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Negotiating a climate convention: The role of prices and quantities
ELSEVIER
Negotiating a Climate Convention: The Role of Prices and Quantities ALFRED ENDRES
University of Hagen, Germany E-mail: [email protected]
In this paper, we consider the economics of negotiating an international greenhouse convention. The agreement is either on emission charges ("prices") or on emission quotas ("quantities"). We show that negotiations between non-identical countries generally lead to Pareto suboptimal conventions. The extent of the deviation of worldwide equilibrium emissions from Pareto optimal emissions depends upon whether the agreement takes the pricing or the quantity approach. Counterintuitively, it turns out that under certain circumstances the quantity convention is Pareto superior to the pricing agreement. © 1997 by Elsevier Science Inc. I. Introduction
Methods and results of traditional environmental economics can be widely applied to global environmental issues. However, there is a specific point that sharply distinguishes global environmental problems from problems at the level of an individual country: In traditional environmental economics it has been (often implicitly) assumed that there is a central agency willing and able to apply environmental policy instruments even if the weffare of some decision makers (e.g., the polluters) is reduced by this activity. Taking a public choice-oriented view, this presumption seems to be doubtful, even in a national context. In a global setting, however, it is particularly unwarranted. It is an essential property of global environmental policy that it must be agreed upon by sovereign countries. In this paper we show that the requirement of countries' consent has important consequences for the equilibrium emissions reduction achievable by the application of alternative environmental policy instruments. One of the most important results of this paper is that a fundamental "folk theorem" of environmental economics maintaining that "effluent charges are allocatively superior to effluent standards ''l does not necessarily hold. The purpose of this paper is to explain the results of international agreements and to demonstrate how they vary with the choice of the "object" of the agreement. These International Review of Law a n d Economics 17:147-156, 1997 © 1997 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010
0144-8188/97/$17.00 PII S0144-8188(96)00057-9
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Negotiating a climate convention
objects are emission reduction quotas a n d effluent charges. For simplicity we assume that countries negotiate u n i f o r m quotas, or an identical effluent charge rate, respectively. Moreover, the p r o c e e d s o f the charge are assumed to r e m a i n in the country where they are raised. For simplicity a n d in a c c o r d a n c e with most real-world environmental a g r e e m e n t s there are no transfer payments between the two countries in the m o d e l p r e s e n t e d below. ~ T h e bargaining process is m o d e l e d as follows: T h e countries are assumed to be cost minimizers. ~ Each country's total cost consists o f e n v i r o n m e n t a l d a m a g e cost a n d pollution a b a t e m e n t cost. Given that the negotiations are on a r e d u c t i o n quota, each o f the two countries proposes a quota minimizing its own total cost. If the proposals o f the countries differ, they agree u p o n the "smallest c o m m o n d e n o m i n a t o r , " i.e., the smaller o f the two r e d u c t i o n quotas. Given that the negotiations are a b o u t an effluent charge rate, either country proposes the rate that minimizes its own total cost. In this case, the principle o f the smallest c o m m o n d e n o m i n a t o r makes t h e m agree on the lower o f the two charge rates proposed. T h e country o p t i n g for the smaller quota (tax rate), thus d e t e r m i n i n g the result o f the negotiations, is called the " b o t t l e n e c k country," below. 4
H. Countries with Diverging Interests Assume two h e t e r o g e n e o u s countries negotiating the emissions o f a global pollutant. T h e i r diverging interests r e g a r d i n g the level o f pollution are m o d e l e d by differences in the countries' a b a t e m e n t cost and d a m a g e functions. Using standard functions quite c o m m o n in the literature, total costs o f country i (i e {1,2}) are ~I'C1 = T D 1 + T A C 1 = 2E'~ + ~ -~ - E 1
(1)
and TCu = TD~ + T A C ~ =
2 + 2 t b - E2
'
(2)
where TDi stands for total d a m a g e a n d T A C i is total a b a t e m e n t cost. Total damage d e p e n d s on aggregate emissions, E = E a + F~, total abatement cost depends u p o n country-specific emissions reductions ( a / b - Ei), where a/b is the level o f emissions generated by either of the countries 5 without any abatement activity ( T A C i = 0). T h e p a r a m e t e r s a, b, oL, d~, a n d )t are s u p p o s e d to be constant a n d non-negative, where q~, ~ ¢ 1 ensures that the countries are heterogeneous. Emissions a n d emission reductions are assumed to be non-negative, implying a
0 ~< E i ~< -~.
(3)
To make things both simple a n d brief, a numerical example is c o n s i d e r e d below, taking the p a r a m e t e r s to be 2 1 a = 12, b= 12, et = 1, ~b = ~ a n d k = ~
(4)
A. ENDRES It should be noted that this is ronmental negotiations. These show that the "folk t h e o r e m " sufficient to provide a counter (4), above.
149
sufficient to highlight certain problems of global enviproblems do not vanish in more general settings. To quoted in the introduction does not always hold, it is example using the parameter values given in equation
III. Pareto Optimal Emi~.sions The globally optimal level of pollution is defined by minimizing the sum of aggregate total costs, T C = T A C 1 + T A G 2 + T D 1 + T D 2, The necessary optimality conditions are MAC1 = MD and MAC~ = MD, where MD = MD 1 + M D 2 and M A C i stands for marginal abatement cost, and MD i (MD) are country-specific (aggregate) marginal damages. Using the functions and parameter values specified above, it follows that the Pareto optimal, country-specific and aggregate emission levels are 41 31 El** = E** 51' 2 - 51 24 E** 17
(5)
Substituting (5) into the total cost function leads to 40 TC**
-
17
(6)
IV. The Agreement on Emissions Reduction Quotas In this section we will investigate the individual and the aggregate equilibrium emission levels that are chosen in a convention on emission reduction quotas. As explained in the introduction the bargaining process is constrained by the assumption that equal percentage reductions are negotiated. 6 Given equations (1) and (2), the individual starting point emission levels from which reductions are measured in the process of the negotiations are equal. 7 Therefore, in a context of an equal percentage emissions reduction the absolute emission reduction quantities of the two countries are also equal. It follows from these two observations that the individual equilibrium emission levels u n d e r such an agreement are also equal to each other and equal to half of the worldwide emissions. So E 1q = E ~ = E Q / 2
follows.
(7)
To find each country's optimal strategy u n d e r these circumstances, equations (1) and (2) are minimized u n d e r the constraint of (7).8 Using the parameter values given in (4) the results are 3 9 E/Q(1) = ~ and E/Q(2)- 13 where the superscripts in brackets indicate which country's optimization the respective value is taken from. E~ (a) is the residual emission level of country i minimizing the first country's total costs u n d e r the quota agreement. So this country proposes to agree u p o n reducing
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Negotiating a climate convention
emissions by 1 - ~/(1), where 1 (= a/b, given equation (4)) is the starting p o i n t emission level for each country. Analogously, the proposal o f the s e c o n d country r e g a r d i n g the level o f emission reductions is 1 - E~ (2). Because E~ (1) > E~ (2), the first country (suggesting the lower r e d u c t i o n quota, implying the h i g h e r level o f residual emissions) turns out to he the bottleneck. Therefore, total residual emissions u n d e r the quota a g r e e m e n t are twice the first country's equilibrium residual emissions, i.e., E Q = 2E Q(1) =
(8)
T h e result that Country 1 serves as the bottleneck, given the p a r a m e t e r values assumed above, is quite plausible. T h e second country suffers two-thirds o f the first country's d a m a g e (6 -- 2 / 3 ) , but a b a t e m e n t costs are lower by a factor o f 2 (~ = 1 / 2 ) . Thus, in the "process ''9 of both countries r e d u c i n g emissions on a one-on-one basis the second country is motivated to go further than the first, securing a h i g h e r n e t benefit o f pollution control. Thus, the first country is the o n e o p t i n g out o f the negotiations "first," taking over the b o t t l e n e c k role. Substituting equation (8) into (1) a n d (2), using equation (7) shows country specific a n d aggregate cost u n d e r the quota convention to be 3 TC Q = ~
(9a)
15 TC~= 1--6
(9b)
and 39 TC Q = - 16
(9c)
V. The Agreement on Emimion Charges To find o u t a b o u t the individually optimal charge rate, each country must form expectations a b o u t what the situation will be after its own industry a n d the industry o f the o t h e r country have adjusted to a given charge rate. Particularly, each country has to assess equilibrium individual a n d total emissions to be able to estimate its own welfare position after the negotiations. To forecast the o t h e r country's a d j u s t m e n t to a given charge rate (which is essential to calculate total equilibrium pollution) each country must assess the o t h e r country's marginal a b a t e m e n t cost function. For simplicity, we assume below that this information r e q u i r e m e n t is met. In the pricing equilibrium, the marginal a b a t e m e n t costs o f the two countries are identical. This is so because (following c o m m o n e n v i r o n m e n t a l e c o n o m i c knowledge) within each country emissions are adjusted to a given charge rate such that marginal a b a t e m e n t costs are identical to this rate. So, using equations (1), (2), a n d (4), 12 - 12E a = 6 - 6E~ = t a n d therefore t E 1 = 1 - 1"-2
(10)
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151
t E 2 = 1 - ~ hold.
(11)
and
Thus, in the tax-adjusted equilibrium the second country's reduction load is double that of the first country's. This is not a big surprise because the second country's marginal abatement cost is half of the first country's cost. We find out about the tax rate proposed by either country during the negotiations, by substituting equations (10) and (11) into equations (1) and (2). Differentiating with respect to t leads to t (1) -
24
(12)
7
and t(2) _
24 15
(13)
So t (1) > t (2) holds, and the countries agree u p o n a tax rate t =/(2).
(14)
Substituting equations (14) and (13) into equations (10) and (11), we find the country-specific and the total equilibrium emissions u n d e r the pricing agreement to be p
13
11
E1 -~ "i5' E~ = "~ and Ep = 8 5
(15)
104 TCP = 7 5 '
(16a)
p 16 TC2=-i-g
(16b)
The respective total costs are
and TC P -
184 75
( 16c )
VI. Comparative Welfare Analysis of Quota and Pricing Conventions Comparing equations (5), (8), and (15) we find that E** (=1.4118) < EQ(=I.5) < EP(=I.6). Thus, in the equilibrium of both kinds of negotiations, aggregate emissions turn out to be higher than the social o p t i m u m would prescribe. Moreover, the result u n d e r the
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N e g o t i a t i n g a climate c o n v e n t i o n
quota agreement is "ecologically superior" to the result u n d e r the pricing approach. Furthermore, and perhaps more surprisingly, the quota convention is Pareto superior to the pricing convention: Comparing equations (6), (9c), and (16c) we find that TC**
(=2.3529) <
TC Q
(=2.4375) <
TC P
(=2.4533).
Thus, the environmental economics "folk t h e o r e m " maintaining that a market-based environmental policy instrument is allocatively superior to the non-market approach does not hold in the specific case analyzed in this paper. This possibly counterintuitive result can be understood by considering two countervailing welfare properties of the two policy instruments. O n the one hand, the pricing agreement is certainly more efficient than the quota agreement: Each given reduction in aggregate emissions is realized at a lower cost using charges rather than quotas, as is well known from traditional environmental economic reasoning. On the other hand, to assess total welfare, the level of aggregate pollution agreed u p o n u n d e r the two frameworks and its relation to the Pareto optimal level has to be taken into account. In the above example the pricing agreement deviates from the Pareto optimal aggregate emission level to a larger extent than the quota agreement does. Total welfare depends on which one of these two countervailing tendencies is the stronger. In the example, the "quantity effect" overcompensates the "efficiency effect," leaving the quota convention to be the Pareto superior arrangement, x° VH. Issues o f Unilateral Action
We now turn to the question of whether there is any incentive for either country to individually deviate from the agreements reached. The question is whether each country's total costs are minimized in the negotiated equilibrium, i.e., whether the contract represents a Nash equilibrium. More specifically, to have no incentive to unilaterally deviate, T C i = T D i + T A C i must be minimized. The necessary condition for the Nash equilibrium is MD i MAGi 11 Thus, the incentive to modify the situation agreed on in the convention can be measured by the "distortion index" =
D i = MAC i - MD i
(17)
If in the contracted equilibrium D i < 0 holds, there is an incentive for country i to reduce emissions by more than agreed on in the contract. O n the other hand, if D i > 0 holds true in the bargaining equilibrium, country i is tempted to increase pollution above the level negotiated. Calculating the distortion index for the quantity convention by substituting equation (8) into (17), using equations (1), (2), and (7), we find that 3 1 D Q = ~ and D Q - 2 Thus, in the quota convention both countries have an incentive to breach the contract by increasing pollution, a2. Analogously, for the pricing convention the distortion index shows 8 = 0 and D~2- 15 Thus, u n d e r the pricing agreement the first country plays its best response to the second
A. ENDRES
153
country's emission level p r o v i d e d that the s e c o n d country sticks to what has b e e n a g r e e d on. However, the s e c o n d country has an incentive to cheat. 1~ A c c o r d i n g to this r e a s o n i n g the contracts discussed in this p a p e r suffer from the " i n h e r e n t instability" often l a m e n t e d in the c o n t e x t o f i n t e r n a t i o n a l pollution problems. 14 T h e r e are two possible solutions to this p r o b l e m . First, the countries m i g h t submit to a s u p r a n a t i o n a l agency, e m p o w e r e d to enforce a contract once it has b e e n negotiated. This is a sacrifice o f sovereignty less severe than also leaving the design o f international e n v i r o n m e n t a l policy to such an agency in the first place. Yet, the countries must give u p some power, a n d they may hesitate to d o so. Second, the n e g o t i a t e d results may turn o u t to be stable if the relationship between the two countries is i n t e r p r e t e d n o t to be a one-shot g a m e b u t r a t h e r a r e p e a t e d game. It is well known from the g a m e theoretic folk t h e o r e m 15 that any b a r g a i n i n g result can be s u p p o r t e d in a r e p e a t e d g a m e given that the payoff is h i g h e r than the o n e each p a r t i c i p a n t can secure for himself a n d the involved parties are n o t too impatient. T h e payoff each party can a u t o n o m o u s l y secure is generally taken to be the MinMax payoff. S o m e t i m e s the payoff in the Nash e q u i l i b r i u m is c o n s i d e r e d to be the relevant benchmark.16 To see w h e t h e r the results of the negotiations derived above are stable in this sense, we calculate the MinMax a n d Nash payoffs for the two countries involved. Calculating the MinMax payoff for the first country, we solve max(E~) min (E 1) ( TC 1(E 1,E2) ) using equations (1), (2), (3), a n d (4) to find 11 E 1 = ]-~ a n d E2 = 1. So E 1 = 11/13 is the emission level of the first country minimizing its own cost given that the emissions o f the o t h e r country are at a level E.2 = 1, maximizing the cost o f the first country. Substituting these values into equation (1) using (4), we find the first country's MinMax payoff to be 24
(18a)
Tc~I M - 13
By analogous r e a s o n i n g the MinMax payoff for the s e c o n d country is identified to be 6
T~ M = g
(18b)
C o m p a r i n g equation (18a) to (9a) a n d (16a), respectively, as well as c o m p a r i n g equation (18b) a n d (9b) a n d (16b) respectively, we find
TcM1 M (=1.8462)> TC~(--1.5), TcMIM> TC~1(=1.3867), T ~ M ( = I . 2 ) > T~Q(=0.9375) a n d T ~ M >
T~(--1.0667).
So each country is b e t t e r off in the b a r g a i n i n g equilibrium than in the MinMax situation, irrespective o f w h e t h e r the negotiations are c o n d u c t e d on prices o r on quantities. Thus, these n e g o t i a t e d equilibria are stable, p r o v i d e d the MinMax solution serves as a b e n c h m a r k a n d the parties involved are patient. 17
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Negotiating a climate convention
T u r n i n g to the Nash e q u i l i b r i u m payoffs, we solve TC/= m i n ! to f i n d TC~l = 2808 1849
(19a)
T ~ V = 1920 1849
(19b)
and
C o m p a r i n g these values to the country-specific costs in the two b a r g a i n i n g e q u i l i b r i a we find Tc]v1(=l.5187) > TC~a, TCiVl> TC~'I, T~V(=l.0384) > T ~ 2 a n d T ~ V < T ~ ' . T h u s , c h a n g i n g the b e n c h m a r k f r o m M i n M a x to Nash does n o t t h r e a t e n the stability o f the q u a n t i t y c o n v e n t i o n . However, the p r i c i n g c o n v e n t i o n t u r n s o u t to be u n s t a b l e b e c a u s e the s e c o n d c o u n t r y is b e t t e r off in the Nash e q u i l i b r i u m t h a n u n d e r the e f f l u e n t c h a r g e regime. T h e r e f o r e , if the Nash e q u i l i b r i u m is t a k e n to b e the b e n c h mark, the c o n v e n t i o n o n charges seems to b e u n f e a s a b l e , s t r e n g t h e n i n g the case in favor o f the q u a n t i t y a g r e e m e n t m a d e in the p r e s e n t paper. VIH. Conclusion Two c o u n t r i e s n e g o t i a t i n g a p u b l i c bad-type p o l l u t a n t have b e e n analyzed in a very simple a n d t h e r e f o r e very restrictive m o d e l . Still, the analysis provides a c o u p l e o f i m p o r t a n t conclusions: • W i t h o u t transfer p a y m e n t s , n e g o t i a t i o n s b e t w e e n n o n - i d e n t i c a l c o u n t r i e s g e n e r a l l y lead to P a r e t o s u b o p t i m a l emissions levels. • T h e b e h a v i o r o f a n e g o t i a t i n g c o u n t r y does n o t d e p e n d o n its a b a t e m e n t a n d d a m a g e cost f u n c t i o n s a l o n e b u t also o n the policy i n s t r u m e n t n e g o t i a t e d . We have shown that even t h o u g h e f f l u e n t charges are m o r e efficient t h a n quotas, it c a n n o t be said that a n a g r e e m e n t o n taxes always leads to b e t t e r results t h a n a n a g r e e m e n t o n quotas. 18 O n the contrary, the quality o f the a g r e e m e n t d e p e n d s o n the differences b e t w e e n the n e g o t i a t i n g c o u n t r i e s r e g a r d i n g their a b a t e m e n t a n d d a m a g e costs.
Notes This paper is based on the work done by the author as a Visiting Professor at the Economics Department and the Law and Economics Center of the University of Miami. The author is indebted to Professors L. De Alessi and IL Clarkson for many stimulating discussions. Support by the Volkswagen-Foundation, Germany, is gratefully acknowledged. The paper also benefited from helpful comments by Professor R. Thomas, University of Iowa, M. Finus and B. Rundshagen, University of Hagen, Germany, and three anonymous referees. The numerical results presented in the paper have been produced by using Maple. 1. Using market forces (like effluent charges or transferable discharge permits) in environmental policy to secure allocative advantages has been the main quest of environmental economics as an applied field. As Goodstein (1995), pp. 267/8, 283, observes, there has been a "25-years struggle to influence the pollution control debate . . . . . maintaining a steady drumbeat of support for the more flexible incentive based approach." Given the consensus regarding the superiority of the pricing approach over the quota approach, there is an obvious need to explain why the latter is generally preferred to the former in practical environmental policy. This demand is met by the Public Choice literature on environmental policy, arguing that special interests prevent the use of efficient instruments. [See the seminal paper by Buchanan and Tullock (1975) and many subsequent analyses.]
A. ENDRES
155
2. T h e few practical conventions that allow for compensations, like the Montreal Protocol, are n o t designed to fulfil the stipulations of e c o n o m i c optimization models. 3. This is a very traditional approach: T h e g o v e r n m e n t r e p r e s e n t i n g either country in the negotiations is a s s u m e d to maximize the country's welfare. O f course, alternatively, a public choice-oriented perspective could be taken. However, this is b e y o n d the scope of this paper. 4. T h e smallest c o m m o n d e n o m i n a t o r principle follows from the a s s u m p t i o n that there are n o compensation payments. W i t h o u t such transfers there is n o t h i n g the country with the m o r e ambitious e n v i r o n m e n t a l goal can do to prevent the less interested country from opting o u t of the negotiations. T h e r e are m a n y examples for the application o f this principle in real-world international politics. 5. Because the level of pollution g e n e r a t e d without a b a t e m e n t is identical for the two countries, they are a s s u m e d to be of "equal size." Given the process of emission reduction for the two countries starts with these emission levels, E~I = / ~ , an equal percentage reduction of emissions is the same as an equal reduction in absolute terms. This "trick" simplifies the algebraic structure of the model. [See also Barrett (1992); Endres (1996); Hoel (1991).] 6. A g r e e m e n t s o n u n i f o r m emission reductions are very often used in practice, even t h o u g h they are generally inefficient. O n e of the reasons is that information asymmetries make the negotiation of differentiated reduction loads difficult. See Hoel (1991), p. 64. 7. O t h e r candidates for starting p o i n t emission levels are the Nash equilibrium emission levels. However, r e d u c i n g emission levels before negotiations start m i g h t weaken the position of the acting party a n d is therefore possibly avoided. [This has b e e n shown by Hoel (1991) a n d B o h m (1993).] In practice, s o m e historical emission level is often used as a b e n c h m a r k ; possibly a level between actual Nash emission levels a n d emissions at the point of zero emission reductions. For the sake of simplicity the p o i n t of zero emissions reduction is taken to be the b e n c h m a r k in this paper. 8. T h e necessary conditions for a m i n i m u m are M A C J 2 = MD i. See Endres (1996), p. 207, a n d Hoel (1991), p. 64. 9. O f course, the m o d e l p r e s e n t e d in the p r e s e n t p a p e r is static. So the word " p r o c e s s " is used for illustration only. 10. Clearly there is a set of p a r a m e t e r constellations, where the efficiency effect overcompensates the quantity effect and, therefore, the pricing convention is the superior institution. T h e r e is also a third set of parameters, where the pricing equilibrium is closer to the Pareto o p t i m u m t h a n the q u o t a equilibrium. In this case the quantity a n d the efficiency effect both work into the same direction; a clear case of the pricing a r r a n g e m e n t b e i n g Pareto superior to the quantity approach. 11. See, e.g., Hoel (1991), p. 57, a n d Welsch (1995), p. 219. It s h o u l d be n o t e d that marginal a b a t e m e n t costs are obtained by differentiating total a b a t e m e n t costs with respect to emission reductions (not with respect to emissions). 12. It should be n o t e d that there are p a r a m e t e r constellations (different to the o n e p r e s u p p o s e d in this paper), where o n e of the countries is i n d u c e d to " o v e r e n f o r c e " the contract. 13. E n d n o t e 12 applies. 14. See Barrett (1992), p. 27, who identifies an "irresistable urge o n the part of all the countries to cheat." T a h v o n e n et al. (1993) analyze an a g r e e m e n t between Finnland a n d the f o r m e r Soviet U n i o n calling for a u n i f o r m reduction in sulfur emissions in Finnland a n d adjacent regions of Russia. T h e y show that the a g r e e m e n t is strategically unstable a n d give an empirical assessment of the incentive to cheat. (There is no information on w h e t h e r cheating has actually occurred.) P u n i s h m e n t strategies to deter breaches o f contract, like the trigger strategy, are discussed in Barrett's a f o r e m e n t i o n e d paper (see pp. 27-32). In the political a r e n a trade sanctions as used in Article 4 of the Montreal O z o n e Protocol of 1987 are considered as having b e e n quite effective. 15. See, e.g., Eichberger (1993), Ch. 8, F r i e d m a n (1986), pp. 103-104, a n d Sabourian (1989), p. 66. This g a m e theoretic folk t h e o r e m is n o t to be confused with the " e n v i r o n m e n t a l e c o n o m i c folk t h e o r e m " which has b e e n discussed earlier in this paper. 16. See the literature in E n d n o t e 15. 17. Moreover, the equilibria are renegotiation proof. See Endres a n d Finus (1996).
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Negotiating a climate convention
18. A system of transferable discharge permits does not ahvays lead to better results than an agreement on quotas, either. See Endres and Finus (1996).
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Negotiating a Climate Convention: The Role of Prices and Quantities ALFRED ENDRES
University of Hagen, Germany E-mail: [email protected]
In this paper, we consider the economics of negotiating an international greenhouse convention. The agreement is either on emission charges ("prices") or on emission quotas ("quantities"). We show that negotiations between non-identical countries generally lead to Pareto suboptimal conventions. The extent of the deviation of worldwide equilibrium emissions from Pareto optimal emissions depends upon whether the agreement takes the pricing or the quantity approach. Counterintuitively, it turns out that under certain circumstances the quantity convention is Pareto superior to the pricing agreement. © 1997 by Elsevier Science Inc. I. Introduction
Methods and results of traditional environmental economics can be widely applied to global environmental issues. However, there is a specific point that sharply distinguishes global environmental problems from problems at the level of an individual country: In traditional environmental economics it has been (often implicitly) assumed that there is a central agency willing and able to apply environmental policy instruments even if the weffare of some decision makers (e.g., the polluters) is reduced by this activity. Taking a public choice-oriented view, this presumption seems to be doubtful, even in a national context. In a global setting, however, it is particularly unwarranted. It is an essential property of global environmental policy that it must be agreed upon by sovereign countries. In this paper we show that the requirement of countries' consent has important consequences for the equilibrium emissions reduction achievable by the application of alternative environmental policy instruments. One of the most important results of this paper is that a fundamental "folk theorem" of environmental economics maintaining that "effluent charges are allocatively superior to effluent standards ''l does not necessarily hold. The purpose of this paper is to explain the results of international agreements and to demonstrate how they vary with the choice of the "object" of the agreement. These International Review of Law a n d Economics 17:147-156, 1997 © 1997 by Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010
0144-8188/97/$17.00 PII S0144-8188(96)00057-9
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Negotiating a climate convention
objects are emission reduction quotas a n d effluent charges. For simplicity we assume that countries negotiate u n i f o r m quotas, or an identical effluent charge rate, respectively. Moreover, the p r o c e e d s o f the charge are assumed to r e m a i n in the country where they are raised. For simplicity a n d in a c c o r d a n c e with most real-world environmental a g r e e m e n t s there are no transfer payments between the two countries in the m o d e l p r e s e n t e d below. ~ T h e bargaining process is m o d e l e d as follows: T h e countries are assumed to be cost minimizers. ~ Each country's total cost consists o f e n v i r o n m e n t a l d a m a g e cost a n d pollution a b a t e m e n t cost. Given that the negotiations are on a r e d u c t i o n quota, each o f the two countries proposes a quota minimizing its own total cost. If the proposals o f the countries differ, they agree u p o n the "smallest c o m m o n d e n o m i n a t o r , " i.e., the smaller o f the two r e d u c t i o n quotas. Given that the negotiations are a b o u t an effluent charge rate, either country proposes the rate that minimizes its own total cost. In this case, the principle o f the smallest c o m m o n d e n o m i n a t o r makes t h e m agree on the lower o f the two charge rates proposed. T h e country o p t i n g for the smaller quota (tax rate), thus d e t e r m i n i n g the result o f the negotiations, is called the " b o t t l e n e c k country," below. 4
H. Countries with Diverging Interests Assume two h e t e r o g e n e o u s countries negotiating the emissions o f a global pollutant. T h e i r diverging interests r e g a r d i n g the level o f pollution are m o d e l e d by differences in the countries' a b a t e m e n t cost and d a m a g e functions. Using standard functions quite c o m m o n in the literature, total costs o f country i (i e {1,2}) are ~I'C1 = T D 1 + T A C 1 = 2E'~ + ~ -~ - E 1
(1)
and TCu = TD~ + T A C ~ =
2 + 2 t b - E2
'
(2)
where TDi stands for total d a m a g e a n d T A C i is total a b a t e m e n t cost. Total damage d e p e n d s on aggregate emissions, E = E a + F~, total abatement cost depends u p o n country-specific emissions reductions ( a / b - Ei), where a/b is the level o f emissions generated by either of the countries 5 without any abatement activity ( T A C i = 0). T h e p a r a m e t e r s a, b, oL, d~, a n d )t are s u p p o s e d to be constant a n d non-negative, where q~, ~ ¢ 1 ensures that the countries are heterogeneous. Emissions a n d emission reductions are assumed to be non-negative, implying a
0 ~< E i ~< -~.
(3)
To make things both simple a n d brief, a numerical example is c o n s i d e r e d below, taking the p a r a m e t e r s to be 2 1 a = 12, b= 12, et = 1, ~b = ~ a n d k = ~
(4)
A. ENDRES It should be noted that this is ronmental negotiations. These show that the "folk t h e o r e m " sufficient to provide a counter (4), above.
149
sufficient to highlight certain problems of global enviproblems do not vanish in more general settings. To quoted in the introduction does not always hold, it is example using the parameter values given in equation
III. Pareto Optimal Emi~.sions The globally optimal level of pollution is defined by minimizing the sum of aggregate total costs, T C = T A C 1 + T A G 2 + T D 1 + T D 2, The necessary optimality conditions are MAC1 = MD and MAC~ = MD, where MD = MD 1 + M D 2 and M A C i stands for marginal abatement cost, and MD i (MD) are country-specific (aggregate) marginal damages. Using the functions and parameter values specified above, it follows that the Pareto optimal, country-specific and aggregate emission levels are 41 31 El** = E** 51' 2 - 51 24 E** 17
(5)
Substituting (5) into the total cost function leads to 40 TC**
-
17
(6)
IV. The Agreement on Emissions Reduction Quotas In this section we will investigate the individual and the aggregate equilibrium emission levels that are chosen in a convention on emission reduction quotas. As explained in the introduction the bargaining process is constrained by the assumption that equal percentage reductions are negotiated. 6 Given equations (1) and (2), the individual starting point emission levels from which reductions are measured in the process of the negotiations are equal. 7 Therefore, in a context of an equal percentage emissions reduction the absolute emission reduction quantities of the two countries are also equal. It follows from these two observations that the individual equilibrium emission levels u n d e r such an agreement are also equal to each other and equal to half of the worldwide emissions. So E 1q = E ~ = E Q / 2
follows.
(7)
To find each country's optimal strategy u n d e r these circumstances, equations (1) and (2) are minimized u n d e r the constraint of (7).8 Using the parameter values given in (4) the results are 3 9 E/Q(1) = ~ and E/Q(2)- 13 where the superscripts in brackets indicate which country's optimization the respective value is taken from. E~ (a) is the residual emission level of country i minimizing the first country's total costs u n d e r the quota agreement. So this country proposes to agree u p o n reducing
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Negotiating a climate convention
emissions by 1 - ~/(1), where 1 (= a/b, given equation (4)) is the starting p o i n t emission level for each country. Analogously, the proposal o f the s e c o n d country r e g a r d i n g the level o f emission reductions is 1 - E~ (2). Because E~ (1) > E~ (2), the first country (suggesting the lower r e d u c t i o n quota, implying the h i g h e r level o f residual emissions) turns out to he the bottleneck. Therefore, total residual emissions u n d e r the quota a g r e e m e n t are twice the first country's equilibrium residual emissions, i.e., E Q = 2E Q(1) =
(8)
T h e result that Country 1 serves as the bottleneck, given the p a r a m e t e r values assumed above, is quite plausible. T h e second country suffers two-thirds o f the first country's d a m a g e (6 -- 2 / 3 ) , but a b a t e m e n t costs are lower by a factor o f 2 (~ = 1 / 2 ) . Thus, in the "process ''9 of both countries r e d u c i n g emissions on a one-on-one basis the second country is motivated to go further than the first, securing a h i g h e r n e t benefit o f pollution control. Thus, the first country is the o n e o p t i n g out o f the negotiations "first," taking over the b o t t l e n e c k role. Substituting equation (8) into (1) a n d (2), using equation (7) shows country specific a n d aggregate cost u n d e r the quota convention to be 3 TC Q = ~
(9a)
15 TC~= 1--6
(9b)
and 39 TC Q = - 16
(9c)
V. The Agreement on Emimion Charges To find o u t a b o u t the individually optimal charge rate, each country must form expectations a b o u t what the situation will be after its own industry a n d the industry o f the o t h e r country have adjusted to a given charge rate. Particularly, each country has to assess equilibrium individual a n d total emissions to be able to estimate its own welfare position after the negotiations. To forecast the o t h e r country's a d j u s t m e n t to a given charge rate (which is essential to calculate total equilibrium pollution) each country must assess the o t h e r country's marginal a b a t e m e n t cost function. For simplicity, we assume below that this information r e q u i r e m e n t is met. In the pricing equilibrium, the marginal a b a t e m e n t costs o f the two countries are identical. This is so because (following c o m m o n e n v i r o n m e n t a l e c o n o m i c knowledge) within each country emissions are adjusted to a given charge rate such that marginal a b a t e m e n t costs are identical to this rate. So, using equations (1), (2), a n d (4), 12 - 12E a = 6 - 6E~ = t a n d therefore t E 1 = 1 - 1"-2
(10)
A. ENDRES
151
t E 2 = 1 - ~ hold.
(11)
and
Thus, in the tax-adjusted equilibrium the second country's reduction load is double that of the first country's. This is not a big surprise because the second country's marginal abatement cost is half of the first country's cost. We find out about the tax rate proposed by either country during the negotiations, by substituting equations (10) and (11) into equations (1) and (2). Differentiating with respect to t leads to t (1) -
24
(12)
7
and t(2) _
24 15
(13)
So t (1) > t (2) holds, and the countries agree u p o n a tax rate t =/(2).
(14)
Substituting equations (14) and (13) into equations (10) and (11), we find the country-specific and the total equilibrium emissions u n d e r the pricing agreement to be p
13
11
E1 -~ "i5' E~ = "~ and Ep = 8 5
(15)
104 TCP = 7 5 '
(16a)
p 16 TC2=-i-g
(16b)
The respective total costs are
and TC P -
184 75
( 16c )
VI. Comparative Welfare Analysis of Quota and Pricing Conventions Comparing equations (5), (8), and (15) we find that E** (=1.4118) < EQ(=I.5) < EP(=I.6). Thus, in the equilibrium of both kinds of negotiations, aggregate emissions turn out to be higher than the social o p t i m u m would prescribe. Moreover, the result u n d e r the
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N e g o t i a t i n g a climate c o n v e n t i o n
quota agreement is "ecologically superior" to the result u n d e r the pricing approach. Furthermore, and perhaps more surprisingly, the quota convention is Pareto superior to the pricing convention: Comparing equations (6), (9c), and (16c) we find that TC**
(=2.3529) <
TC Q
(=2.4375) <
TC P
(=2.4533).
Thus, the environmental economics "folk t h e o r e m " maintaining that a market-based environmental policy instrument is allocatively superior to the non-market approach does not hold in the specific case analyzed in this paper. This possibly counterintuitive result can be understood by considering two countervailing welfare properties of the two policy instruments. O n the one hand, the pricing agreement is certainly more efficient than the quota agreement: Each given reduction in aggregate emissions is realized at a lower cost using charges rather than quotas, as is well known from traditional environmental economic reasoning. On the other hand, to assess total welfare, the level of aggregate pollution agreed u p o n u n d e r the two frameworks and its relation to the Pareto optimal level has to be taken into account. In the above example the pricing agreement deviates from the Pareto optimal aggregate emission level to a larger extent than the quota agreement does. Total welfare depends on which one of these two countervailing tendencies is the stronger. In the example, the "quantity effect" overcompensates the "efficiency effect," leaving the quota convention to be the Pareto superior arrangement, x° VH. Issues o f Unilateral Action
We now turn to the question of whether there is any incentive for either country to individually deviate from the agreements reached. The question is whether each country's total costs are minimized in the negotiated equilibrium, i.e., whether the contract represents a Nash equilibrium. More specifically, to have no incentive to unilaterally deviate, T C i = T D i + T A C i must be minimized. The necessary condition for the Nash equilibrium is MD i MAGi 11 Thus, the incentive to modify the situation agreed on in the convention can be measured by the "distortion index" =
D i = MAC i - MD i
(17)
If in the contracted equilibrium D i < 0 holds, there is an incentive for country i to reduce emissions by more than agreed on in the contract. O n the other hand, if D i > 0 holds true in the bargaining equilibrium, country i is tempted to increase pollution above the level negotiated. Calculating the distortion index for the quantity convention by substituting equation (8) into (17), using equations (1), (2), and (7), we find that 3 1 D Q = ~ and D Q - 2 Thus, in the quota convention both countries have an incentive to breach the contract by increasing pollution, a2. Analogously, for the pricing convention the distortion index shows 8 = 0 and D~2- 15 Thus, u n d e r the pricing agreement the first country plays its best response to the second
A. ENDRES
153
country's emission level p r o v i d e d that the s e c o n d country sticks to what has b e e n a g r e e d on. However, the s e c o n d country has an incentive to cheat. 1~ A c c o r d i n g to this r e a s o n i n g the contracts discussed in this p a p e r suffer from the " i n h e r e n t instability" often l a m e n t e d in the c o n t e x t o f i n t e r n a t i o n a l pollution problems. 14 T h e r e are two possible solutions to this p r o b l e m . First, the countries m i g h t submit to a s u p r a n a t i o n a l agency, e m p o w e r e d to enforce a contract once it has b e e n negotiated. This is a sacrifice o f sovereignty less severe than also leaving the design o f international e n v i r o n m e n t a l policy to such an agency in the first place. Yet, the countries must give u p some power, a n d they may hesitate to d o so. Second, the n e g o t i a t e d results may turn o u t to be stable if the relationship between the two countries is i n t e r p r e t e d n o t to be a one-shot g a m e b u t r a t h e r a r e p e a t e d game. It is well known from the g a m e theoretic folk t h e o r e m 15 that any b a r g a i n i n g result can be s u p p o r t e d in a r e p e a t e d g a m e given that the payoff is h i g h e r than the o n e each p a r t i c i p a n t can secure for himself a n d the involved parties are n o t too impatient. T h e payoff each party can a u t o n o m o u s l y secure is generally taken to be the MinMax payoff. S o m e t i m e s the payoff in the Nash e q u i l i b r i u m is c o n s i d e r e d to be the relevant benchmark.16 To see w h e t h e r the results of the negotiations derived above are stable in this sense, we calculate the MinMax a n d Nash payoffs for the two countries involved. Calculating the MinMax payoff for the first country, we solve max(E~) min (E 1) ( TC 1(E 1,E2) ) using equations (1), (2), (3), a n d (4) to find 11 E 1 = ]-~ a n d E2 = 1. So E 1 = 11/13 is the emission level of the first country minimizing its own cost given that the emissions o f the o t h e r country are at a level E.2 = 1, maximizing the cost o f the first country. Substituting these values into equation (1) using (4), we find the first country's MinMax payoff to be 24
(18a)
Tc~I M - 13
By analogous r e a s o n i n g the MinMax payoff for the s e c o n d country is identified to be 6
T~ M = g
(18b)
C o m p a r i n g equation (18a) to (9a) a n d (16a), respectively, as well as c o m p a r i n g equation (18b) a n d (9b) a n d (16b) respectively, we find
TcM1 M (=1.8462)> TC~(--1.5), TcMIM> TC~1(=1.3867), T ~ M ( = I . 2 ) > T~Q(=0.9375) a n d T ~ M >
T~(--1.0667).
So each country is b e t t e r off in the b a r g a i n i n g equilibrium than in the MinMax situation, irrespective o f w h e t h e r the negotiations are c o n d u c t e d on prices o r on quantities. Thus, these n e g o t i a t e d equilibria are stable, p r o v i d e d the MinMax solution serves as a b e n c h m a r k a n d the parties involved are patient. 17
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Negotiating a climate convention
T u r n i n g to the Nash e q u i l i b r i u m payoffs, we solve TC/= m i n ! to f i n d TC~l = 2808 1849
(19a)
T ~ V = 1920 1849
(19b)
and
C o m p a r i n g these values to the country-specific costs in the two b a r g a i n i n g e q u i l i b r i a we find Tc]v1(=l.5187) > TC~a, TCiVl> TC~'I, T~V(=l.0384) > T ~ 2 a n d T ~ V < T ~ ' . T h u s , c h a n g i n g the b e n c h m a r k f r o m M i n M a x to Nash does n o t t h r e a t e n the stability o f the q u a n t i t y c o n v e n t i o n . However, the p r i c i n g c o n v e n t i o n t u r n s o u t to be u n s t a b l e b e c a u s e the s e c o n d c o u n t r y is b e t t e r off in the Nash e q u i l i b r i u m t h a n u n d e r the e f f l u e n t c h a r g e regime. T h e r e f o r e , if the Nash e q u i l i b r i u m is t a k e n to b e the b e n c h mark, the c o n v e n t i o n o n charges seems to b e u n f e a s a b l e , s t r e n g t h e n i n g the case in favor o f the q u a n t i t y a g r e e m e n t m a d e in the p r e s e n t paper. VIH. Conclusion Two c o u n t r i e s n e g o t i a t i n g a p u b l i c bad-type p o l l u t a n t have b e e n analyzed in a very simple a n d t h e r e f o r e very restrictive m o d e l . Still, the analysis provides a c o u p l e o f i m p o r t a n t conclusions: • W i t h o u t transfer p a y m e n t s , n e g o t i a t i o n s b e t w e e n n o n - i d e n t i c a l c o u n t r i e s g e n e r a l l y lead to P a r e t o s u b o p t i m a l emissions levels. • T h e b e h a v i o r o f a n e g o t i a t i n g c o u n t r y does n o t d e p e n d o n its a b a t e m e n t a n d d a m a g e cost f u n c t i o n s a l o n e b u t also o n the policy i n s t r u m e n t n e g o t i a t e d . We have shown that even t h o u g h e f f l u e n t charges are m o r e efficient t h a n quotas, it c a n n o t be said that a n a g r e e m e n t o n taxes always leads to b e t t e r results t h a n a n a g r e e m e n t o n quotas. 18 O n the contrary, the quality o f the a g r e e m e n t d e p e n d s o n the differences b e t w e e n the n e g o t i a t i n g c o u n t r i e s r e g a r d i n g their a b a t e m e n t a n d d a m a g e costs.
Notes This paper is based on the work done by the author as a Visiting Professor at the Economics Department and the Law and Economics Center of the University of Miami. The author is indebted to Professors L. De Alessi and IL Clarkson for many stimulating discussions. Support by the Volkswagen-Foundation, Germany, is gratefully acknowledged. The paper also benefited from helpful comments by Professor R. Thomas, University of Iowa, M. Finus and B. Rundshagen, University of Hagen, Germany, and three anonymous referees. The numerical results presented in the paper have been produced by using Maple. 1. Using market forces (like effluent charges or transferable discharge permits) in environmental policy to secure allocative advantages has been the main quest of environmental economics as an applied field. As Goodstein (1995), pp. 267/8, 283, observes, there has been a "25-years struggle to influence the pollution control debate . . . . . maintaining a steady drumbeat of support for the more flexible incentive based approach." Given the consensus regarding the superiority of the pricing approach over the quota approach, there is an obvious need to explain why the latter is generally preferred to the former in practical environmental policy. This demand is met by the Public Choice literature on environmental policy, arguing that special interests prevent the use of efficient instruments. [See the seminal paper by Buchanan and Tullock (1975) and many subsequent analyses.]
A. ENDRES
155
2. T h e few practical conventions that allow for compensations, like the Montreal Protocol, are n o t designed to fulfil the stipulations of e c o n o m i c optimization models. 3. This is a very traditional approach: T h e g o v e r n m e n t r e p r e s e n t i n g either country in the negotiations is a s s u m e d to maximize the country's welfare. O f course, alternatively, a public choice-oriented perspective could be taken. However, this is b e y o n d the scope of this paper. 4. T h e smallest c o m m o n d e n o m i n a t o r principle follows from the a s s u m p t i o n that there are n o compensation payments. W i t h o u t such transfers there is n o t h i n g the country with the m o r e ambitious e n v i r o n m e n t a l goal can do to prevent the less interested country from opting o u t of the negotiations. T h e r e are m a n y examples for the application o f this principle in real-world international politics. 5. Because the level of pollution g e n e r a t e d without a b a t e m e n t is identical for the two countries, they are a s s u m e d to be of "equal size." Given the process of emission reduction for the two countries starts with these emission levels, E~I = / ~ , an equal percentage reduction of emissions is the same as an equal reduction in absolute terms. This "trick" simplifies the algebraic structure of the model. [See also Barrett (1992); Endres (1996); Hoel (1991).] 6. A g r e e m e n t s o n u n i f o r m emission reductions are very often used in practice, even t h o u g h they are generally inefficient. O n e of the reasons is that information asymmetries make the negotiation of differentiated reduction loads difficult. See Hoel (1991), p. 64. 7. O t h e r candidates for starting p o i n t emission levels are the Nash equilibrium emission levels. However, r e d u c i n g emission levels before negotiations start m i g h t weaken the position of the acting party a n d is therefore possibly avoided. [This has b e e n shown by Hoel (1991) a n d B o h m (1993).] In practice, s o m e historical emission level is often used as a b e n c h m a r k ; possibly a level between actual Nash emission levels a n d emissions at the point of zero emission reductions. For the sake of simplicity the p o i n t of zero emissions reduction is taken to be the b e n c h m a r k in this paper. 8. T h e necessary conditions for a m i n i m u m are M A C J 2 = MD i. See Endres (1996), p. 207, a n d Hoel (1991), p. 64. 9. O f course, the m o d e l p r e s e n t e d in the p r e s e n t p a p e r is static. So the word " p r o c e s s " is used for illustration only. 10. Clearly there is a set of p a r a m e t e r constellations, where the efficiency effect overcompensates the quantity effect and, therefore, the pricing convention is the superior institution. T h e r e is also a third set of parameters, where the pricing equilibrium is closer to the Pareto o p t i m u m t h a n the q u o t a equilibrium. In this case the quantity a n d the efficiency effect both work into the same direction; a clear case of the pricing a r r a n g e m e n t b e i n g Pareto superior to the quantity approach. 11. See, e.g., Hoel (1991), p. 57, a n d Welsch (1995), p. 219. It s h o u l d be n o t e d that marginal a b a t e m e n t costs are obtained by differentiating total a b a t e m e n t costs with respect to emission reductions (not with respect to emissions). 12. It should be n o t e d that there are p a r a m e t e r constellations (different to the o n e p r e s u p p o s e d in this paper), where o n e of the countries is i n d u c e d to " o v e r e n f o r c e " the contract. 13. E n d n o t e 12 applies. 14. See Barrett (1992), p. 27, who identifies an "irresistable urge o n the part of all the countries to cheat." T a h v o n e n et al. (1993) analyze an a g r e e m e n t between Finnland a n d the f o r m e r Soviet U n i o n calling for a u n i f o r m reduction in sulfur emissions in Finnland a n d adjacent regions of Russia. T h e y show that the a g r e e m e n t is strategically unstable a n d give an empirical assessment of the incentive to cheat. (There is no information on w h e t h e r cheating has actually occurred.) P u n i s h m e n t strategies to deter breaches o f contract, like the trigger strategy, are discussed in Barrett's a f o r e m e n t i o n e d paper (see pp. 27-32). In the political a r e n a trade sanctions as used in Article 4 of the Montreal O z o n e Protocol of 1987 are considered as having b e e n quite effective. 15. See, e.g., Eichberger (1993), Ch. 8, F r i e d m a n (1986), pp. 103-104, a n d Sabourian (1989), p. 66. This g a m e theoretic folk t h e o r e m is n o t to be confused with the " e n v i r o n m e n t a l e c o n o m i c folk t h e o r e m " which has b e e n discussed earlier in this paper. 16. See the literature in E n d n o t e 15. 17. Moreover, the equilibria are renegotiation proof. See Endres a n d Finus (1996).
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Negotiating a climate convention
18. A system of transferable discharge permits does not ahvays lead to better results than an agreement on quotas, either. See Endres and Finus (1996).
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