Discounting, Distribution and Disaggregation: Discount Rates for the Rich and the Poor with Climate as a Source of Utility
| Author | Rintaro Yamaguchi |
| DOI | http://doi.org/10.1111/sjpe.12018 |
| Published date | 01 September 2013 |
| Date | 01 September 2013 |
DISCOUNTING, DISTRIBUTION AND
DISAGGREGATION: DISCOUNT RATES
FOR THE RICH AND THE POOR WITH
CLIMATE AS A SOURCE OF UTILITY
Rintaro Yamaguchi
ABSTRACT
To consider the implications of disaggregated consumption and discounting in
the context of climate change, we study discounting in a world composed of the
rich and the poor; a standard setting in the literature of cost–benefit analysis
with distributional considerations. We derive several discount rates for different
num
eraires, which allow us to discuss intergenerational and intragenerational
equity in common terms. In the example of CES-CRRA utility, we also show
that disaggregated discount rates may vary owing to several factors. One impor-
tant parameter, inequality aversion, can be determined in the weighting of inter-
generational and intragenerational concerns.
II
NTRODUCTION
In the series of reports published by the Intergovernmental Panel on Climate
Change (IPCC) over the past decade, it was revealed that one of the most
controversial socioeconomic factors is the choice of the discount factor for
measuring the costs and benefits of future climate change; this was especially
evident in the Second Assessment Report of 1995. Similarly, right after the
launch of the Stern Review, most criticisms (and plaudits) referred to its
choice of a low utility discount rate that could have led to the opposite policy
recommendation, were it higher.
Standard analysis suggests that the consumption discount rate is made up
of a pure rate of time preference and the product of the consumption growth
rate and the elasticity of the marginal utility of consumption. However, the
rate of “consumption growth” appears to be too aggregate to discuss such a
global and durable issue, so some authors scrutinize the prospect of consump-
tion along the lines of the limited substitutability argument of Gerlagh and
van der Zwaan (2002). In such a move, Hoel and Sterner (2007) and Traeger
(2011) assume the consumption of the usual commodities and environmental
quality as arguments of utility. By assigning relative prices to both
consumption and the environment, they illustrate that when discounting the
Nomura Research Institute
Scottish Journal of Political Economy, Vol. 60, No. 4, September 2013
©2013 Scottish Economic Society.
440
environment, the possible increase in the relative price of the environment
should be deducted from the usual consumption discount rate. Applying this
formulation to the DICE model by Nordhaus (2008) would propose that the
optimal amount of carbon dioxide emissions tends to zero within a century
(Sterner and Persson, 2008).
Apart from the relatively oft-debated issue of uncertain consumption,
another route that can be taken to elaborate the consumption prospect is to
disaggregate consumption into rich and poor people. Equity consideration in
cost–benefit analysis dates back to Dasgupta et al.’s (1972) exposition, which
proposed that some unknown redistributional weight be placed on the poor’s
consumption. Since then, however, equity weighting has almost been evicted
from standard analysis under the banner of the Kaldor-Hicks compensation
criterion. However, equity weighting has recently been making a comeback in
the context of climate change. An obvious reason for the comeback is that it
is very costly, or unrealistic, to compensate those who suffer positive net dam-
age from climate change in the present and in the future. Pioneering studies in
this regard include Azar and Sterner (1996) again and Fankhauser et al.
(1997), who have considered weighting the costs and benefits by the elasticity
of the marginal utility of income
1
. Kaplow and Weisbach (2011) clarify that
the elasticity of the marginal utility is essentially a reduced form derived from
the composite of the utility function and the social welfare function.
In debates about climate change, one of the most contentious practical
problems of equity consideration is whether enhancing adaptive behavior of
the vulnerable should be prioritized over costly, uncertain mitigative policies
by rich countries. For example, referring to the relationship between the two
policies as “trade-offs,” Tol (2005) suggests that reducing impacts might be
more efficient than reducing emissions in Africa and Latin America
2
. In this
context as well, discounting based on disaggregated consumption could be of
more significance if we pose the problem as mitigation vs. adaptation, with
each affecting the rich and the poor in a different manner.
All of these explain the motivation of the current paper. Quite a few papers
have accumulated regarding the substitutability and the equity consideration,
but few studies focus on their combination, despite its apparent relevance in
the policy debate. If we disaggregate consumption into the rich and the poor,
while keeping the dual consumption of the composite good and the environ-
ment, we get a more precise idea of what is going on in terms of the discount
rate
3
. In the course of doing so, we start with a general social welfare function
1
Their num
eraires were marginal utility of the rich and the average income group, respec-
tively, but they were shown to be equivalent by Azar (1999).
2
See Lomborg (2008) for a similar non-technical argument.
3
The simultaneous consideration of income or consumption and the environment could be
seen as a dynamic extension of Brekke (1997), who illustrated that the environment as a pub-
lic good leads to different willingness-to-pay values for different individuals, demonstrating
the importance of the choice of a num
eraire in a cost–benefit analysis. Our model echoes this
last point, but is placed in a dynamic context on the rich and the poor, thus arousing the
tension between intertemporal vs. intratemporal equity, in contrast to a static economy of a
materialist and an environmentalist as modeled in Brekke (1997). See also Dr
eze (1998).
DISCOUNTING, DISTRIBUTION AND DISAGGREGATION 441
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