other inputs, a lesser degree ofimprovements, or lower yields on tenant farms than on owner-cultivated farmsor on farms employing wage labor, nor is there evidence that the market valuesof land under tenant cultivation are lower than the values of land under ownercultivation ( Cheung, 1969a, pp. 56-61 , 1980, p. 42 ). And, while it has beenargued that, under share tenancy, certain types of activities -- such asimprovements to farms -- would be contracted inadequately or not at all, Cheung(1980, p. 43) finds that these 'are precisely the activities stated in every writtencontract that I could find'. All of this evidence suggests quite strongly thatcharges that share tenancy is less efficient that other cultivation arrangementscannot easily be sustained.
Even though the theory assumes zero transaction costs where transactioncosts are actually positive, it is able to explain 'much of the observed farmingbehavior' ( Cheung, 1969a, p. 159 ). In this situation of well-defined propertyrights, transaction costs are not so high as to affect resource use at the margin,but, rather, affect the choice among alternative contractual arrangements -- theuse of alternative methods of cultivation reflecting the tradeoff betweencoordination costs and risk, each of which varies across alternative contractualarrangements ( Cheung, 1980, p. 44 ). (For a related discussion, see Cheung(1969b) .) While Cheung's evidence does not conclusively demonstrate theoptimality of share contracts, it certainly does lend strong support for the claimthat, at a minimum, share contracting is no less efficient than other availablecontractual arrangements, and thus that, under the appropriate (and notunrealistic) conditions, the mechanisms of the Coase Theorem can lead to asatisfactory resolution of externality problems through the market.
The other early study by Cheung of the working of Coase-Theorem-typemechanisms is 'The Fable of the Bees ...' (1973) , a study which responds to J.E.Meade's (1952) classic discussion of the positive reciprocal externalities thatexist between beekeepers and the owners of apple orchards: apple blossomsprovide valuable services to beekeepers, whose bees feed on them, while, at thesame time, bees provide valuable pollination services to the apple-orchardowner. While Meade argued that a system of taxes and subsidies can, and must,be imposed in order to achieve efficiency, contractual arrangements betweenfarmers and beekeepers have long been routine in the U.S., and the existence ofa market for nectar and for pollination services can be readily observed in thestate of Washington, the location of Cheung's study -- in some cases merely byconsulting the yellow pages of the telephone directory ( Cheung, 1973, p. 19 ).The question, of course, is whether these markets generate an efficientallocation of resources. Cheung (1973, pp. 24-28) argued that a presumption canbe established in the affirmative, since available data provides substantialsupport for the competitive nature of the market.
How is it that in this externality situation the market avoids the failurepointed to by Meade? To begin with, transaction costs are very low here. Sincethe value of resources devoted to pollination and nectar extraction isinsignificant and farmers could easily and cheaply keep bees themselves (andsometimes do so), the gains from contracting with beekeepers are extremelysmall, which, in turn, suggests that contracting costs are minimal ( Cheung,1980, pp. 46-48 ). There is also a well-developed system of contractual relationsbetween beekeepers and farmers, so well developed, in fact, that, while writtencontracts (sometimes as simple as postcards) are used to secure an initialarrangement among the parties, oral agreements are standard for subsequentrelations. Furthermore, these oral contracts are rarely breached, owing to thepresence of 'extra-legal constraints' in the form of sanctions against those whodo not honor their contracts ( Cheung, 1973, p. 29 ). Yet, in spite of theinformality of these contracts, they tend to be quite comprehensive, specifying'... the number and strength of the [bee] colonies, the rental fee per hive, theterms of delivery and removal of hives, the protection of bees from pesticidesprays, and the strategic placing of hives'. And, where hives are placed merelyfor honey-generating purposes (i.e., no pollination is involved), prices (oftenpaid in honey) are not necessarily fixed -- being allowed to vary with the honeyyield ( Cheung, 1973, p. 29 ). All of these various pieces of evidence leadCheung to conclude that, contrary to Meade's story, 'the allocation of hives andnectar flows approximates that of a smoothly functioning market' whereinresources are efficiently allocated ( Cheung, 1980, p. 50 ).
This having been said, Cheung notes that there are two factors which couldpotentially complicate these arrangements (relative to standard lease contracts),both of which relate to other levels of external effects. First, there are potentialspillovers from one farmer contracting for pollination services, which couldpotentially lead neighbors to take strategic advantage by employing fewer hivesthemselves. Second, the use of pesticide sprays by one farmer may result indamage to the bees kept on nearby farms. But both of these issues are dealt withthrough either custom or explicit contracting (such as the payment of riskpremiums for potential exposure to pesticides), depending on the circumstances.The reliance on customs here is an interesting parallel to Ellickson (1986 , 1991) ,discussed above.
It should be obvious that it is not possible to confirm or refute the efficiencyclaims made by Cheung, and, given this, the results cannot be said to show theapplicability of the Theorem (here, the Stigler (1966) version) per se . Yet, theyoffer important evidence that markets can successfully (if not fully efficiently)deal with potential externality problems under the appropriate conditions.
The importance of the Theorem lies not in whether it is correct, but in thedetailed nature of the assumptions required to make it correct--in that is thenature of transactions costs. The interesting question about the Theorem then isthe nature of the transactions costs associated with those situations in which thetheorem is thought to not be correct. The legacy of the Theorem lies in thesubsequent work attempting to detail the nature of transaction costs and theireffect on the workings of the economic system. The richness and variety oftypes of economic arrangements can now be seen in the richness and variety oftransaction costs and in mechanisms for reducing them.
In this sense the importance of the Coase Theorem lies not in its supposedcorrectness or incorrectness and the corresponding policy relevance or lackthereof, but, rather, in the positive transactions cost propositions that flow fromit. These include both normative and positive propositions. Examples are Posner's (1992, p. 52) normative suggestion that at law '[s]ince transactions arenever costless in the real world, efficiency is promoted by assigning the legalright to the party who would buy it ... if it were assigned initially to the otherparty', and the positive prediction of Lesser et al . (1997) that suits at law insituations where negotiation costs are low will involve considerations ofdistribution not efficiency.
The Coase Theorem has helped to give rise to a extensive body of work,much of it summarized by Eggertsson (1990) , concerned with economicbehavior and institutions and to a more detailed and useful sense of what ismeant by property. The Coase Theorem has made clearer the relationshipbetween transactions cost and property rights and in doing so has begun to givea much stronger basis for understanding how legal regimes change in responseto changes in constraints ( North, 1981 ). One can now define the strength ofproperty rights in terms of lower transaction costs for the exclusion, exchangeand use of property.
In part of the economics literature at least ( Eggertsson, 1990 ) thetransactions cost approach has replaced the market failure model of publicintervention that is expressed by Weimer & Vining (1992, p. 30) :
When is it legitimate for government to intervene in private affairs? Inthe United States, the normative answer to this question has usually beenbased on the concept of market failure -- a circumstance where thepursuit of private interest does not lead to an efficient use of society'sresources or a fair distribution of society's goods.
When the costs of transaction mechanisms are introduced there aredepartures from perfect markets. These departures are in fact externalitiesbecause they represent effects not taken into account in the decision makingprocess. Externalities, then, are found everywhere there are transaction costs,and are ubiquitous. Since the concept of market failure rests on externalities thatare defined by transactions costs, the concept of market failure (and the conceptof externality) does no work for us that is not already done by transaction costs( Zerbe and McCurdy, 1996 ). Externalities are in fact an unnecessarycomplication in the theory of government intervention.
Public goods represent a useful example of a situation in which the marketfailure model can be, and to some extent is being, replaced by a transaction costmodel. The older market failure approach is represented by Samuelson (1954) ,who saw public goods as a class of market failures. For example, in writingabout the classic case of the lighthouse, Samuelson (1964, p. 45) writes:
Here is a later example of government service: lighthouses. These savelives and cargoes; but lighthouse keepers cannot reach out to collect feesfrom skippers. So, says the advanced treatise, 'we have a divergencebetween private advantage and money cost ... and true social advantageand cost ... Philosophers and statesmen have always recognized thenecessary role of government in such cases of 'external-economydivergence between private and social advantage'.
The transaction cost-property rights approach appears to provide a richervehicle of analysis, as shown by Cheung, North, and others. For example, Coase(1974a) shows that the British lighthouse system was once a well-functioningprivate system and that, in general, the system was more complex than thatsuggested by the simplistic market failure diagnostic.
The triumph of the transaction cost approach shows that the true legacy ofthe Coase Theorem lies not in its correctness, but in drawing attention to the roleplayed by transaction costs within the economic system.
In light of the foregoing discussion, three things can be said about the CoaseTheorem. First, it is correct, in the sense that it has withstood all of thechallenges mounted against it to date. Efficiency will obtain, regardless of theinitial assignment of rights, and the result will be invariant keeping in mind thateven income effects are irrelevant if one accepts the Barzel/Allen definition ofzero transaction costs. Second, the Theorem, although correct, is unrealistic, asCoase recognized (see Coase 1960, p. 15 , 1981, p. 187 , 1988a, pp. 174-179 ).The latter point, of course, should have been obvious from the beginning, whichraises the question as to why the debate over the Theorem has been so intense.A small part of the answer, within the economics profession at least, may lie inthe interesting theoretical puzzle that the Theorem poses. Dwarfing this,however, is the normative debate that, implicitly or explicitly, pervades nearlyall aspects of the Theorem's discussion.
Three prescriptions for legal-economic policy are said to flow from the CoaseTheorem.
1. Rights- cum -market solutions are said to be preferable to Pigouvian remediesfor the resolution of externality problems.
2. Property and contract are efficient; any interference with the outcomes sogenerated will make matters worse rather than better. It is this implication thatmakes the Coase Theorem, in the minds of some, 'the cornerstone of alaissez-faire legal and economic policy regarding contract and property law'( Hoffman and Spitzer, 1986, p. 151 ).
3. When transaction costs are positive, rights should be assigned to those whowould possess them in the end-state if transaction costs were zero, as seen in theprescriptions of wealth maximization, or 'mimic the market'.
But the Coase Theorem says none of these things. The Theorem is a positivestatement with no normative implications; it is an 'is' statement, not an 'ought'statement. Each of the above propositions rests on the assumption thatefficiency is the goal of legal-economic policy. But the Coase Theorem goesmerely to the presence of absence of efficiency; it does not tell us that it is allthat matters or even that it matters at all. It is this normative leap that seems tounderlie most of the hostility to the Coase Theorem -- and, by extension, to lawand economics generally. (See, for example, Baker (1975) , Kelman (1979) , the Symposium on Efficiency as a Legal Concern (1980) and A Response to theEfficiency Symposium (1980) , Schlag (1986) , Gjerdingen (1986) , Johnston(1990) , and Crespi (1991) .) For a response to these types of criticisms see Zerbe(1998a) . Compounding the hostility to the normative use of the Coase Theoremare the use of incorrect definitions of economic efficiency by proponents of lawand economics ( Zerbe, 1998b ).
Furthermore, even if one takes efficiency to be the goal of legal-economicpolicy, the Coase Theorem does nothing to establish the sanctity of property andcontract or the superiority of the market over Pigouvian remedies, owing to theubiquitous nature of transaction costs. If coordination is costless, the market willoptimally allocate rights and resources, but so too will Pigouvian remedies. Onthe other hand, the Pigouvians fare no better in this debate since, after wavingaway the Coase Theorem on the grounds that transaction costs are positive, theytend to immediately fall back on the demonstration that Pigouvian remediesgenerate socially optimal outcomes, using models in which government isassumed to operate with full information and without cost. (But see Baumol(1972) for a more judicious evaluation of Pigouvian remedies.)
Here, we come to the true import of the Coase Theorem. The Theorem isnot, in the end, about markets or about costless bargaining; rather, it is about thecosts of coordination. If coordination is costless, markets function perfectly; butso does government. If coordination is costly, markets function imperfectly; butso does government. The task for legal-economic policy thus becomes that ofascertaining the magnitude and influence of these costs and the resultingimplications for alternative institutional-policy arrangements. The true andvaluable legacy of the Theorem is all of the subsequent work on transactionscosts that explore the costs of coordination under different regimes and indifferent situations. Like the Coase Theorem itself, this, too, is without directnormative implications. However, it has led to certain normative claims, asnoted above. One, from an analytical perspective, is that the received conceptionof externalities should be abandoned. Another, this time from a policyperspective, is that judgments as to the appropriate form of governmentintervention should be made on the basis of what institutional arrangementproduces the lowest combination of coordination costs. In this regard, it isinteresting to note that much of the normative debate and the propositions wenoted above in that regard can be turned into a series of positive predictionsabout which arrangements will promote economic efficiency. Where theaffected parties could reach a solution through negotiation but choose litigationor regulation, the real issue is likely to be who is to be assigned property rightsrather than how to realize gains from trade (See, for example, Lesser, Dobbs,and Zerbe (1997) ).
Finally, the meaningfulness of the Coase Theorem must be understood inepistemological terms. The 'correctness' of the Theorem is a matter of logicalvalidity; in general, the Theorem is a conclusion derived from premises, and therole of the assumptions constituting its premises is to rule out of considerationall those variables which would prevent the derivation of the conclusion as amatter of logic. The validity of the Theorem, therefore, is a function of theassumptions defining away certain limiting conditions. The empirical truth ofthe Theorem -- its descriptive accuracy -- is a separate matter from its logicalvalidity. The Theorem considered empirically is a tendency statement, astatement that under certain conditions such and such behavior and allocativeetc. results can be expected; that is, a law in the Marshallian sense. However,the logical and empirical aspects are closely related to one another in thatchanging the assumptional conditions of the Theorem is tantamount to changingthe conditions in terms of which the Theorem is a tendency statement. TheTheorem is a tendency or probability statement in a further empirical sense, towit: the experimental literature indicates that the results expected on the basisof certain specifications of the Theorem are realized something less than onehundred percent of the time.
Given the foregoing, it becomes clear that much of the literature on theCoase Theorem not only overreaches in terms of the normative implicationsmore or less improperly drawn from the Theorem, but fails to specify themeaningfulness of the Theorem in such terms -- readily leading to practiceswhich make claims for and take the Theorem far beyond what logicality andempiricism permit.
The authors would like to thank Douglas Allen, James Buchanan, RobertCooter, Robert Ellickson, Elizabeth Hoffman, Richard Posner, Warren Samuels,and participants in the Workshop in the History of Economic Thought andMethodology at Michigan State University for comments and suggestions onprevious drafts of this essay and for helping to clarify our thinking on certainpoints raised herein. The excellent research assistance of Mary Therese Cogeosis also gratefully acknowledged. Of course, the authors are solely responsiblefor any remaining errors.
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