a long tail of high estimates. These tails can be attributed to uncertainty about
feedbacks (Roe and Baker, 2007), related for example to clouds and water vapour,
and about the cooling effect of aerosols.
In Nordhaus’ (2008) risk analysis with DICE, the random climate-sensitivity
parameter is normally distributed with a mean of 3oC and a standard deviation of
1.1oC. Compared with the evidence compiled by IPCC, however, this distribution
may significantly underestimate the probability of very high values. For example, a
value of 6.3oC, which is three standard deviations from the mean of Nordhaus’ normal
distribution, is assigned a probability of only around 0.1%, whereas several of the pdfs
in IPCC (2007) put the corresponding probability at 5-10%. Similarly, in his review
of the evidence, Weitzman (2009) considers that there is a 1% chance of the climate
sensitivity exceeding 10oC. According to the above normal distribution, this is less
likely than a ‘six sigma’ event, so it has a probability of less than 10-7%. Therefore we
specify the random climate-sensitivity parameter as lognormally distributed. With
the parameterisation in Table 1, it can easily be verified that a value of at least
6.3oC, for example, is associated with a 3% probability.
3.2 The damage function
The final parameter in Table 1 is one element of the damage function linking tempera-
ture and utility-equivalent losses in output. In recent years, there has been increasing
focus in climate-change economics on this critical function (e.g. Weitzman, 2010a),
which is unsurprising when one considers that, without the damage function, the
accumulation of atmospheric CO2 has no consequence for social welfare. In many
past studies, including those with DICE, the approach has been to specify losses in
output as a quadratic function of global mean temperature:
Ω(T) = 1, ɪ, τ, , (7)
1 + α1Tt + α2Tt
where Ω, to keep our nomenclature consistent with Nordhaus (2008), is the propor-
tion of output lost at time t, T is the increase in global mean temperature over the
pre-industrial level, and α1 and α2 are coefficients.
The coefficients α1 and α2 are calibrated on the large literature devoted to es-
timating the cost of climate change in particular sectors of the economy, such as
agriculture, energy, and health (summarised in Parry et al., 2007). This literature
provides estimates of varying reliability and validity, but it can generally be concluded
that the loss in utility for warming of up to about 3o C is relatively well constrained,
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