and

In this paper we update our earlier estimates of the cost of the Kyoto Protocol using the G-Cubed model, taking into account the new sink allowances from recent negotiations as well as allowing for multiple gases and new land clearing estimates. Rather than comparing this to the original Kyoto Protocol as other studies have done, we compare the estimates from the current Kyoto Protocol to a realistic alternative to the Kyoto Protocol outlined by McKibbin and Wilcoxen ( 1197a, 1997b, 2002). A key part of the comparison between the two alternatives is not to predict exactly what the outcome for emissions reduction might be at a future date under each approach. What we want to focus on is the importance of the inherent uncertainty about the future that should be at the heart of the design of a suatainable climate policy. To show how important uncertainty is to the design of the climate policies, we take two alternative plausible assumptions about a single aspect of the future predictions and compare the two regimes under these alternative assumptions. Since climate change is all about policy making under uncertainty it is important in comparing regimes to explore how the regimes handle aspects of uncertainty as well as the average performance of the regimes. This comparison illustrates a fundamental difference between the Kyoto Protocol and the Blueprint.


Introduction
The likelihood that the Kyoto Protocol will achieve significant real reductions in greenhouse gas emissions is very low. The United States withdrew from the protocol in March 2001, a move which was angrily denounced by surprised commentators in Europe and around the world. It was described as arrogant, isolationist, and a "betrayal [by the Bush Administration] of their responsibilities as global citizens". 1 Yet the announcement was really nothing more than a blunt public acknowledgment of a fact that was well known within the policy community: the Kyoto Protocol was already dead in the United States. The U.S. Senate, which must ratify all international treaties by a two-thirds majority, overwhelmingly opposed the protocol and had voted 95-0 against U.S. participation as early as July 1997, five months before the protocol was signed. 2 Opposition was so great that the Clinton Administration, which negotiated and signed the protocol, never bothered to submit it to the Senate for ratification. Even if the Bush Administration had enthusiastically supported the treaty -which it did not -there was little it could have done.
What doomed the protocol in the Senate is a critical flaw in its design: it requires each participating industrialized country to agree to achieve a specified emissions target regardless of the cost of doing so. 3 The focus on rigid targets also makes the treaty impractical as a long-term climate policy for the rest of the world as well. Because the costs of reducing emissions are unknown and could be very large, countries with substantial emissions have insisted on increasingly lax targets as a condition for their continued participation. Japan, Canada and Russia, for example, were able to negotiate large increases in their "sink" allowances during COP6bis, held in Bonn, and COP7, held in Marrakesh. 4 Between the U.S. withdrawal and the increase in sink allowances, the protocol has been relaxed substantially. The effect on estimated emissions permit prices in the 2008-2012 period is dramatic. Relative to the original Kyoto agreement, permit prices are likely to be reduced by 14 percent (Bohringer, 2001) to 85 percent (Kemfert, 2001). 5 In this paper we update our earlier estimates 6 of the cost of the Kyoto Protocol using the G-Cubed model, taking into account the new sink allowances from recent negotiations as well as allowing for multiple gases and new land clearing estimates. We then move on to the paper's main topic, which is an examination of the protocol's core flaw -the sensitivity of compliance costs to unexpected changes in future economic conditions. To explore this point we consider two plausible alternative assumptions about a single aspect of the future world economy and evaluate the protocol under each assumption. The two cases we examine are: (1) moderate productivity growth in Russia sufficient to produce a 3.24% average rate of economic growth from 2000 to 2012; and (2) higher productivity growth leading to a 4.24% average rate of economic growth over 2000 to 2012. 7 Comparing the two sets of results shows the sensitivity of greenhouse gas abatement costs to variables that are very difficult to predict. The cost of the protocol in foregone GNP, for example, varies by up to 50 percent. The comparison thus illustrates the risks created by the protocol's focus on rigid emissions targets.
We also evaluate an alternative climate change policy described in Wilcoxen (1997a,b and2002a,b) under both Russian growth scenarios. The alternative policy, hereafter called the "Blueprint", differs sharply from the protocol because it does not impose fixed emissions targets. 8 Its design, which will be discussed in more detail below, takes explicit account of the vast uncertainties surrounding climate change. As a result, the policy's costs are predictable and are affected very little by the change in Russian economic growth. 9 Predictability of costs is essential because a climate agreement will have to remain in force indefinitely: The remainder of the paper is structured as follows. In section 2, we give a brief overview of the Kyoto Protocol and highlight the quantitative changes that have occurred to the effective 8 The name "blueprint" comes from the title of McKibbin and Wilcoxen (2002a). 9 In this paper our focus is uncertainty in the costs of reducing emissions. Pizer (1997), Newell and Pizer (1999), and Hoel and Karp (2002) examine uncertainty in benefits as well as costs, although in a more abstract level. targets facing countries from COP3 to COP7. 10 In section 3, we present a brief critique of the protocol and describe the alternative Blueprint proposal. Section 4 gives an overview of G-Cubed, the multi-country, multi-sector general equilibrium model we use to evaluate each of the policies. Section 5 discusses the key elements of our baseline simulation and presents our results. The baseline is particularly important because the rate at which emissions grow in the absence of a climate change policy is a major determinant of the cost of the Kyoto Protocol: the more emissions rise in the baseline, the more they must be reduced to hit the protocol's targets.

Climate Negotiations and the Kyoto Protocol
International negotiations on climate change policy began in earnest in 1992 at the Rio Earth Summit organized by the United Nations. The result of the summit was the United Nations Framework Convention on Climate Change (UNFCCC), a non-binding agreement aimed at reducing atmospheric concentrations of greenhouse gases so as to achieve the goal of "preventing dangerous anthropogenic interference with the Earth's climate system." 12 It was signed and 10 The original COP3 version of the protocol has been analyzed extensively; see Weyant (1999). 11 Because of the difference in baselines, the results in this paper are not directly comparable to our previous work. Direct comparisons of the COP3 and COP7 versions of the protocol, holding baseline assumptions constant, can be found in Bohringer (2001), Buchner et al (2001), Kemfert (2001), and Löschel and Zhang (2002). The papers use different models but reach similar overall insights. 12 For more information about the UNFCCC and the various COP meetings that followed it, see the UNFCCC web site: http://www.unfccc.org/. ratified by most of the countries in the world, including the United States, and entered into force in 1994.
The Convention's intent was to stabilize emissions of greenhouse gases at 1990 levels by the year 2000 through voluntary measures taken by individual countries. Most of the burden was to be assumed by 40 industrialized countries listed in Annex I to the Convention. In particular, Article 4, Paragraph 2(a) required each of these countries to "adopt national policies and take corresponding measures on the mitigation of climate change" in order to reduce its emissions.
Annex I countries were also required to contribute to a financial fund (subsequently merged into the Global Environment Facility, or GEF) to be used to help pay for climate-friendly projects in developing countries.
In the subsequent decade, however, few substantive policies were implemented and global emissions of greenhouse gases rose considerably. From that perspective, the UNFCCC failed to achieve its goal. However, its real contribution was to set up a mechanism under which negotiations could continue as periodic "Conference of the Parties" (COP) meetings.
The first Conference of the Parties, COP 1, was held in Berlin in March and April of 1995. The second Conference, COP 2, was held in Geneva in July of 1996. COP 3 was held in Kyoto in December of 1997. The result of the meeting was document called the "Kyoto Protocol," a treaty that formalized the "targets and timetables" approach that had been taking shape since COP 1. The Protocol set explicit emissions targets for 39 countries listed in its Annex B, which included essentially all industrialized countries who were signatories. 13 Each of these countries was to reduce its greenhouse gas emissions so that its total emissions, when converted to a carbon-equivalent basis, did not exceed a specified percentage of its "base period" emissions. For most countries the base period was 1990 but countries having economies in transition were allowed to choose other base periods during COP 2. 14 Average emissions over the "budget period" 2008-2012 were to be at or below the target. 15 The Annex B limits are shown in Table 1 ; countries designated as "economies in transition" are marked with an asterisk.

Table 1 : Kyoto Protocol Emissions Limits or Reduction Commitments
The commitments in Table 1 amount to about a 5 percent reduction below 1990 emissions for the Annex B countries as a group, or about 245 million metric tons of carbon. 16 The Protocol was designed to allow Annex B countries flexibility in meeting their commitments. For the Protocol to come into force it must be ratified by 55 percent of its signatories, and they must jointly account for at least 55 percent of total carbon dioxide emissions in 1990 from Annex I countries. Most of the operational details of the Protocol's international mechanisms -IET, JI and the CDM -were left for future COP meetings to resolve. There was no negotiation over issues of compliance, how institutional structures would work, or on how developing countries might be involved beyond the CDM. Meetings after COP 3 were devoted to working out the operational details of the Kyoto Protocol. Details can be found in McKibbin and Wilcoxen (2002a). For the purposes of this paper, the key issues are the relaxation of targets through changes in allowed sinks. 16 The exact reduction depends on the treatment of land use changes, which had not been finalized by the end of COP6. 17 The European Union, in particular, was in favor of limiting the degree to which compliance could be achieved by trading and JI. The United States was opposed to any restrictions.
When the second part of COP6 was convened in Bonn in July of 2001, it was intended to resolve all remaining implementation details of the Kyoto Protocol. The outcome was a package of proposals known as the "Bonn Agreements" which included, among other things, an increase in the sink allowances for forestry and land-use changes that were granted to several countries. 18 The total increase in sink allowances was large and reduced the overall stringency of the protocol by 54.5 million metric tons of carbon. Countries given sink allowances greater than one million metric tons of carbon-equivalent emissions are shown in Table 2. Although the Bonn Agreements were formulated during the second part of COP 6, they were not adopted as official decisions of the Conference. Instead, further discussion and formal adoption were deferred until COP 7. the Bonn Agreements in three main areas: (1) defining the "principles, nature and scope" of the international flexibility mechanisms; (2) finalizing the accounting rules for sinks derived from land use changes and forestry; and (3) designing an enforcement mechanism to discourage noncompliance. The result was a document called the "Marrakesh Accords" that COP participants hoped would remove all remaining obstacles to ratification of the Kyoto Protocol.
Finally, COP 7 further relaxed the Kyoto emissions target by granting a Russian request that its sink allowance be increased from 17.63 MMT to 33 MMT. Thus sinks have relaxed the 18 Sink allowances enable countries to offset a portion of their carbon emissions by enhancing activities, such as Kyoto targets by roughly 70 MMT, which together with the withdrawal of the United States makes the Kyoto Protocol's targets through 2012 very loose. Indeed, if world economic growth remains slow for a few years, the protocol's emissions targets may not be binding.

An Alternative to the Kyoto Protocol
At the heart of the climate change debate are two key facts. The first is the familiar and undisputed observation that human activity is rapidly increasing the concentration of greenhouse gases in the atmosphere. Each year, worldwide fossil fuel use adds about six billion metric tons of carbon to the atmosphere, and the concentration of carbon dioxide is now about 30 percent higher than it was at the dawn of the Industrial Revolution.
The second fact, however, is that no one fully understands how the climate will respond. 19 The increase in greenhouse gases could lead to a sharp rise in global temperatures with severe consequences for ecosystems and human societies. On the other hand, it's possible that the temperature rise could be modest, easy to mitigate and far in the future. The most likely outcome is probably somewhere between the two but the intrinsic complexity of the climate makes it impossible to know precisely what will happen with any degree of confidence.
Determining the costs and benefits of policies that would limit greenhouse gas emissions is even more difficult. Costs, for example, depend heavily on how fast emissions would grow in the absence of a climate policy: the more quickly emissions rise, the more expensive it will be to reduce them to any given level. The rate of emissions growth, however, depends on that are impossible to predict accurately over long spans of time: population growth, educational forestry, that remove carbon dioxide from the atmosphere. attainment, productivity growth within different industries, convergence (or lack thereof) in incomes between developing and developed countries, fossil fuel prices, and many others.
Plausible alternative assumptions about these factors can lead to vastly different estimates of future emissions.

The Kyoto Protocol
The most important problem with the Kyoto Protocol (outlined in the previous section) is that it fails to recognize and address this uncertainty. The heart of the Protocol is a set of "targets and timetables" requiring developed countries to reduce their greenhouse gas emissions. To ratify the protocol, each country must agree to reduce its emissions to a specified level-typically about 5 percent below in the country's emissions in 1990-during the period from 2008 to 2012.
By requiring participants to meet rigid emissions targets on a fixed timetable, however, the treaty implicitly adopted the position that the risks posed by climate change are so great that emissions must be reduced no matter what the cost. However, too little is known about the dangers posed by climate change, and about the costs of avoiding it, to draw that conclusion. Nor is there any evidence that the targets set by the protocol are the optimal levels of greenhouse gas emissions, either for an individual country or for the world as a whole. If anything, cost-benefit calculations based on studies to date tend to suggest that the costs exceed the benefits, at least in developed countries. 20 The Blueprint is 19 For an exhaustive survey of the scientific literature on climate change, see Intergovernmental Panel on Climate Change (2001). 20 See, for example, Nordhaus and Boyer (1999) or Tol (1999).
The Protocol's lack of clear cost-benefit justification was not, however, the fatal flaw that lead to such strong opposition in the U.S. Senate. After all, governments often face uncertainty when evaluating potential policies. Because the damages caused by climate change could be very large, a prudent legislature might want to adopt a climate policy to hedge its bets as long as it could keep the policy's costs within bounds. But Kyoto's "targets and timetables" design makes that impossible. Governments that adopt the protocol risk taking on a disastrously expensive commitment. It was this aspect of the Protocol that lead to the nearly unanimous opposition it faced in the U.S. Senate.
The Senate also objected to the absence of emissions limits for developing countries.
Developing countries account for only a small portion of historical emissions and are especially reluctant to incur large costs in a climate change agreement. As a result, they were specifically exempted from emissions restrictions in the Kyoto Protocol. However, developing country emissions are growing far more rapidly than those of developed countries, and no climate agreement can succeed in the long run without developing country participation. As a result, the Senate insisted that the U.S. refrain from participating in an agreement that did not include significant commitments by developing countries. Although it received considerable attention in the press, however, this consideration was subordinate to the Senate's concern about the cost of the policy. Had the cost of the policy been known to be low, the Protocol's asymmetrical treatment of developed and developing countries would have been a much less important issue.
The Senate routinely approves other agreements having asymmetries between the U.S. and other countries.
One additional problem with the Kyoto Protocol is that it lacks credible compliance measures and fails to give governments any incentive to police the agreement. Monitoring polluters is expensive, and punishing violators imposes costs on domestic residents in exchange for benefits that will go largely to foreigners. Governments would be strongly tempted to look the other way when firms exceed their emissions limits. Negotiators have tried to devise a strong international mechanism to monitor compliance and penalize violations, but so far have failed to produce a mechanism that is a credible deterrent for anything beyond very minor violations. 21

The Blueprint: A More Realistic "Hybrid" Approach
The uncertainties surrounding climate change have sharply polarized public debate. In There are elements of truth in both positions but neither is an appropriate response to climate change. A balanced reading of the current scientific literature indicates that a moderate degree of effort should be made to slow the growth of greenhouse gas emissions. Taking some sort of action is clearly warranted: although climatologists disagree about how much warming will occur and when it will happen, no one seriously suggests that mankind can continue to add 21 The main penalty that would be imposed on a country violating the protocol is a reduction in the amount of carbon dioxide it would be allowed to emit in the period following 2012. However, emissions limits beyond 2012 are not increasing amounts of carbon dioxide to the atmosphere every year without any adverse consequences. Moreover, climate change is essentially irreversible, so it makes sense to avoid causing more of it than necessary, at least until the potential risks are better understood. At the same time, current evidence does not justify a draconian cut in emissions: the cost would be enormous and the environmental benefits might be small. It's easily possible that the resources needed for a sharp reduction would be better spent on more immediate social problems. As a matter of common sense, therefore, the right approach must be a policy between the two extremes: it should provide incentives to reduce greenhouse gas emissions but avoid imposing unreasonably large costs.
In addition, a climate policy's political prospects will be substantially better if it does not require large transfers of wealth -either between countries or between households and firms within a country -or the surrender of a significant degree of national sovereignty. Finally, the system will need to remain in effect for many years so it must be designed to allow new countries to enter with minimum disruption and to survive the exit of some of its participants.
Neither of the standard market-based economic policy instruments satisfies all of these criteria. An ordinary tradable permit system would require participants to achieve a rigid emissions target regardless of cost. An emissions tax, on the other hand, would involve huge transfers of wealth and would be politically unrealistic. However, a hybrid policy, combining the best features of the two, would be an efficient and practical approach. 22 specified in the protocol and remain to be negotiated. A country violating the agreement could simply insist on a correspondingly higher post-2012 limit. 22 The economic theory behind regulation under uncertainty is due to Weitzman (1974), and the theory underlying hybrid regulatory policies is due to Roberts and Spence (1976). A hybrid approach to climate change was first proposed by McKibbin and Wilcoxen (1997)  Once distributed, the perpetual permits could be traded among firms, or bought and retired by environmental groups. 24 In addition, the government itself could buy back permits in future years if new evidence on climate change indicates that emissions should be cut more sharply.
Annual permits would be sold at a stipulated price determined by international negotiations, such as US$ 10 per ton. To put the fee in perspective, in the United States, US$ 10 23 The Kyoto reduction to 95 percent of 1990 emissions would slow climate change but not eliminate it entirely. Atmospheric concentrations of carbon dioxide, and hence global temperatures, would continue to rise. Stabilizing the temperature would require stabilizing the concentration of carbon dioxide, which would require net anthropogenic carbon dioxide emissions to be reduced to nearly zero. See McKibbin and Wilcoxen (2002a) for a discussion of how the Blueprint could be used to reduce emissions below the Kyoto target over the long run. 24 Countries could participate in the Blueprint even if they lacked appropriate markets where permits could be traded. In that case, a firm's allocation of perpetual permits would essentially be an emissions quota. Without tradability, the country would no longer be guaranteed of reducing its emissions at minimum cost. However, the existence of annual permits would reduce the excess cost caused by an inefficient allocation permits.
dollars per ton of carbon is equivalent to a tax of US$ 1.40 per barrel of crude oil, raising the price of a US$ 20 barrel of oil by about 7 percent. There would be no limit on the number of annual permits that could be sold in a given year.
Because it has two kinds of permits, the Blueprint is a bit more complicated than a simple permit system. However, it has all of the strengths of a traditional permit system and has additional advantages as well. It performs especially well in comparison to the Kyoto Protocol.
Like the Kyoto Protocol, the Blueprint encourages energy producers to keep emissions steady or, even better, to cut them. Firms that can cut emissions cheaply will do so and then sell unneeded perpetual permits to those whose emissions are increasing. As a result, emissions in each country will be reduced, and in a cost-effective manner.
Unlike the Protocol, however, the Blueprint provides an upper limit on the cost of compliance. No firm would have to pay more than US$ 10 per ton to reduce its emissions A key strength of the Blueprint is that it would be very stable with respect to changes in the mix of participating countries. Because permit markets are separate between countrieslinked only by the common price of an annual emissions permit -the entry or exit of one country from the system would have no effect on the price of permits circulating in other countries. In contrast, a change in list of countries participating in the Kyoto Protocol would cause windfall gains or losses to ripple through permit markets around the world.
Another advantage is that countries would manage their own domestic permit trading system independently, using their own legal systems and financial institutions. International cooperation, although helpful, would not be essential beyond the initial design of the system.
Monitoring firms to make sure they comply with the policy would be an internal matter for each country. Unlike the Kyoto Protocol, the Blueprint provides incentives for governments to monitor and enforce the agreement within their borders. One incentive is the revenue that could be raised from the sale of annual permits: low compliance would cause a government to sell fewer annual permits that it could have, lowering permit revenue. In addition, and perhaps more importantly, holders of perpetual permits will pressure their governments to be vigilant in order to maintain the market value of long term permits: low compliance would reduce prices in the permit market. The Kyoto Protocol, in contrast, requires international monitoring and a new international institution to ensure compliance. Moreover, poor monitoring and compliance in one country could debase the entire global permit trading system because it would affect emissions permit prices throughout the developed world.
Overall, the Blueprint is a practical and politically realistic approach to reducing greenhouse gas emissions. The main criticism leveled against it is that it does not guarantee precisely how much abatement will take place each year. If firms discover that it is very expensive to keep their emissions below their holdings of perpetual permits, the option to buy annual permits allows them to emit more, although at a cost of US$ 10 per ton. As a practical matter, however, the Blueprint would do far more to reduce emissions than a stronger treaty that could never be ratified or enforced.
In the following sections we illustrate the strengths of the Blueprint relative to the Kyoto Protocol especially when taking the considerable uncertainty about the future into account. But first we summarize the economic simulation framework being used.  Table 3 presents an overview of the model; its country and sectoral breakdowns are listed in Table 4. The range of countries modeled to date include the United States, Japan, Australia, Europe, the rest of the OECD, China, Oil Exporting developing countries (OPEC), Eastern Europe and states of the former Soviet Union (EFSU), and all other developing countries (LDCs). Production in each region is divided into twelve sectors. There are five energy sectors (electric utilities, natural gas utilities, petroleum processing, coal extraction, and crude oil and gas extraction) and seven non-energy sectors (mining, agriculture, forestry and wood products, durable manufacturing, non-durable manufacturing , transportation and services). This disaggregation enables us to capture the sectoral differences in the impact of alternative environmental policies.

An Overview of the G-Cubed Multi-Country Model
Each economy or region in the model consists of several economic agents: households, the government, the financial sector and firms in the 12 production sectors listed above. The behavior of each type of agent is modeled. Each of the twelve sectors in each country in the model is represented by a single firm in each sector which chooses it inputs and its level of investment in order to maximize its stock market value subject to a multiple-input production function (defining technological feasibility) and a vector of prices it takes to be exogenous. For each sector, output is produced with inputs of capital, labor, energy, materials and a sectorspecific resource. The nature of the sector specific resource varies across sectors. For example in the coal industry it is reserves of coal, in agriculture and forestry/wood products it is land which is substitutable between these two sectors. The capital stock in each sector changes according to the rate of fixed capital formation and the rate of geometric depreciation. It is assumed that the investment process is subject to rising marginal costs of installation, with total real investment expenditures in each sector equal to the value of direct purchases of investment plus the per unit costs of installation. These per unit costs, in turn, are assumed to be a linear function of the rate of investment. One advantage of using an adjustment cost approach is that the adjustment cost parameter can be varied for different sectors to capture the degree to which capital is sector specific.
Households consume a basket of composite goods and services in every period and also demand labor and capital services. Household capital services consist of the service flows of consumer durables plus residential housing. Households receive income by providing labor services to firms and the government, and from holding financial assets. In addition, they also receive transfers from the government. The household decision involves predicting expected future income from all sources (i.e. wealth) as well as current income. This information together with the relative prices of different goods and services then determine the pattern of consumption spending over time and the pattern of spending across the available goods.
It is assumed that the government in each country divides spending among final goods, services and labor according to the proportions in the base year input-output table for each country. This spending is financed by levying taxes on households and firms and on imports.
Households, firms and governments are assumed to interact with each other in markets for final goods and services; financial; and factor markets both foreign and domestic. The result of this interaction, given the desires of each economic entity, determine a set of relative prices than feed back into decision making by the different economic agents.
In summary, the G-Cubed model embodies a wide range of assumptions about individual behavior and empirical regularities in a general equilibrium framework. The complex interdependencies are then solved out using a computer. It is important to stress that the term "general equilibrium" is used here to signify that as many interactions are possible are captured, not that the economy is in a full market clearing equilibrium at each point in time. Although it is assumed that market forces eventually drive the world economy to a long run steady state equilibrium, unemployment does emerge for long periods due to different labor market institutions in different economies.

Some Estimates of Costs of Kyoto Versus The Blueprint
In this section we used the G-Cubed model to estimate the emissions reductions and changes in key economic variables that would arise under both the Marrakesh version of the Kyoto Protocol and the Blueprint.

Baseline Business-As-Usual Projections
To solve the model, we first normalize all quantity variables by each economy's endowment of effective labor units. This means that in the steady state all real variables are constant in these units although the actual levels of the variables will be growing at the underlying rate of growth of population plus productivity. Next, we must make base-case assumptions about the future path of the model's exogenous variables in each region. In all regions we assume that the long run real interest rate is 5 percent, tax rates are held at their 1999 levels and that fiscal spending is allocated according to 1999 shares. Population growth rates vary across regions as per the 2000 World Bank population projections. Assumptions are contained in Table 5.
A crucial group of exogenous variables are productivity growth rates by sector and country. The baseline assumption in G-Cubed is that the pattern of technical change at the sector level is similar to the historical record for the United States (where data is available). 25 In regions other than the United States, however, the sector-level rates of technical change are scaled up or down in order to match the region's observed average rate of aggregate productivity growth over the past two decades. This approach attempts to capture the fact that the rate of technical change varies considerably across industries while reconciling it with regional differences in overall growth. This is clearly a rough approximation; if appropriate data were available it would be better to estimate productivity growth for each sector in each region.
Given these assumptions, we solve for the model's perfect-foresight equilibrium growth path over the period 1999-2080. This a formidable task: the endogenous variables in each of the 82 periods number over 7,000 and include, among other things: the equilibrium prices and quantities of each good in each region, intermediate demands for each commodity by each industry in each region, asset prices by region and sector, regional interest rates, bilateral exchange rates, incomes, investment rates and capital stocks by industry and region, international flows of goods and assets, labor demanded in each industry in each region, wage rates, current and capital account balances, final demands by consumers in all regions, and government deficits. 26 At the solution, the budget constraints for all agents are satisfied, including both intratemporal and inter-temporal constraints.

Simulating The Kyoto Protocol and the Blueprint
Given the baseline scenario, we then impose the applicable post-COP7 Kyoto targets on each country or region. 27 In terms of the model's aggregation, we assume that Japan, Europe,  For a more detailed discussion of the importance of accounting for heterogeneity in sector-level productivity growth rates see Bagnoli, McKibbin and Wilcoxen (1997). 26 Since the model is solved for a perfect-foresight equilibrium over an 82 year period, the numerical complexity of the problem is on the order of 82 times what the single-period set of variables would suggest. We use software developed by McKibbin (1992) for solving large models with rational expectations on a personal computer. agreement, for example, reduces cumulative emissions over the period by less than 2 percent. This point can be made even more stark if we compare the impacts of both regimes on cumulative emissions since the industrial revolution.
The second point to note from Figure 1 is that the nominal stringency of a climate policy is a poor indication of its effectiveness. A moderate policy, such as the Blueprint, can have a substantially larger effect on cumulative emissions than the Kyoto Protocol if it is enacted sooner and has broader participation. In other words, a modest policy that takes effect in the next few years and has relatively broad participation will do more to reduce climate change than the Kyoto Protocol, which constrains only a few countries and imposes its constraints a decade in the future.

Conclusion
The Kyoto Protocol never had much chance of reducing greenhouse gas emissions significantly because its design was deeply flawed. Following the withdrawal of the United States and the weakening of the protocol's targets at COP6 and COP7, it is likely to do nothing to reduce global emissions through the end of the 2008-2012 commitment period. The protocol's core flaw is its focus on "targets and timetables" that, in effect, require participants to agree to reduce greenhouse gas emissions to specified levels regardless of the cost. Our results confirm that the costs of the protocol are very sensitive to key economic variables that cannot be predicted with any precision. A single, modest change in projected productivity growth in Russia changes the costs of the protocol substantially. Many other variables would have similarly large effects. In order to ratify the protocol, therefore, a country must be willing to undertake an uncertain and possibly very expensive commitment. Moreover, unexpected future changes in economic conditions could raise the cost of the protocol sharply, which would create strong pressures for participating countries to withdraw at that point. In short, the protocol's emphasis on emissions targets undermines participation for two reasons: (1) it discourages countries from ratifying the agreement; and (2) it causes the protocol to be particularly vulnerable to future events.
The Blueprint policy, in contrast, is more attractive to initial participants because it does not require an open-ended commitment, and it is more sustainable over long periods because future events have little effect on compliance costs. The Blueprint, in other words, is transparent: the upper bound on annual permit prices allows a potential participant to determine its maximum compliance costs in any future period without having to know in advance how the myriad uncertainties surrounding climate change will be resolved. A country considering participation in the agreement will know exactly what to expect and will have little reason to abandoning the policy later. Moreover, the Blueprint has the potential to achieve greater cumulative emissions reductions than the Kyoto Protocol, and to achieve them at lower cost, because it would encourage wider participation and earlier reductions. Overall, it is a viable and promising alternative to the Kyoto Protocol.  Specification of the demand and supply sides of economies;° Integration of real and financial markets of these economies;° Intertemporal accounting of stocks and flows of real resources and financial assets;° Extensive econometric estimation of key elasticities of substitution from disaggregated data at the sectoral level;° Imposition of intertemporal budget constraints so that agents and countries cannot forever borrow or lend without undertaking the required resource transfers necessary to service outstanding liabilities;° Short run behavior is a weighted average of neoclassical optimizing behavior and ad-hoc "liquidity constrained" behavior;° Disaggregated to allow for production and trade of multiple goods and services within and across economies;° Full short run and long run macroeconomic closure with macro dynamics at an annual frequency around a long run Solow/Swan/Cass neoclassical growth model;° Solved for a full rational expectations equilibrium at an annual frequency with an horizon of more than a century.