climate change, integrated assessment, computable general equilibrium

Richard s.J. Tol

Roberto Roson

English

Research Papers in Economics

AN INTEGRATED ASSESSMENT MODEL OF ECONOMY-ENERGY-CLIMATE – 
THE MODEL WIAGEM: A COMMENT 
 
Roberto Roson
a,b and Richard S.J. Tol
c,d,e 
 
a Ca’Foscari University of Venice, Venice, Italy 
b Fondazione Eni Enrico Mattei, Venice, Italy 
c Centre for Marine and Climate Research, Hamburg University, Hamburg, Germany 
d Institute for Environmental Studies, Vrije Universiteit, Amsterdam, The Netherlands 
e Center for Integrated Study of the Human Dimensions of Global Change, Carnegie Mellon 
University, Pittsburgh, PA, USA 
 
May 28, 2003 
 
Working Paper FNU-26 
 
 
Economic assessments of the impacts of climate change are rare. Even rarer are papers on the 
higher order economic impacts. The paper by Claudia Kemfert (2002) is therefore welcome. 
Most economic impact studies use direct costs as an approximation of welfare losses. 
According to the direct cost method, a welfare loss is approximated by price times quantity, 
where the quantity is the physical impact of climate change (see Pearce et al., 1996, and 
Smith et al., 2001, for an overview). The direct cost method ignores that the impact may 
change the price (the partial equilibrium effect), that changes in one market may have effects 
on other markets (the general equilibrium effect), and that climate change may alter 
investments (the growth effect). Using a dynamic computable general equilibrium model, 
Kemfert is able to look at all economic effects of climate change impacts on nature, human 
health, forestry, water resources, and energy consumption. 
Only four other papers use a similar methodology. Scheraga et al. (1993) use now outdated 
climate change scenarios and climate change impact studies, and only sketch the assumptions 
and results. The papers by Darwin et al. (1995) and Darwin and Tol (2001) are limited to the 
impacts on agriculture and coastal zone, respectively; the model used there is a static CGE. 
Deke et al. (2001) come closest to Kemfert, but only look at agriculture and coastal 
protection. Kemfert clearly improves on these papers. 
Kemfert proceeds as follows. She takes a selection of the welfare losses estimated by Tol 
(2002a,b), and runs part of his model with her scenarios of population, income and climate. 
She sums the impacts, and calibrates a power function to the results (Equation 3.14). 
Figure 1 compares Kemfert’s “approximation” (read from her Figure 8 and inferred from her 
Table 11; the latter is probably what she used, see below) and Tol’s original model (run with 
the IS92a scenario and the climate sensitivity lowered to 0.6 to reproduce the reported 
warming in Kemfert’s Figure 6). It is clear that Kemfert’s impacts and Tol’s differ 
substantially. Indeed, if we inspect Kemfert’s model a bit closer, differences emerge. For 
instance, Kemfert’s extrapolating function (3.11) for “mortality” corresponds to Tol’s 
separate intrapolating functions for cardiovascular and respiratory mortality. In equations 
(3.12) and (3.13), Kemfert reinterprets Tol’s changes in welfare due to changes in energy 
consumption as changes in energy demand. As Kemfert is silent about the reasons for these 
changes – indeed, she does not alert the reader to the fact that changes have been made – we 
do not pursue this particular point further. Figure 1. Impacts of climate change according to Tol’s original model and Kemfert’s 
approximations according to her Figure 8 and Table 11. 
 
Kemfert reports climate change impacts of around 1.7% of GDP for a global warming of 
0.25￿C. Let’s follow Kemfert in assuming that impacts are proportional to áT
â where T is the 
global mean temperature and á and â are parameters; 0.5 > â > 1.5. The impact of climate 
change for a 2.5￿C warming, say due to a doubling of the atmospheric concentration of carbon 
dioxide, would be 17.0% of GPD if â = 1.0 (5.4% if â = 0.5; 53.8% if â = 1.5). These 
numbers are substantially higher than the even the maximum numbers reported in the Second 
and Third Assessment Reports of the IPCC (Pearce et al., 1996; Smith et al., 2001). 
The numbers apart, Kemfert also makes a methodological point, namely that of adding 
general equilibrium effects to the direct costs of climate change. Unfortunately, she does not 
compare the two, and we have not been able to construct this comparison from her paper. The 
economics effects of climate change “lower[…] other investments”. This is a bit 
disappointing. The great advantage of computable general equilibrium models is that one can 
look at economy-wide effects of different shocks to different sectors. If the shock to the 
economy is uniform, and only affects investments, one might as well use a growth model. 
Let us use a Solow-Swan model, for instance, with a Cobb-Douglas production function and 
constant growth rates of population and technology (see Romer, 1996). The equations of 
motion of this economy are: 
(1) 
1 (1)(1)()()()()(1()) KtKtAtKtLtDt
aa ds
- +=-+-  
(2)  (1)(1());(1)(1()) AL AtgAtLtgLt +=++=+  
where K is capital, A is total factor productivity, and L is labour; ä=0.1, ó=0.2, á=0.2, gA=1.01 
and gL=1.01 are parameters; t is time measured in years; and D is the climate change impact. 
In the first scenario, we set D=0 and the other variables initially to their relative steady state 
values. In the second scenario, we let D grow linearly from 0.005 to 0.018, as suggested by 
Kemfert’s Table 11. Figure 2 displays the direct impact of climate change as well as the 
induced reduction in GDP. Figure 2 qualitatively resembles Figure 1; the direct costs (Table 
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111) were just copied; the reduction of GDP starts at zero and rises, more or less linearly, to 
just above the direct costs in 50 years time. 
 
Figure 2. The direct costs and the indirect costs (growth effect only) of climate change, using 
a Solow-Swan model with inputs after Kemfert’s Table 11; two estimates of the growth effect 
are shown, one after Kemfert (“growth effect”) and one after Nordhaus (“GE, Nordhaus”). 
 
Results in all CGE models critically depend on the model structure. Unfortunately, Kemfert 
does not fully explain all key characteristics and assumptions of the WIAGEM model. 
However, some choices seem fairly standard, whereas others are not. In the following, let us 
consider a few non-conventional model characteristics, and their implications in terms of 
realism and reliability of the simulation findings. 
First, the modelling of international trade is very ad hoc. Although any national economy 
includes 11 industries, all non-energy sectors enter into a single composite macro good. 
Furthermore, the macro-good is split, in a CET function, between domestic and exported 
products. Only the exported macro-composite is traded internationally. Does this matter for 
climate change impacts? Yes! An important feature of climate shocks is the differentiated 
impact among industries and regions: some sectors are more vulnerable than others; some 
sectors are more integrated than others in the national and international economic structure. 
This is why one wants to use a CGE model: to explore the systemic effects of changes in 
relative competitiveness. Unfortunately, these important effects cannot be captured in a model 
in which a single good is traded internationally. This composite good includes everything: 
from non-tradable personal services to quasi-homogeneous materials. 
Second, Kemfert is largely silent on the process of investment and capital formation. 
However, one model characteristic seems clear: there is one world interest rate, and only one 
capital market, equalizing capital yields in the alternative investment destinations. This is a 
grossly unrealistic assumption. Capital returns vary widely around the world; investment 
portfolios exhibit a very significant “home bias”; domestic savings and investments are highly 
correlated, despite the apparent integration of international capital markets. Neglecting this 
feature would imply a large overestimation of economic growth in developing countries, 
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sunless one uses ad hoc capital controls. Does this matter for estimating climate change 
impacts? Yes! Vulnerability to climate change depends, inter alia, on poverty and 
development, which in turn depend on national and international investment. Furthermore, the 
estimated growth effect of climate change is driven by the formulation of the process of 
capital formation. 
In WIAGEM, optimal savings are endogenously determined using a Ramsey formulation. 
However, the initial calibration is to observed savings. Do these match? Kemfert (p. 288) 
claims that “the intertemporal optimal dynamic allocation is characterized by a steady state 
growth path”. Is the model in steady state also at the initial time step? Is there a transition 
phase from the initial state to the optimal path? Presumably, the steady state with climate 
change (policy) differs from the steady state without. What are the transition dynamics from 
one steady state to the other? Without fully understanding the model dynamics, it is hard to 
assess the model results. These issues may explain the occasionally irregular results in 
Kemfert’s Table 11. 
Third, on the consumption side, Kemfert models the utility function of the representative 
consumers as a sort of CES production function. The CES is a homothetic function: the 
income elasticity for all consumption goods is unity. (Other CGE models use, instead, more 
sophisticated functions, allowing for differentiated income elasticities.) Does this matter for 
long-run simulations? Yes! When economies grow, consumption shifts away from energy 
intensive basic needs to more elaborated goods and services. This has obvious implications 
for the forecasting of greenhouse gases emissions, but also for the relative competitiveness of 
each nation, and, particularly, for the relative importance of sectors vulnerable to climate 
change. 
Given these simplifying assumptions used in Kemfert’s CGE, it is not altogether surprising 
that we are able to mimic its behaviour with a Solow-Swan model: the growth engine of 
WIAGEM is very simple. 
Kemfert produces an indirect, growth effect of climate change that is very large. The question 
is whether this estimate is realistic. In Kemfert’s formulation, climate change melts away 
investment. That is, if the impact of climate change is equivalent to 1% of GDP, investment 
falls by 5% (using a savings’ rate of 20% as above). In Nordhaus’ (1994) DICE model, 
climate change melts away production, so that a 1% reduction in GDP reduces investment 
only by 1%. Figure 2 also shows the growth effect using this formulation. It is, as expected, 
considerably smaller. (See Fankhauser and Tol, 2001, for a more extensive discussion.) 
However, the growth effect even as estimated by Nordhaus’ method may be too large. For, 
the direct impacts include many intangibles. The “ecological impact”, for instance, is the 
income loss equivalent, in welfare terms, to a loss in biodiversity. The ecological impact is 
not an income loss, and it does not directly affect output or investment. A similar argument 
holds for health impacts. 
As to the general equilibrium effects of climate change, Kemfert unfortunately does not 
estimate these. This is not a trivial exercise, anyway. Typically, climate change impact studies 
report results either in physical units (e.g., change in total yield) or in welfare equivalents 
(e.g., percent GDP). A CGE outputs welfare estimates, so welfare losses are useless as an 
input. Similarly, a CGE outputs changes in total agricultural production, and cannot use 
estimates of such changes as inputs. In order to include climate change impacts in a CGE, the 
outputs of impact studies need to (painstakingly) reworked into variables that can be used in a 
CGE. Such variables include changes in endowments (e.g., for land lost to sea level rise), 
changes in productivity (e.g., for agriculture), changes in demand (e.g., for energy), changes 
in government expenditures (e.g., for coastal protection), and changes in the (expected) return on investment (as a result of the above changes). To date, nobody has succeeded in doing this 
in an internally consistent manner for a comprehensive set of climate change impacts. 
 
Acknowledgements 
We had useful discussions about the topics of this paper with Francesco Bosello, Carlo 
Carraro, Sam Fankhauser, Claudia Kemfert, Hans Kremers, Marco Lazzarin and Kerstin 
Ronneberger. The Volkswagen Foundation through the ECOBICE project, the US National 
Science Foundation through the Center for Integrated Study of the Human Dimensions of 
Global Change (SBR-9521914) and the Michael Otto Foundation provided welcome financial 
support. 
 
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AN INTEGRATED ASSESSMENT MODEL OF ECONOMY-ENERGY-CLIMATE – THE MODEL WIAGEM: A COMMENT

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AN INTEGRATED ASSESSMENT MODEL OF ECONOMY-ENERGY-CLIMATE – THE MODEL WIAGEM: A COMMENT

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