Revisions since DICE

The DICE-2007 model is the fifth generation of the aggregated global dynamic model. For those who are familiar with earlier versions, particularly Nordhaus 1994 and Nordhaus and Boyer 2000, this section describes the major revisions.8

DATA INPUTS

All the economic and geophysical data have been updated, and the new first period is centered on 2005. The first period for the last full revision of the model (in Nordhaus and Boyer 2000) was centered on 1995. Economic data for the current revision use IMF estimates for major economic aggregates with preliminary data from 2005. Energy data are from the World Bank and U.S. Energy Information Agency (EIA). Carbon dioxide emissions are from the EIA and the Carbon Dioxide Information Analysis Center. Geophysical data are from multiple sources, including primarily the Goddard Institute for Space Studies and the Hadley Centre. The revision incorporates some results from the IPCC Fourth Assessment Report, as well as more comprehensive revisions from the IPCC

Derivation of the Equations of the DICE-2007 Model 47

Third Assessment Report. Data on CO2 emissions generally go through 2004, with some preliminary data for 2005 and 2006. Prices have been updated to 2005 U.S. dollars. The conceptual basis for outputs has been changed from market exchange rates to purchasing-power-parity (PPP) exchange rates.9

REGIONAL AGGREGATION ALONG WITH ECONOMIC AND EMISSIONS PROJECTIONS

The economic, emissions, and impact estimates are based on 12 regions and are then aggregated to the global total using PPP exchange rates. The 12 regions are the United States, the European Union, other high-income countries, Russia, Eastern Europe and the non-Russian former Soviet Union, Japan, China, India, the Middle East, sub-Saharan Africa, Latin America, and other Asia. Estimates for each region are built up from data on the 71 largest countries. These countries represent 97 percent of emissions, 94 percent of world output, and 86 percent of population. For each region, we project population, output, carbon intensity, and baseline CO2 emissions by decade. We then aggregate to the global total for each year. Figure 3-1 shows the historical emissions-output ratios for five important regions and the global total, displaying a steady decarbonization after 1960. However, the most recent trend is for a stable global CO2-GDP ratio, due in part to the rise in CO2 emissions from China.

Figure 3-2 shows the emissions projections for the baseline run of the DICE-2007 model along with those from several "SRES scenarios" developed in the Special Report on Emissions Scenarios for the IPCC (IPCC 2000). The DICE-model projections are developed completely independently

Derivation of the Equations of the DICE-2007 Model

1.00

0.05

Figure 3-1. Historical ratios of CO2 emissions to GDP for major regions and globe, 1960-2004. Trends in the ratio of CO2 emissions to GDP for five major regions and the global total. We call the decline in this rate "decarbonization." Most major economies have had significant decarbonization since 1960. The rates of decarbonization have slowed or reversed in the last few years and appear to have reversed for China. With the changing composition of output by region, the world CO2-GDP ratio has remained stable since 2000. Note that "W C Eur" is Western and central Europe and includes several formerly centrally planned countries with high CO2-GDP ratios.

1960 1965 1970 1975 1980 1985 1990 1995

2000

Figure 3-1. Historical ratios of CO2 emissions to GDP for major regions and globe, 1960-2004. Trends in the ratio of CO2 emissions to GDP for five major regions and the global total. We call the decline in this rate "decarbonization." Most major economies have had significant decarbonization since 1960. The rates of decarbonization have slowed or reversed in the last few years and appear to have reversed for China. With the changing composition of output by region, the world CO2-GDP ratio has remained stable since 2000. Note that "W C Eur" is Western and central Europe and includes several formerly centrally planned countries with high CO2-GDP ratios.

using different methods and more recent data (the SRES scenarios used in the latest IPCC projections were developed approximately a decade ago). The DICE emissions projection is toward the low end of the SRES range until the middle of the twenty-first century and then rises relative to some of the lower SRES scenarios.

1960 1980 2000 2020 2040 2060 2080 2100

Figure 3-2. Industrial CO, emissions. A comparison of baseline CO, emissions in the DICE-2007 model with the emissions projections of major SRES scenarios prepared for the IPCC. Source for SRES is IPCC 2000. The heavy lines are the high (mean plus one standard deviation), mean, and low (mean minus one standard deviation) projections of the DICE model. The uncertainty range for the DICE-model projections is described in chapter 7. The range between the high (DICE +1 sigma) and low DICE — 1 sigma) projections is designed to capture 68 percent of the distribution of likely outcomes.

50 Derivation of the Equations of the DICE-2007 Model

SOCIAL WELFARE FUNCTION

One of the major concerns about the earlier DICE model was their assumption of a relatively high pure rate of social time preference (3 percent per year). We note first, as discussed earlier, that the interpretation of the economic parameters is that they are designed to provide the most accurate projections rather than to be normative in nature. Additionally, the earlier assumptions were heavily influenced by numerical problems with alternative specifications and the requirement that the rate of return on capital be calibrated with observed market data.

In the revised version, we have lowered the pure rate of social time preference to 1.5 percent per year and have recalibrated the utility function to match market returns, yielding an elasticity of the marginal utility of consumption of 2. This revision moves the model closer to one that displays intergenera-tional neutrality while maintaining the calibration of the model's rate of return on capital with empirical estimates. Users should be aware that the sharp nonlinearity of the revised utility function may cause major scaling problems in computations and may therefore prove difficult to solve numerically; indeed, the unitary-elastic utility function was used in previous versions because we were unable to solve these computational problems in the earlier DICE models with higher elasticities.

DAMAGE FUNCTION

The basic structure of the regional damage functions follows the approach used in the RICE-1999 model. The major revisions involve recalibrating the costs of catastrophic damages, refining the estimates for regions with high temperature

Derivation of the Equations of the DICE-2007 Model

Derivation of the Equations of the DICE-2007 Model

—A— RICE-1999 —O— DICE-2007

y/

//

Mean temperature increase (°C)

Figure 3-3. Damage function. The damage function used in the DICE-2007 model compared with the earlier study using the RICE-1999 model. The arrow shows the estimated range from IPCC 2007a, which reports that "global mean losses could be 1-5% GDP for 4°C of warming" (p. 20).

Mean temperature increase (°C)

Figure 3-3. Damage function. The damage function used in the DICE-2007 model compared with the earlier study using the RICE-1999 model. The arrow shows the estimated range from IPCC 2007a, which reports that "global mean losses could be 1-5% GDP for 4°C of warming" (p. 20).

changes, and using revised estimates of the overall impacts for low damages. One result is that for small temperature changes, we estimate that there are positive damages, whereas in the 1999 model damages for small temperature changes were negative (that is, there were estimated positive net benefits). In addition, using PPP estimates of output results in a significantly higher world output; because damages are generally estimated as a fraction of output, total damages are also significantly higher in the 2007 model. The damage functions continue to be a major source of modeling uncertainty in the DICE model. Figure 3-3 shows the damage function contained in the DICE-2007 model compared with the earlier RICE model and the latest results from the IPCC Fourth Assessment Report (IPCC 2007a).

52 Derivation of the Equations of the DICE-2007 Model

ABATEMENT-COST FUNCTION

The basic functional form for the abatement-cost function follows the structure assumed in the earlier DICE models. However, the structure has been reformulated over time to correct for an earlier modeling mistake. The implicit specification in the DICE model is that there is a "backstop technology." As noted earlier, this is a technology that can replace all carbon-emitting processes at a relatively high cost; that is, the backstop technology takes over when the emissions-control rate is 100 percent. The prior version used a functional form that implicitly and mistakenly assumed that the cost of the backstop technology increased over time.

The new version redefines the emissions-reduction equations by calibrating them to an explicit price and time profile of the backstop technology. The calibration of the new emissions-cost function is based on recent modeling efforts that calculate the cost of deep emissions cuts, the IPCC special report on sequestration (IPCC 2005), the IPCC Fourth Assessment Report, as well as modeling estimates provided by Jae Edmonds. In the new model, the cost of the backstop technology starts around $1,200 per metric ton of carbon and declines to $950 per metric ton by 2100.

The cost of the backstop technology appears high relative to other estimates, but it should be noted that this is the marginal cost of reducing the last unit of carbon emissions and not the cost for relatively inexpensive sources, such as coal-fired electricity generation. A substitute for fossil fuels such as nuclear power might be a backstop at $500 per ton of carbon replaced, but it might substitute only for electrical power. In other words, the $1,200 reflects the cost of replacing carbon from the last high-value use, such as plastics or jet fuel

Derivation of the Equations of the DICE-2007 Model 53

or solvents. Although this new specification makes little difference in the short run (to the tactics of climate policy, so to speak), it turns out that it makes a major difference over the long run (to the strategy or vision).10

CARBON CYCLE

The new version of the DICE model does not change the basic structure of the carbon-cycle model, but it recalibrates the initial stocks and the flow parameters. As noted earlier, the basic strategy is to calibrate the DICE model to the MAGICC model, primarily to the emissions scenarios that most closely resemble those in the DICE projections, such as the A1F1 scenario.

For reference purposes, we show in Table 3-1 a comparison of the concentrations projections for the DICE model with a model comparison from the Fourth Assessment Report of the IPCC. (This review became available after the completion of the modeling design.) The table shows the fraction of cumulative anthropogenic CO2 concentrations that are retained in the atmosphere by the IPCC models and by the DICE model. For the historical period, the DICE model is at the upper end of the models, with an atmospheric retention ratio of 0.54, compared with 0.45 for the model ensemble. For the total period, however, the DICE model has a slightly lower atmospheric retention ratio of 0.51, versus 0.55 for the model mean. The major omission in the DICE model is the absence of ocean carbonate chemistry that generates lower ocean uptake over time in the more complete models. It should be noted that the SRES scenario examined, A2, has relatively flat emissions compared with the DICE-model baseline.

54 Derivation of the Equations of the DICE-2007 Model

Table 3-1. Comparison of Projections of Atmospheric CO2 Retention Rate in DICE Model and IPCC Model

Fraction of Cumulative Emissions Retained in Atmosphere

Table 3-1. Comparison of Projections of Atmospheric CO2 Retention Rate in DICE Model and IPCC Model

Fraction of Cumulative Emissions Retained in Atmosphere

Model

1850-2000

1850-2100

IPCC FAR

Model mean

0.45

0.55

Range

0.43-0.61

0.45-0.72

DICE-2007

0.54

0.51

Note: These estimates in the DICE-2007 model and the IPCC Fourth Assessment Report (FAR) model show the fraction of total anthropogenic CO2 emissions that were retained in the atmosphere for the periods 1850-2000 and 1850-2100. The emissions trajectories are not exactly comparable because the DICE model uses the baseline emissions, while the IPCC used the SRES scenario A2. Source for IPCC is IPCC 2007b, figure 7.13.

Note: These estimates in the DICE-2007 model and the IPCC Fourth Assessment Report (FAR) model show the fraction of total anthropogenic CO2 emissions that were retained in the atmosphere for the periods 1850-2000 and 1850-2100. The emissions trajectories are not exactly comparable because the DICE model uses the baseline emissions, while the IPCC used the SRES scenario A2. Source for IPCC is IPCC 2007b, figure 7.13.

CLIMATE MODEL AND DATA

The basic structure of the climate model has not been significantly revised in the current DICE model. The timing has been changed to shorten the lag from radiative forcing to temperature change. The parameterization has been slightly revised, increasing the climate sensitivity from 2.9°C to 3.0°C per equilibrium CO2-equivalent doubling, which is in line with the IPCC central estimate. In addition, the short-run adjustment parameters have been calibrated to fit the estimates from general circulation models and impulse-response experiments, particularly matching the forcing and temperature profiles in the MAGICC model. The estimates of non-CO2 forcing and nonindustrial CO2 emissions have been revised in light of recent estimates and the findings in the IPCC Third and Fourth Assessment Reports.

Derivation of the Equations of the DICE-2007 Model 55

Figure 3-4 shows a comparison between the calibrated DICE model and the MAGICC model. For technical reasons, both are calibrated to a 2.6°C temperature-sensitivity parameter, but similar results hold for a 4.5°C temperature-sensitivity parameter. The DICE model has slightly lower projections for the same emissions path; over the twenty-first century the DICE-model structure projects a 3.61°C increase, while the MAGICC structure projects a 3.71°C increase.

INCOMPLETE PARTICIPATION

Earlier versions of the DICE model assumed that policies were harmonized among different regions and that all regions participated. The current version introduces a participation function. This allows model runs in which a subset of countries has emissions reductions (in a harmonized fashion), while the balance of countries undertakes no emissions reductions. Because of the functional form of the emissions equation in the DICE model, we can derive an exact mathematical representation of the result of incomplete participation. This new specification allows estimates, in the structure of an aggregate model, of the impact of alternative groupings of countries such as occurs in the Kyoto Protocol. We describe the participation structure and some results of incomplete participation in Chapter 6.

LIMITED FOSSIL-FUEL RESOURCES AND HOTELLING RENTS

Earlier versions of the DICE model focused on short-term projections and policies ("short-term" being up to 2100). In the current version, given the increased attention to long-term projections of climate, geophysical systems, and ecology, the o.o H-1-1-1-1-1-1-1-1-1-

2005 2015 2025 2035 2045 2055 2065 2075 2085 2095

Figure 3-4. Comparison of temperature change. A comparison between the temperature profiles for the DICE-2007 model with a 2.6°C temperature sensitivity and the MAGICC programs with the same temperature sensitivity. The MAGICC runs are generated by the software at MAGICC 2007. The runs use the A1F1 CO, emissions and the radiative forcing for non-CO, greenhouse gases assumed in the MAGICC runs.

Derivation of the Equations of the DICE-2007 Model 57

modeling has paid more attention to long-run consistency with major geophysical models and economic constraints. One major change has been to introduce long-run fossil-fuel availability constraints. In the new model, total resources of economically available fossil fuels are limited to 6,000 billion metric tons of carbon equivalent (approximately 900 years at current consumption rates). This constraint generates Hotelling rents that in the long run rise to drive consumption to the backstop technology. Although these constraints are unimportant in the base case for the short run (up to a century), they become important in cases of rapid economic growth or low rates of carbon-reducing technological change.

REAL RETURNS ON CAPITAL

One of the major economic variables for constructing a capital-based model is the real return on capital. We have constructed our model by using the Cobb-Douglas production function with explicit estimates of the capital stocks of different regions derived by the perpetual inventory method. As a check, we have compared the projections of the real return on capital in the DICE model with estimates of the real return from various studies. Table 3-2 shows the collation of the real returns on assets from the IPCC Second Assessment Report.11 For the United States, the estimated returns are around 5 percent for most well-measured sectors, while numbers for other countries and sectors are sometimes much higher. In the DICE model, the estimated return on capital is between 5 and 6 percent per year for the first five decades. A further discussion of this question is contained in Chapter 9.

58 Derivation of the Equations of the DICE-2007 Model

Table 3-2. Estimated Real Returns to Capital from IPCC Second Assessment, Various Periods and Sources

Real Return

Asset Period (Percent)

High-income industrial countries

Real Return

Asset Period (Percent)

High-income industrial countries

Equities

1960-1984 (a)

5.4

Bonds

1960-1984 (a)

1.6

Nonresidential capital

1975-1990 (b)

15.1

Govt. short-term bonds

1960-1990 (c)

0.3

United States

Equities

1925-1992 (a)

6.5

All private capital, pretax

1963-1985 (d)

5.7

Corporate capital, posttax

1963-1985 (e)

5.7

Real estate

1960-1984 (a)

5.5

Farmland

1947-1984 (a)

5.5

Treasury bills

1926-1986 (c)

0.3

Developing countries

Primary education

various (f)

26

Higher education

various (f)

13

Source: Arrow et al. 1996. The letters refer to the sources provided in the background document.

Source: Arrow et al. 1996. The letters refer to the sources provided in the background document.

0 0

Post a comment