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Part 3 - Energy-economy interactions in stabilizing CO₂ emissions

7. Modelling economically efficient abatement of greenhouse gases
8. Macroeconomic costs and other side-effects of reducing CO₂ emissions
9. The effects of CO₂ reduction policies on energy markets
Comments on part 3
Appendix to part 3 examining the macroeconomic effects of curbing CO₂ emissions with the Project LINK world econometric model

7. Modelling economically efficient abatement of greenhouse gases

William R. Cline

1. Introduction

Cline (1992a) sets forth a comprehensive economic analysis of the greenhouse problem. That study develops estimates of the damage that may be expected from global warming; reviews other model estimates of the costs of abatement; and, after an in-depth examination of appropriate discounting methodology, presents cost-benefit calculations that find it is socially efficient to pursue an aggressive international policy of abatement of greenhouse gases (GHGs). The study suggests a two-phase policy approach, with more moderate action in the first decade pending further scientific confirmation.

Subsequent papers synthesize these findings and extend the analysis in various directions (North-South policy interaction, in Cline, 1992c; optimization using the Nordhaus, 1992a, DICE model in Cline, 1992b and 1992d; and a review of new benefits estimates, a survey of abatement cost models, and policy synthesis in Cline, 1993). To minimize duplication of these earlier studies, this paper presents only a summary statement of the cost-benefit analysis in Cline (1992a), and invites the reader to consult that study directly for further elaboration.

The emphasis here is on the evolving shape of the analytical debate. Recent scientific work tends to confirm the emphasis in Cline (1992a) on the much greater warming and damage that may be expected over a very long horizon (three centuries). New scientific results also underscore the risks of sudden and catastrophic effects. New damage estimates widen the menu of conceptual and regional effects even for the conventional doubling of CO₂. Ongoing comparisons of models provide a clearer emerging picture on the side of abatement costs as well.

For the overall cost-benefit comparison, it is becoming increasingly clear that the rate of time discounting is the single most important source of difference between analyses showing aggressive action to be socially efficient (Cline, 1992a) and conclusions in the opposite direction (Nordhaus, 1992b) Accordingly, this paper presents new estimates applying differing discount rates to the Nordhaus (1992a) optimization model, and incorporating backstop technology into that model as well. The analysis here also identifies the corresponding field of "carbon shadow prices," representing the socially efficient penalties for carbon emissions over time.

2. Damage from 2xCO₂ benchmark warming

The primary benefits of GHG abatement are the value of global warming damage thereby avoided. There are also secondary benefits, principally the reduction of urban pollution as a side-effect of reducing fossil fuel combustion. Most analyses examine these effects for the "equilibrium" warming associated with the doubling of carbon dioxide above pre-industrial levels ("2xCO₂").¹

For this conventional benchmark, and the corresponding equilibrium mean global warming of 2.5°C (the "best guess" estimate of the Intergovernmental Panel on Climate Change, IPCC, for the climate sensitivity parameter L ), Cline (1992a) places damage to the US economy in a range of 1-2 per cent of GDP. The greatest damage occurs in agriculture (losses of 0.3 per cent of GDP), where careful attention to the appropriate allowance for "carbon fertilization" tends to leave greater net damage than is sometimes suggested.² Other major damage categories include the costs of increased energy for the excess of higher air-conditioning requirements over savings on heating (0.17 per cent of GDP); sealevel rise (0.12 per cent); losses in water supply (0.12 per cent); and increased losses of human life (0.1 per cent). On conservative valuations, forest loss, species loss, and increased air pollution from warmer temperatures (tropospheric ozone) add another 0.18 per cent of GDP to damage. More liberal allowances for species loss might place this damage alone on the order of 0.7 per cent of GDP. The secondary benefit of reduced air pollution could be of a comparable magnitude.

The 1 per cent of GDP damage estimate for 2xCO₂ in Cline (1992a: table 3.4) is thus best viewed as a moderate central value, with the figure easily reaching 2 per cent of GDP. Moreover, if upper-bound warming (L = 4.5°C) is applied, and with even modest non-linearity (damage exponent = 1.3), the corresponding range for damage reaches 2-4 per cent of GDP.

Important additional damage estimates have been made by Titus (1992) and Fankhauser (1992). For the United States, Titus suggests extremely large potential damage in forest loss (0.8 per cent of GDP) and in increased water pollution associated with decreased stream flow (0.6 per cent of GDP, for a damage category not even considered in Cline, 1992a). The larger figure for forest loss incorporates a broader concept of the consumer value of forest use, whereas the much smaller estimate in Cline (1992a) is based narrowly on the market value of lumber forgone.

For his part, Fankhauser (1992) extends the damage estimates to other countries, estimating them at 1.5 per cent of GDP for the European Communities, 0.7 per cent for the former Soviet Union, a remarkably high 6.1 per cent for China, and 2.8 per cent for non-OECD countries overall.³ His estimate for the United States is 1.3 per cent of GDP, which is comparable to the range in Cline (1992a). Fankhauser's estimate of an average of 1.4 per cent of GDP damage globally is comparable to that used by Nordhaus (1993b). It should be emphasized, however, that this is a GDP-weighted measure. Because of the relatively higher damage in developing countries, weighting by population would give a higher global estimate.

3. Very-long-term warming and damage

Cline (1992a) places heavy emphasis on the fact that, in the absence of policy intervention, global warming is likely to extend far beyond the amount associated with a doubling of pre-industrial atmospheric concentrations of carbon dioxide. A doubling of the carbon dioxide equivalent of all GHGs is expected to occur as early as 2025 (IPCC, 1990). In contrast, the proper time-horizon for analysis is at least three centuries. Thus, Sundquist (1990) estimates that the atmospheric concentration of carbon dioxide may be expected to rise until the end of the twenty-third century, after which time mixing into the deep ocean could cause a limited reversal.

As calculated in Cline (1992a), with reasonable baselines for population and economic activity and given abundant coal resources, global emissions would multiply approximately threefold by 2100 and ninefold by 2300. With the atmospheric retention ratio at its recent level of approximately 50 per cent of emissions, over this horizon atmospheric concentrations of carbon dioxide could multiply some eightfold. Taking other GHGs into account, and applying the radiative forcing relationships identified in IPCC (1990), the implication is a central warming projection of 10°C by 2300 for the IPCC's "best guess" climate sensitivity parameter of L = 2.5°C. This would take the earth back to the climate of the mid-Cretaceous period 100 million years ago, when mean temperatures were an estimated 6°C to 12°C higher than today (Hoffert and Covey, 1992). If instead the upper-bound climate sensitivity parameter is applied (L = 4.5°C), verylong-term warming could reach approximately 18°C.

Recent simulations of the GFDL (Geophysical Fluid Dynamics Laboratory) general circulation model (GCM) at Princeton University tend to confirm the central very-long-term baseline in Cline (1992a). Manabe and Stouffer (1993) examine the effects of a quadrupling of pre-industrial carbon dioxide equivalent by 140 years from now. They note that this level amounts to a 1 per cent annual increase in CO₂ - equivalent concentration, and is consistent with the IPCC "business-as-usual" scenario. The equilibrium mean surface air temperature increase reaches 7°C.⁴ This estimate turns out to be slightly more severe than that in my study (a central estimate of 7°C warming commitment by the somewhat later date of 2150; Cline, 1992a 52).⁵

Manabe and Stouffer do not argue that atmospheric concentrations will in fact stop rising after 140 years. Instead, their interest is in examining the consequences of this specified century-scale scenario. They find that the sealevel rise from thermal expansion alone reaches 1.8 metres by the 500th year, and would presumably be much greater if the effect of melting of ice sheets were taken into account. In contrast, the IPCC's estimate for the sealevel rise by 2100 is only two-thirds of a metre (IPCC, 1990: fig. 9.6).

Damage is highly likely to be non-linear in warming. As just one example, water runoff is a residual between precipitation (which rises with global warming but primarily in the high latitudes) and evapotranspiration, which rises more than linearly with warming. Cline (1992a) uses a relatively modest degree of non-linearity for most effects: an exponent of 1.3. (In contrast, Nordhaus, 1993b, applies a quadratic damage function.) The Cline (1992a) estimate of very-long-term damage corresponding to 10°C warming is in the range of 612 per cent of GDP for central estimates. Even with moderate non-linearity, the damage reaches an average of 20 per cent of GDP for higher-damage cases (upper-bound warming; with base damage for 2xCO₂ at 1 or 2 per cent of GDP).

4. Catastrophic effects

One of the most disturbing findings of the new Manabe-Stouffer simulation for 4xCO₂ is that:

... the ocean settles into a new stable state in which the thermohaline circulation has ceased entirely and the thermocline deepens substantially. These changes prevent the ventilation of the deep ocean and could have a profound impact on the carbon cycle and biogeochemistry of the coupled system. (Manatee and Stouffer, 1993: 215)

In other words, the GFDL model simulated for just 4xCO₂ finds that in the base case one of the feared "catastrophes" occurs: the ocean conveyor belt shuts down, and along with it presumably the flow of the Gulf Stream that keeps Northern Europe from being as cold as its latitudinal peer, Canada's Hudson Bay region.⁶ Moreover, the same phenomenon would largely close off the potential large reservoir of the deep ocean as a sink for carbon dioxide, presumably raising the atmospheric retention ratio and accelerating atmospheric build-up as a consequence.

Other recent evidence on the risk of catastrophe comes from the climate records in Greenland ice cores, which suggest that warming can come in extremely compressed periods. Thus, there was an estimated 7°C (local) warming within the space of only 50 years in the Younger Dryas period some 12,000 years ago (Dansgaard et al., 1989); and a collapse and rebound of temperature by 14°C within a 70-year period near the end of the last (Eemian) interglacial period before the present (Holocene) interglacial, some 115,000 years ago (Anklin et al., 1993). The extreme speed of such warming would seem highly likely to increase the non-linearity of damage, perhaps to catastrophic levels.

In the benefit-cost analyses examined below, these and other catastrophic scenarios are simply absent. The possibility of catastrophic outcomes must be kept in mind as a consideration that could warrant more aggressive abatement than indicated by the central benefit-cost analysis.

5. The costs of greenhouse gas abatement

Cline (1992a: chap. 4) provides a survey of economic models of the cost of reducing carbon dioxide emissions. Conceptually this cost equals the output loss imposed by restricting the use of a productive input, energy, in the "production function" for economic output. The central range of results in these models indicates that, by 2050, it would cost some 2-3 per cent of gross world product (GWP) to reduce emissions by 50 per cent from their business-as-usual baseline. This range is consistent with the production function approach.⁷

The OECD has investigated standardized simulations of several of the carbon abatement models (Dean, 1993). In an aggressive intervention scenario in which carbon emissions are reduced by 2 per cent annually from their business-as-usual time-path, by 2050 emissions would stand 70 per cent below baseline; and by 2100, 88 per cent below baseline. This scenario is broadly consistent with the aggressive action plan examined in Cline (1992a), where emissions are cut by one-third from present levels and then held constant at 4 billion tons of carbon (4 GtC) annually.⁸

The results of this standardized exercise show that, for the United States, the costs of the aggressive reduction by 2050 are in a range of 1.3 per cent of GDP (OECD's "GREEN" model) to about 2.6 per cent of GDP (the Manne-Richels, MR, model; and the Rutherford model). The extremely deep cut by 2100 imposes costs of 3.1 per cent of GDP in the MR model and 2.6 per cent of GDP in the Rutherford model (Dean, 1993. 11).⁹

For global costs, the models show somewhat (but not dramatically) higher costs. The simple average for these three models is a cost of 2.9 per cent of GWP for the 70 per cent cut from baseline by 2050, and 4.2 per cent of GWP for the 88 per cent cut from baseline by 2100. For the former Soviet Union, China, and other developing countries, costs are in the range of 4.0-5.5 per cent of GDP for the deep cuts by 2100 (MR and Rutherford models). Importantly, the somewhat higher costs of abatement for developing countries parallel the relatively higher damage of greenhouse abatement suggested by Fankhauser (as noted above), implying that for developing countries the benefit-cost trade-off may be comparable to that in industrial countries but at higher levels on both sides of the ledger.

Although costs can be substantially non-linear with respect to the depth of emissions cut-back at a given technology, they need not be so if it is recognized that the deeper reductions tend to come later in the time-horizon when the array of technological alternatives is wider. In particular, the advent of a "backstop technology" providing unlimited non-carbon-emitting energy at a fixed price premium above fossil fuels makes a critical difference to the cost of deep carbon cutbacks late in the horizon. Manne and Richels (1992) estimate that such technologies (e.g. advanced nuclear, solar, or biomass) should be available by about 2030, at a premium of about US$200 per ton of carbon (in 1990 dollars) above the opportunity cost of energy from carbon-emitting backstop technologies (e.g. synthetic fuels from coal).

Cline (1992a: chap. 5) emphasizes that abatement costs can be held lower initially through two strategies: forestry measures; and a move to the efficiency frontier using existing technology (as stressed in the "bottom-up" models). Reduced deforestation can remove carbon emissions at a cost of less than US$10 per ton. Afforestation can sequester carbon at costs under US$20 per ton (Moulton and Richards, 1990). However, additional carbon is sequestered only during the forest's growing stage, suggesting that afforestation is primarily an option for the first three decades or so.

The National Academy of Sciences (NAS, 1991) has estimated that, by moving to the efficiency frontier of existing technology, it would be possible to reduce US carbon emissions by 10-40 per cent at zero or very low cost. Information costs, utility pricing distortions, and other market failures help explain the gap between actual practice and potential efficiency. It is important to emphasize, however, that closing this gap is a one-time proportionate gain. Once the economy has moved to an "efficient" baseline, the new path parallels the original business-as-usual baseline at a lower absolute level that none the less still rises over time. It is unrealistic to expect a constant succession of additional movements to ever-shifting efficiency frontiers at zero cost, because the market failures in the revised baseline have already been removed. This is particularly so if the business-as-usual baseline already incorporates a widening array of technological alternatives (as in the Manne-Richels 1992 model). Thus, adherents of the bottom-up school cannot reasonably expect cost-free carbon abatement over the whole time-horizon.

Finally, costs can be substantially reduced if revenues from a carbon tax are used to correct existing distortions in fiscal structure. Existing taxes (e.g. on income and capital gains) impose disincentives that result in an economic loss of about 30 cents for each dollar of revenue collected (estimates for the United States by Jorgenson and Yun, 1990). Similarly, McKibbin (1992: 41) estimates that whereas an OECD-wide tax of US$15 per ton of carbon reduces US GDP by about 0.4 percentage points from baseline over the next two decades, if the revenues are used to reduce the budget deficit (rather than returned in a "lump sum" to households) the adverse output effect would be reduced to a 0.3 per cent reduction from baseline. The reason is that a lower fiscal deficit would reduce interest rates and stimulate investment and growth.

6. Benefit-cost comparison

Figure 7.1 shows the benefit-cost trade-off over time that emerges for an aggressive action programme that cuts global carbon emissions by one-third (to 4 billion tons of carbon annually) and then holds them constant over time (Cline, 1992a: chap. 7). In lieu of specific estimates for other countries, the figure assumes that the US damage profile is representative globally.

The benefits of abatement are set at only 80 per cent of the damage from baseline warming, on the grounds that even with aggressive action warming cannot be avoided completely. Similarly, abatement costs are expanded by 20 per cent above those for carbon alone, to take account of other GHGs. The cost curve is low at first, because of a 20 per cent "free" reduction assumed for the move to the efficiency frontier, as well as the availability of forestry measures. The abatement cost time-path then peaks at about 3.5 per cent of GWP, and thereafter declines to a plateau of about 2.5 per cent, because the cost function in Cline (1992a) allows for lower cost at later dates as the consequence of widening technological alternatives.¹⁰

Over the horizon, the benefits of abatement as a percentage of GWP substantially exceed costs in the high-damage case but are moderately below costs on average in the moderate central case. Moreover, the costs of abatement tend to be concentrated early in the horizon, whereas the greenhouse damage and thus benefits of abatement occur later. As a result, two factors drive the cost-benefit comparison: risk weighting, and the time discount rate for comparison across different points in time. Cline (1992a) places heavier weight (0.375) on the high-damage case than on the low-damage case (0.125) in aggregating with the central case (weight of 0.5) to capture risk aversion. Perhaps the single most important methodological issue, however, is the proper rate for time discounting.

Fig. 7.1 The costs and benefits of aggressive abatement of greenhouse warning

The discount rate

When consumption is available at alternative time-periods, the proper discounting procedure applies a "social rate of time preference" equal to:

where g is the rate of growth of per capita income, a is the elasticity of marginal utility of consumption, and r is the rate of pure time preference (Cline, 1992a: chap. 6; Nordhaus, 1992b: 1319). That is, the term a (< 0) tells how rapidly marginal utility drops off as per capita income rises; and the term r tells how much society prefers consumption today rather than tomorrow even for an unchanged level of per capita income.

Cline (1992a) adopts the classic view of Ramsey (1928) and others that the rate of pure time preference (r ) should be set to zero for the purposes of social welfare analysis. Especially for intergenerational comparisons, from the point of view of society it makes no sense to value a dollar of consumption for the future at less than a dollar of consumption today when per capita consumption is held constant between the two periods. In contrast, utility-based discounting for income and consumption growth is appropriate, and is incorporated in the second term ().

Many econometric studies use a logarithmic utility function, which sets the elasticity of marginal utility (a ) equal to -1.0 (Blanchard and Fischer, 1989). Two specific investigations of the elasticity of marginal utility independently place it at -1.5 (Fellner, 1967; Scott, 1989), indicating a somewhat more rapid drop-off in marginal utility than in the usual logarithmic utility function.

Cline (1992a) sets per capita income growth over the three-century horizon at about 1 per cent annually. With r = 0, = 1.5, and g = 1, the result is a social rate of time preference of 1.5 per cent per annum. Even at this rate, which some economists would consider low, US$1 of consumption today equates with US$20 (in real terms) 200 years in the future.

Following modern discount theory, Cline (1992a) further incorporates the influence of the portion of resources diverted from capital investment (on which the rate of return is higher) by applying a shadow price on capital and converting these resources to consumption equivalents. The overall effect is a discount rate of about 2 per cent.

Returning to figure 7.1, when this discounting procedure is applied, and when greater weight is applied to the high-damage case than to the low-damage case (not shown), the result is that the risk-weighted benefit/cost ratio for aggressive policy action comfortably exceeds unity (at 1.3). Thus, the economic benefits of the aggressive abatement of greenhouse gases would appear to warrant the corresponding economic costs, adding an economic basis for action to any case that might be made on ecological or scientific grounds alone.

Optimal emissions paths and the DICE model

In sharp contrast, Nordhaus (1992b) finds that even freezing emissions at their current level would have net social costs equivalent to 0.7 per cent of discounted future consumption. His optimal path would cut emissions by only 10 per cent from baseline, rising to 15 per cent in the next century. Because baseline emissions multiply more than threefold by 2100, his result indicates that it is economically efficient to allow the great bulk of emission increases to proceed unhindered.

To reach these conclusions, Nordhaus uses his Dynamic Integrated Climate-Economy (DICE) model (Nordhaus, 1992a). The DICE model is a potentially important advance in economic analysis of greenhouse policy. The model directly integrates emissions and global warming with savings, investment, and growth over time. The model appropriately takes a very-long-term view of the problem, as its simulations span 400 years (although Nordhaus, 1992b, reports results only through 2105). In principle the model provides the basis for identifying an optimal path of emissions over time, although in practice this path is extremely sensitive to assumptions.

Cline (1992b) implements the DICE model and examines its sensitivity to key parameters. As might be expected for an analysis over such a long horizon, the time discount rate turns out to be the principal reason for the sharp divergence between the Nordhaus results and those of the cost-benefit analysis in Cline (1992a).

In the DICE model, utility-based discounting (equivalent to the term discussed above) takes place through the combined effect of the logarithmic utility function (in which a 1 per cent rise in per capita income causes a 1 per cent decline in the marginal utility of consumption), on the one hand, and the model's optimal allocation of resources between present consumption and capital formation through saving (which drives the per capita growth rate, g), on the other. The model then explicitly further discounts by incorporating the rate of pure time preference, r . Its objective function is thus:

where P is population, c is per capita consumption, t is the year, and T is the final year in the horizon (400 in DICE).

Alternative simulations with DICE

The impact of alternative discount rates

Figure 7.2 reports the results of simulating DICE with alternative values for the rate of pure time preference, r . The figure shows the proportionate cut of carbon emissions from baseline (business as usual). For comparison, the path of proportionate cuts implied by the ceiling of 4 GtC annually is also shown, identified as "Cline."

The lowest path of cut-backs in the figure represents results setting the rate of pure time preference at 3 per cent, the value assumed by Nordhaus. As indicated, the implementation here successfully replicates the Nordhaus result of optimal cut-backs limited to only 10-15 per cent over the first 100 years when r = 3 per cent. However, the figure also shows that, if lower values are assigned to r , the DICE model itself generates much more aggressive optimal abatement paths. Indeed, if the rate of pure time preference is set equal to zero on the grounds argued above, the optimal abatement path in DICE becomes approximately equivalent to the 4 GtC ceiling of the aggressive abatement programme found to have a favourable risk-weighted benefit-cost ratio in Cline (1992a).

For comparability with the results in Cline (1992a), the appropriate value for the rate of pure time preference in figure 7.2 is in the range of 0.5 per cent per annum. The reason is that the DICE model applies a lower elasticity of marginal utility (a = -1 instead of -1.5). This difference can be approximately compensated for by raising the rate of pure time preference (r ) from the conceptually appropriate level of zero to 0.5 per cent.¹¹

Fig. 7.2 The optimal rate of emissions reduction

As may be seen in figure 7.2, if the rate of pure time preference is set at 0.5 per cent per annum, the optimal cut-back from baseline reaches about 50 per cent by 2100. Although this reduction is far greater than the optimal cut-back of 14 per cent identified by Nordhaus (1993b) for that period, the reduction remains considerably smaller than that implied by the aggressive international programme of limiting emissions to 4 GtC. However, adjustment of other elements of the DICE model could easily close this gap, including incorporation of the risk of higher-damage cases and imposition of a backstop-technology ceiling on abatement costs (as discussed below).

It should come as no surprise that the most profound policy decision that must be made on greenhouse policy turns on the rate of pure time preference, or how much weight we place on our own consumption in preference to that of our descendants. Global warming is inherently a problem involving small sacrifice in the present for large damage avoided for future generations. The 3 per cent value for r assumed by Nordhaus would seem to give far too little weight to future generations. 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).

In this debate, Nordhaus (1993a) has replied that a zero rate of pure time preference is "lower than would be consistent with observed real interest rates." Even if this were true it would not be the proper basis for policy determination. Society would be irresponsible to impose a US$370/US$1 trade-off against our descendants even if the markets today stated that this rate is what currently obtains in financial transactions. Policy should seek to correct market distortions where they exist, and a rate of 3 per cent for pure time preference would strongly imply a severe distortion in the inter-temporal consumption and assets markets. Indeed, it would be inconsistent to rule out the application of second-best pricing to compensate for market failure on the key analytical parameter the discount rate - in addressing a policy issue that takes as its point of departure the need for second-best correction of market failure on another central price - that of carbon (for which the market price does not incorporate the external diseconomy of greenhouse damage).

Moreover, it is by no means clear that observed market behaviour places a rate as high as 3 per cent on pure time preference. The closest asset to this concept is the real rate of return on Treasury bills, which involve no risk. This rate has averaged only 0.3 per cent over the past 60 years (Cline, 1992a: 258).¹²

Nordhaus himself has examined the sensitivity of the DICE results to the discount rate (Nordhaus, 1993b). However, his sensitivity test is a weak one, because he maintains the sum of the pure rate of time preference (r ) and the "growth discounting" () constant at 6 per cent. In his base case, r = 3 per cent, and growth rate, g, under "today's conditions" equals 3 per cent; so that, with a =-1 (logarithmic utility), the left-hand side of equation (1) above equals 6 per cent, which he judges is the market rate for the present "real interest rate on goods." When he reduces the rate of pure time preference from 3 per cent to zero for purposes of sensitivity analysis, he compensates by increasing the elasticity of marginal utility from -1 to -2, so that the left-hand side of (1) remains 6 per cent with today's growth rate at g = 3 per cent. The result is that setting the rate of pure time preference to zero only increases optimal abatement from a 12.5 per cent cut-back from baseline in 2050 to a 25 per cent reduction; and from a 14.3 per cent cut-back by 2100 to a 28 per cent reduction (Nordhaus, 1993b: table 6-4). Moreover, even this increase in optimal abatement stems solely from the fact that growth is decelerating in Nordhaus's baseline. If growth were constant, there would be no change in optimal emissions, because the reduction of pure time preference would be wholly offset by the increase assumed for the elasticity of marginal utility.

As discussed above, insistence that equation (1) above must equal a "market" rate of 6 per cent would appear misguided. As noted, it is highly doubtful that the proper concept, the consumption rate of time preference, is anywhere near this high. Moreover, a "second-best" approach would consider the social rate of time preference rather than an observed market rate, as argued above.

Other model assumptions

There are other assumptions in DICE that may warrant change as well. The model's near-cubic cost curve for carbon reduction causes an extremely high marginal cost for deep cut-backs. This pattern stems in part from the fact that the cost curve has no time variable: the sacrifice for a 70 per cent cut-back of carbon from baseline is identical whether the cut-back occurs today or in the latter part of the next century.¹³

The high cost of deep carbon reductions in DICE is revealed by considering the "shadow price" on carbon (the marginal cost of reducing carbon by 1 ton) under alternative simulations. Figure 7.3 reports these prices. It is evident that, with the much steeper optimal carbon reductions identified with lower rates of pure time preference, it is optimal to pay even very high marginal costs for carbon reduction (and thus very high carbon taxes). At r = 0, the optimal carbon tax reaches about US$220 per ton by 2025, and US$590 per ton by 2105.

These marginal costs would appear to overstate the expense of reducing carbon emissions. In particular, the marginal costs in the DICE model can rise far above the level of about US$200 per ton of carbon identified by Manne and Richels (1992) as an appropriate range for the ceiling associated with backstop technology.

Cline and Hsieh (1993) show that the imposition of a backstop-technology ceiling on the marginal cost of avoiding carbon emissions causes the optimal abatement path to jump to nearly complete elimination of carbon at the period when the shadow price of carbon (and thus the marginal benefit of its removal) begins to exceed the backstop price. Thus, with a ceiling of US$200 per ton of carbon removed, and with a rate of pure time preference of 1 per cent, the optimal cutback from baseline jumps from 33 per cent in 2125 to 45 per cent in 2145 and nearly 100 per cent in 2155, compared with an optimal cutback of only 43 per cent at the latter date in the absence of the backstop ceiling.

Another crucial source of understatement of optimal abatement in the Nordhaus (1992b) DICE results is that they do not incorporate the risk of upper-bound warming and upper-bound damage in the damage function. The analysis is strictly central-case, yet the essence of the greenhouse problem is dealing appropriately with risk. 14 Indeed, without risk weighting, the Cline (1992a) analysis shows a benefit/cost ratio for aggressive action of only 0.7. Moreover, both analyses omit the potential of catastrophic impact. Thus, neither Nordhaus (1992b) nor Cline (1992a) quantifies the economic damage that would result from a shutting down of the "ocean conveyor belt" that generates the Gulf Stream. Similarly, the damage functions are at most quadratic, and assume gradual warming.

The Nordhaus formulation of DICE would also appear to understate baseline carbon emissions, and thus prospective warming. The model sets business-as-usual emissions at 25 GtC by 2100 and only 31 GtC by 2275. In contrast, Cline (1992a) places emissions at 21 GtC by the first date and 56 GtC by the second. For their part, Manne and Richels (1992) set baseline emissions at 39 GtC already by 2100. The principal reason for the low emissions late in the horizon in the Nordhaus baseline is his assumption of low economic growth, driven by decelerating technological change (as discussed in Cline, 1992b).

Fig. 7.3 The shadow price of carbon with alternative discount rates

Moreover, the climate module in DICE would appear to understate the prospective extent of even central-case warming. The global mean temperature rise never exceeds 5.5°C over four centuries in the model as specified; yet the IPCC (1990: chap. 6) places the commitment to global warming at 5.7°C already by 2100 under business as usual. One reason for the low very-long-term warming is the low emissions baseline, as noted. Another reason for the apparent understatement is that DICE specifies a low contribution of greenhouse gases other than carbon dioxide, which at their maximum add only 1.24 watts/m² (wm^-2) in radiative forcing as opposed to the level of 3.06 wm^-2 already by 2100 estimated for these gases by the IPCC (1990: table 2.7).15 Still another reason would appear to be that the DICE specification involves a declining atmospheric retention ratio for carbon dioxide emissions, which falls to only 37 per cent by 2100, 29 per cent by 2200, and 26 per cent by 2270 (Cline, 1992b). Yet Wigley has indicated that, under business as usual, a relatively constant atmospheric retention ratio of about 45 per cent can be expected to persist.¹⁶

Shadow prices and carbon taxes

Returning to figure 7.3, the alternative simulations with DICE provide a basis for identifying appropriate penalties to assign for carbon emissions. For a given point in time and a specified rate of pure time preference, the "shadow price" tells the marginal benefit of reducing emissions by an additional 1 ton of carbon and thereby reducing global warming; or, equivalently, the marginal economic cost of doing so. Accordingly, the shadow price also tells the optimal marginal carbon tax, because only a tax of this amount will send the proper price signal to economize on carbon emissions.

As indicated in figure 7.3, for a rate of pure time preference of 0.5 per cent, the shadow price of carbon (optimal carbon tax) rises from US$45 per ton initially to US$84 per ton by 2025, US$133 by 2055, and US$243 by 2105. As suggested above, this range for r corresponds roughly to the assumptions in Cline (1992a), albeit still with understatement of abatement from the standpoint of not incorporating the risk of upper-bound warming or cost limits from backstop technology.

In comparison, Fankhauser and Pearce (1993) identify a lower and flatter trajectory for the shadow price of carbon, rising from US$20 per ton in 1991-2000 to US$28 per ton by 2021-2030. An important source of the difference is that Fankhauser and Pearce use a probabilistic approach to the range of discount rates, thereby including considerable weight on rates substantially higher than suggested here. Conceptually their method differs as well, because it seeks to identify the shadow price on a basis of discounted greenhouse damage under probability-weighted scenarios of public action and inaction, rather than by identifying an optimal emissions path that takes account of the costs of abatement.

7. Policy implications

The analysis in Cline (1992a) recommends an aggressive programme of international abatement of greenhouse gases. However, it suggests a two-phase strategy. In the first decade, more moderate measures would be applied. Thereafter, pending further scientific confirmation, policy measures would be intensified to limit emissions to a path similar to that of a 4 GtC ceiling.

In the event, industrial countries essentially committed at the Earth Summit in Rio de Janeiro in 1992 to return greenhouse gas emissions to 1990 levels by the year 2000. In view of the rising business-as-usual path, this commitment is equivalent to a cut-back somewhere on the order of 10-15 per cent.

There is a surprising convergence of the various analyses on action approximately consistent with this degree of restraint in the first decade. The Cline (1992a) aggressive action programme is a reduction of one-third; but, with a milder first phase, cut-back from baseline by some 10-15 per cent in the first decade is consistent with the overall strategy. The Nordhaus (1992b) optimal cut-back of 9 per cent by 1995 is not far from the same outcome. Similarly, the hedging strategy of Manne and Richels (1992) also leads to a cut-back from baseline of about 12 per cent by the year 2000.

Similarly, the carbon tax tends to converge for this initial period. Thus, the range suggested here of US$45 per ton in the 1990s (fig. 7.3 at r = 0.5 per cent) suggests that something like US$20-25 per ton might be appropriate in the initial decade of more moderate action pending further scientific confirmation. This range is consistent with the Fankhauser-Pearce initial shadow price (optimal carbon tax) of about US$20 per ton of carbon. This tax is even within reach of the Nordhaus Monte-Carlo results. Those sensitivity results place Nordhaus's optimal carbon tax at an expected value of about US$12 per ton of carbon in 1995, and as high as US$45 per ton at the 95th percentile of the distribution. Considering the suggestion of Yohe (1992) that incorporation of risk recommends "focusing on a scenario which describes something around the 75th percentile of potential economic damage," an intermediate point between the two Nordhaus Monte-Carlo estimates would also tend to converge in the US$20-25 per ton range for 1995. The policy prescriptions would begin to diverge more sharply only beyond the first decade, assuming scientific confirmation of the seriousness of the problem.

During this first decade, in addition to the moderate cut-backs and carbon taxes suggested here for the first phase, there should be intensive scientific research. One important area is in the narrowing of discrepancies among general circulation models on cloud feedback, the principal source of divergence generating the IPCC range of L from 1.5°C to 4.5°C. However, another key area for further research is on the very-long-term prospects for warming and damage. It would appear that, until recently, the scientific community may have been discouraged from looking at horizons beyond a century by the presumed tyranny of the economists' discount rate. That is, more distant results may have been thought to matter little because of time discounting in the policy process. However, as suggested here (and in Cline, 1992a), proper discounting methodology can leave room for serious damage even after a century to play a significant role in the analytical outcome. Economists should encourage the scientists to extend their analyses to these longer horizons (as in Manabe and Stouffer, 1993), rather than discourage such analysis.

In addition, there is a need in the coming decade for much more extensive analysis of the benefits and costs of GHG abatement for developing countries. Most of the economic analyses to date have been for the United States and other industrial countries. However, the fragmentary evidence for developing countries suggests that the stakes for limiting global warming may be even higher in these regions. Confirmation of this diagnosis, and its broader dissemination, could help the international community move toward a more global response in a second phase of policy action. It may be appropriate that abatement efforts in the first phase be concentrated in the industrial countries (including "joint" measures they might undertake with developing countries). In the longer run, however, ceilings on emissions in China and other developing countries will be necessary as well, if the problem of global warming is to be seriously addressed (Cline, 1992a: 336-342; Manne and Richels, 1992: 91).

Notes

1. Because of ocean thermal lag, equilibrium warming occurs perhaps some three decades after the corresponding radiative forcing from the increase in atmospheric concentrations of GHGs above pre-industrial levels. "Transient" or actual warming is thus less than the commitment" to equilibrium warming at a point in lime, unless atmospheric concentrations have been at a stable plateau for several decades.

2. Because of other trace gases, there is much less than twice the amount of carbon dioxide in the atmosphere when 2xCO₂-equivalent radiative forcing is attained.

3. The high estimate for China is driven by damage amounting to about 2 per cent of GDP each in two categories: agriculture and human mortality. The former reflects the large share of the agricultural sector in GDP. The latter is the consequence of applying a statistical value of life for China at US$150,000 only about one-tenth the typical range for industrial countries but relatively high compared with per capita income.

4. The actual transient warming by the 140th year is 5°C.

5. Note that the GFDL GCM has A = 3.5°C; Cline (1992a) uses A = 2.5°C.

6. The argument is that, with greater high-latitude precipitation and glacier melting, the waters near Greenland would become less saline and therefore less dense. In addition, warming (which would be much greater at this latitude than the global mean) would reduce the gradient of the thermocline. Together, the changes could mean that the cold surface waters there might no longer sink into the deep ocean as they currently do, shutting down the ocean conveyor belt.

7. Energy claims some 68 per cent of GDP. Economic theory states that this 'factor share" is also the "elasticity" of output with respect to the factor. The models tend to show that a 50 per cent cut-hack in carbon requires only a 25 per cent cut-back in energy. The resulting output loss would be 25% x 0.07 = 1.75 per cent of GDP, based on the factor elasticity approach.

8. Thus, the average baseline in the OECD survey is about 15 GtC by 2050 and 27 GtC by 2100 (Dean, 1993: 8).

9. The study also reports much higher cost estimates from simulations by Barns, Edmonds, and Reilly. However, those estimates apply an unreliable "GDP feedback parameter" in the Edmonds Reilly model. Unfortunately, the OECD survey did not use the methodologically preferable variant in the model, which instead estimates costs by integrating the area under the marginal carbon tax curve a method that gives much lower costs. See the discussion in Cline (1992a: 160-161).

10. Indeed, a floor is set on costs to prevent this influence from reducing them to extremely low levels late in the horizon.

11. Note also that the Nordhaus DICE technical change parameter generates an optimal growth path with considerably less per capita consumption growth than in Cline (1992a). Per capita consumption grows at 1.1 per cent in the first 50 years, 0.5 per cent in the second 50 years, and more slowly thereafter, with average growth of 0.4 per cent over three centuries (compared with 1 per cent in Cline, 1992a). Note further that there is an inherent compensation for this difference in the growth-discounting effect. Slower growth depresses late-period GDP and therefore the economic base to which the proportionate excess of damages over abatement costs present late in the horizon applies (fig. 7.1). In compensation, the growth-discounting component of the discount rate,, is lower because of the lower growth rate, g. The lower discount rate enhances the importance of later periods. neutralizing their diminution from the standpoint of the size of the economic base. Finally, note that the use of pure time preference at r = 0.5 per cent to compensate for a lower elasticity of marginal utility probably introduces an upward bias in the discount rate for DICE compared with Cline (1992a). That is, with the low growth rate of 0.4 per cent in DICE, the appropriate discount rate would be: r = 0.4 x 1.5 + 0 = 0.6 per cent (equation 1). Instead, the approximation suggested as comparable in figure 7.2 here is r = 0.5, so that r = 0.4 x 1 + 0.5 = 0.9 per cent.

12. It is true that observed real rates of return on capital of as much as 8 per cent imply that there is a large wedge between the social rate of time preference to savers in equation (1) and the return on capital. Under perfect markets, we would have the rate of return on capital i equal to the social rate of time preference r, or:. However, private capital return includes substantial project risk, and in addition includes a wedge representing marginal tax rates. As a result, i = r + w, where w is a wedge incorporating risk, tax distortions, and other market imperfections. Importantly, it is practically inconceivable that real return on capital could remain as high as 8 per cent over three centuries. Such a rate is strictly inconsistent with the size of GWP in both the Nordhaus and Cline projections. Thus, an investment of just 1 per cent of today's GWP, or US$200 billion, earning a steady 8 per cent real return would grow to 1.3 million times projected GWP at the end of the 300-year horizon. What these considerations do suggest is that there may he undersaving and underinvestment in a wide range of areas from society's viewpoint. However, the existence of such underinvestment is no justification for a social decision to underinvest in greenhouse abatement, where the consequences build up to proportionately much greater magnitudes because of the extremely long time-horizon.

13. The Nordhaus cost function is: c = 0.0686z^2.887 where c is cost as a fraction of GDP and z is the proportionate cut-back of carbon emissions from baseline.

14. Although the subsequent version in Nordhaus (1993b) does conduct sensitivity analysis and address risk aversion through "Monte-Carlo" runs in which parameters are varied, that approach does not identify the optimal path under risk aversion with the key discount rate parameters set at r = 0 and a = -1.5. Even so, the sensitivity estimates indicate somewhat more forceful optimal action. Thus, in Nordhaus's base case, the optimal carbon tax is only US$5.32 per ton in 1995, rising to US$13.68 by 2045, and US$21.03 by 2095. The corresponding rates of reduction from baseline are 9 per cent, 12.5 per cent, and 14.3 per cent, respectively. In contrast, with 400 Monte-Carlo runs, the expected (probability-weighted) carbon tax is US$11.83 per ton by 1995; and the tax for the 95th percentile in the distribution is US$42 per ton in that year.

15. Adjustment for the more recent findings that radiative forcing from CFCs tends to be neutralized by reduced forcing from the stratospheric ozone stripped by CFCs would not alter this estimate by much.

16. T. M. L. Wigley, University of Colorado, personal communication, 16 July 1993, using the model described in Wigley (1993). Note that Wigley has warned that his model may not provide reliable estimates for atmospheric concentration and retention for concentration levels above 1,000 ppm. because of the possible effect of a large increase in the ocean sink from the influence of dissolution of oceanic carbonates and near shore sediments. However. Eric Sundquist of Woods Hole Oceanographic Institute has indicated that the three-century horizon investigated here is too short for this influence to have much effect on atmospheric concentration. Personal communication. 5 February 1993.

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