temperature is roughly 11oC above the pre-industrial level. Thus the mean value of
function (8) remains fairly conservative at high temperatures. However, when α3 is
three standard deviations larger than the mean, 5o C warming triggers an output loss
of around 25% of output, and 50% of output is lost when warming reaches just 6o C.
This is very close to the specification of Weitzman (2010b). Conversely, at three
standard deviations below the mean, α3 is small enough that function (8) virtually
collapses to function (7), so our risk analysis on the damage function can be said
to span the approaches taken by Nordhaus on the one hand and Weitzman on the
other.
4 Results
As reported in Section 2, a necessary, but insufficient, condition for SDU welfare to
be below DU welfare is that there exists some period t ≥ 0 such that ct > ct+1.
This period t has to be smaller than the model’s terminal period T , as we impose
constant consumption beyond T . Satisfying this condition will in general depend on
severe climate-change damage, since the DICE model, in line with other integrated
assessment models, predicts strong growth in production in the absence of such
damage. For example, when all the coefficients αi of the damage function are set
to zero, so that damages are ‘switched off’, global mean consumption per capita in
DICE is forecast to grow in real terms from US$6,667 in 2005, the base year, to
US$26,159 in 2105, and onwards to over US$80,000 in 2205.10 Hence the probability
that ct > ct+1 for 0 ≤ t < T may be low, but as long as it is not zero, SDU may lead
to a different evaluation of policies to cut CO2 emissions than will DU. Therefore we
begin our analysis of the modelling results by investigating the probability that per-
capita consumption is falling at some point over the modelling horizon, conditional
on the schedule of emissions cuts pursued.
To begin with, we examine three such climate-change policies. They are, first,
‘business as usual’, second, a schedule of emissions cuts to limit the atmospheric
concentration of CO2 to twice its pre-industrial level (560 parts per million, hereafter
referred to as the 2 CO2 policy), and, third, a more aggressive schedule of cuts to
limit the concentration of CO2 to only one-and-a-half times its pre-industrial level
(420ppm, hereafter referred to as the 1.5 CO2 policy). The latter two schedules, the
abatement schedules, have both been prominent in recent international negotiations
10Using Nordhaus’ (2008) standard values for DICE’s variables and parameters.
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