Developing Countries' Greenhouse Emissions: Uncertainty and Implications for Participation in...

Randall Lutter [*]

Developing countries can participate in the Kyoto Protocol to limit greenhouse gas emissions by adopting national emissions limits. Such limits could offer economic gains to developing countries, cost savings to industrialized countries, and environmental benefits.

They could also address concerns of the U.S. Senate. On the other hand, uncertainty about greenhouse gas emissions in developing countries is so great that emissions limits may impose substantial costs if they turn out to be unexpectedly stringent. To manage risks arising from emissions limits, developing countries should index any emissions limits to variables that predict emissions in the absence of limits. This paper presents such an index--similar to one recently adopted by Argentina--and develops estimates showing that it could lower the risk of economic losses to developing countries from about 40 percent to about 35 percent.

INTRODUCTION

The biggest issue facing policy-makers concerned with climate change is how developing countries should contribute to international efforts to limit greenhouse gas emissions. The 1997 Kyoto Protocol sets stringent emissions limits for industrialized countries (Framework Convention on Climate Change, 1997). But the merit of the Protocol, in particular its cost-effectiveness, will depend on the actions of developing countries as well. Recognizing this, the U.S. Senate in July 1997 overwhelmingly adopted the Byrd-Hagel Resolution, which stipulates that the United States should not accept new commitments to limit or reduce greenhouse gas emissions until developing countries have "new specific scheduled commitments to limit or reduce greenhouse gas emissions... within the same compliance period." [1] The Clinton Administration has indicated it will not submit the Kyoto Protocol for ratification by the Senate until there is "meaningful participation" by key developing countries (Eizenstat, 1998). Growing concern t hat climate change is partly anthropogenic ensures a continued debate in public and in the Senate about developing countries' policies to limit greenhouse gas emissions.

Developing countries could participate in the Kyoto Protocol by following the example of the industrialized countries and adopting national emission limits. Kazakhstan has already taken steps in that direction, and Argentina has adopted a binding target (Framework Convention on Climate Change, 1999; Argentine Republic, 1999). National emission limits are suggested by a common interpretation of the Byrd-Hagel Resolution and are more consistent with the existing Protocol than policies that would reduce emissions without specific limits.

National emissions limits can provide economic advantages apart from the benefit of lower emissions. They facilitate international trading of emissions permits among participating countries, because they make clear each country's obligations. Developing countries that adopt national limits can profit if the emissions limits are set close to the emissions levels projected to occur anyway (that is, the business as usual (BAU) emissions levels), insofar as the marginal cost of reducing emissions is below the international permit price. In this case, a developing country could reduce emissions at a cost of, say, $10 per ton and sell the permits that would no longer be needed at the international price of, say, $50 per ton. Profit from international permit sales offers a key rationale for developing countries to accept emissions limits. Moreover, such sales, by lowering international permit prices, would lower the costs to the United States and other countries of complying with the Kyoto Protocol.

But national emissions limits also create economic risks. Such limits may raise costs much more than expected, if an economic boom raises emissions in the near-term and so increases the reductions needed to meet a national limit for the 2008 to 2012 period established in Kyoto. Many analyses suggest that a five-percent underestimate in BAU emissions would quadruple the costs of limiting emissions to five-percent below the estimated BAU. [2] Economic risks from emissions limits are greater than those from emissions taxes designed to achieve the same emissions reductions, [3] because a fuel's carbon content determines how its price changes with a carbon emissions tax. Although enforceable limits provide good assurance that emissions are capped during given periods, the value of such assurance is small because climate change is a long-range problem that can be controlled without large emissions reductions in specific periods (Pizer, 1997; Manne and Richels, 1999; Wigley et al., 1996).

Emissions limits for developing countries may also pose risks to the environment. In general, if a developing country takes on an emissions limit that is too lax, it can sell emissions permits that it does not need. Such sales would increase emissions from other countries that have emissions limits and participate in international permit markets. A similar but more subtle environmental risk is related to recessions and financial crises, which in the absence of emissions limits lower emissions. If a developing country adopts an emissions limit set to the expected BAU emissions level, an unexpected recession that lowers its emissions would still increase the supply of emissions permits available for sale through the international trading mechanism in the Kyoto Protocol. And an increase in the supply of emissions permits would increase emissions from developed countries. Yet such an increase would not occur if the developing country had not adopted the emissions limits. Thus emissions limits for developing coun tries may increase global emissions relative to a situation in which no such limits exist.

The problems from uncertain emissions projections are not hypothetical. For Canada, news about unexpected stringency of its emissions limits arrived only weeks after the Kyoto Protocol. Officials at Natural Resources Canada received revised emissions projections suggesting that by 2010, Canada's emissions could be nearly 40 percent higher than the estimates officials used to negotiate emissions limits in Kyoto (Eggertson, 1998). In another example, the 1997-98 East Asian financial crisis led to sharply lower emissions projections for some countries.

The possibility of high costs may reduce developing countries' propensity to accept emissions limits as well as eventual compliance, because the Kyoto Protocol is to be enforced through voluntary national actions. Yet avoiding these risks by proceeding without national emissions limits for developing countries is also costly. The U.S. Administration's analysis suggests that U.S. costs could rise by two-thirds if key developing countries use an alternative project-by-project approach called the clean-development mechanism instead of national emissions caps set equal to emissions projected under BAU policies (Eizenstat, 1998; U.S. Administration, 1998, Table 4). The clean development mechanism may be seen as an attempt to approximate the effect of a national emissions cap set equal to BAU, although it entails much larger transaction costs, and therefore gains from trade will be smaller than with national emissions caps.

In this paper, I address uncertainty about the emissions expected under BAU policies and its implications for developing country participation in the Kyoto Protocol. Although the costs of the Kyoto Protocol have been extensively studied, the risks to individual developing countries of accepting emissions limits have apparently escaped close scrutiny (see, for example, Weyant and Hill, 1999). This paper provides rough estimates of the magnitude of risks to national economies and the global environment and presents ways to manage these risks. I show that emissions forecasts in the United States are typically slightly below estimates of realized values, and there is even less reason for confidence in emissions estimates for developing countries. Countries with smaller economies have emissions that are more variable and intrinsically harder to forecast. In addition, models as sophisticated as those used by the U.S. Energy Information Administration are available in only a subset of developing countries, and fore casts based on national data on emissions and GDP are very inaccurate. Such forecasts imply that a developing country could face a forty percent probability that it will be worse off by accepting an emissions limit set equal to emissions projected under BAU policies. This result depends however, on the international price of emissions permits, the cost curve for reducing emissions, and the value of reductions in other emissions that result from controlling carbon emissions. I recommend that emissions limits for developing countries be indexed to variables that predict their uncapped emissions, so as to reduce the risk of inadvertent stringency (for related ideas: Frankel, 1999; Baumert et al., 1999). I develop such an index and estimate how much it could reduce the risk of economic losses.

The broad points presented here are applicable beyond the Kyoto Protocol. They also apply to international efforts to limit developing country emissions in later commitment periods or through an agreement other than the Protocol, as long as such efforts are built on national emissions caps.

Section 1 of the paper presents a simple model of the effect of uncertainty on emissions reductions and costs. Section 2 assesses uncertainty in the retrospective estimates of emissions for the United States, since retrospective estimates are necessary to evaluate the precision of prospective estimates. Section 3 evaluates the uncertainty around forecasts of emissions for the United States, using information from the Energy Information Administration. Section 4 develops several reduced form estimates of emissions applicable to developing countries and evaluates the uncertainty implicit in these models. In section 5, I synthesize the different evidence about uncertainty of emissions forecasts. Section 6 assesses the risk of economic losses under limits set equal to emissions expected under BAU policies and the reduction in such risk from indexing. Finally, policy recommendations and conclusions are presented in section 7.

1. A SIMPLE MODEL

The social cost of emissions limits is determined in part by the gains from trading emissions permits in international markets, which I illustrate in Figure 1. In Figure 1a, the country accepts an emissions limit equal to 100 tons, which is also the level of emissions under BAU policies. Given the marginal cost curve [MC.sub.a], the country could gain from trade in international permits by reducing emissions from 100 tons to [E.sup.*], the point at which further reductions cost more than the international price of permits, [P.sub.I]. The magnitude of the gain (that is, the revenue from international permit sales less the cost of reducing emissions) is A.

In Figure 1b the economy booms after the emissions limit is established and so uncapped emissions would equal 110 tons and exceed the limit of 100 tons. The actual emissions in the absence of a cap in this case are 110 tons, so the marginal cost curve is [MC.sub.b], which departs from 110 tons. Given the international permit price [P.sub.I], the gains from trade are D, the net gains from reducing emissions below the limit, less the cost, C, of achieving the emissions limit itself. If D exceeds C, the country is better off with such an emissions limit and the gains from trade than with none. However, if the emissions limit were more stringent or abatement costs higher, the net gains from trade would vanish and D would be less than C. For any particular true baseline emissions level, a world price and a marginal cost curve, there is a "breakeven" emissions limit, where the gains from trade vanish: D = C. In the special case where the marginal cost curve is linear and has no intercept, the point at which the ga ins from trade vanishes is the level of true baseline emissions less half of the emissions reductions necessary to raise marginal abatement cost to the international permit price. [4] I use this "breakeven emission limit" in section 6 below.

Finally, in Figure 1c, a recession lowers BAU emissions to 90 tons, which is less than the emissions limit of 100 tons. The country can sell permits for 10 tons of emissions in world markets, without any specific policies to reduce emissions. Permits sold on this basis, without any accompanying emission reductions, are sometimes called paper permits. Their sale on international markets increases global emissions. In addition, the country can profitably reduce emissions below 90, as long as the cost of additional reductions is less than the international price [P.sub.I]. Thus in this case the total gain from trade in permits is E + F. In reality it is practically impossible to distinguish emissions abatement associated with specific policies from emission reductions due to weather or energy price changes.

2. REVISIONS TO RETROSPECTIVE EMISSIONS ESTIMATES

Retrospective estimates are the best benchmark to evaluate prospective estimates, but even they are uncertain. To assess that uncertainty, I examine revisions to estimates from the highly regarded U.S. Energy Information Administration (ETA). I focus on 1990 emissions because they are the basis of the targets in the Kyoto Protocol. [5]

As shown in Figure 2, The EIA's estimates of 1990 carbon emissions have been revised nine times since 1992, most recently in July 2000 (Reiser and Holte, 2000, Table 18). Carbon emissions for 1990 were first reported by the EIA in 1992 to be 1340.5 million metric tons of carbon (MMTC), about 0.34 percent less than the EIA's most recent estimate of the same emissions. [6] The EIA, in its Emissions of Greenhouse Gases in the United States 1997, changed its estimate to 1355.9 MMTC, an increase of 15.4 MMTC. Most recently, EIA has again reduced its retrospective estimate in its Annual Energy Outlook Forecast Evaluation to 1345.2 MMTC, an increase of 5.2 MMTC over its 1992 estimate. Slight modifications in methodology and underlying data account for these changes in the estimates of 1990 carbon emissions. [7]

Such uncertainty has implications for implementation of the Kyoto Protocol that are distinct from my evaluation of prospective estimates. While revisions of 15 MMTC may seem relatively small, they would affect permits valued at between $150 million and $1.5 billion, given a market price of between $10 and $100 per ton. Avoiding the costly litigation associated with such uncertainty may require better monitoring and reporting of emissions or a de minimis exemption for small violations.

3. ASSESSMENT OF UNCERTAINTY IN PROSPECTIVE CARBON EMISSION FORECASTS

To assess the uncertainty of prospective emissions forecasts, I would like to compare prospective emissions forecasts with estimates of realized values. Such a comparison is limited to emissions forecasts for carbon, however, because I know of no model of emissions of other greenhouse gases that provides prospective forecasts that can be compared with estimates of realized values. [8]

In the absence of a set of carbon emissions forecasts for developing countries that extends over a period long enough to allow meaningful comparisons with realized values, [9] I pursue two second-best approaches. First, I turn to the track record of forecasts of U.S. emissions prepared by the U.S. EIA; these forecasts represent a sort of gold standard. Although this track record cannot tell us how accurate the ETA would be if it developed emissions forecasts for, say, Mexico, it can tell us how accurate current forecasting technology is for a large industrialized country. Second, for developing countries I forecast emissions using a simple reduced-form model of carbon emissions and compare those forecasts with realized values.

The EIA recently published its first evaluation of the accuracy of earlier carbon emission forecasts appearing in Annual Energy Outlooks between 1992 and 1999 (Reiser and Holte, 2000, Table 18). For my purposes, however, EIA's evaluation is of limited value because it assesses only 28 separate prospective annual estimates, and only three of these are for forecasts more than five years into the future (Reiser and Holte, 2000, Table 18). [10] Therefore, while I summarize EIA's conclusions below, I also develop implicit forecasts of carbon emissions from the EIA's forecasts of energy use for different types of fossil fuels (Reiser and Holte, 2000, Tables 3, 4, and 5). These implicit forecasts cover 112 separate annual estimates, and 47 are for periods more than five years ahead. (See Table 1 below.)

My point of departure in developing implicit emissions forecasts is the EIA's Annual Energy Outlook Forecast Evaluation 2000 (Reiser and Holte, 2000), which compares various forecasts of consumption of different fuels to actual realized values from 1985 to 1999. With these consumption data, thermal conversion factors (Energy Information Administration, 1999a, Appendix A), carbon coefficients, [11] combustion fractions (Energy Information Administration, 2000a, Assumptions), and annual tons of sequestered carbon, [12] I develop the carbon emissions forecast implied by the estimated fuel consumption in a given year.

To test the precision of these implicit forecasts, I compared them with 28 contemporaneous EIA explicit forecasts for the years beginning in 1992 and ending 1999 (Reiser and Holte, 2000, Table 18). The error ranged from -0.89 percent to 1.4 percent, with an average absolute difference of 0.52 percent of EIA's explicit forecasts. These relatively small errors appear acceptable for the current purposes.

Assessing the reliability of these implicit forecasts requires a good proxy for actual emissions. Several proxies of uncertain quality are available. The EIA has published explicit retrospective estimates for 1990 and years since 1992. The Oak Ridge National Laboratory has made retrospective estimates for years since 1950, but differences between their retrospective estimates for carbon emissions from fossil-fuel consumption and those of EIA ranged from about 2 to 5 percent (Marland et al., 1998). [13] I therefore develop implicit retrospective estimates following the same approach used to develop implicit prospective estimates. The implicit retrospective estimates differ from the implicit prospective estimates only insofar as fuel consumption is adjusted based on Reiser and Holte (2000, Tables 3, 4 and 5). Other coefficients described above are constant for each year of emissions because revisions are often unavailable and variability across years is small. The implicit retrospective estimates are closer to EIA's explicit retrospective estimates than the Oak Ridge numbers and have the additional advantage of consistency with the implicit prospective estimates. Implicit EIA forecasts and most recent implicit retrospective estimates appear in Table 1.

Summary statistics about the errors in these implicit forecasts and in EIA's explicit forecasts (Reiser and Holte, 2000, Table 18) are shown in Table 2 below. [14] The average absolute forecast error rises from about 1 to 2 percent in the forecasts for only one or two years ahead to between 4.6 percent and 7 percent for the forecasts that are 12 or 14 years ahead. Both the implicit and the explicit forecasts tend to be less than the realized values.

The five-year commitment period specified in the Kyoto Protocol may be long enough to allow many surprises related to the business cycle and weather to average out. Using forecasts from the preceding tables, I construct forecasts for non-overlapping five-year intervals by grouping the annual estimates into the most recent such intervals for which data are available. I then compare the forecasts for such intervals with the retrospective estimates and calculate the errors. Summary statistics for these errors appear in Table 3.

Nearly 87 percent of the forecasts are too low. Although medium term forecasts have errors between 2 and 3 percent, for the ten-year-ahead forecast the error is nearly 7 percent. A continuation of this pattern would imply that the costs to the United States of meeting the emissions cuts specified in the Kyoto Protocol will exceed forecasts by a small amount. Moreover, EIA-type models of emissions built up from disaggregated forecasts of consumption of different fuels may have a tendency to underpredict that warrants further examination before their widespread adoption by developing countries.

4. REDUCED FORM MODELS OF EMISSIONS

For most developing countries there is no readily available source of energy use forecasts detailed enough to give implicit carbon emissions forecasts. In the absence of such forecasts for these countries, the best method of forecasting emissions is to develop a model relating aggregate data on emissions to relevant variables such as income and population, although such a model may be inferior to the detailed fuel-specific and sector-specific model used by, for example, the EIA. Models relating aggregate data on emissions and income have been developed for the purposes of forecasting global emissions (Schmalensee et al., 1998), but I am unaware of a publication that gives forecasts for individual countries and describes the uncertainty of such forecasts.

My model uses data on three key variables--emissions of carbon dioxide, GDP, and population--for 117 countries for the time period 1950-1992. The carbon dioxide emissions data, measured in metric tons of carbon, are from the Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Department of Energy (Marland et al., 1998). The data on population, GDP, and investment (the latter measured in 1985 international dollars) are from the Penn World Table Mark 5.6a (Summers et al., 1998).

I compute reduced-form regressions of five-year average carbon emissions on GDP and other variables. The unit of observation is emissions over a five-year interval because this interval corresponds to the five-year commitment period in the Kyoto Protocol. The forecast errors from these regressions give estimates of the likelihood of different degrees of inadvertent stringency.

I assess errors for forecasts made outside the sample period because I am concerned with all types of uncertainty, including uncertainty related to structural change and model specification. In particular, I exclude the last period of data (1988 to 1992) from the regressions and then assess the errors in emissions forecasts for the years 1988 to 1992. Since I am concerned with both inadvertent stringency and paper permits, I measure the error both in terms of the percent difference from the emissions level and as metric tons of carbon.

I employ two distinct forecasting approaches. The first uses an autoregressive approach, in which emissions are a function of lagged emissions and other lagged variables such as income and population. This approach is simpler for the present purpose than that of Schmalensee et al. (1998), who use regressions of emissions per capita and pre-existing estimates of growth in population and income to forecast emissions. Applying their approach would require information about forecasts of developing countries' populations and income made one, six and eleven years before the out-of-sample period 1988 to 1992, because I also explore how the forecast errors fall as the predictions are made closer to the commitment period. The model I develop is consistent, however, with Schmalensee et al. in that it allows emissions per capita to be non-linearly related to income per capita. The second approach assumes that emissions are a function of concurrent variables such as income, so that forecasts of future emissions require forecasts of future gross domestic product. The Appendix gives details.

The results suggest how emissions limits for developing countries could be indexed to variables that predict what emissions would be in the absence of such limits. As shown in the Appendix, a model that predicts relatively well a country's emissions (in logs) over a five-year period is: [15]

emissions = const + 0.5 lagged emissions + 0.6 lagged GDP

+ 0.06 (lagged GDP / capita) + error term (1)

Thus a one percent increase in emissions over a five-year period is associated with about a 0.5 percent increase in emissions over the subsequent five-year period, holding other things constant. In addition, a one percent increase in GDP over a five-year period is associated with about a 0.6 percent increase in emissions over the subsequent five-year period, holding other things constant.

Therefore an emissions limit intended to be a fixed value below BAU emissions should rise 0.6 percent with every 1 percent increase in GDP over the period from 2003 to 2007, and 0.5 percent with every 1 percent increase in emissions over the same period.

Indexing emissions limits to earlier emissions would create a perverse incentive for developing countries, because they could increase emissions from 2003 to 2007 and so receive a higher emissions cap during 2008 to 2012. It is unclear, however, whether the costs of this perverse incentive are large relative to the benefits. There are environmental costs of increases in greenhouse gas emissions from 2003 to 2007. But the reduced risk of inadvertent stringency from emissions limits in the 2008 to 2012 period may be an important benefit because it increases the likelihood of developing country participation in the Kyoto Protocol and compliance with agreed-upon limits. More research evaluating this tradeoff seems worthwhile.

The out-of-sample forecast errors in the regressions used to derive (1) are very large. As shown below in Table 4, the average of the absolute value of the errors is about 19 percent when forecasts are made based on data only one period before the forecast period but rise substantially when earlier data are used. The standard deviation of the errors rises from 31 percent to 33 percent to 43 percent as the number of five-year lags rises from one to two to three. Although forecasts are less than the realized value they are large enough in absolute terms, (more than 100 million metric tons) to suggest that there is a possibility of substantial paper permits.

Argentina's recent announcement accepting an emissions target indexed to GDP provides some evidence about interest in this type of index. Argentina's index limits emissions to 151.5 [GDP.sup.1/2], a formula that implies an elasticity of emissions with respect to GDP of 0.5, which is fairly close to the value of 0.6 included in the preceding formula (Argentine Republic, 1999). Unlike (1) however, Argentina's emissions limit is independent of lagged values and instead depends on the "five year average GDP corresponding to the commitment period [2008 to 2012]" (Argentine Republic, 1999, Chapter 6).

For a "best-case" model in which emissions are a function of concurrent values of GDP, population, and lagged emissions, errors are little improved and average 21 percent. [17] For Mexico the error in this case is 13 percent. (See Table A3 in the Appendix). Of course, adjusting national emissions limits based on information available only after the 2008 to 2012 period raises profound questions of implementation. Yet, this is the approach adopted by Argentina.

5. SYNTHESIS

Are the errors from the reduced form regressions larger than the EIA's forecast errors because the forecasting ability of the EIA's models is superior to the simpler reduced form models presented here? Or are the errors larger because of the greater instability of smaller, less diversified economies that are more susceptible to shocks related to weather, monetary or financial systems, terms of trade and other causes?

To assess those questions, I first evaluate how the variability of GDP and emissions changes with the size of the economy. I then assess how forecast errors vary with the size of an economy.

It is well known that economic activity in small economies is more variable than economic activity in large economies (for example: Lucas, 1988). [18] Emissions of small economies should therefore be more variable than the emissions of larger economies. Data in Figure 3 relating variability of emissions to GDP support this point. In Figure 3, variability in emissions is the absolute value of the difference in logs of emissions in one five-year period and the preceding five-year period.

Results of regressions of emissions variability on GDP appear in Table 5 below.

In general, the smaller economies have emissions that are more variable than large economies. [18] As shown in Table 5, the estimated effect of the lagged value of GDP on variability of emissions is approximately -0.027 on average, in a model that accounts for period-specific effects. Based on the results of model (3), which allows GDP effects to vary with time, the effect rises from -0.049 at the beginning of the sample to about -0.02 at the end. This rise may result from increased specialization and diversification of economic activities in all countries during the sample period.

These regressions imply that comparing an economy with the GDP of Mexico to one with the GDP of the United States, the average change in emissions between successive five-year periods falls from about 18 to 11 percent. In general, a ten-fold increase in the size of the economy leads to a decrease in variability of approximately seven percentage points.

Since emissions are less variable in larger economies, I expect forecast errors to decline as the size of an economy grows, and Table 6 shows this to be the case for the same forecast errors summarized in Table 4 above. For forecast errors that are one-period ahead, a one percent increase in GDP is associated with a reduction in the forecast error of about 0.1 percent. For forecasts that are two periods ahead (that is, for a five-year period at least six years in the future) the forecast errors are about 7 percent for an economy with the GDP of Mexico and about 4 percent for an economy with the GDP of the United States.

The forecasting errors that these equations predict for the United States are greater than the errors for five-year periods calculated in Table 3 above, although the number of observations in Table 3 is so small the difference could be attributable to chance. The implicit emissions forecasts that I developed based on the EIA energy-use forecasts have errors for forecasts one period ahead and two periods ahead of roughly 1.3 percent and 2 percent respectively. [19] For forecasts one period ahead, the results of the reduced form model suggest average errors of 6 percent for a GDP the size of the United States', while for forecasts two periods ahead it predicts errors of about 4 percent.

The reduced form approach gives forecast errors that are larger for countries with smaller economies and that are larger than the errors from the forecasts implicit in EIA's fuel use estimates. A model of developing country emissions that had multiple fuels and multiple energy uses might be expected to yield forecasts more reliable than those implied by the preceding regressions. But it would be less reliable than the EIA forecasts for the United States because of the larger variability of emissions in smaller economies.

6. LIKELIHOOD OF NET COSTS FROM NATIONAL EMISSIONS LIMITS

What is the likelihood that a developing country that accepts an emissions limit set at the level of BAU emissions would be made worse off as a result of inadvertent stringency? To simplify the analysis, I assume that the world permit price is predetermined and independent of surprises pertaining to emissions in the country in question. In addition, I assume that the marginal cost curves developed from the Second Generation Model of the Pacific Northwest Laboratories reflect true social marginal cost, and I ignore the value of other environmental benefits that might result from reduced carbon emissions. [20] I ignore indirect costs, which might include equilibrium effects of changes in the price of oil and in subsidies and taxes. Given these simplifying assumptions, the likelihood of economic losses--that is costs in excess of any gains from trade--depends on the difference between forecast emissions and emissions realized under BAU policies.

I use estimates of the marginal cost of abatement developed by the President's Council of Economic Advisers (CEA) based on results of different runs of the Second Generation Model (SGM) [21] Two versions of the marginal cost curves are presented in Figures 4 and 5. The first shows the emissions reductions in tons of carbon; the second shows emissions reductions as a percent of the SGM baseline forecast. In both figures the hatched lines represent extrapolations to the origin.

These cost curves suggest that the potential gains to India from trade in emissions permits, if it accepted an emissions limit equal to BAU emissions, could reach $1 billion per year if the international permit price reached $40 per ton. [22] They also imply that China could supply a very large number of low cost emissions permits to world markets, if it were to accept an emissions cap at BAU. China's large supply of carbon permits results from its extensive and relatively inefficient use of coal. The assumption that China and India adopted such caps was key to the Administration's estimate that the marginal cost of meeting the Kyoto Protocol would be $23 or less per ton of carbon. [23]

For countries that take international permit prices as given, the roughly linear nature of the marginal cost curve suggests the breakeven emissions cap can be easily approximated. Recall that the breakeven emissions limit is the level of BAU emissions less half the emissions reductions needed to raise the marginal abatement cost to the international permit price. For India and Mexico, a cap inadvertently 10 percent below BAU emissions would yield losses unless the world permit price were above about $45 per ton.

For these two countries I calculate the likelihood of negative gains from trade by assuming it is equivalent to the likelihood that the emissions forecast will be too stringent by at least 10 percent. [24] Those probabilities are 0.37, 0.38, and 0.41 for the forecasts that are one, two and three periods ahead respectively. [25] This estimate should clearly be viewed as preliminary; use of a more sophisticated model should reduce these forecast errors. Finally, these probabilities assume an international permit price of $45 per ton.

The probability of economic losses is lower if international permit prices are higher. For India and Mexico, international permit prices of about $100 per ton correspond to a breakeven emissions cap of about 20 percent below BAU emissions. In this case the probabilities of losses are 0.26, 0.27 and 0.32 for the forecasts that are one period ahead, two periods ahead and three periods ahead respectively.

In general, the reduction in risk of economic losses from indexing is higher with moderate permit prices than with either very high or very low permit prices. Figure 6 below illustrates this point by showing the probability of economic losses with different world permit prices. The illustration assumes that the marginal cost of abating carbon is proportional to emissions reductions and that a ten percent reduction costs only $20 per ton. Thus the costs are similar to the curves for Mexico or India shown in Figure 5. It also assumes that the cap is set equal to emissions expected under BAU and that the standard deviation of the difference between realized BAU and the cap is 25 percent of BAU without indexing, but only 20 percent with indexing.

7. CONCLUSIONS

Developing country participation in the international effort to limit greenhouse gas emissions is the biggest issue facing policymakers concerned with global climate change. Binding national emissions limits--the form of participation most consistent with the Byrd-Hagel Resolution, the Kyoto Protocol and the Administration's estimates that the Costs of Kyoto would be modest--have economic advantages but also pose potentially significant risks to the economies of developing countries. This analysis suggests that if a developing country agrees now to a fixed national emissions cap equal to the emissions expected between 2008 to 2012 under BAU policies, then the likelihood of economic losses could be as high as 40 percent. Limits on developing country emissions may also increase global emissions, if emissions limits were so lax that countries could sell permits in international markets without undertaking real reductions.

To control such risks, international negotiators should index developing country emissions limits to variables that predict BAU emissions. A simple indexing approach might adjust the emissions limit by the level of GDP in the years before 2008, when the Kyoto limits take effect. It could adjust the cap upwards by 0.6 percent for every one percent increase in GDP above a projected value, and downwards by 0.6 percent for every one percent shortfall of GDP relative to its projected value. In addition, developing country emissions limits might be indexed to emissions prior to 2008, at the rate of 0.5 percent for every one percent change in pre-2008 emissions. This preliminary analysis suggests that indexing would lower the likelihood of net losses for a developing country accepting an emissions limit set equal to expected BAU by about 5 percent.

An indexing approach should complement statistically unbiased forecasts of BAU emissions. Even a well-respected institution like the U.S. EIA appears to systematically underestimate future carbon emissions. Developing countries may continue to be reluctant to accept greenhouse gas emissions limits without demonstrably unbiased estimates of future emissions. More research on the reliability of emissions forecasts is needed.

Argentina recently accepted an emissions target indexed to its gross domestic product during the 2008 to 2012 commitment period for Kyoto. Its example suggests that indexing emissions limits is an attractive way to control the costs to developing countries of adopting emissions limits, the key way to participate in the Kyoto Protocol. Notwithstanding Argentina's example, there is a need for much more research about what indexing approaches are best. Future research and international negotiations about developing country participation in the Kyoto Protocol should therefore on indexed emissions limits.

The author thanks Beth Mader for her outstanding assistance, Bob Hahn and the anonymous reviewers for helpful comments, and Joe Aldy for many constructive discussions. The author alone is responsible for the views expressed in the paper.

(*.) Fellow, AEI-Brookings Joint Center for Regulatory Studies, and resident scholar at the American Enterprise Institute for Public Policy Research, 1150 Seventeenth Street, N.W., Washington, DC 20036, USA. E-mail: rlutter@aei.org

(1.) See Senate Resolution 98, Senators Byrd, Hagel et al., reported by Senator Helms July 21, 1997, Section (l)(A).

(2.) This calculation assumes for simplicity that emissions permits cannot be traded internationally and that the cost curves are linear. Many of the industrialized country cost curves presented by Weyant and Hill (1999), however, are non-linear in a way that implies even greater sensitivity of cost to underestimates of emissions under BAU policies.

(3.) Emissions limits, or quotas, provide certainty about the number of tons emitted, while emissions taxes provide certainty about the cost of the last ton of emissions avoided. For a review of the implications of the economic uncertainty associated with quotas (see Weitzman, 1974; Pizer, 1997).

(4.) A simple geometric proof substantiates this point.

(5.) Revisions to these estimates by the Energy Information Administration do not, however, affect these targets.

(6.) This Annual Energy Outlook 1993 (AEO) was published in December1992 and therefore was presumably based on energy consumption and carbon coefficient data from almost a year earlier (Energy Information Administration, 1992).

(7.) Verbal communication with EIA representative, November 15, 1999.

(8.) This focus on carbon has uncertain effects on the results.

(9.) The International Energy Agency, for example, does not regularly publish estimates of emissions for individual developing countries. The International Energy Agency (IEA) has published two climate-change reports that include international carbon emissions estimates for past years, the most recent was [CO.sub.2] Emissions from Fuel Combustion 1971-1996, published in October 1998; but these publications do not include forecasts of emissions. An IEA representative confirmed that no carbon emission or energy use forecasts for individual developing countries are available from IEA and could not suggest an alternate source for these data.

(10.) This table includes 'forecasts' made for the same year as the year they were published; such forecasts are not prospective (for example, AEO95, published in 1994, presents a 'forecast' for 1994).

(11.) Carbon coefficients (millions of metric tons of carbon/quadrillion Btu) from Marland and Pippin (1990) as cited in Annual Energy Outlook 1993 were used for all estimations before 1995. In 1995, the EIA updated its carbon coefficients; these modified coefficients were used for all estimates after and including 1995 and were taken from Annual Energy Outlook 2000. When possible, carbon coefficients for each fuel type were modified by combustion fractions to account for carbon that is not emitted to the atmosphere. When combustion fractions were not available, annual tons of sequestered carbon for each fuel type were used. Because the consumption data was given for petroleum as a whole, weighted averages were found for thermal conversion fractions, combustion fractions and carbon coefficients.

These weighted averages and annual sequestered carbon data are the main source of error for these carbon emission estimates. Both weighted averages and sequestered carbon data are based on actual fuel-type use each year, not on the forecasted proportion of fuel-types used. This approach was necessary because the combustion data used for this paper reported fuel-types only as petroleum, natural gas and coal. Thanks go to Daniel Skelly and Perry Lindstrom, who helped with the development of this approach and to Susan Holte and Eugene Reiser for help interpreting the Forecast Evaluation 2000.

(12.) From the spreadsheet 'extener.xls' obtained from the Energy Information Administration for years before 1998. For 1998 and 1999, sequestered carbon was determined using non-fuel use estimates from Annual Energy Review 1999 (Energy Information Administration, 2000b) and sequestration rates from Emissions of Greenhouse Gases in the United States 1998 (Energy Information Administration, 1999b).

(13.) These discrepancies, for the four years beginning in 1992, may result from unidentified differences in definitions. EIA staff could offer no insight into these differences.

(14.) Note because Annual Energy Outlooks are printed in the year before the forecasts (for example, AEO99 was printed late in 1998), we consider an AEO99 forecast for 1999 as one year ahead.

(15.) All variables are in logs. Other terms, described in Table Al in the Appendix are excluded here for simplicity. In an effort to maximize the predictive power of the model I include some variables whose effects are not statistically significant.

(17.) These results are not strictly comparable to the regressions in Table 4 because of differences in sample size.

(18.) The Penn Mark 5.6 GDP data also show that larger economies have less variability than smaller economies. The data indicate that the absolute value of the annual change in GDP = 0.0921 - 0.00339 lagged log of GDP. The robust standard error for the coefficient is 0.00042.

(18.) Since my key objective is to make a cross-country comparison, I concentrate on simple ordinary least squares as opposed to fixed-effects estimators. I use robust Huber-White estimates of the standard errors, because of heteroskedasticity apparent in the scatter-plot (see White, 1980).

(19.) These should reflect the forecasts labeled one and six years ahead in Table 3, but given the lack of data I consider the forecasts for one and two years ahead and five and seven years ahead.

(20.) Substituting low-carbon fuels for high-carbon coal reduces emissions of nitrogen oxides, sulfur and fine particles, which contribute to potentially harmful local air pollution. Estimating the value of these emissions reductions is complicated by uncertainties in the assessment of environmental impacts, in their valuation and in when (and whether) emissions limits required to comply with recent regulations will be fully met. See Burtraw and Toman (1997) for a detailed discussion.

(21.) The data are on CEA worksheets made public by the Commerce Committee of the U.S. House of Representatives. See also U.S. Administration (1998).

(22.) The gains are approximately (1/2) ($40 x 50 million).

(23.) See U.S. Administration (1998, page 48 and Table 5).

(24.) I do not calculate the likelihood of inadvertent stringency for China. Inadvertent stringency in China's emissions limit would likely affect international permit prices because it would could not be seen as a small player in international permit markets.

(25.) I calculate these probabilities by assuming a normal distribution and using the estimated standard deviations for the out-of-sample forecast errors presented in Table 5.

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APPENDIX

FORECASTING DEVELOPING COUNTRY EMISSIONS

To forecast developing country emissions I use primarily a set of regressions of emissions on lagged emissions and lagged measures of income (GDP), income per capita (gdp), and investment. The results of this approach appear in Table A1 below. In these regressions the unit of observation is a five-year average of carbon emissions.

I focus on fixed effects models because the estimates of fixed effects pass the Hausmann test and offer better out-of-sample predictions than random effect models.

The estimates of out-of-sample forecast errors that 1 report in the text are constructed to underestimate the true extent of uncertainty in forecasts two or three periods ahead. In particular, the forecasts are based on regressions using all the data prior to 1988. Thus the forecast errors do not reflect uncertainty associated with unexpected structural changes in the period prior to 1988.

I also develop regressions of emissions on current variables, such as current values of GDP and GDP per capita. When these regressions are coupled with equations that predict GDP and GDP per capita, this method yields out-of-sample forecasts, but the associated errors are no less than with the lagged approach, so I do not present them here.

I use models of emissions as a function of current variables to assess whether current economic information predicts emissions substantially better than past data. Table A2 summarizes such models. In model (1), GDP per capita has an elasticity of about -0.04, although this is statistically insignificant. In model (2), a term for the square of the log of gdp is introduced. Its coefficient is negative but the linear term is still statistically insignificant when this equation is estimated using fixed effects. In model (3) I introduce a term defined as the product of GDP and gdp. I find that this term has a negative and statistically significant effect on emissions. Hausmann's test points to the superiority of the fixed effects model.

In Table A3, I present estimates of out-of-sample forecast errors from model 3 of Table A2.

These forecasts show average absolute errors of approximately 20 percent for the best case forecast. These estimates reflect errors across the 86 countries for which the forecasts are made.