Some papers on estimating cliinate chailge damage have advocated the use of uiliform unit values for damage (e.g., Ayres and Walter, 1991; Hohmeyer and Gartner, 1992; Ekins, 1995; Meyer a.nd Cooper, 1995). Note the differ- ence between a global assessmellt without regional distinctions and a global assessment with regional distinctions. In the former case, the common way t o proceed is t o value everything at a global average, in the same way that Fankhauser and To1 (1995) valued a t regional averages. It is the latter case that we are interested in, where regions are distinguished and damage is regionally assessed and subsequently compared and aggregated. It is im- portant t o note that the case in favor of uniform damage valuation in all these papers is made on the basis of ad hoc decisions, not welfare theoretic reasoning. This sectioil analyzes these value judgements in the framework
of the model of Section 3, a.nd calculates the type of global welfare function implicitly assumed when using uniform unit damage values.
For the sake of simplicity, iildividuals are divided into only two groups, inhabitants of OECD couiltries (clenoted by superscript r ) and inhabitants of non-OECD countries (including middle-income countries such as those with economies in transition; denoted by superscript p). We are interested in the ratio of per unit damage values (e.g., the relative W T P per km2 of wetlands). Suppose the ratio actually observed, based on the current income distribution, is VT/TfP. The goal the11 is t o choose the parameters of the regional and global welfare functions such that the ratio of equity-weighted per unit values is unity. Using equatioil ( I ) , this requirement can be written as
Using equation (3) for global welfare and equation (2) to specify regional welfare, after some mailipulation equatioil (4) becomes
with R = [ln(T/'P) -ln(T/")]/[ln(YT) -111(I,'")]. R.eca,ll that y is the parameter for illequality aversion in the global welfare function, and e is the income elasticity of the ma.rgina1 regional welfare. That is, for any given values for R and e (which are both deterilliiled empirically), the presumption that climate change impacts a,re to be valued equally implies a certain value for y , and thus a certain degree of inequality aversion.'
Table 5 presents y as a functioil of e and VT/Vp. As before, we assume values for e between 0 and 2, with values of 0.8-1.5 being the most likely specification according t o empirical evidence (see Cline, 1992; Pearce and Ulph, 1994). The ratio VT/VP is more difficult t o determine, because empir- ical evidence is scarce. An often used starting point is t o assume an income elasticity of W T P of one (Pearce, 1980). In this case, W T P s as proportions of income are identical for all individuals. That is, V T / Y T = VP/Yp, which in turn implies a value of T f T / T f G Iv/T'P, or a ratio of about four (recall that Y is purchasing-power-corrected per capita income and that the group of poorer countries includes middle-income as well as low-income countries).
The estimates quoted in Pearce et al. (1996) took the same starting point;
however, rounding and extrapolation inaccuracies, as well as deviations from
'Note t h a t we only require equal values between regions, not equal values a t a particular level. T h e l a t t e r would imply an additional rest,riction on (5).
Table 5. Implied illequality aversion ( y ) as a fuilction of risk aversion (e)
this rule for some damage categories, led t o a slightly higher average income elasticity of WTP, in the order of 1.15-1.20. This result implies a Vr/VP ra- tio of about 8-10.~ Flores and Carson (1995) and Kristrom and Riera (1996) argue that elasticities generally tend t o be less than one, and Krupnick et al. (1995), for example, have a.ssumed a value of 0.35-1.0 for statistical life estimates in Eastern Europe. This secoild set of studies would imply a much lower VT/VP ratio, perhaps in the order of 1.3-4.0. Table 5 presents esti- inates of y for both sets of a.ssumptions.
As Table 5 shows, the postulate of uniform per unit values is compatible with many sets of "reasonable" parameter assumptions, but by no means with all of them. For several parameter specifications, common values im- ply degrees of inequality aversion in the utilitarian (y=O) or Bernoulli-Nash range (y = I ) . ~ In the case of a unitary illcome elasticity of WTP, for exam- ple, uniform per unit values imply a Bernoulli-Nash welfare function. Other parameter sets imply higher degrees of inequality aversion, and in the case of a logarithmic regional welfare fuilctioll ( e = l ) , equal values are only com- patible with a inaximin welfare coilcept (y = m).
There are also cases where the notion of common per unit values would seem untenable. As Table 5 shows, there are parameter combinations for which common per unit values imply negative values for y , that is, "in- equality attraction," which could in the limit go t o a maximax (Nietzchean)
'This figure is an average value between middle-income and low-income country ratios, which are all subsumed in the "poor" group. T h e middle-income country ratio assumed by Fankhauser (1995) is about 4:1, and the low-income country ratio is in the order of 10:l t o 15:l.
3 A l t l ~ o u g l ~ y = l is only approached for c 1 oo and e 1. oo.
welfare concept (y = -m). With certain parameter combinations, weighted per unit damage estimates for the LLpoor" region can be higher than those for the "rich" region. The restriction of equal values then favors the rich.
Clearly, this would be an indefensible welfare concept, and it would therefore be hard t o make a case for common per unit values should these particular parameter values prevail. As noted, the question of the appropriate regional welfare and W T P parameters is a n empirical one, about which precious little is known t o date.
5. Conclusions
It is arguable that climate change is such a large and pervasive issue that it is right for equity arguments t o be integrated into a benefit-cost comparison, even though equity weighting is no longer common in benefit-cost analysis.
This paper shows one approach to equity weighting in the aggregation of damage estimates for world regions into a global damage estimate.
In our approach, equity weights depend on regional and global wel- fare functions, notably, the degrees of risk aversion and inequality aversion.
Equity-weighted global damage estimates can be substantially higher than the damage estimates presented by the IPCC SAR (Pearce et al., 1996), although reduced damage cannot be excluded. The simple aggregation un- derlying the figures reported in the IPCC SAR implies unacceptable welfare functions.
T h e degree of inequality aversion required for per unit damage values t o be the same in rich and in poor countries - a notion frequently called for in the debate on the chapter on social costs of the IPCC SAR - is compatible with a wide range of "reasonable" welfare functions, but can also be incongruous with defensible welfare concepts.
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