reduced-form polynomial equation associating a change in temperature with a loss
in utility, expressed in terms of equivalent output. The damage function in DICE
implicitly takes account of the economy and society’s capacity to adapt to climate
change, which reduces the amount of output lost for a given increase in global mean
temperature, so that the representative agent is left to choose how much to invest
in abating CO2 emissions from production. The model is globally aggregated and is
resolved in decadal time steps from 2005 up to 2395.
DICE is described in full in Nordhaus (2008), and for the sake of brevity we
focus our exposition here on those parts of the model we have modified.6 Since un-
certainty is central to climate policy, we select a subset of eight of the most important
parameters in DICE, and specify each as random. Table 1 lists these parameters and
the form and parameterisation of their probability distributions. In selecting these
eight parameters, we have followed the lead of Nordhaus’ (2008) own risk analysis.
However, in the case of two parameters, we have chosen an alternative specification.
They describe the climate sensitivity and the curvature of the damage function, and
we devote special attention to them below. For ease of computation (particularly
with random parameters), the savings rate in our version of DICE is exogenous (set
at 22%). In other versions, the savings rate is chosen by the representative agent.7
We use a standard, iso-elastic utility function, and calculate classical utilitarian so-
cial welfare recursively, using eqs. (4) and (5) for DU and SDU respectively. The
probability distributions of the random parameters are sampled using a Latin Hy-
percube (1000 draws), and social welfare is computed separately for each draw and
then weighted by its (identical) probability as described above.
The first four parameters in Table 1 play a role in determining CO2 emissions. Of
these four parameters, Kelly and Kolstad (2001) showed that growth in TFP and in
population are particularly important. The reason is that, in integrated assessment
models such as DICE, growth in CO2 emissions is proportional to growth in global
6We adapt the MS Excel version of the model, which is convenient for running risk analysis using
the @Risk and Riskoptimizer plug-ins.
7If climate change depresses capital productivity, then the savings rate is likely to fall ceteris
paribus. However, Fankhauser and Tol (2005) show that endogenising the savings rate makes
little difference to the economic impact of climate change. In addition, Nordhaus claims that the
results of DICE simulations with a constant 22% savings rate are virtually identical to results
with endogenous savings, for standard parameter values. We specify exogenous savings in order
to simplify the optimisation task: in our multi-parameter risk analysis, adding a choice variable
increases computational demands hugely.
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