Criticism of economic models
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To evaluate the impact of climate change on world economy, economists use computer models that integrate climate forecasts and economy forecasts. They are called Integrated Assessment Models.

The DICE model
The first such model was developed by economist William Nordhaus at Yale University, USA. It was designated `DICE´, which stands for Dynamic Integrated model of Climate and the Economy; the name also refers to that mankind is playing dice with the natural environment. It was first presented in 1990. In this model, the whole world is treated as one unit. Subsequently a more detailed model was developed, in which the world was divided into a number of regions; this regionalized version was designated RICE and was first presented in 1996 (link).
Both models have subsequently undergone major revisions in 1999 and later in order to incorporate new knowledge on greenhouse gases, energy use and economic data. The models can be downloaded and run by others on their own computers. Much of what Bjørn Lomborg has written in recent years on the economics of climate change is based on Lomborg´s own runs of recent versions of DICE and RICE.

Other models used in Smart Solutions to Climate Change
Many other integrated assessment models have been produced. Some of these are based on DICE or RICE, but have been changed and extended in various ways. This is the case for the WITCH model (link), which was developed at Fondazione Eni Enrico Mattei (FEEM) in Italy.
An independently developed model is the FUND model (link), which was originally developed by the Dutch/German/Irish economist Richard Tol, and is now co-developed by Tol and David Anthoff. Tol is the economist on which Bjørn Lomborg relies most heavily.

A very different model
There exist many models. One that is very different from those mentioned above is the E3MG model developed in Cambridge, England. It does  not directly, like most others, seek to find an optimal path. It combines a top-down and a bottom-up approach where it explicitly incorporates a wide range of low-carbon technologies and focuses inter alia on barriers for implementation of these technologies (link).

Differences between models
The 4th report of IPCC, work group III, compares the outputs of many models. As indicated here, many models give rather similar outputs, but two models differ especially from the rest. One is the FUND model which predicts high fuel prices and is especially pessimistic as to the effect of carbon mitigation on gross world product. The other is E3MG which also predicts rather high fuel prices, but which is especially optimistic in forecasting that rising fuel prices will stimulate technological innovation and give a boost to the growth in world economy. In general, the way of coping with technological innovation is one of the most important features of an economic model. Whereas most earlier models dictated a path of technological change that was unaffected by climate policies, many new models treat technological change endogenously in response to reserach and development, to carbon prices, to policies etc. The effect of including technological change varies much. A main point is to what degree low-carbon energy can be substituted for high-carbon energy - the higher the possibility for substitution, the more are mitigation costs reduced (link).

A crucial finding mentioned in the IPCC report is that most of the differences between models are accounted for by the modellers´ assumptions. For example, the strongest factor leading to lower carbon prices is the assumption of high substitutability between internationally-traded products. This suggests that any particular set of results about costs may well be the outcome of the particular assumptions and characterization of the problem chosen by the model builder, and these results may not be replicated by others choosing different assumptions (link).

Models used in the book `Smart Solutions to Climate Change´ (hereafter abbreviated SSCC)

In SSCC, the DICE or RICE model is the basis for the analysis in the following chapters: 1 (climate engineering), 3 (forestry), 4 (black carbon), 7 (technological innovation) and 8 (technology transfer). The WITCH model is used in chapters 6 (adaptation) and 7.1 (technological innovation). The FUND model is used in chapters 2 (carbon dioxide mitigation) and 5.1 (methane mitigation).

Criticism: the DICE and RICE models

The DICE and RICE models are widely used because they are well known, easily accessible and relatively easy to use. However, they can be criticized on a number of points.

The magnitude of damages
Built into the model are relations that define how much damage occurs to the world economy at a given temperature rise. These relations must be guess-work, because nobody knows for sure what will actually happen. Some people criticize that the damage functions are set too high and that actual damages will be lower than anticipated. Others think that on the contrary, the damage functions are set too low. There are strong arguments that the damage functions are unrealistic. Thus, according to SSCC p. 322, if we manage to keep the temperature rise at a very strict threshold of maximally 1.5° C,  the value of all climate damages is about $10 trillion, whereas if for several centuries nothing is done to mitigate the climate, the damages will be $22.5 trillion. It is simply not plausible that the difference in damages between these two scenarios should be so moderate. There is growing scientific evidence that climate is changing more quickly, and the probable impacts of change may be larger, than was contemplated a decade ago (SSCC p. 330).

Catastrophes and tipping points
Nordhaus has estimated the risk of major climate catatrophes by consulting climate scientists, and has incorporated these risks into the model. When temperature rises by several degrees, the risk of catastrophes makes out a considerable part of the projected costs (SSCC p. 227), even though the low probability of such potential catastrophes makes the `average´ cost quite moderate. Because it is very uncertain if and when such catastrophes occur, the whole estimate of damage costs is extremely uncertain.
On the other hand, the risk that the climate may pass crucial `tipping points´ is not considered. Many politicians acknowledge that if temperatures increase by more than 2° C, there are severe risks that some `tipping point´ is passed and that the course of climate change comes completely out of control. However, in the runs of the DICE model, the world GDP is reduced by only 1 % at an increase of 2° C, by 4 % at an increase of 4° C, and by 8 to 9 % at an increase of 6° C. Consider, however, that a 4° increase is commonly regarded as carrying a significant risk of large-scale, highly disruptive  and possibly catastrophic climate change (SSCC p. 287), and that at 6° there is a risk that most life forms on earth will disappear. The discrepancy between the model runs and these scary projections is so large that we can have little trust in the model.

No dynamic technological change
The model presupposes that there will be a rate of increase in energy efficiency of all uses of household machines etc., but that this rate of improvement will gradually decline. Likewise, there will be a rate of decarbonization of the energy supply, ie. the energy output per ton of C combusted will rise, but this will happen only slowly. The decline of carbon intensity of energy provision is set at 1.03 percent per year, based on the empirically determined rate for the decade 1995-2005. The model contains no possibility for an accelerated technological change that increases the rate of decarbonization. Thus, although the central theme of all political negotiations on the climate issue is to bring down CO2 emissions by replacing fossil fuels with no-carbon energy sources, this central theme is practically left out of the DICE and RICE models. The models include a price signal such thatn when fossil fuels (i.e. coal) become scarce, the price per ton of carbon will rise, but this price signal will be felt only very late, after at least a century (link). The models allow the substition of other energy sources for coal, but the substitution parameter remains practically zero for many decades ahead.
Because the rate of decarbonization is low and fixed in advance in the model, there is little opportunity to switch to other more environmentally friendly energy sources, and when this switch is so heavily restricted, an environmentally friendly development can only happen by forced reductions of energy use, which will be very costly.

No equity
The whole set-up presupposes that climate damages be monetized. That is, such damages as loss of dry land, loss of human lives, and reduced health, must be expressed in economic units. So the modeler has to define what is the value of dry land, what is the value of a human life, etc. Now, the values are set in such a way that they are proportional to the GDP per capita of the region considered. Thus, the loss of a human life or a hectare of land in the rich western world counts more than 10 times as much as the loss of lives or land in poor areas like Bangladesh or Africa south of Sahara. It is possible in the model to correct this by `equity weighting´, but usually such weighting is not applied. That is, the model is used to view the world as if the only thing that counts is money. If you save one life in Western Europe by sacrificing five lives in Africa, then, according to the model, this is a good thing, because the total world economy is improved thereby. In other words, fairness and equity are left out.
According to the available climate projections, the poor parts of the world will be hit most hardly by climate change. This may hamper the much wanted economic growth of just those regions which need the most to grow. But this does not matter to the economic optimization process that is built into the model. Damages in The Third World count very little, and the policy that is preferred by the model as `the best´ will be the policy that is of greatest benefit to those countries that are already rich.

Discount rates
When future economic costs and benefits are assessed, they are usually transformed into a `present value´ by using a discount rate. The choice of discount rate is subjective and crucial for what results are obtained, as explained here on Lomborg-errors. In the first computations made with DICE, the discount rate was set at about 3 % per year which is sufficiently high that expenditures made in the far future play only a very little role. In newer versions, the discount rate is usually set even higher. The model now uses a so-called Ramsey equation, where the discount rate is the sum of two terms, one based on the rate of time preference, or `impatience´, and the other based on the growth rate of the world economy. This is explained on the page on discount rates on Lomborg-errors (scroll down a few pages until you find the term Ramsey in bold letters). When the parameters are set as preferred by Nordhaus, the growth rate is set at a start value of 1.5 % per year, whereas the total discount rate becomes 5.5 % per year. During the run, the growth rate slows down a little, and the total discount rate drops to about 5 % a year in 2100 and 4.5 % a year in 2200. This is called `dynamic discounting´. The parameters are set such as to match the empirical real return rate on invested capital, which is estimated to be 5.5 % per year at present.

A problem with this very high discount rate is the underlying ideology that investments in climate mitigation should be equally profitable as present-day industrial investments. That is, investments in climate mitigation should only be made when they are just as profitable as any other average business, and the reason to mitigate climate should be to make or spare money, not to prevent deterioration of  the environment per se. However, if the world economy grows at 1.5 % per year, nobody can maintain a sustained return on invested capital of 5.5 % per year for any extended period of several decades or even centuries. This is the time-scale of climate change, and a discount rate as high as 5.5 % on this time scale makes no sense. Actually, climate economists have failed to resolve the discrepancy that arises because short-term returns on invested capital are much higher than the long-term growth rate of the total economy. This is explained in more detail on the page on discount rates on Lomborg-errors.

So, by insisting on very high discount rates that are out of tune with the long time scales of climate change, Nordhaus obtains that the future counts very little, and future climate catastrophs do not really count. One might even postulate that with such discount rates, the model would show that it might pay off to follow a path that maintains a high rate of economic growth right now, but leads to the destruction of all life on the globe in 500 years or 1,000 years from now.

The WITCH model

The WITCH model allows for endogenous technological change that can potentially improve energy efficiency  or the production of energy from various sources. Seven different energy-generating technologies are modeled: coal, oil, gas, wind and solar, nuclear, electricity, and biofuels (SSCC p. 261).  The world is divided into twelve regions. Climate policy and development of energy sources differ in different regions. Each region chooses its optimal path regarding investments in physical capital, in research and development of energy technologies, and in consumption of fossil fuels. The model takes into account the effects of prices of fossil fuels, the effects of research in energy technology, increased efficiency via learning-by-doing, and transfer of energy technology between regions. Population growth and growth in the world economy are coded into the model,  but may be adjusted.

Thus, the model allows analysis of the interplay between economic growth, energy prices, and changes in energy technology - just those crucial elements which cannot be studied in the DICE and RICE models.

In many other respects, the WITCH model contains the same elements as RICE. For instance, the relationship between temperature and climate damages is kept unchanged from the RICE model. Thus, the criticism that such damages may be underestimated apply also to WITCH (SSCC p. 260). Those runs of the model which are reported in SSCC are made without including the risk for catastrophes. Final effects are dominated by impacts on crop productivity and on the tourism industry (SSCC p. 267), which is a nearly ridiculous result. The effects of loss of dry land, effects on health etc. do not count very much. Weather related disasters as were seen e.g. in 2010 (deadly heat wave in Russia, huge floodings in Pakistan and Queensland) are hardly reflected in the model output.
Like in the RICE model, there is no equity between rich and poor.
There may be rised many more points of criticism, as may be seen by the perspective paper by Frank Jotzo in SSCC pp. 284-291.

The FUND model

As stated on the FUND web site, people who are not experts are discouraged from using FUND. The developer, Richard Tol, claims that models are often quite useless in unexperienced hands, and no one is smart enough to master in a short period what took someone else years to develop. If you download the model, you will have to make a real effort to let it do something. It should be reserved for scientists working in an `ivory tower´. This implies that others have little chance to judge if the results are trustworthy and based on sound assumptions.

Published criticism
The FUND model is heavily criticized by Roberto Roson (SSCC pp. 109-113) and by Frank Jotzo (SSCC p. 287). Among the points of criticism are that in the model, neither climate change impacts nor choices of policy affect economic growth. Instead, growth in population and world economy follow scenarios that are exogenously defined. Also, the degree to which policies aim at fostering climate-friendly technologies is set exogenously. There are no backstop-technologies, i.e. expensive but carbon-free technologies used to replace fossil fuels if energy prices rise too much. It is possible in the model to introduce various types of carbon tax, but it is not clear how this brings about a reduction of emissions in the model and how tax revenue is transferred to other sectors of the economy.

No equity
Like the DICE model, FUND is usually run without equity weighting. The value of a statistical life is set to be 200 times the annual per capita income (SSCC p. 89), so a life in Switzerland is worth many times more than a life in Mozambique. This means that effects in the rich parts of the world count much more heavily than effects in poor regions.

Biased damage functions
The estimates of damages due to climate change are also known from various papers authored by Richard Tol, and Lomborg relies heavily on these estimates. Major climate effects are on the death rates due to excessive heat and cold, and to changed consumption of fossil fuels for heating.
Now, Tol assumes that in the rich countries, there will be a large reduction in deaths due to cold, and only a small rise in deaths due to heat. This assumption is rather hypothetical, as the basis for the assumption is very uncertain (see here on Lomborg-errors). Actually we have had large death tolls due to heat waves (70,000 dead in Western Europe in 2003, 56,000 dead in Russia in 2010). Still, the model assumes that the effect of moderate temperature rises in temperate regions will be a considerable reduction in the number of deaths due to unfavourable temperatures. As the model is run with no equity weighting, excessive heat deaths in tropical countries does practically not count. Instead, the main effect is a postulated reduction in number of deaths in rich countries, and the overall effect of a moderate temperature rise will therefore be positive.

Also, a main effect is that moderate warming will cause less consumption of fuel for heating in the rich countries. It seems that the model does not consider that this reduced consumption of fuel is counteracted by rising fuel costs. And it is postulated that increased use of fuel for air conditioning in hot climates is too small to outweigh the decreased use in colder climates.

Needless to say, no catastrophes or tipping points are built into the FUND model.

The effect of a high discount rate
The model is run with a fixed discount rate of 5 %. This is a very high rate for an analysis that extends 100 years into the future, and the use of such a high rate may be criticized on a theoretical basis (see the Lomborg-errors page on discount rates). It means that damages that occur 100 years from now are reduced to less than 1 percent, whereas benefits that occur e.g. 25 years from now are reduced only to about 30 %.
Now, consider that in the FUND model, the effect of global warming will be net positive 25 years from now, because of fewer cold deaths in the rich countries, whereas the effect will be net negative 100 years from now. But with a discount rate of 5 %, what happens in 25 years has a weight neraly 40 times higher than what happens in 100 years. So the overall discounted value of climate damages will be very moderately negative, or maybe even positive.

Overall trend
The FUND model appears as if it were tailored to reduce the impacts of global warming as much as possible. There is no possibility for an endogenously determined shift away from fossil fuels; benefits in the rich countries a few decades from now count much more heavily than damages that lie 100 years ahead; benefits in the rich countries count much more heavily than damages in the poor countries. And on top of that, the model is reserved for specialists with little opportunity for others to see through the built-in mechanisms.

A figure in SSCC (fig. 6.2 page 225) compares the output from various economic models. For the other models, the result is that climate change causes a net damage that is very small at first, but gradually grows, whereas the FUND model shows that there will be large initial benefits. This is a contrast to a statement elsewhere (SSCC p. 224), where it is stated that based on the occurence on great natural catastrophes, estimated losses are in the iorder of 0.5 % of current world GDP, and damages are increasing at a rate of 6 % a year in real terms. In comparison, the FUND model does not include damages from such catastrophes. In the FUND model, there will be a net benefit even up to a temperature rise of 2° C, which is the point at which others fear a run-away effect when the climate may pass some tipping point.

Thus, although the FUND model may have some functions that are superior to other models, the overall output is not particularly credible, and there is a crucial lack of possibility to let price signals induce technological innovation. This is a part of the explanation why this model is more pessimistic about the effects of climate mitigation than nearly all other models, as stated on top of this page.