3.2 Simulation results and model selection
Based on the estimates presented in Table 1, we simulate 100.000 possible future discount rate
paths for each model starting in 2002 and extending 400 years into the future.6 The expected
discount factors and CERs are calculated from equations (1) and (2) and are reported in Tables
2 and 3. We also comment on the empirical distribution of interest rates.
The SS model yields the highest discount factors followed by the RS and AR(4) model.
These differences are more pronounced during the first half of the forecast horizon. Only SS
sustains some value in the distant future (400 years). Naturally, the corresponding certainty-
equivalent discount rates reveal largely the opposite picture. The AR (4) model yields the
higher rates during the first half of the sample, while the RS model yields the higher rates in
the second half. The SS model gives consistently lower CERs that fluctuate in the range of 2.2%
to 1.4%. Turning to the simulated distribution of discount factors, the model with the lowest
coefficient of variation (i.e. the ratio of standard deviation over mean) is SS, whereas the AR(4)
model yields the highest coefficient.7 Alternatively, as a measure of uncertainty, we employ the
5% and 95% empirical percentiles. This measure seems to favor the RS model, which has the
tightest confidence intervals, suggesting that uncertainty over the expected discount factor is
considerably reduced. On the other hand, the percentiles of the SS model are relatively wide.
Evaluating the forecasting performance of our models for the long run is impossible due to
limitation of data. However, since forward rates exist for a period of 30 years we undertake a
comparison of forecasting performance over this time horizon using available real data. Specifi-
cally, we make use of the term structure of the inflation-indexed UK government bonds and use
the Mean Square Forecast Error (MSFE) as our selection criterion. For completeness we calcu-
late four modified MSFE criteria by incorporating four kernels8 which attach different weights
to observations based on their proximity to the present. The results are presented in Table 4.
Interestingly, the various specifications of the MSFE criterion unanimously rank the SS model
first followed by the RS model and then the AR(4) model. In sum, if we select the models on
the basis of their ability to characterize the past and their accuracy concerning forecasts of the
future we are inclined to prefer the SS model.
4 Policy Implications
In this section we highlight the policy implications of DDRs and model selection by looking at
the long-term policy arena. Firstly we follow N&P and consider the present value of carbon
sequestration: the removal of 1 ton of carbon from the atmosphere. Secondly, we look at nuclear
build in the UK. The two are directly related since nuclear power can benefit from carbon credits
under a system of joint implementation and carbon trading (see Pearce et al. 2003).
Regarding our first case study, we establish the present value of the removal of 1 ton of
carbon from the atmosphere, and hence the present value of the benefits of the avoidance of
climate change damages for each of our models.9 The results, reported in Table 5, suggest that
the lower valuation is given by the conventional 3.5% discounting, followed by the AR(4) model.
Interestingly, when employing the SS model, the present value of carbon emissions reduction is
over 200% larger compared to the case of constant discounting.
Our second case study highlights a sense in which DDRs are limited in accounting for
intergenerational equity. We, specifically, consider new nuclear build in the UK which is still
being considered as an option to ensure security of energy supply and adherence to Kyoto targets
6 The process of picking parameters and shocks is available from the authors upon request. Initial values for
any lags of the real interest rate necessary for the simulation are set at 3.5 per cent, the rate used for CBA by
the UK Treasury (HM Treasury 2003).
7The relevant tables are not reported for brevity, but are available upon request.
8The Bartlett, the Parzen, the Quadratic-Spectral (QS) and the Tukey-Hanning (TK) kernels are the weighting
functions used in our evaluation.
9See N&P for the assumptions concerning the modeling of carbon emissions damages.