Comparing Greenhouse Gases 

for Policy Purposes* 

Richard Schmalensee** 

In order to derive optimal policies for greenhouse gas emtsswns 

control, the discounted marginal damages of emissions from different gases must 

be compared. 1he greenhouse warming potential (GWP) index, which is most 

often used to compare greenhouse gases, is not based on such a damage 

comparison. 1his essay presents assumptions under which ratios of gas-specific 

discounted marginal damages reduce to ratios of discounted marginal 

contributions to radiative forcing, where the discount rate is the difference 

between the discount rate relevant to climate-related damages and the rate of 

growth of marginal climate-related damages over time. If there are important 

gas-specific costs or benefits not tied to radiative forcing, however, such as 

direct effects of carbon dioxide on plant growth, there is in general no shortcut 

around explicit comparison of discounted net marginal damages. 

INTRODUCTION 

David Wood understood early on both the high economic stakes 

involved in debates about global climate change and the potentially huge 

contribution that careful and objective economic analysis could make to those 

debates. While I was serving on the Council of Economic Advisers and 

concerned with climate change policy, David was actively and effectively 

building interest in climate change among energy economists at MIT and 

elsewhere. He and I ~lked about the economics of global change several times 

The Energy Journal, Volume 14, Number 1. All Rights Reserved. 

*I began work on this paper while a member of the Council of Economic Advisers and 

(finally) completed it with support from the MIT Center for Energy and Environmental Policy 

Research. I am indebted to Richard Eckaus and John Reilly for very useful discussions. 

**Center for Energy and Environmental Policy Research, Massachusetts Institute of 

Technology, Cambridge, MA 02139. 

245 
246 I The Energy Journal 

during 1990 and the early spring of 1991. We agreed about many things, 

including the ongoing fusion of energy and environmental policies that this issue 

exemplifies, but we argued about the subject of this paper. I like to think that 

David would have found my ideas more persuasive in their present form. 

THE PROBLEM 

In its first report, Working Group I of the Intergovernmental Panel on 

Climate Change (the IPCC) observed that 

The earth's climate is dependent upon the radiative balance of the 

atmosphere, which in turn depends upon the input of solar radiation and 

the atmospheric abundances of radiatively active trace gases (i.e., 

greenhouse gases), clouds and aerosols. (IPCC, 1990, p. 7) 

Global anthropogenic emissions of the various greenhouse gases are not in fixed 

proportions.• Thus, for instance, the ratio of total methane (C~) emissions to 

total carbon dioxide (CO:J emissions caused by human activity can be affected 

by a variety of governmental and intergovernmental policies. It follows that the 

design of an efficient global policy aimed at slowing the rate of climate change 

would necessarily involve decisions on how much, over time, to spend on the 

margin to reduce CH4 emissions and how much to spend to reduce C02 

emissions. This choice in turn must logically reflect the marginal damages 

associated with emissions of each kilogram of CH4 and C02• 

As the intensity, as well as the substance, of the debate on global 

climate change makes clear, future damages attributable to current greenhouse 

gas emissions are highly uncertain. This reflects uncertainty about at least (a) 

how changes in today's emissions would affect future atmospheric abundances 

of greenhouse gases and thus future radiative forcing, (b) how changes in the 

time-path of radiative forcing would affect future climates, and (c) how changes 

in future climates would affect some appropriate measure of human welfare. 

Perhaps because the second and third of these sources of uncertainty have 

seemed particularly important and intractable and because damage analysis 

involves difficult problems of economic valuation, a number of authors have 

proposed schemes for comparing the relative values of reducing emissions of 

greenhouse gases that reflect only atmospheric abundances and their radiative 

forcing implications. 

1. Here and in what follows "greenhouse gases" should be understood to include both radiatively 

active gases and aerosols as well as other gases and aerosols that affect the formation or destruction 

of such gases and aerosols. 
Comparing Greenhouse Gases I 247 

This essay argues that comparisons among greenhouse gases that are 

useful for analysis of abatement policies cannot be made without significant 

economic input; the physical sciences cannot supply all necessary information. 

If greenhouse gas comparisons are to inform policy design, they must be 

ultimately based on analysis of marginal costs and benefits. As the next section 

demonstrates, it follows that comparisons which begin and end with summaries 

of contributions to radiative forcing over time have no welfare-economic or 

policy-analytic justification. The section that follows then shows that under 

certain assumptions, comparisons of discounted marginal damages reduce to 

comparisons of appropriately discounted marginal effects on global radiative 

forcing. The welfare-economic foundations developed there can support rigorous 

evaluation of alternative discount rates. 

The final section considers the implications of relaxing two key 

assumptions. First, if changing concentrations of individual greenhouse gases 

produce important costs or benefits that are unrelated to global radiative forcing, 

explicit calculations of discounted net marginal damages cannot in general be 

avoided. In particular, if the effects of changes in atmospheric concentrations of 

C02 on plant growth are economically important, it will generally be impossible 

to make policy-relevant comparisons between C02 and other greenhouse gases 

without explicit computation of gas-specific marginal discounted net damages, 

including those associated with C02 fertilization. Second, following essentially 

all the relevant literature, the formal analysis that follows does not explicitly 

consider uncertainty. Some of the issues that would be encountered in doing so 

are also discussed in the last section of this paper. 

STARTING WITH RADIATIVE FORCING 

Because none of the relevant physical, chemical, or economic 

relationships can be guaranteed to be linear, and some are clearly nonlinear, the 

analysis here focuses on derivatives with respect to gas-specific emissions 

evaluated along some baseline economic/environmental trajectory. Let R(r) be 

instantaneous radiative forcing (the net radiative flux change at the tropopause, 

usually measured in watts per square meter) at timer, let E;(O) be emissions of 

gas i (usually measured in kilograms) at time 0, perhaps the present, fori = 1, 

, N, and let 

T ~ 0, i = 1, ... ' N. (1) 

For any i and T, a;(r) depends on the instantaneous radiative forcing associated 

with increases in the atmospheric concentration of gas i, on the dynamics of 

removal of gas i from the atmosphere, and on the impact of increases in the 
248 I The Energy Journal 

concentration of gas i on the concentration over time of other greenhouse gases 

and their precursors. These functions are often thought of as inputs to economic 

analysis, but this is incorrect. The marginal radiative forcing effect of increasing , 

the concentration of any one gas depends on initial concentrations of that gas 

(because of saturation of absorption bands) and on initial concentrations of other 

gases (because of chemical interactions and overlap of absorption bands). Since 

these initial concentrations at any time depend on earlier emissions, the a;(r) 

Junctions inevitably depend to some extent on an explicit or implicit long-run 

economic forecast. It also follows that the a1 functions may depend importantly 

on what date is taken as time zero and on the impact of any large-scale 

emissions reductions policies. 

The most frequently-cited approach to comparing greenhouse gasses is 

the index of global warming potential (GWP) presented by Lashof and Ahuja 

(1990) and by the IPCC (1990, 1992): 

i = 1, ... , N, (2) 

where T must be specified and, by convention, gas 1 is C02• Thus GWP1 = 1, 

and the idea is that if GWP2 = 2, for instance, then one can argue that reducing 

emissions of gas 2 is twice as valuable, kilogram for kilogram, as reducing 

emissions of C02• 

The most obvious problem with the GWP measure is that the horizon, 

T, is completely arbitrary. The choice of horizon can be important in this setting 

because the atmospheric lifetimes (half-lives) of the various greenhouse gases 

differ substantially. The second IPCC report (1992, p. 56), for instance, lists 

estimated lifetimes that vary from "days" (for NOx) to "> 500" years (for CFC14 and CFC-116). 

The first IPCC report (1990, p. 60) dealt with the lack of any welldefined, defensible procedure for choosing T by showing values of a set of 

GWP1 for T = 20, 100, and 500. 2 The corresponding GWPs for HCFC-123, 

which has an estimated lifetime much shorter than that of C02, are 310, 85, and 

29. Considering only major greenhouse gases, the corresponding GWPs shown 

2. The second IPCC report (1992) acknowledged the severity of uncertainties attached to the 

"indirect effects" of emissions of several greenhouse gases and did not present "total" GWPs 

comparable to those in the first report. 

l'~ .-
Comparing Greenhouse Gases I 249 

for methane (CH.J are 63, 21, and 9. 3 Since 20 years is clearly too short an 

horizon for this problem, while 500 years seems an awfully long time in any 

context, the reader's attention is naturally drawn to T = 100 as some sort of. 

reasonable compromise. This is an old trick: drafters of decision memoranda in 

the White House learn quickly to fight to have their preferred choice in the 

middle of the list of options presented. Any of a wide range of values of T can 

be made to appear a reasonable compromise in this fashion. 

Moreover, some have argued that extreme values ofT should be used 

instead of compromise values. Hammond, Rodenburg, and Moomaw (1990, p. 

705) advocate treating one unit of gas i at time zero as equivalent to a;(O)IalO) 

units of C02• They argue that using only very short-run changes in radiative 

forcing serves to tie "observable current results directly to policy actions .... " 

At the other extreme, Smith and Ahuja (1990) seem to argue that it is most 

appropriate to consider the total effects over time of current emissions, and this 

seems to imply setting T = oo. Nordhaus (1991) presents only this measure in 

his recent survey. 

Lashof and Ahuja (1990, p. 531) note that "current radiative forcing 

may be considered more important from a policy viewpoint than radiative 

forcing occurring in the distant future ... " Accordingly, they consider discounted 

GWP (DGWP, say) measures based on discounted integrals of the a;(r) 

functions: 

DGWP, 

I a;(r) e-" dr 

0 

"" 

i = 1, ... , N, (3) 

where r is a discount rate that must be specified. Nordhaus (1990) appears to 

have arrived independently at this same approach. 

The use of a fixed horizon as in (2), with everything occurring before 

Ttreated identically and everything after Tignored, has no support in economic 

theory. Because of this, T is arbitrary in a fundamental sense: there are no 

sound economic arguments that could be used to fix its value. 

On the other hand, discounting cash flows- either actual cash flows 

or values of costs and benefits of various sorts- or utility flows over an infinite 

horizon is commonplace and easily justified. Thus the main problem with (3) is 

3. The second IPCC report (1992, p. 56) indicates that these numbers incorporate the effects of 

a typographical error. The corresponding numbers given there for the direct effects only of CH4 are 

35, 11, and 4. 
250 I The Energy Journal 

different: it applies discounting to a physical quantity, incremental radiative 

forcing, that is only by coincidence proportional to either an actual or potential 

stream of cash or utility over time. As Eckaus (1992, p. 27) puts it, "Adding up 

physical measures of radiative forcing in different periods resulting from 

emissions at different times and places is, in an economic policy sense, like 

adding apples and oranges: it cannot be done." Because discounting has no 

economic rationale here, there is no way to apply economic analysis to the 

determination of an appropriate value of r. Thus, though (3) has a more familiar 

and defensible weighting than (2), it is in the end equally arbitrary because there 

is no principled way to fix r. 

ENDING WITH RADIATIVE FORCING 

This section considers comparisons based on the relation between 

changes in quantities of emissions at time zero, the E;(O), and D(t), the dollar 

value of damages at time t caused by climate change. As above, the analysis 

deals with derivatives along some baseline economic/environmental trajectory; 

here the focus is on derivatives of discounted damages with respect to emissions. 

Nordhaus (1991), Reilly (1991), Uzawa (1991), Eckaus (1992), and others have 

analyzed the first-order conditions for optimality of such a trajectory. 4 While 

the approach taken here is formally somewhat more general because it considers 

derivatives along trajectories that may not be optimal, it should be clear that the 

same gas-specific derivatives are central to both approaches. 

Suppose that the only external effects of greenhouse gas emissions are 

on the global climate and that the state of the global climate can be adequately 

summarized for cost-benefit purposes by M variables, where M is finite. Let 

~(t) be the value of the/' of these climate variables at time t. The most 

discussed such variable is global mean temperature, but other quantities, such 

as regional values of soil moisture and tropical storm frequencies may be 

considerably more important. We use the following notation for the marginal 

relations between climate and damages (conditional on whatever assumption 

regarding adaptation seems most reasonable): 

4. Eckaus (1992) considers cost minimization subject to an exogenously-imposed time-path of 

mdiative forcing, while the others treat mdiative forcing as determined by the optimization. While 

the resulting formulae differ somewhat in form, there is no substantive difference relevant to the 

issues considered here. 
Comparing Greenhouse Gases I 251 

fJD(t)lfJS(u) = f3p,u), t ~ u, j = 1, ... , M. (4) 

Since climate variables depend on the historical time-path of radiative forcing 

(and, perhaps, other quantities that will be assumed to be exogenous), we can 

define 

fJS(u)!fJR(r) = 'Y}Il,T), IJ ~ T, j = 1, ... ' M. (5) 

Using (4) and (5), the marginal relation between radiative forcing and 

climate-related damages becomes: 

fJD(t)lfJR(r) = E [I"' [fJD(t)lfJCiu)][fJS(u)tfJR(r)Jdu] 

}•I 0 

(6) 

= t [I"' f3p,u)'Yiu,r)du] = q,(t,r). J•l 0 

Finally, the present discounted value of damages associated with a small unit 

increase in the emissions of gas i at time zero can be written as 

I [fJD(t)/fJE1

(0)]e-"dt = I [ i [fJD(t)lfJR(r)][fJR(r)/fJE1

(0)]dr] e-"dt 

0 0 0 

I [ 1 ~(t,r)a,(r)dr] e~dt - I a,(r) [ I ~(t,r)e-"dt] dr (1) 

= I a1

(r)o(r)dr. 

0 

That is, the discounted damage caused by a unit increase in ElOJ is equal to a 

weighted integral of alr}, where the weights do not depend on i. This follows 

because emissions of greenhouse gases are (for the moment) assumed to cause 

only climate-related net damages, and such damages are only caused by changes 

in radiative forcing. The quantity o(r) is the derivative of the present discounted 

value of marginal damages with respect to radiative forcing at time T. 
252 I The Energy Journal 

Note that in (7) the discount rate, r, is applied to the dollar values of 

incremental damages over time. In this setting, as in general, the rationale for 

discounting of monetary values rests on some mixture of impatience and the 

productivity of investment, and the choice of an appropriate discount rate for 

public policy analysis involves choosing the right mixture, as well as adjustment 

for risk and the effects of taxes.5 While a detailed analysis of this issue is 

beyond the scope of this essay, the important point is that the economic problem 

of choosing the "correct" r in (7) is well-defined, which it was not in the context 

of (3). 

If o(r) in (7) were known for aliT, the argument so far implies that it 

should be used to replace the discount factor in (3) to compute indices of global 

warming damage, and ratios of those indices could then be used to compare 

greenhouse gases. But this function is not known, importantly because great 

uncertainty surrounds the level of damages associated with any particular pattern 

of climate change. Nonetheless, under some assumptions, the shape of o(t) takes 

on a familiar form, and uncertainties regarding the level of that function cancel 

out across gasses when comparisons are made in ratio form, as in (2) and (3). 

Sufficient conditions for this to be true are that following hold for j = 1 , ... , M: 

f3p,v) = f3J e 8' for t = v, = 0 for t > v; 

riv,r) = riv-r) for v ~ 1'. 

(8) 

Setting the {31 = 0 for t > v can be viewed as simply a convention on 

the measurement of damages. The assumption that the f3/t,t) grow at rate g for 

all j and t is quite restrictive in principle but less so in practice, given the 

sketchy nature of our knowledge of the likely costs of global change. Nordhaus 

(1991, p. 925), for instance, argues in effect that g should be set equal to the 

rate of economic growth in "resource steady state" -when "all physical flows 

in the global economy are constant even though (because of resource-augmenting 

technical change) the real value of economic activity may be increasing." Out 

of such an equilibrium, one might argue that g should be less than the rate of 

aggregate economic growth, since marginal physical damages to natural systems 

seem unlikely to grow as rapidly as the global economy, and the share of 

economic activity accounted for by agriculture and other climate-sensitive 

activities is secularly declining. On the other hand, the value of damages to 

natural systems may rise quite rapidly because environmental amenities are 

luxury goods, and, depending on the baseline pace of climate change, marginal 

sensitivity to climate-related damages may rise more rapidly than damages 

5. In general, see Lind (1984) and the literature he cites. Heal (1991) and Cline (1992) focus 

on discounting issues that arise in the context of climate change. 
Comparing Greenhouse Gases I 253 

themselves. At any rate, it is possible to have an intelligent economic argument 

about what value or values of g best summarize available information on likely 

future changes in the marginal effects of climate change. 

The second line of (8) assumes local linearity of the important climatedetermining natural processes. In the absence of discontinuous changes or sharp 

nonlinearities within the relevant range, this assumption should not be seriously 

misleading. It is, of course, a modest generalization of the single linear 

differential equation that determines climate in the models of Nordhaus (1991) 

and others. 

Substituting from (8) into the definition of o(7) given in (7), we obtain 

oo 

00

[N ] o(r) = J 4>(t,r)e-''dt = f ~ f3J-yp-r)e8' r r J I 

(9) 

where 8 = r-g, and A is a constant, independent of r. Thus a comparison of 

greenhouse gases based on discounted climate-related damages, using what might 

be called a relative damage index (RDJ), reduces to a comparison of discounted 

radiative forcing, with discount rate 8:6 

00 l [iW(t)/c3E1

(0)]e-''dt l Ot1

( r) e -Br dr 

RDI; 0 0 1, ... 'N. 00 l [c3D(t)/c3E1

{0)]e-''dt 

0 

l a 1

(r)e-8

'dr 

0 (10) 

As discussed above, the economic problem of choosing rand g, and thus(}, is 

in principle well-defined. In contrast, simply writing down (3) provides no 

economic (or other) basis for selecting a particular discount rate. 

6. This conclusion also follows from the steady-state optimal growth analysis of Nordhaus 

(1991). 
254 I The Energy Journal 

SOME COMPLICATIONS 

While the RDI developed above is an improvement on the GWP and the 

DGWP, there are at least two reasons why it is unlikely to be an adequate basis 

for policy decisions. First, as Reilly (1991) notes, the assumption that the only 

external effects of greenhouse gas emissions are climate-related is both strong 

and crucial to the sort of analysis performed above. CFC emissions have 

important effects on stratospheric ozone, for instance, and plant growth may be 

sensitive to atmospheric concentrations of C02• Efficient control strategies must 

take such effects into account if they surpass some threshold level of economic 

importance. Since external effects that are not climate-related do not operate via 

changes in radiative forcing, the presence of such effects in general rules out the 

sort of cancellation that produced (10). Specifically, even under assumptions (8), 

discounted net damages in general simplify only to 

00 I [oD(t)loE,(O)]e-"dt = A I ci;(r)e-8

'dr + J'1

, 

0 0 

i = 1, ... , N, 

where 'Yi is the discounted present value of the derivative of non-climate-related 

net damages with respect to emissions of gas i at time 0. In order to compare 

greenhouse gases for policy purposes in this case, both A and the 'Yi must be 

explicitly calculated. 7 

The second reason why (10) is unlikely to provide a sound basis for 

policy decisions is that an analytical framework that took full and explicit 

account of the uncertainties and irreversibilities that are important in the climate 

change context would likely imply a basically different approach to comparing 

greenhouse gases. 8 Over time, scientific and economic research will likely 

reduce uncertainties regarding natural climate-rated processes, damage functions, 

and costs of adaptation and abatement. Most climate-related policy actions that 

have been widely discussed, both those focused on abatement of greenhouse gas 

emissions and on adaptation to changed climates, would have long-lived effects, 

and changes in emissions of at least some greenhouse gases will have long-lived 

effects on radiative forcing. 

All else equal, a policy that puts primary near-term emphasis on 

relatively long-lived gases (C02 in particular) would seem to be attractive 

because it provides insurance against learning that climate change is a more 

7. See Reilly and Richards (forthcoming) for an illuminating development of this point and some 

interesting calculations of discounted net damages. 

8. For explorations of the policy implications of two aspects of the uncertainty that is pervasive 

in this context, see Heal (1984, 1991) and Hendricks (1991). 
Comparing Greenhouse Gases I 255 

serious problem than it now seems. This effect is necessarily absent from any 

analysis that neglects uncertainty. Of course, to go beyond this intuitive 

argument, or even to provide an adequate defense for it, would require a fullblown analysis of uncertainty in this context. Such an analysis would be quite 

valuable for a host of reasons that go well beyond the issues considered in this 

essay. 

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