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1.
Lawrence R. Klein
2.
Warwick J. McKibbin
3.
Kenji Yamaji
Uncertainty in environmental analysis
Statistical model building is a natural procedure to use in studying environmental impacts on social activity and also in examining the effects of alternative environmental policies. There are, however, uncertainties in this, as in any other, approach. It appears to me that some of the discussion at the conference was based on the assumption that model findings are correct, and accurate beyond their abilities.
I simply want to caution those among us who would speak as though certain estimates - say, of CO2 pollution or many other environmental measures - are quite correct. The discussion has been based on "point" estimates with more digits or decimals than can be justified, on the basis either of observational accuracy or of our precision in estimating technical or behavioural reactions.
The models that are being used are based on meagre data samples, often with large measurement errors. If the errors were to be evaluated by appropriate statistical formulas, we would undoubtedly find that the estimated confidence intervals, based on standard errors of extrapolation, are quite large. These intervals (or regions in higher dimensions) are often so wide that a surprisingly large number of qualitatively different social consequences could plausibly occur, yet I notice people speaking of societal results that are deceptively implied to be quite precise. For example, there is great uncertainty about the amount of carbon reduction in the atmosphere that would be associated with a given carbon tax.
My guess is that the interval of uncertainty, for a given degree of probability (such as two-thirds), is as great as 1,000 million metric tons. Those who confidently expect that emission levels can be held to the global amounts that prevailed in 1990 as a result of the imposition of a moderate tax of less than US$75/ton may well be wrong. It may require a much steeper tax to hold emissions at 1990 levels, and this good, in itself, would not be a very satisfactory outcome for the world. In fact, the different models that are used for the projection of CO2 emissions come to very different conclusions as to the effectiveness of taxation in reducing emissions. The spread among different model estimates is as large as a carefully evaluated confidence interval based on any one model.
Some of the main sources of error and uncertainty are the following:
- the estimation of the rate and volume of emissions from prevailing technologies;
- reactions of consumers and producers to price changes, either by market forces or by tax changes, in the use of energy;
- a flawed global database, such that some magnitudes are not available and the combustion effects, on a global basis, from the burning of fuel are not precisely known;
- the effects of climate and other natural conditions in which the model is assumed to operate not being fully (or even "well") known.
There are formidable obstacles to accurate projections of the economy and the physical environment, in tandem. These obstacles do not mean that we can say nothing about the problem or that we should remain silent in the face of the obstacles. They do imply, however, that we should describe our findings in general terms, with both point values and regions of uncertainty.
How can this be done? In the first place, well-known statistical methods for the estimation of standard errors of extrapolation or projection should be employed as far as possible. In some cases, sample data will be too sparse to permit careful evaluation of the underlying estimates of error variances.
A second step involves the calculation of stochastic simulations of the associated models. The investigation must assess all entry-points in the model design that admit error, and use drawings of numerical disturbance values (random in many cases) for the computation of alternative extrapolations. If this process is replicated, over and over again, an entire distribution of extrapolations can be assembled. Error variances or ranges can be determined from the replicated set of extrapolations. Of course, a minimal first or preliminary step should be to make a sensitivity analysis of the effect of assigning very different values, in a plausible range, to key parameters of the system. These different parameter estimates should not be purely one-at-a-time, because many of the key parameter estimates are interrelated with one another. This is an important point that is frequently overlooked in sensitivity analysis.
There is one saving aspect in this approach. If analysts concentrate on the examination of deviations from baseline cases they can take advantage of the phenomenon of "error cancellation." To the extent that some of the underlying uncertainties are the same, both in the baseline case and in the scenario case, there will tend to be high correlation between the same magnitude extrapolated from the two cases.
In the well-known statistical formula for the variance of a difference,
var(xs - xb) = varxs - 2covxsxb + varxb,
we find that large positive values for covxsxb can help offset the cumulative effects of var xs plus var xb. In this formula, xs stands for a scenario value, xb for a baseline value, var for variance and cov for covariance. If xs and xb are highly correlated, as one might suspect, then covxsxb will be large, relative to varxs + varxb.
This issue does not necessarily make the analysis accurate, in an absolute sense, but it does help to restrain the inherent degree of uncertainty.
It should also be noted that many environmental phenomena take a very long time to build up to serious magnitudes, i.e. serious for the quality of life. It is my conviction that the error of extrapolation grows with the length of the extrapolation horizon. Statements about the year 2020, or in some cases 2050, are extremely uncertain. We must try to look ahead, but we must be aware of the high degree of uncertainty associated with an attempt to extrapolate that far into the future.
The three papers in part 3 have a number of common themes. The central theme is the costs and benefits of implementing policies to reduce the expected increase in CO2 emissions over the next 10-300 years. I found that all three papers offered useful insights on the issues that they address, but they also highlight the need for more detailed research and better modelling efforts in this area. I will raise comments on specific aspects of each paper and then present some results from a new report to the US Environmental Protection Agency that uses a model called G-Cubed that I have developed jointly with Peter Wilcoxen. This model has a time-horizon of 300 years but integrates the short-run macroeconomic adjustment process in a model with multiple sectors in production and trade. It also explicitly deals with the interaction of asset flows and goods flows in international trade which are ignored in all other models that examine carbon taxes. In addition, this model is participating in the next round of OECD model comparisons. Each of the authors refers to results from the last round of model comparisons and thus these new results from G-Cubed will supplement the discussion of these earlier studies.
The paper by William Cline presents further extensions to his important contributions over the past several years, related to the issue of the benefits of reducing greenhouse gas emissions. His main argument is that more aggressive action is needed to combat the emission of CO2 than is likely to be implemented. His basic argument is that standard calculations of costs and benefits ignore the potential of a major disaster if nothing is done. In addition, economists have used discount rates that are high so that major problems that occur more than 100 years in the future are discounted away. Although I disagree with his arguments on this point, I agree with his policy prescription for the next decade. That is, to introduce a carbon tax of US$20-25 per ton and to increase investment in scientific research so as to improve our understanding of where we are and where we may be going. In addition, at the end of these comments I will provide some evidence that will support Cline's position that more can be done to reduce carbon emissions by illustrating that there need not be a trade-off between carbon emission reduction and lower economic growth. It is possible to reduce CO2 emissions with only short-term loss of GDP if the revenue that is generated by the tax is invested appropriately.
I would also like to raise several issues that Cline touches upon in his paper. First, in my opinion, the cost-effectiveness of planting trees to absorb CO2 is significantly overestimated. The sort of estimates for the United States from the studies that Cline cites are that around 20 per cent of the arable land in the United States should be planted to significantly reduce net projected increases in US carbon emissions. The general equilibrium effects of this are potentially large, given that it will raise the price of land, especially in agriculture. These general equilibrium effects have been ignored in the studies to date. The G-Cubed modelling work to which I have referred is attempting to focus more on this issue. We do not yet have a clear picture of the cost-effectiveness of the tree-planting strategy on a scale sufficiently large to lead to a reduction in baseline emissions.
Cline is right to point out the important role played by the discount rate in cost-benefit calculations. But also of great importance in any of these evaluations are: the extent of baseline emissions; the existence of backstop technologies; and how the revenue from the carbon tax is used.
Specifically on the question of discount rates, I tend to agree with the standard economists, approach of using a pure rate of time preference closer to 3 per cent. Cline points out when criticizing Nordhaus's assumption of 3 per cent: "This rate means that, under conditions of equal per capita income today and 200 years in the future, we can justifiably ask our descendants to give up US$370 in consumption to permit us to enjoy just US$1 of extra consumption today (in constant price dollars)." But it can easily be countered that, with a 3 per cent marginal product of capital, why should we be expected to give up US$1 of extra consumption today so that our descendants 200 years from now will have US$370 in extra consumption? In standard intertemporal consumer theory, where we have a representative consumer who dives forever, it can be shown that the marginal product of capital (or the real interest rate) is driven to the pure rate of time preference in steady state. If the discount rate is greater than the real interest rate then it pays to borrow and raise consumption today because the forgone consumption is less valuable in terms of future utility. If the discount rate is less than the real interest rate then it pays to forgo consumption today, invest the saving in physical capital, and get a future return that in terms of utility makes you better off. As consumption is forgone, the capital stock rises and the marginal product of capital falls until the interest rate equals the rate of time preference. In terms of valuing per capita consumption between any two periods, then the rate of time preference equal to the marginal product of capital is the logical assumption to use (at least in steady state).
I remain unconvinced by Cline's argument about discount rates, although I agree with Cline that more should be done, especially in the United States, to limit the emission of greenhouse gases. My view is based on the argument below that there need not be a linear relationship between reductions in CO2 emissions and GDP loss.
Professor Amano also addresses the consequences of reducing CO2 emissions through carbon taxes. He does this by comparing results from the models used in the OECD global model comparison project with results from Japanese studies. He makes a number of important points with which I agree. I will provide evidence in support of his contentions below.
Amano argues that many of the Japanese models have a larger loss of GDP per unit of carbon tax than the models in the OECD study because they place more weight on short-run changes in aggregate demand. Secondly, the Japanese models allow for unemployed resources in the short run, which computable general equilibrium (CGE) models typically do not. Thirdly, he points out that what is done with the revenue from the tax is very important. In addition, he raises questions about the extent of trade diversion leading to leakage of the effects of a unilateral tax levied by one country. Amano argues that to capture the overall effects requires a model with disaggregated sectoral detail because the carbon tax does not fall uniformly across the economy.
As already mentioned, I agree with many of Professor Amano's points. One aspect of the paper with which I disagree is the link between GDP growth and carbon emissions. Despite making the point that the impact of a carbon tax falls differentially on different sectors of the economy, Amano then summarizes the model results, as many commentators in this debate do, by inferring that a 1 per cent reduction in CO2 emissions requires a carbon tax of US$2-10 per ton. This tax then implies a reduction in GDP of between 0.02 and 0.05 per cent. Below, I will show that in the G-Cubed model a 1 per cent reduction requires a carbon tax of around US$8 per ton but the outcome for GDP depends crucially on how the revenue is used. By 2010 it could lead to a fall in GDP of 0.3 per cent if revenue is rebated back to consumers or to a rise of 0.4 per cent if the revenue is recycled to fund an investment tax credit.
In the final paper John Ferriter presents a baseline scenario out to the year 2010 from the International Energy Agency model. He then presents results for a US$100 per ton carbon tax, US$300 per ton carbon tax, and an increase in energy efficiency. I have little to argue with in the baseline scenario, but I question the usefulness of the model results. From my reading of the paper, it is assumed that between 1993 and 2010 there is no feedback from the change in energy prices after tax to aggregate GDP and then back to energy demand. This result is counter to most other model studies, including those of the models he refers to in his paper. I also found the results that a carbon tax of US$300 per ton by 2010 is the stabilizing level for the United States to be at the high end of the evidence from other models. Part of the reason a large tax is required is that there is no aggregate reduction in GDP that drives down the demand for energy. I will now present some results for the impact of a US$15 per ton carbon tax in the G-Cubed model to add evidence to that presented by the three papers as well as to show the crucial importance of the assumption about how the revenue from the tax is used. In addition, the difference between short-run aggregate demand consequences and long-run production substitution that is pointed to by Professor Amano will be highlighted.
The G-Cubed model
The G-Cubed model is documented in McKibbin and Wilcoxen (1992). This model is a multi-sector dynamic general equilibrium growth model. The key features of G-Cubed can be summarized as follows:
• specification of the demand and supply sides of industrial economies;
• integration of the real and financial markets of these economies;
• intertemporal accounting of the stocks and flows of real resources and financial assets;
• imposition of intertemporal budget constraints so that agents and countries cannot forever borrow or lend without undertaking the resource transfers necessary to service outstanding liabilities;
• short-run behaviour is a weighted average of neoclassical optimizing behaviour and ad hoc "liquidity constrained" behaviour;
• disaggregation of the real side of the model to allow for the 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 neoclassical growth model;
• the model is solved for a full rational expectations equilibrium at an annual frequency from 1993 to 2200.
The model consists of seven economic regions - the United States, Japan, the European Economic Community (EUR), the rest of the OECD (ROECD), oil-exporting developing countries (OPEC), Eastern Europe and states of the former Soviet Union (EFSU), and all other developing countries (LDCs) - with 12 sectors in each region. 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, fishing, and hunting, 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.
G-Cubed's seven regions can be divided into two groups: four industrial regions and three others. For the industrial economies, the internal macroeconomic structure as well as the external trade and financial linkages are completely specified in the model.
Figure 3C.1 presents results from McKibbin and Wilcoxen (1993a). This simulation shows the path of gross national product (GNP) in the United States after the imposition of a permanent US$15 per ton carbon tax in the United States commencing in 1993. The results are expressed as percentage deviations from the model baseline; thus zero implies no change in GNP relative to the baseline path. Each line in figure 3C.1 is for a different assumption about how the revenue from the tax is used. The five alternative assumptions are:
1. deficit reduction;
2. a lump-sum rebate to households;
3. an investment tax credit (ITC) to all sectors except housing;
4. a cut in the household income tax rate;
5. a cut in the corporate tax rate.
It is clear from figure 3C.1 that the consequences of the different assumptions are important. For example, with a lump-sum rebate of the revenue (which is the standard assumption many studies use) GNP remains below baseline well past the year 2022. However, by giving an investment tax credit, GNP is back to baseline by 1995. Secondly, in each case the aggregate demand consequence of the policy is important in the short run and the production substitution is important in the long run. This supports Professor Amano's argument.
Figure 3C.2 presents the consequences for carbon emissions of the alternative assumptions about the use of the tax revenue. Although there are some differences between the resulting paths for carbon emissions, it is clear that in each case the policy is effective in reducing emissions. The reason is that the dominant effect of the carbon tax is to reduce carbon, especially in the coal industry. None of the alternative revenue assumptions stimulates the coal industry sufficiently to negate the carbon tax in that industry, because the policies are economy wide rather than sector specific. Thus they can change economy-wide production and income but not carbon emissions that are concentrated in the coal, oil, and natural gas extraction industries. The two figures together show that there need not be a linear relationship between carbon emissions and GNP. This is because of the sectoral substitution possibilities plus the differential impact across sectors of the policies.
Fig. 3C.1 Consequences for US real GNP of a US$15/ton carbon tax under alternative revenue recycling assumptions, 1993-2022 (Source: McKibbin and Wilcoxen, 1993a)
Fig. 3C.2 Consequences for US carbon emissions of a US$15/ton carbon tax under alternative revenue recycling assumptions, 1993-2022 (Source: McKibbin and Wilcoxen, 1993a)
Finally, the question of offset through trade flows resulting from unilateral carbon taxes has been assessed using the G-Cubed model in McKibbin and Wilcoxen (1993b). In that paper, we show that a unilateral US carbon tax reduces carbon emissions in the United States by about 15 per cent less than when all OECD countries also impose a carbon tax. Thus there is evidence of some offset from unilateral action but nowhere the complete offset suggested by the estimates discussed in Amano's paper.
References
McKibbin, W. and P. Wilcoxen. 1992. G-Cubed: A Dynamic Multi-Sector General Equilibrium Growth Model of the Global Economy: Quantifying the Costs of Curbing CO2 Emissions. Washington, D.C.: Brookings Institution, Discussion Paper in International Economics No. 98, September.
McKibbin, W. and P. Wilcoxen. 1993a. "Global costs of policies to reduce greenhouse gas emissions II." Report prepared for the Office of Policy Analysis, US Environmental Protection Agency, on the 2nd-year results from a multi-year research grant.
McKibbin, W. and P. Wilcoxen. 1993b. "The global consequences of regional environmental policies: An integrated macroeconomic, multi-sectoral approach." In: Y. Kaya, N. Nakicenovic, W. Nordhaus, and F. Toth (eds.), Costs, impacts and Benefits of CO2 Mitigation. Austria: International Institute for Applied Systems Analysis, CP-93-2.
Many interesting topics are raised and discussed in part 3. Dr. Cline makes a persuasive argument for his two-phase policy approach with the first phase of CO2 stabilization through the application of "integrated" economic analysis. By "integrated" I mean that both the cost of greenhouse gas control and the damage resulting from climate change are treated.
Professor Amano is rather neutral in a sense. He surveys the macroeconomic cost evaluations of a CO2 tax and studies of its side-effects, and he also talks about his own study on the sensitivity of the optimal climate control using a version of the integrated model originally developed by Professor Nordhaus.
Mr. Ferriter is the most pragmatic and cautious of the three. He introduces an IEA study on the carbon tax with relatively high rates and regulatory approach for promoting energy efficiency improvements. He suggests that the regulatory approach would have effects equivalent to those that can be expected with a carbon tax of US$300/tC.
I would like to comment on three points related to these presentations.
The first point is the macroeconomic impact of a carbon tax. As Professor Amano points out, the macroeconomic cost varies depending on several factors, such as the time-horizons of the models and the treatment of tax revenues. He also mentions the difference in the types of model employed. I would like to emphasize here the influence of the basic structure of the models used. On the basis of actual past performances, the general equilibrium type model and a more explicit optimization model tend to produce a smaller macroeconomic cost compared with simulation models that simulate the performance of actual imperfect market functions.
My own study on carbon tax, which is included in Professor Amano's survey, is based on a simulation type model. The cost I obtained is rather high even when the tax revenue is assumed to be recycled through income tax reduction. Of course, there is also a regional difference. I think my result reflects the higher marginal cost of CO2 reduction in Japan. But the difference of model type makes a more significant impact.
My second comment concerns the policy implications of integrated economic analysis, or optimal climate control with minimum total social cost. The uncertainties involved in damage cost evaluation are huge, particularly in the case of climate change. We have too little knowledge to do a full cost-benefit analysis of climate control. In this context, sensitivity analyses, as demonstrated by Dr. Cline and Professor Amano, are very interesting and important. However, optimal control may be very close to the business-as-usual case, and very far from CO2 stabilization, which is the path many OECD countries (including Japan) are now choosing. But, as Dr. Cline says, CO2 reduction, which is a more stringent control than CO2 stabilization, could be the optimal path depending on the choice of discount rate and the time-horizon.
It is clear that more study should be done in this field. My personal feeling is that we should take action now to deal with climate change. There are two aspects that are not mentioned in the presentations: one is that there could be a catastrophic positive feedback such as triggering a burst of methane emission from tundra in Siberia, and the second is that technology development could, eventually, dramatically reduce the cost of CO2 control. These issues are not short-term ones and therefore appear not to be suitable topics of discussion here. But I believe short-term policy should also be rooted in long-term considerations.
The last point I would like to raise is the global perspective of climate control, or more specifically the issue of "carbon leakage," which Professor Amano mentions as a side-effect. I think inter-regional equity is important as well as intergenerational equity. In this sense? the developed regions should take the lead in climate control and CO2 limitation. However, unilateral efforts by developing regions are quite likely to be accompanied by leakage; i.e. CO2 reductions in a developed region may result in CO2 increases in other regions. And such leakages can be very large. On the other hand, the assertion that joint implementation between developed and developing regions can be one of the most effective and efficient schemes to reduce global CO2 emissions is mostly maintained in qualitative terms; as far as quantitative analysis is concerned, there is not enough research in this field. Through analyses addressed to these global perspectives, pessimism about carbon leakage could be turned into positive opportunities.