Measuring sustainable development for the future with climate change mitigation; a case study of applying an integrated assessment model under IPCC SRES scenarios

Abstract

The Intergovernmental Panel on Climate Change (IPCC) described mainstreaming climate change mitigation into development choices in its Fourth Assessment Report, chapter 12 of Working Group III. It also pointed out that “few macro-indicators include measures of progress with respect to climate change” despite the needs for the inclusion. This paper tackled this point in the following ways by applying an integrated assessment model. First, this study applied shadow prices and production, endogenously obtained from the model, instead of using market prices and statistical data used in preceding studies in the economics literature. Second, this study measured forecasts of genuine saving (GS) and wealth globally up to the year 2100, while preceding studies were constrained to past and current savings and wealth. Third, this study examined changes in GS and wealth in different future scenarios on IPCC SRES (Special Report on Emissions Scenarios) with CO₂ emissions constraints. Finally, the authors adopted a GS estimation methodology of shadow prices in imperfect economies by Kenneth Arrow and Partha Dasgupta, instead of that of perfect economies by Kirk Hamilton et al., on which the authors had based previous studies. This makes the indicator consistent with changes of wealth.

Appendix

1.1 A brief outline of our model

1.1.1 Objective function

We assume a social planer who maximizes (intertemporal) social welfare, V(t), expressed by the present discounted value of utility streams:

$$ \max V(t) = \int\limits_{s = t}^{\infty } {N(s) \cdot \log \left( {\frac{C(s)}{N(s)}} \right){\text{e}}^{{ - \rho \left( {s - t} \right)}} {\text{d}}s} $$

(14)

where N(s) is population (exogenously given), C(s) is consumption (endogenous), utility is given by the product of the logarithm of per capita consumption and population, and ρ is the pure rate of time preference or utility discount rate, assumed to be 2 %/year here (see Appendix, Table 5). Here, a caution is warranted that our model is described not in continuous time, but in terms of 10-year time steps (denoted as “yr” hereafter) from 2010 to 2150. The period after 2150 is added by using the sum of an infinite geometric series (unshown in Eq. 15). Geographically, the model divides the world into ten regions (denoted as “rg” hereafter), which are North America, Western Europe, Japan, Oceania, China, East-South Asia (including India), Middle East and North Africa, Sub-Sahara Africa, Latin America, and the former Soviet Union and Eastern Europe. Hence, Eq. (14) is expressed as follows, where c is per capita consumption:

$$ \max V(2010) = \sum\limits_{rg} {Neg_{rg} \cdot \left( {\sum\limits_{yr = 2010}^{2150} {\left( {\frac{1}{1 + \rho }} \right)^{yr - 2010}\,\cdot\,N_{rg,yr}\,\cdot\,\log c_{rg,yr} } } \right)} $$

(15)

Table 5 Nomenclature of mainframe of the model

For population, the scenario from the Special Report on Emissions Scenarios (SRES) by the IPCC (Intergovernmental Panel on Climate Change) is used as exogenous scenario N _rg,yr by time step and world region. Neg _rg is known as the “Negishi weight,” whose interpretation is that “optimization” determines the efficient competitive-market equilibrium of the different regions.

1.1.2 A macro-economy submodel

Consumption is derived endogenously within a model, similar to the RICE (Nordhaus and Boyer 2000), in which macroeconomic relations are determined among output, investment, capital stock depreciation, intermediate inputs (supply cost of fuel mineral resources, non-fuel mineral resources, and land use), and external damage costs. Specifically, we have:

$$ C_{rg,yr} = Y_{rg,yr} - I_{rg,yr} + IM_{rg,yr} - XP_{rg,yr} $$

(16)

where output, Y, is given by the nested production function, subtracted by costs involved in intermediate inputs such as FC, NFC, LUC, DC:

$$ Y_{rg,yr} = A_{rg,yr} \cdot F_{rg,yr} \left( {K,H,EL,NE,M,LU} \right) - FC_{rg,yr} - NFC_{rg,yr} - LUC_{rg,yr} - DC_{rg,yr} $$

(17)

$$ F_{rg,yr} \left( {K,H,EL,NE,M,LU} \right) = \left[ {\left[ {\left\{ {a_{1} \left( {K_{rg,yr}^{\alpha } H_{rg,yr}^{1 - \alpha } } \right)^{ - \varepsilon } +\,a_{2} \left( {\left( {EL_{rg,yr}^{\beta } \cdot NE_{rg,yr}^{1 - \beta } } \right)^{\gamma } \cdot M_{rg,yr}^{1 - \gamma } } \right)^{ - \varepsilon } } \right\}^{{ - \frac{1}{\varepsilon }}} } \right]^{ - \lambda } + a_{3} \cdot LU_{rg,yr}^{ - \lambda } } \right]^{{ - \frac{1}{\lambda }}} $$

(18)

where K is physical capital stock, H is human capital, EL is electricity, NE is non-electric energy resources, M is non-fuel mineral resources, LU is land resources, and a₁, a₂, a₃, α, β, γ, ε, λ are the parameters. The dynamics of the capital stock is described by:

$$ K_{rg,yr + 1} = \left( {1 - \delta } \right)^{10} \cdot K_{rg,yr} + I_{rg,yr} $$

(19)

where δ is the annual depreciation rate.

A _rg,yr is the calibration term between F _rg,yr (K,H,EL,NE,M,LU) and the sum of intermediate input costs (FC _rg,yr  + NFC _rg,yr  + LUC _rg,yr ) plus value added (refGDP _rg,yr ), which is the benchmark GDP of SRES-B2 scenario adopted in Nakićenović and Swart (2000):

$$ A_{rg,yr} = \frac{{refGDP_{rg,yr} + FC_{rg,yr} + NFC_{rg,yr} + LUC_{rg,yr} }}{{F_{rg,yr} \left( {K,H,EL,NE,M,LU} \right)}} $$

(20)

The aggregate stock of human capital H _rg,yr is obtained by multiplying labor population L _rg,yr by an individual human capital stock ϕ through average education years S _rg,yr (i.e., exp(ϕ(S))), and human health (i.e., exp(Ψ ASR)).

$$ H_{rg,yr} = \exp (\varphi (S)) \cdot \exp (\psi \cdot ASR) \cdot L_{rg,yr} $$

(21)

FC _rg,yr , NFC _rg,yr , LUC _rg,yr , DC _rg,yr are fuel mineral supply cost, non-fuel mineral supply cost, land-use cost for food supply, and damage cost, respectively, which are explained in the following sections.

1.1.3 Fuel and non-fuel minerals (FC, NFC)

The submodel of mineral resources treats fuel minerals (fm; oil, gas, coal, uranium) and non-fuel mineral resources (nfm; iron, bauxite, copper, lead, zinc, limestone). This is a demand and supply model, in which supply deals with mining, milling, dressing, smelting, and refining for nfm, the electrical or chemical conversion process for energy, transportation among the ten global regions, to the final demand of both energy (EL _rg,yr and NE _rg,yr ) and materials (MD _{sec,nfm,rg,yr} ) by three representative manufacturing sectors (electricity and machinery, construction and building, motor cycles). The nfm exist as in-use stocks of goods produced during the assumed products lifetime, after which they become out-of-use stocks and then are finally disposed of or recycled.

1.1.4 Land use and land-use change (LUC)

The land-use submodel calculates the endogenous five categories of land use (forestry, grassland, cropland, urban, others) and 20 kinds of land-use change among the categories (= five times four), by satisfying exogenous demand for food and area of urban land (i.e., land area requirement for human settlement), by the use of exogenous costs of land rent, land conversion, and food production.

The food demands are expressed as both calorie based and protein based, which are satisfied by crop productions in croplands and by meat productions in grasslands. Each production is converted by use of yield to area of cropland and grassland (pasture land). The area of urban land is calculated from population and population density. Forest area is calculated via (1) deforestation and reforestation due to carbon release and absorption, (2) conversion to cropland and grassland for food production requirements. The land category of “other” includes all others such as desert terrain and reservation land, whose area will be kept constant. In short, the land area of “others” is constant, urban area is decided by population and population density, forestry is driven by food demand and global warming constraints, and both grassland and cropland satisfy aggregated food demand.

1.1.5 External damage costs (DC)

Damage cost (DC) can be calculated by:

$$ DC_{rg,yr} = \sum\limits_{sgo} {WF_{sgo,rg,yr} \cdot \sum\limits_{sbs} {DR_{sgo,sbs,rg,yr} \cdot Inv_{sbs,rg,yr} } } $$

(22)

where

$$ WF_{sgo,rg,yr} = WF_{{sgo,JPN,yr_{0} }} \cdot \left( {\frac{{{{Y_{rg,yr} } \mathord{\left/ {\vphantom {{Y_{rg,yr} } {N_{rg,yr} }}} \right. \kern-\nulldelimiterspace} {N_{rg,yr} }}}}{{{{Y_{{JPN,yr_{0} }} } \mathord{\left/ {\vphantom {{Y_{{JPN,yr_{0} }} } {N_{{JPN,yr_{0} }} }}} \right. \kern-\nulldelimiterspace} {N_{{JPN,yr_{0} }} }}}}} \right)^{\sigma } $$

(23)

sgo = human health, social capital, net primary production (NPP), and biodiversity, sbs = greenhouse gases, ozone depletion substances (ODS), extraction and disposal of nfm, LU&LUC.

The weighting factor, WF (or MWTP), and the dose–response relation, DR, are exogenously given by LIME. They are related to four endpoints (or safe guard objects) by way of the DR relationship described in (Itsubo and Inaba 2000; Itsubo et al. 2005) then aggregated into monetary terms by WF obtained through conjoint analysis (Itsubo et al. 2005, 2012). INV is inventories treated in the model, such as CO₂, SO _x , and NO _x from fuel combustion, CO₂ release via deforestation, five kinds of non-CO₂ greenhouse gas GHG (NCGHG), 14 kinds of ozone depletion substances (ODS), and extraction and disposal of nfm, LU&LUC. NCGHG and ODS are exogenous; all the others are endogenous. DR and WF in LIME are adjusted to be compatible with all regions and time steps in our model. The WF is transferred by using benefit transfer expressed in Eq. (A10) (income elasticity σ of 0.5 from Pearce 2003).

The Dose–Response relations in Japan are indicated in LIME, which is adjusted to all regions and time steps to suit our model. The differences in region and time compared to present-day Japan are reflected by using a zero-order approximation that considers the damage and impact to safe guard objects (Kosugi et al. 2009). To be specific, the ratio (between the value in a region in a time step as numerator and the value of the present day as a denominator) is multiplied by values of dose–response in present-day Japan. The ratio of population density ratio for human health, the ratio of population density for human health per capita GDP for social capital, potential NPP for NPP, and the extinction risk of vascular plants for biodiversity, are applied to the multiplication.

1.2 Impact categories treated in our model (see Appendix Table 6)

1.2.1 Global warming

In order to develop damage functions for the safeguard subjects of human health (WHO 2010), social assets (Uchida et al. 2002) and biodiversity (Thomas 2004), (1) damage due to the impact pathway with and without emissions perturbations for CO₂, NOx, SOx, as was carried out in papers by R.S.J. Tol (e.g., Tol 2005), by using the MAGICC/SCENGEN 5.3 model (Wigley 2010); (2) time series impacts were estimated by interpolation and extrapolation based on the benchmark impacts considering regional population change and economic development (United Nations 2003, Nakićenović et al. 1998, WHO 2004); (3) the damages were aggregated as functions of global mean temperature rise.

Table 6 Category endpoints considered in LIME in relation to impact categories and safeguard subjects

1.2.1.1 Damages for human health

The human health impacts till the end of this century are extrapolated from WHO 2004, for malaria, diarrhea, malnutrition, coastal floods, inland floods and landslides. The damage is calculated between damages between with and without the perturbations for the following equation: (global mean temperature rise) * (baseline scenario for outbreaks of illness) * (relative risks − 1) * (baseline scenario for population) * (DALY per case).

1.2.1.2 Damages for social capital stock

Future crop productions without CO₂ fertilization effects were extrapolated results from the model of potential crop productivity developed by Kyoto University and the National Institute of Environmental Studies, Japan (Takahashi et al. 1997). In addition, the CO₂ fertilization effect was calculated based on the study by (Cure and Acock 1986). To estimate the change in energy consumption for heating and cooling resulting from global warming, future heating and cooling degree days were calculated, and the interaction between economic growth and heating and cooling energy consumption was analyzed using empirical energy consumption data for Japan (EDMC/IEEJ 2002). The land elevation dataset ETOPO5 accessible via GRID-Tsukuba, originally developed by the NOAA National Geophysical Data Center (NGDC), was used to calculate the areas of submergence in the case of a 0.5-meter sea-level rise that plausibly corresponds to a doubled CO₂ concentration in 2100.

1.2.1.3 Damages for biodiversity

Relationships between relative change for land use and global mean temperature are derived from Thomas 2004 using species-area relationships. The impacts are converted into relative risk changes modeled in the original LIME model (Itsubo 2010), as a function of global mean temperature rise.

1.2.2 Land use

The increment of extinction risk of vascular species and the decrement of net primary production (NPP) of vegetation, as indicators of biodiversity and primary productivity, respectively, were assessed as damage indicators (Nakagawa et al. 2002). These damages were considered to be incurred by land use (land occupation) and land-use change (land transformation).

1.2.2.1 Damages to biodiversity

The extinction risk as employed in LIME is defined as the inverse number of the average years from the present until the extinction of a threatened vascular plant, originally based on the idea of extinction probability. A statistical model developed by Matsuda (Matsuda 2000; Matsuda et al. 2003) based on the Red Data Book (RDB) in Japan (Environment Agency of Japan 2000) was applied to estimate extinction probability. The damage factor corresponding to the location of land use was established by assessing regional biodiversity using the distribution of the RDB public species, which is called the hot spot map, accessible via the Internet from the Biodiversity Center of Japan.

1.2.2.2 Damages to primary productivity

NPP loss due to land use was derived by subtracting the actual NPP from the potential NPP, whereas that due to land-use change was assessed in terms of the potential decrease of NPP based on when the former area of land use would be recovered, taking into account the time necessary for recovering an area’s potential. The recovery time was set according to the results reported by (Numata 1987). The Chikugo model (Uchijima and Seino 1985) including climatic data was applied to the calculation of the potential NPP. The field-surveyed NPP data compiled by (Iwaki 1981) were utilized for the actual NPP.