Equitable and Efficient International Schemes to Control Carbon Dioxide Emissions

Transcription

1 Equitable and Efficient International Schemes to Control Carbon Dioxide Emissions Arthur J. Caplan Department of Economics John B. Goddard School of Business and Economics Weber State University Ogden, Utah and Emilson C.D. Silva Department of Economics Tulane University New Orleans, LA September 12, 2000 Abstract: We examine three noncooperative global warming games where carbon dioxide emissions and transfers are determined. An international agency implements transfers from rich to poor nations. In each game, the transfer mechanism obeys a predetermined equity principle horizontal, proportional or green GNP. Participation in each transfer scheme is voluntary. We find that implementable horizontal and proportional equity schemes are Pareto efficient. The green equity scheme, however, is generally inefficient. Unlike the others, our proposed proportional equity scheme is necessarily implementable all nations always choose to participate. We conclude that proportional equity transfer schemes may be powerful instruments in controlling global warming. JEL Classification: C72, D62, D78, H41, H77, Q28. Acknowledgements: Caplan thanks the John B. Goddard School of Business for summer research support which led to the completion of this manuscript.

2 1 1. Introduction The Kyoto Protocol to the United Nations Framework Convention on Climate Change, completed December 10, 1997, will probably be remembered most for its innovative use of emissions trading to control global greenhouse gas emissions. 1 However, it will also be remembered for the promulgation of another type of incentive: international transfers between rich and lower-income nations. 2 As stated in Article 12 of the protocol, transfers should be used as a means to: (1) provide new and additional financial resources to meet the agreed full costs incurred by [lower-income] countries in advancing the implementation of existing commitments, and (2) provide such financial resources, including for the transfer of technology, needed by [lower-income] countries to meet the agreed full incremental costs of advancing the implementation of existing commitments. It is, therefore, apparent that there will be a significant amount of resources transferred from rich to poor nations and that the implementation of international transfer schemes will have tremendous effects on the allocation of global resources. Such international transfers may provide rich and poor nations with incentives to efficiently abate their carbon dioxide emissions. 1 That emissions trading is a cost-effective means of controlling pollution is not much in debate. The theory behind its use is generally clear, simple, and favorable: compared to command-and-control policies, such as uniform quotas, emissions trading induces firms to obtain the same aggregate level of control at lower total cost (c.f. Tietenberg, 1992; Hanley, et al., 1997). Moreover, similar types of marketable permit programs in the U.S. used to control water, lead, and air pollution, have proven effective (Hahn, 1989; Stavins, 1998). All told, an impressive amount of research and experience underscores the benefits and costs associated with emissions trading programs (see Maloney and Yandle (1984), Coggins and Swinton (1996), Burtraw (1996), and references therein). 2 The protocol also introduces a third market mechanism to control greenhouse gas emissions, known as clean development mechanisms (see Article 11). We examine the efficiency properties of this mechanism in a separate paper.

3 2 In this paper, we examine how rich and poor nations allocate their resources when they anticipate that transfers will be made from rich to poor nations in order to satisfy a particular equity principle. We investigate the efficiency properties of international transfers that emerge from voluntary participation of rich and poor nations in three types of international schemes designed to induce the nations to control carbon dioxide emissions. Each scheme obeys a specific equity principle, namely, horizontal equity, proportional equity and green equity. Under horizontal equity, the amount of the transfer effected follows from a condition that equates utilities of representative residents of rich and poor nations. This is undoubtedly an extreme form of international justice, but it provides a useful benchmark for future comparisons. Under proportional equity, the transfer is determined by a condition that preserves the status-quo relative ranking of international welfare levels: the welfare of rich and poor nations are equated as proportions of their respective reservation welfare levels. Under green equity, the transfer is derived from a condition that equates green GNP s across rich and poor nations. 3 Interestingly, we find that rich and poor nations efficiently curb their carbon dioxide emissions whenever they participate in the transfer schemes that obey horizontal and proportional equity principles. However, under green equity, both types of nations find it desirable to emit more than the efficient level of carbon dioxide. The Kyoto Protocol s promotion of international transfers as a means to reduce global carbon dioxide emissions is apparently a step in the right direction. As Sandler (1997) points out, the control of global warming requires stronger effort to bring about collective action than 3 For a comprehensive discussion of various green GNP measures presently in use, see Hamilton and Lutz (1996) and World Bank (1999).

4 3 that required to control other types of regional and global externalities, such acid rain and CFC emissions. For example, both the Helsinki Protocol (1985) to control sulfur emissions and the Sofia Protocol (1988) to control nitrogen oxide emissions merely codified reductions that the parties had either already independently implemented or were soon to achieve (Murdoch, Sandler, and Sargent, 1997). Similarly, the Montreal Protocol (1987) to control CFC emissions did not impose any new constraints on its signatories. Rather, the protocol served to legitimize the strategically chosen status quo (Murdoch and Sandler, 1997). Primarily because the benefits of curbing their carbon dioxide emissions are greatly outweighed by the associated costs, nations independently have less incentive to abate. Incentives such as transfers are therefore more likely to be effective in controlling global warming. It may not be difficult to implement some of the international transfer schemes studied in this paper. There are already several international schemes that transfer resources from rich to poor nations. Despite the well-documented decline in foreign aid among OECD-member nations (measured as percentages of GDP over time), poverty-reduction remains a primary objective of this aid (OECD, 1995 and 1996). In addition, the widespread movement toward debt relief for poor nations points up the fact that official foreign aid statistics tend to underestimate the extent of transfers taking place between rich and poor nations (Phillips, 1999). Controlling global warming, therefore, may provide yet another rationale for international transfers. In fact, the Conference of the Parties to the United Nations Framework Convention on Climate Change, which represents the supreme body of the Convention, has delegated the responsibility of operating the Convention s financial mechanism to the Global Environment Facility (GEF). The GEF was established in 1990 by the World Bank, the United Nations

5 4 Development Programme (UNDP), and the United Nations Environment Programme (UNEP). The role of the convention s mechanism is to transfer funds and technology from rich to poor nations. The GEF, however, lacks political and economical powers to design and enforce international mechanisms to control emissions of carbon dioxide. In other words, the GEF is not capable of punishing regions that do not comply with international standards. The interregional transfers implemented by the GEF are redistributive, namely, they are effected after the regions choose their own environmental actions. Perhaps the best method of measuring the strength of international equity constraints is to track changes in the ratio of green GNP s across regions over time. For example, a 1994 World Bank (1999) estimate of the ratio of aggregate green GNP between South American, Central American, African, and Asian nations on the one hand, and North American, Pacific OECD, and Western European nations on the other is approximately Transfers from the latter group of nations might therefore be targeted toward either maintaining or perhaps increasing this ratio over time. The paper is organized as follows. Section 2 introduces the basic model and examines both Pareto efficiency and the Nash equilibrium in absence of transfers. Section 3 explores the efficiency properties of three transfer schemes, horizontal equity, proportional equity and green equity. Section 4 concludes the study with a brief summary of our findings. 2. The Model We assume two coalitions of countries indexed r (rich) and p (poor), respectively, where countries are identical within a coalition. We further assume that population sizes across the

6 5 coalitions are equal and normalized to one, so that a representative agent s utility may also be interpreted as regional welfare. Regional welfare is expressed as U j = U(x j, y j ), j = r, p (1) where x j represents a good whose production results in carbon dioxide emissions, and y j represents a non-carbon dioxide-producing good (e.g. an agricultural good), which will serve as our numeraire good. We assume that U is increasing in both arguments, quasiconcave and twice continuously differentiable. Given normalized populations and equalized rates of diffusion and absorption, we assume that the total flow of carbon dioxide emissions, G, is given by G = j x j = x r + x p. (2) Region j s resource constraint is as follows: (3) where the unit of the industrial good is chosen so that its price equals 1. While on the left-hand side of (3) we have the region j s consumption expenditure, on the right-hand side we have the region s net income. The quantity I j > 0 represents region j s exogenously-given initial endowment in absence of carbon dioxide emissions. We assume that each unit of carbon dioxide emitted depletes the region j s endowment at a rate j (0, 1), so that region j s net income equals I j j G. We assume that 1 > p > r in order to capture the common belief that a greater proportion of poor nations are more sensitive than rich nations to the negative effects of global warming, as a result of both geographic location and economic structures (Poterba, 1993). For future reference, it is important to note that the terms I j j G, j = r,p represent the respective

7 6 regions green GNP s, since these quantities should equal the regions national incomes net of damages caused by the global externality. 4 By adding the individual resource constraints, we obtain the global resource constraint: (4) A Pareto efficient allocation can be determined by choosing {x j, y j,; j = r,p} in order to maximize U r subject to (2), (4) and U p = K, where K > 0 is some constant. By varying K, we can derive the entire Pareto frontier. In addition to (4) and U p = K, the first order conditions that characterize the Pareto efficient allocation are as follows: 5 (5) Equations (5) show that the marginal rates of substitution left-hand side should be set equal to the common marginal social rate of transformation right-hand side. The marginal social rate of transformation between industrial and agricultural goods is the sum of the added 4 This is an obvious abstraction from how green GNP is actually defined for individual nations. For instance, degradation of the environment due to local externalities and the depletion of non-renewable natural resources is also netted out of the standard GNP measure in calculating a nation s green GNP or genuine savings measures (see Hamilton and Lutz, 1996). However, holding constant these types of more localized deletions from GNP, our representation of green GNP allows for an accurate measure of the global externality s relative effects on initial endowments. 5 Throughout the paper, we assume that interior and locally unique solutions and that the first order conditions are not only necessary but also sufficient for a maximum.

8 7 value of agricultural good forgone and of the (negative) externality effects on available resources in each region. For the purpose of comparison, consider the simultaneous Nash game played by rich and poor regions in absence of international transfers. In this game, region j independently chooses {x j, y j } in order to maximize U j, subject to (2) and (3). The resulting first order conditions for the Nash equilibrium without transfers are as follows: (6) Equations (6) indicate that the regions equate their marginal rates of substitution to their respective private marginal rates of transformation, rather than the social marginal rate. This follows because the regions neglect the external effects of their carbon dioxide emissions. This fact provides a rationale for some form of intervention to improve global welfare. Let U j0 denote the utility level obtained by region j in the simultaneous Nash equilibrium. In what follows, this will represent region j s reservation utility level. It is important to note that 0 since I r - r G > I p - p G, U r > U p0. See Figure 1. [INSERT FIGURE 1 HERE] 3. International Equity Constraints Henceforth, let denote the amount of nonnegative income, in terms of the numeraire good, that is transferred from the rich region to the poor region in order to satisfy a predetermined equity principle. These transfer instruments are controlled by an international

9 8 agency, say the Global Environment Facility (GEF). In the presence of international income transfers, we obtain the following resource constraints for the rich and poor regions, respectively: (7a) and (7b) Our benchmark equity principle is horizontal equity. Under horizontal equity, the rich region transfers income to the poor region in an amount that equates regional welfare levels (i.e., U r = U p ). This is an extreme form of equity, which might be feasible when initial resource endowments are approximately equal across regions. Under proportional equity, the transfer amount follows from equalization of the proportions of regional welfare levels to respective noncooperative Nash welfare levels (i.e., U r / U r0 = U p / U p0 ). Finally, under green equity, the transfer is determined so as to equate regional green GNP s. Transfers are implemented by the GEF after the regions choose their resource allocations. We postulate that each region s participation in the transfer scheme is voluntary. To be implementable, the transfer scheme must satisfy participation constraints for both regions, namely, it must provide each nation with a utility level that it is at least as large as each nation s reservation utility level. The games examined below are three-stage games (see, e.g., Caplan, et al. (1999), Caplan and Silva (1999) and Silva and Caplan (1997) for examples of similar multistage games involving transboundary externalities). In the first stage of each game, both regions decide whether or not to participate in the particular transfer mechanism. In the second

10 9 stage of the game, the rich region chooses x r while the poor region chooses x p, taking the choices of each other as given. In the third stage of each game, the GEF determines the amount of the transfer that should be implemented in order to satisfy the underlying equity principle. Both regions anticipate the transfer and its effects on resource allocation when they move in the first two stages of the game. The games are solved by backward induction, and the equilibrium concept used is subgame perfect equilibrium. 3.1 Horizontal Equity In the third stage of this game, the GEF chooses {y j, ; j = r,p} to maximize U r subject to (7a), (7b) and U r = U p, taking {x j, j = r,p} as given. It is important to note that since the agricultural good is our numeraire and income is measured in terms of the numeraire, the transfer instruments essentially endow the GEF with the ability of determining the allocation of the total endowment of agricultural good available at the beginning of the third stage of the game between the two regions. Furthermore, since by adding up equations (7a) and (7b) we get equation (4), the GEF problem simplifies to choosing {y j ; j = r,p} to maximize U r subject to (4) and U r = U p. The solution to this problem is given by: (8). (9)

11 In writing (8) and (9), we have already utilized the fact that the solution equations can be used to define the implicit functions y j1 (x r, x p ), j = r,p. 6 Differentiating the equations above yields: 10 (10a) (10b) (10c) (10d) Equations (10a) and (10c) tell us that the sum of the marginal responses to an increase in industrial production should equal the negative of the marginal transformation rate. Equations (10b) and (10d) show us how the utilities have to be adjusted when industrial production is increased in order to satisfy the horizontal equity property. In the second stage, region j chooses {x j } to maximize U j subject to y j = y j1 (x r, x p ), j = r,p. The first order conditions are as follows: (11) 6 For the remainder of the paper, superscript k, k = 1,2,3, will be used to distinguish functions and equilibrium quantities of the three different games.

12 11 As the marginal utilities of agricultural consumption are positive, equations (10b), (10d) and (11) imply that: (12) (13) Rewrite equations (11) as follows: (14) Now, note that equations (13) and (14) together imply equations (5). Since, as we have already seen, the transfer scheme also satisfies equation (4), we obtain the following result: Proposition 1: The transfer scheme based on the horizontal equity principle is Pareto efficient. This is a powerful result. Because each region finds it desirable to produce and consume the industrial good at an amount that satisfies the efficient conditions (5), we may conclude that each region unilaterally realizes that non-internalization of the global externality will only harm itself regional utilities are equated in the third stage of the game in spite of the actions taken in the second stage. In a sense, the incentives introduced by the transfer scheme are powerful enough to nullify each region s potential gain in ignoring the externality that its carbon dioxide emission generates. Such a perfect equivalence reasoning was first derived by Boadway (1982) and later extended by Myers (1990), but for settings with no interregional externalities. Our Proposition 1

13 12 extends this perfect equivalence reasoning to a situation involving interregional externalities. Similar results are available in the fiscal federalism literature (see, e.g. Wellisch (1994), Silva (1997), Silva and Caplan (1997), Nagase and Silva (2000) and Hoel and Shapiro (2000)). These works, however, neglect the issue of whether or not it is individually rational for a region to participate in a interregional scheme (or federation) designed to internalize externalities and implement transfers. We now turn our attention to the first stage of the game. Is the transfer scheme based on the horizontal equity principle implementable? To be implementable, the transfer scheme must be individually rational, that is, each region must find it desirable to participate. Let U j1 denote the utility level of region j in the subgame perfect equilibrium for the last two stages of the game. Formally, the transfer scheme under horizontal equity is implementable if and only if: (15) Figure 2 demonstrates the potentially large area of non-implementability corresponding to the horizontal equity solution. Point C on the Pareto frontier is the horizontal equity solution. A move to point C from any Nash solution located within box OABC is Pareto improving, while a move to point C from anywhere inside the area ADB is not (region r's welfare will decrease). 7 [INSERT FIGURE 2 HERE] 7 U r 0 > U p 0 implies that a noncooperative Nash solution will never lie below the 45 o line, thus ruling out area BCE as a non-implementation area.

14 Proportional Equity This game follows the same pattern as that presented for the horizontal equity scheme, except that the equity constraint faced by the GEF in the third stage is now U r / U r0 = U p / U p0. The solution to the GEF's problem is given by (4) and (16) Inserting the implicit functions y j2 (x r, x p ) into (4) and differentiating the implied equation together with (16) yields: (17a) (17b) (17c) (17d) In the second stage of the game, region j chooses {x j } to maximize U j subject to y j = y j2 (x r, x p ). The first order conditions are: (18)

15 14 It is now easy to see that equations (17a) - (17d) and (18) together imply equations (5). Since the proportional equity transfer scheme also satisfies equation (4), the subgame perfect equilibrium for the last two stages of the game is Pareto efficient. Similar to the horizontal equity principle, the incentives introduced by the proportional equity transfer scheme are powerful enough to nullify each region s potential gain in ignoring the externality that its emissions generate. In sum, the proportional equity scheme also leads to perfect incentive equivalence. Our result clearly demonstrates that it is possible to obtain perfect incentive equivalence without the equal utility condition. That is, the equal utility condition is sufficient but not necessary for perfect incentive equivalence. Our analysis enlarges the set of circumstances under which the perfect incentive equivalence reasoning derived by Boadway (1982) and extended by Myers (1990), Wellisch (1994), Silva (1997), Silva and Caplan (1997), Silva and Nagase (2000) and Hoel and Shapiro (2000) among others, is applicable. Indeed, it is straightforward to show that if we replace equation (16) by U r = f(u p ), where f is continuous and differentiable, the subgame perfect equilibrium for a two-stage game similar to the one investigated above is Pareto efficient. 8 In this new game, the regions independently choose how much of the industrial good they wish to consume in the first stage and the GEF chooses the allocation of the numeraire good across both regions in order to satisfy the overall resource constraint and the utility constraint, U r = f(u p ). When the regions anticipate that the utility constraint will always be satisfied, whether they behave efficiently or not, they realize that making choices that internalize the interregional 8 This claim assumes that the maximization problems are characterized by interior solutions and that the corresponding first order conditions in each problem are necessary and sufficient for a locally unique maximum. For the sake of brevity, we chose not to include the proof of this claim here. It is, nonetheless, available from the authors upon request.

16 15 externalities is in each region s best interest. The Pareto efficient allocation implied by the subgame perfect equilibrium for this game lies on the intersection of the function f and the Pareto frontier. The striking and distinguishing feature of the transfer scheme based on proportional equity relative to the transfer scheme based on horizontal equity, however, is that it necessarily leads to a Pareto improvement relative to the simultaneous Nash equilibrium allocation. In other words, it is always individually rational for each region to participate in the current transfer scheme. To see this, let U j2 denote the level of utility obtained by region j in the subgame perfect 0 equilibrium for the last two stages of the game. From U r / U r0 = U p / U p, we obtain U r = (U r0 / U p ) U p. The inefficient allocation (U p0, U r0 ) is located, on the line of slope U r / U p > 1, inside of the Pareto frontier. See line OA in Figure 3. The point (U p2, U r2 ), on the other hand, lies on the intersection of line OA and the Pareto frontier, since the subgame perfect equilibrium for the 2 last two stages of the current game is Pareto efficient and U r2 / U r0 = U p / U p0. In sum: Proposition 2:The transfer scheme based on the proportional equity principle is both Pareto efficient and fully implementable. This result is good news for environmental policy makers who are concerned with abating carbon dioxide emissions. It should be easier to convince the citizens of rich nations of the merits of proportional equity, as proposed here, than of the merits of horizontal equity. 3.3 Green Equity The equity constraint faced by the GEF in the third stage of this game is: (19) from which it follows that:

17 16 (20) Equation (19) tells us that the exact amount of the income transfer obey the rule that green GNP s must be equated. Equation (20) then shows us that this transfer amount equals half of the green GNP differential between the rich and poor regions. Substituting equation (20) into equations (7a) and (7b) and rearranging yields: (21) Differentiating equations (21) leads to: (22a) (22b) In the second stage of the game, region j chooses x j to maximize U j subject to y j = y j3 (x r, x p ). These maximization problems yield (23) Combining (23) with (21a), we obtain: (24) Equations (24) reveal that the marginal rates of substitution will be equalized across regions. However, the marginal rates of substitution do not equal the social marginal rate of

18 17 transformation, as required by Pareto efficiency. Hence, the scheme is inefficient. Interestingly, the right-hand sides of (24) correspond to the average of the private marginal rates of transformation see equations (6). We infer from this that the scheme induces the regions to partially internalize the externalities they generate. Is this scheme implementable? It may or may not be. There is no guarantee that each region s payoff from participation in the scheme exceeds its reservation utility level. Hence, besides being inefficient, the scheme based on green equity may also be non-implementable. 4. Concluding Remarks Our results suggest that rich and poor regions may behave efficiently in the presence of international resource transfers that satisfy horizontal or proportional equity. Because transfer schemes motivated by horizontal or proportional equity link the welfare levels of rich and poor regions, they create strong incentives for the regions to internalize the global externality. The efficiency properties of these transfer schemes are noteworthy in light of the call for international transfers in the Kyoto Protocol. Further, the proportional equity transfer scheme has the added advantage of being fully implementable. This full implementability property of the proportional equity transfer scheme makes it a more attractive scheme for policy purposes than the horizontal equity transfer scheme. We also find that a transfer scheme from rich to poor regions motivated by equalization of green GNP s not only fails to induce both regions to simultaneously behave efficiently, but may also fail to induce both regions to participate. By the efficiency criterion, the green equity scheme is certainly dominated by both horizontal equity and proportional equity schemes. By the implementability criterion, our proposed proportional equity scheme is undoubtedly the victor.

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21 20 Wellisch, D., (1994), Interregional Spillovers in the Presence of Perfect and Imperfect Household Mobility, Journal of Public Economics, 55: World Bank, (1999), Expanding the Measure of Wealth: Indicators of Environmentally Sustainable Development, Environmentally Sustainable Development Studies and Monograph Series No. 17, Environmental Department, Washington D.C.

22 21 Figure 1 Figure 2

23 Figure 3 22