# 2. The RICE99 model

Nordhaus and Boyer (2000)’s RICE is the most recent version of a regional dynamic general equilibrium model originally proposed by Nordhaus for the study of the economic aspects of climate change (Nordhaus and Yang, 1996). The RICE model basically considers a single sector optimal growth model suitably extended to incorporate the interactions between economic activities and climate. There is one such model for each of the eight macro regions into which the world is divided: USA, Other High Income countries (OHI), OECD Europe (Europe), Russia and Eastern European countries (REE), Middle Income countries (MI), Lower Middle Income countries (LMI), China (CHN), and Low Income countries (LI).

Within each region a central planner chooses the optimal paths of fixed investment and carbon energy input that maximizes the present value of per capita consumption. Nordhaus and Boyer’s starting assumption is that a Social Planner optimally runs his/her own region, indexed by n, by maximizing the following discounted utility function:

(1)

Where C(n,t) stands for consumption, b is the discount factor and L(n,t) is the population level. The maximization process is subject to some constraints that capture the economic dynamics as well as the environmental ones.

The Resource Constraint of each region links consumption with net output Y and with physical investments I. The following equation identifies the Resource Constraint:

C(n,t) = Y(n,t) – I(n,t) (2)

The gross value added obtained from the production process is described by the following equation:

Q(n,t) = A(n,t)[K(n,t)gCE(n,t)anL(n,t)(1-g-an)] - pe(n,t)CE(n,t) (3)

Where A(n,t) denotes the state of the technology, K(n,t) is physical capital, CE(n,t) is carbon energy, and pe(n,t)is the price of carbon energy. Apart from A(n,t) and L(n,t), all the inputs of this value-added equation are endogenously determined. Note that the evolution of A(n,t) accounts for productivity growth by production-enhancing technical change. In the model this index follows an exogenously determined increasing path over time.

There is a wedge W between gross and net output production due to climate alterations; this wedge is inversely related to and driven by the damage function D(n,t):

Y(n,t) = W(n,t)Q(n,t) (4)

W(n,t) = 1/D(n,t) (5)

D(n,t) =1+ q1,nT(t) + q2,nT(t)2 (6)

Where D(n,t) is the environmental damage per unit of gross output, T(t) is the temperature increase and q1,n, q2,n are regionalized parameters capturing the temperature impact.

The environmental damage is a key variable explaining how the model describes capital accumulation by including environmental resources. We refer to natural resources (intended as a flow) and not about environmental capital stocks, because the basic assumptions of this model are that there is an unlimited stock of natural resources and that carbon energy demand is always satisfied by supply. The scarcity is reflected only in the carbon price.

The factors affecting the PIR are expressed in the model by a set of equations and variables. The scale effect (in our case represented by the industrial technological innovation A(n,t) influencing the scale of the economy) and environmental technical progress (in the model the emissions/carbon energy ratio) are included in Grossman’s EKC decomposition. Regulation (in our case an international agreement intended as a “Kyoto forever” emission constraint) is an important factor affecting the PIR, as suggested by Arrow et al. (1995). Unfortunately the RICE-family models cannot include hypotheses concerning the composition effect as defined by Grossman, nor can they include preferences, because they are one-good models and they do not include a commodity market.

Specifically the green technological effect is included in the following equation:

E(n,t) = V (n,t)CE(n,t) (7)

Where E(n,t) represents the level of emissions. Notice that the coefficient V(n,t) in (7) represents the emissions/carbon-energy ratio and captures the second form of technical change of the RICE99 model: the environmental friendly technical change. This index of carbon intensity is exogenously determined and follows a negative exponential path over time. In this way, Nordhaus and Boyer (2000) make the assumption of a gradual, costless improvement in green technology gained by the agents as time passes.

Regulation, included in the model as a “Kyoto forever” emissions constraint, is described by the following equation:

(8)

Where Kyoto(n) is the idiosyncratic emission target set in the Kyoto protocol for the signatory countries (i.e. USA, Other high income countries, OECD Europe and Eastern Europe countries in the model) over time and the BAU (Business as usual) levels for the non-signatory ones. In our simulations we will introduce an emissions permits market.

The scale effect is influenced by total factor productivity A(n,t) which explains the industrial technology and is an exogenous and increasing parameter over time with a decreasing growth rate.

In RICE99 we are allowed to isolate EKC factors individual effects and to turn on and off their contribution on model results. This analysis was already implemented by econometric tools (Stern 2002) in order to assess EKC factors contribution on the PIR and by Integrated Assessment Models (Galeotti (2003)) to investigate if in developed countries environmental technology can decouple economic growth. Galeotti in two versions of RICE96 including endogenous technological change runs counterfactual simulations in which:

- He suppresses the role of the environment-friendly “green” technical progress by imposing a value of the emissions intensity value σ(n,t) = E(n,t)/Y(n,t) = σ(n,1) which implies a constant value of the carbon content for each unit of produced output over time.

- He analyses scenarios in which regulation in the form of an emissions stabilizing policy (“Kyoto forever scenario”) is imposed together with the possibility of emission trading for all Annex I countries (including United States).

Differing from Galeotti in our paper:

We also run counterfactual simulations in which we suppress the role of the scale effect by guessing a constant rather increasing exogenous industrial innovation (A(n,t)=A(n,1)) in every period.

We impose a constant value of the carbon intensity (V (n,t)= E(n,1)/CE(n,1) =1) rather than emissions intensity because of the different equations describing green technological change in the RICE96 and the RICE99 models.

Finally, though a “Kyoto forever” scenario is not realistic given the recent USA’s rejection of the Kyoto Protocol we impose an emissions cap also for the United States as in Galeotti (2003) since we are interested in analyzing the impact of international policies involving the widest and significant coalition of developed countries. The next table (Table 1) summarizes the scenarios.

The next step will be to rank these scenarios, on the basis of meaningful indicators highlighting economic, environmental and social indicators. The sustainable development literature, in the last 15 years, stresses the importance of measuring sustainable development in order to address policy design and evaluation (Pearce et al., 1998).

In order to rank alternative policies we evaluate the impact of different scenarios using the following indicators:

For environmental impact, the level of CO2 emissions.

For social impact, the welfare as assessed by the Atkinson’s (1972) theorem. By the Atkinson’s theorem we are allowed to implement equity based ordering of income distributions among scenarios over time. A scenario is welfare improving if shows higher levels of income per capita and equity assessed by Lorenz curves.

These scenarios are run by the non-linear program solver GAMS for 15 periods from 1995 to 2135. For each sustainability dimension we get a ranking as follows:

Economic impact: the best scenario is the one showing the highest world consumption per capita.

Environmental impact: the best scenario is the one showing the lowest level of CO2 emissions.

Social impact: the best scenario is the one showing the highest welfare on the basis of the Atkinson’s theorem.