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The contrasting assumptions often adopted in the mitigation scenarios are cases of stabilizing emissions or temperature increases. In Case E, the annual level of CO2 emissions is stabilized at the 1990 level, and, in Case T. the temperature rise from the pre-industrial level is constrained below or equal to 1.5C. The required emission reductions in these two cases are, of course, substantial. The carbon taxes required in Case E, for instance, are US$46/tC in 2000, US$130/tC in 2010, US$280/tC in 2020, and so on; and in Case T they are somewhat higher in the near term and register US$697/tC in 2050 and US$1,704/tC in 2100. The rate of reduction in world GDP in 2100 is a mere 0.8 per cent in Case O, but it is much higher in Cases E and T (5.8 per cent and 9.3 per cent, respectively).

Against the view that deems continuing global warming optimal, there can be a criticism that it discriminates against future generations. Indeed, Cline argues that the application of a 3 per cent discount rate is inappropriate. On the basis of the facts that the elasticity of marginal utility of consumption is around 1.5 and that the long-term rate of growth of per capita income is roughly 1 per cent per annum, he considers that the annual rate of social time discount should be around 1.5 per cent. He also points out that, if a logarithmic utility function is used, the elasticity of marginal utility with respect to consumption is unity so that consumption growth at an annual rate of 1 per cent implies built-in discounting of 1 per cent per annum.

Case O' in tables 8.3-8.7 reports the results where only the rate of time discount is changed, from 3 per cent per annum to 0.5 per cent per annum, all other conditions being kept unchanged as in Case O. It can be seen that both the rates of emission reduction and carbon taxes are higher now, although the rates of emission reduction hardly exceed 40 per cent even in the 22nd century. Moreover, the time profile of temperature rise does not change very much. When the rate of social discount is lowered, a larger weight is given to the utility from future consumption. Therefore, when optimization involves savings-investment decisions, as in the present model, this change tends to induce larger investments and hence larger future output and CO2 emissions. On the other hand, the lower discount rate also attaches a larger weight to future damage, so that it raises rates of emission reduction in the nearer term. Because these two opposing forces cancel each other out, the two scenarios look very similar as far as physical conditions are concerned. This means that lowering the discount rate can explain only a part of the differences between the Nordhaus and Cline results.

Let us now turn to the remaining five cases of tables 8.3-8.7. In these cases, I set the rate of discount at 0.5 per cent per annum. The first three cases distinguish climate sensitivity and the extent of damage from global warming as follows:

LT - low climate sensitivity parameter (1.5C) and low damage parameter (1 per cent with the degree of non-linearity 1.3);

MT - medium climate sensitivity parameter (3.0C) and medium damage parameter (1 per cent with the degree of non-linearity 2.0);

HT - high climate sensitivity parameter (4.5C) and high damage parameter (2 per cent with the degree of non-linearity 3.0).

The central case, MT, is identical to Case O'. Comparing the results for these three cases, we can observe that climate and damage parameters can change the nature of optimal time paths substantially. Emission reduction rates and carbon taxes are higher in Case HT than in Case MT, with smaller emissions but larger temperature increases and larger output reductions in Case HT. The reverse holds for Case LT. However, none of the three cases would satisfy those who prefer stabilizing emissions or temperature rise. The temperature increases in 2200 lie in the range of 2.6-6.1C, which is much higher than in Cases E and T.

In the last two columns of tables 8.3-8.7, I take up two extreme cases: for Case LL I assigned the lowest parameter values for climate sensitivity and output damage as well as for the rates of population growth, and similarly for Case HH I assigned the highest set of parameter values. I can point out two interesting similarities. First, Case LL has many points in common with Case O. This means that the application of rather high time discount rates is tantamount to assuming the most favourable global climate conditions in many important aspects: low temperature increases, little damage, less severe non-linearity of damage, and low rates of population growth. Second, Case HH, in turn, has many similarities with Cases E and T. CO2 emissions are severely controlled by high carbon taxes, resulting in fairly large output losses in the long run. However, there is one important difference: even with such severe emission controls global warming will not be mitigated in Case HH as sufficiently as in cases E and T.

One might think that if the expected damage caused by global warming were much more substantial, then further stringent emission controls would lessen global warming. Thus, I considered two higher-damage scenarios in table 8.8: one with a higher degree of non-linearity of the damage function (power 3.5) and the other with an even higher damage parameter (4 per cent of world output at 2 x CO2). In both cases carbon tax rates in 2100 are in the range of US$1.200-$1,500/tC, and rates of emission reduction in 2200 become 100 per cent. Indeed, in the case where damage is 4 per cent, the extent of temperature rise becomes lower than that in Case HT or HH. However, it is still larger than those of Cases E and T. Thus we must conclude that, even enlarging the size of the damage parameter by twice the most pessimistic estimate and making other assumptions most amenable to substantial damage, we cannot obtain optimal abatement paths that would justify immediate emission stabilization at about current levels. It appears that we need some other sort of social valuation function that incorporates much broader non-market values, or that takes a more serious view of uncertain, catastrophic situations in the distant future.

Table 8.8 Two high-damage scenarios


Emission reduction (%)

Carbon tax (US$/tC)

Emissions (GtC)

Temperature rise (C)

Power 3.5

Damage 4%

Power 3.5

Damage 4%

Power 3.5

Damage 4%

Power 3.5

Damage 4%

2000 47 56 257 357 4.2 3.5 1.7 1.7
2010 52 60 338 461 4.9 4.0 1.7 1.7
2020 54 62 409 551 6.2 5.0 1.7 1.7
2050 59 67 671 868 7.9 6.3 1.9 1.8
2100 79 86 1,235 1,467 10.3 6.9 2.6 2.3
2150 96 100 1,874 2,075 4.4 0.1 3.5 2.8
2200 100 100 2,365 2,572 0.2 0.2 3.8 2.7

As I mentioned at the beginning of this section, Fankhauser and Pearce arrived at the conclusion that the social costs of carbon emissions for the period 1990-2030 are in the range of US$20-30/tC. I shall conclude this section by summarizing my own estimates in table 8.9. It is clear that Case O. which attempts to reproduce the Nordhausian situation, does not seem to be normal when we apply the discount rate of 0.5 per cent per annum. My MT scenario gives slightly higher estimates than those of Fankhauser and Pearce, but it should be noted that these numbers are only for a relatively short period. My Case MT shows that the estimates would rise as we move further into the future, and will approach US$200/tC by 2100.

I add one more simulation in table 8.9 within brackets. This case is based on exactly the same assumptions as Case MT, but the terminal year is 2250 rather than 2300. Thus, shortening the time-horizon tends to reduce the social costs of carbon emissions. Since the problem of global warming arises from stock externality, higher discounting of the future will make the social costs smaller. By shortening the time-horizon, we simply discount the events beyond the time-horizon by an infinite discount rate. We must therefore take a fairly long view in evaluating the social costs of greenhouse gas emissions.

Table 8.9 The social costs of carbon emissions (US$/tC)






Optimization la Nordhaus 5 7 8 11
Emission stabilization 48 130 280 375
Stabilization of temperature rise 94 146 219 331
Low temperature rise 41 50 56 62
Medium temperature rise 60 76 89 103
(With shorter time horizon 54 69 80 92)
High temperature rise 117 149 174 201
Low population growth, etc. 23 27 30 32
High population growth, etc. 263 344 415 497
High damage: power 3.5 257 338 409 493
High damage: damage parameter 4% 357 461 551 655

5. Summary and conclusions

In this paper I first examined the magnitudes of the macroeconomic costs of carbon emission reductions based upon the OECD project of global model comparisons. I found that a 1 per cent reduction in carbon emissions generally requires a 0.02-0.05 per cent decline in GDP in developed countries, and that corresponding carbon tax rates are around US$2-10/tC.

I also showed that many Japanese research results had found much larger macroeconomic costs, because these models are fairly short term in scope involving demand-determined output responses. Also, the treatment of tax revenue is different. These findings suggest that interpretation of simulation results should be based upon clear understanding of the nature of the model.

Economic measures to limit carbon dioxide emissions, such as carbon taxes, usually have some side-effects as well. There is some empirical evidence that carbon taxes would have regressive distributional implications, but there seem to exist appropriate instruments to accommodate these undesirable domestic side-effects.

International side-effects need careful distinction. Any change in the structure of comparative advantage induced by an efficient, international scheme to internalize the external costs of carbon emissions should not be counteracted. Sectoral adjustment problems should be handled as in many other cases of changing environments. Carbon leakages resulting from trade diversion and from changes in international energy prices can theoretically be large enough to negate the initial effort of limiting carbon emissions, but the available evidence seems to suggest that unilateral action by OECD countries, for example, will still be largely effective. Finally, due consideration should be given to the possibility of an international scheme to limit carbon emissions causing large-scale international redistribution of income against fossil-fuel-exporting countries.

In contrast to the macroeconomic cost estimates based upon some sort of stabilization objectives for the emission or atmospheric concentration of greenhouse gases, the optimal response approach suggested by William Nordhaus has led to the conclusion that optimal abatement paths are much closer to the business-as-usual scenario path than to stabilization paths. The questions of the appropriate rate of time discount and of proper estimates of damage from global warming do not seem to resolve the wide gap between the optimization approach and the stabilization approach It appears that we need to investigate further if we are to broaden our scope of non-market values and take a more serious view of uncertain, catastrophic situations in the distant future.

Appendix: A simple Nordhaus-type model of climate and the world economy

This appendix gives a short summary of a simple Nordhaus-type model of climate and the world economy to evaluate optimal emission control paths under various alternative assumptions. The model consists of the following 12 equations:


Variable and parameter names and parameter values as well as initial conditions are as given below.


At: production technology factor
ACt: atmospheric stock of carbon dioxide
Ct: consumption
Et: carbon dioxide emissions
GDPt: gross domestic product
gA annual growth rate of A
ga annual rate of change in a
a t: emission factor
m t emission control variable
F t damage factor
It investment
Kt capital stock
Lt population
Tt temperature rise
equilibrium temperature rise
U discounted sum of consumption utility
d K capital depreciation rate
d M fraction of CO2 transferred to deep ocean


a: percentage loss of world GDP due to GHG abatement
b: percentage loss of world GDP due to global warming damage
ACP pre-industrial level of atmospheric stock of carbon dioxide
N time horizon
temperature rise at the benchmark
b feedback parameter
q power of the damage function
g 1,g 2 coefficients in the damage function
k fraction of CO2 remaining in the atmosphere
l adjustment coefficient
p share of capital
r social discount rate

Parameter values and initial conditions

a = 1%
ACP = 580(GtC)
AC0 = 750(GtC)

b = 1% or 2%
E0 = 6.003 (GtC)
gA = 0.85% p.a.
ga = -1.0% p.a.
GDP0 = 25.8 (tril. $)

a 0 = E0/GDP0
g 1 = a/100/0.53

d K = 0.05
d M = 0.002
q = 1.3, 2.0, or 3.0
k = 0.5
l = 0.2
K0 = 70.32 (tril. $)
L0 = 5.292 (bil.)
N = 2300
p = 0.25
r = 0.005 or 0.03


The author thanks Kenji Yamaji of the University of Tokyo and Tsuneyuki Morita of the National Institute of Environmental Studies for helpful comments and valuable suggestions. Of course, the author is solely responsible for any remaining errors.


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