with strict inequality if both U(c0) < W (1c) and U(c0) > W (1c) are assigned positive
probability. The left-hand side corresponds to the approach of first valuing each
realization and then assign probability weights to the different realizations, while
the right-hand side corresponds to the approach of first determining a certainty
equivalent for each generation and then valuing the stream of certainty equivalents.
We have used the former approach for calculating SDU welfare in the empirical
analysis. To determine what axiomatic basis exists for each of these two approaches
and thereby shed light on which one fits more naturally with SDU is a topic for
future research. Note that the two approaches are identical under DU, because then
the function that aggregates present utility and future welfare is linear.
We also make the assumption that the utility function U not only expresses
aversion to inequality over time, but also aversion to risk. It is of interest to separate
inequality aversion from risk aversion, but this is outside the scope of the present
paper. In any case, the identity between aversion to inequality over time and to risk
is standard in the empirical literature on climate-policy evaluation, so our results
will be easier to compare to previous studies in this way.
3 Risk analysis with DICE
In order to examine empirically the differences between climate policy evaluation
under SDU and DU, we employ the DICE integrated assessment model of the joint
climate-economy system, built by William Nordhaus (we adapt the 2007 version
of the model, described in Nordhaus, 2008). In brief, DICE couples a neoclassical
model of economic growth to a simple model of the climate system.4 Output of a
composite good is produced using aggregate capital and labour inputs, augmented by
exogenous total factor productivity (TFP) in a Cobb-Douglas production function.
However, industrial production is also associated with the emission of carbon dioxide,
which is an input to the simple climate model,5 resulting in radiative forcing of
the atmosphere and an increase in global mean temperature. The climate model
couples back to the economy by means of a so-called ‘damage function’, which is a
4IPCC (Houghton et al., 1997) coined the term ‘simple climate model’ to denote models, which
specify the atmosphere, surface and deep oceans as one-dimensional, uniformly mixed boxes, which
exchange heat and/or CO2 with each other. By contrast, atmosphere-ocean general circulation
models (AOGCMs), the most complex type of climate model, divide the atmosphere and ocean into
a detailed three-dimensional grid, with many longitudinal, latitudinal and vertical points.
5 Alongside exogenous emissions of carbon dioxide from land use.
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