Many areas of the natural and social sciences involve complex systems that link together multiple sectors. Integrated assessment models (IAMs) are approaches that integrate knowledge from two or more domains into a single framework, and these are particularly important for climate change. One of the earliest IAMs for climate change was the DICE/RICE family of models, first published in Nordhaus (1992), with the latest version in Nordhaus (2017, 2017a). A difficulty in assessing IAMs is the inability to use standard statistical tests because of the lack of a probabilistic structure. In the absence of statistical tests, the present study examines the extent of revisions of the DICE model over its quarter-century history. The study finds that the major revisions have come primarily from the economic aspects of the model, whereas the environmental changes have been much smaller. Particularly sharp revisions have occurred for global output, damages, and the social cost of carbon. These results indicate that the economic projections are the least precise parts of IAMs and deserve much greater study than has been the case up to now, especially careful studies of long-run economic growth (to 2100 and beyond).
The dominant underlying change in the results of this IAM has been in the economic sectors, particularly in the measurement or prospect of current and future global output per capita. A useful example is the revision in global output for 2015. The level of 2015 output (in 2010$) was revised upwards by 35% over the period. Most of this was conceptual, involving the change from market exchange rates to purchasing power parity. The major revision in the 2100 outlook for output was a change from the stagnationist view of global growth in the 1980s and 1990s to a view of continued rapid growth today. This change can be seen by comparing the survey in Nordhaus and Yohe (1983) with that of Christensen et al (2017). As a result of these two changes, projected 2100 output per capita was revised upward by a factor of 3½ over the period. This major upward revision drove all economic variables, including damages and the social cost of capital.
A further major revision has been in the damage function. There was essentially no established aggregate damage function in the early 1990s, and this module of the DICE model was put together based on very rudimentary primary information.
Another large change has been in the rate of decarbonization, where the revisions have been to lower emissions per unit output over the period. This was largely due to the upward revision in output (which was not well measured) compared to a stable estimate of emissions (which was relatively well measured).
Perhaps the most dramatic revision has been the social cost of carbon (SCC). The SCC for 2015 has been revised upwards from $5 to $31 per ton of CO2 over the last quarter-century. This is the result of several different model changes as shown in Table 6. While this large a change is unsettling, it must be recognized that there is a large estimated error in the SCC. The estimated (5%, 95%) uncertainty band for the SCC in the 2016R model is ($6, $93) per ton of CO2. This wide band reflects the compounding uncertainties of the temperature sensitivity, output growth, damage function, and other factors. Moreover, it must be recognized that analyses of the social cost of carbon were not widespread until after 2000. Finally, estimates of the SCC are both highly variable across model and specification and have increased substantially over the last quarter-century. If we take early estimates of the SCC from two other well-known models (PAGE and FUND), these were close to estimates in the DICE1992 model.
A final result concerns the estimated uncertainty of the estimates. Because of their non-statistical structure, it is difficult to estimate the uncertainties associated with future forecasts of IAMs. Two sets of formal estimates of uncertainty for the model (in 2008 and 2017) were examined and compared with actual errors. While a complete comparison is not available, the actual errors to date (measured as forecast revisions) are reasonably within the error bands. This suggests that studies of the uncertainties of IAM projections are an important companion to standard projections as a way of signaling the reliability of different projections (a recent multi-model study of uncertainty is in Gillingham et al. 2015).
by William D. Nordhaus
National Bureau of Economic Research (NBER) www.NBER.org
NBER Working Paper No. 23319; Issued in April 2017