The Representative Agent Must Die:
Using Demographics to Inform Social Discount Rates
January 30, 2016
Eli P. Fenichel, Matthew J. Kotchen, and Ethan Addicott
Abstract
Benefit-cost analyses of long-lived public projects—such as those related to
environmental protection, infrastructure, education, and health—require a social discounting
process. The Ramsey Rule provides the backbone for modern discounting. A critical parameter
in the Ramsey Rule is the utility discount rate, UDR, (or rate of pure time preference). There is a
split in the literature as to whether the UDR is a purely normative decision or should be backed
out from market behavior. We offer a third approach, based life expectancy. We exploit the fact
that multiple generations are extant at any point in time, and the UDR can reflect an aggregation
over how these generations care about their own future utility. We use the approach to derive
estimates of the UDR for nearly all countries of the world, and find UDRs range between 1.5 and
4.0 percent, with a global estimate of 2-3 percent. We also place our empirical results in the
context of deriving the overall social discount rate, and find results that are strikingly close to
those often used in practice. For example, we derive social discount rates between 2 and 6
percent for the United States, which compares well to OMBs 3-7 percent range.
Introduction
Few topics in economics are as fundamental and generate as much controversy as
discounting. Benefit-cost analyses of long-lived public projects—such as those related to
environmental protection and investments in infrastructure, education, and health—require a
social discounting process. While most regulatory agencies have established procedures for
discounting future benefits and costs, economists continue to debate what constitutes an
appropriate discount rate and fundamentally how discounting should be applied—and the stakes
are high. Small changes to discount rates and procedures can significantly affect the present
1
value calculations for long-lived projects, so questions about discounting often play a critical role
in policy evaluation.
Economic analysis of climate change has brought many of the important issues to the
fore. Policies to address climate change are generally associated with near term costs of reducing
emissions in order to avoid damages that would otherwise occur far into the future. Hence the
extent to which more or less aggressive climate policy passes a benefit-cost test will depend
critically on the social discount rate. This is the main insight that comes from the highly
influential and contrasting research of Stern (2007) and Nordhaus (2007).1 Both employ the
Ramsey-Koopmans-Cass framework for discounting, yet they differ primarily in their underlying
assumptions about the utility discount rate (UDR), which reflects the time discount rate between
generations irrespective of differences in consumption.2 While Stern uses a very low rate that
supports more aggressive climate policy relative to Nordhaus, the differences in how they justify
their assumptions are of greater interest here. Stern follows classical economists and argues that
the choice should be based on ethical considerations, whereas Nordhaus argues that discounting
should be backed out of behavior reflected in actual market interest rates.
The Stern-Nordhaus exchange rekindled a long-standing debate about “descriptive”
versus “prescriptive” approaches to discounting (Arrow et al. 1996), and subsequent papers have
sought to further clarify the role of positive and normative assumptions implicit in the economics
of climate change and discounting more generally.3 While this literature furthers the
understanding of conceptual issues surrounding the choice of social discount rates, there remains
relatively little empirical guidance on how to choose the underlying parameters, especially with
regard to the UDR. Researchers and policy makers are left to choose based on various ethical
criteria, some of which can push in different directions, or to back out values after determining
other parameters, including an a priori assumption about what the social discount rate should be.
In this paper, we develop a demographic approach for estimating the UDR that serves as
a useful benchmark. Rather than make a judgment about how a social planner is to compare
utilities across generations, we exploit the fact that multiple generations are extant at any point in
1
Both Nicholas Stern and William Nordhaus have written several subsequent papers directly on the topic, but here
we reference the original two in which the distinction first arose.
2
This parameter of the Ramsey equation is sometimes referred to as the rate of societal pure time preference, in
addition to other variants.
3
Examples include Weitzman (2007), Dasgupta (2008), Goulder and Williams (2012), Arrow et al. (2012), and
Gollier (2012).
2
time, and the UDR can reflect an aggregation over how these generations care about their own
future utility. We begin with an (admittedly extreme) assumption that individuals care about the
future only to the extent that they live to enjoy it; that is, individuals discount future utility
according to mortality risk. We then derive estimates of the UDR based on the age structure of a
population and life expectancy at each age. Given life expectancies, the estimates inform periods
considered long-term for many policies (50 to 80 years), and they can apply even further into the
future to the extent that population structures are stable, which we investigate. In effect, our
approach is “descriptive” at the individual level, and “prescriptive” in the aggregation, for which
we estimate and discuss various alternatives. One advantage is that normative judgments are
anchored in tradeoffs among the current population rather than abstract notions about future
generations not yet born.
We use the approach to derive estimates of the UDR for nearly all countries of the world
using detailed demographic data from the World Health Organization. A striking feature of our
results—which range between 1.5 and 4.0 percent—is that they fall within the range many
economists consider reasonable.4 Overall, the approach yields a global estimate of the UDR
between 2 and 3 percent depending on whether aggregation is based on the median or mean
individual, respectively. We emphasize how the results are dependent on the aggregation rule,
which reflects normative judgments. While there is heterogeneity in the estimates across
countries, differences tend to be attenuated because of two demographic features that push in
opposite directions. When one’s concern about the future depends entirely on whether s/he will
live to enjoy it, we would expect countries with a younger aged population to discount the future
less. However, the demographics, which are influenced by levels of economic development, are
such that countries with younger populations also tend to have lower life expectancies at age, and
this implies greater discounting of the future all else equal. The result, as we discuss, is that two
countries can have very similar estimates of the UDR, but for very different reasons.
Our primary contribution is the development of a demographically based approach for
estimating the UDR, along with its application to all countries individually and collectively, but
we also place our empirical results in the context of deriving the overall social discount rate (also
referred to as the consumption discount rate). Specifically, we combine our estimates of the UDR
4
For example, in various studies, Nordhaus uses rates that range from 1.5 to 3 percent (see Nordhaus and Yang
(1996) and Nordhaus (2007),(2014)). Moreover, a recent survey of expert opinion among economists finds a mean
estimate of the UDR of 1.1 percent, with a range between 0 and 8 percent (Drupp et al. 2015)
3
with other parameters of the Ramsey equation using the International Monetary Fund’s 20-year
forecasts of economic growth for each country, along with expert opinion about the elasticity of
the marginal utility of consumption (Drupp et al. 2015).5 We again find results that are strikingly
close to those often used in practice. For example, we derive social discount rates between 3 and
6 percent for the United States when aggregation is based on the median or mean individual,
respectively. These compare very closely with the Office of Management and Budget’s range
between 3 and 7 percent. Across all countries we find that social discount rates are not driven
primarily by estimates of the UDR or forecasts about economic growth, but rather a roughly
equal weighting of both. Our approach thus provides a new methodology for deriving regionallyspecific discount rates for use in integrated assessment models of climate change, in addition to
more general applications of cost-benefit analysis.
2. Conceptual Framework
To motivate our conceptual framework, we begin with the standard discounted utility
model for a representative individual, who has an intertemporal utility function of the form
,…,
where
1/ 1
,
is the discount factor and
is the individual’s pure rate of time preference.
It has long been recognized that uncertainty about survival affects the way individuals discount
the future and therefore make intertemporal choices. Fredrick, Loewenstein, and O'Donoghue
(2002) provide a nice quotation from Rae (1834) that goes back almost two centuries:
When engaged in safe occupations, and living in healthy countries, men are much more apt to be
frugal, than in unhealthy, or hazardous occupations, and in climates pernicious to human life.
Sailors and soldiers are prodigals. In the West Indies, New Orleans, the East Indies, the
expenditure of the inhabitants is profuse. The same people, coming to reside in the healthy parts of
Europe, and not getting into the vortex of extravagant fashion, live economically. War and
pestilence have always waste and luxury, among the other evils that follow in their train. (Rae
1834 p. 57)
There are many more recent references that make the same point with specific reference to life
expectancy. Moreover, it is mortality risk in a catastrophe that has been used to motivate
5
We discuss other possibilities as well, which can easily be incorporated as alternative assumptions.
4
discounting in an intergenerational context (Weitzman 2009; Dasgupta 2007; Goulder and
Williams 2012).
We can explicitly account for life expectancy in the discounted utility model.6 We begin
simply by assuming a constant probability of death, , between periods. The discount factor can
account for this as follows:
1
,
1
where
represents the pure rate of time preference assuming certain survival. When
1, the
future is discounted entirely, because of certain death. In contrast, immortality leads to
0, in
which case the discount factor entirely depends on the pure rate of time preference.
Two observations are helpful before generalizing the framework further. First, the
original formulation of the discount factor can account for the probability of death, whereby
1
1
(1)
1
Second, it is easy to see that the probability of survival 1
assuming
is an upper bound for ,
0. In other words, the individual discounts future utility by at least the probability
of not being around to enjoy it.
A clear limitation of this formulation is that
is constant through time, whereas life
expectancies are such that the probability of death generally increases with age. To account for
this reality, assume the individual is age
0, and that the probability of death is known at
at
. The model can then be written as
each age, denoted as
,…,
,where
1
1
.
Assuming that the probability of death in any year is increasing with age, this model implies that
is decreasing over time, or equivalently, the discount rate is getting larger, reflecting less
concern about the future when one is less likely to be around to enjoy. A further implication is
that for any , a younger initial age
implies a lower discount rate in period because of
greater chances of survival. These results, as we will show, play an important role as offsetting
effects in our empirical estimates over populations.
6
Our approach here is similar to that of Eckstein (1961) and Kula (1997).
5
Thus far we have considered only a single individual, but our aim of deriving a social
UDR requires consideration of an entire population. We assume the population consists of
individuals denoted
same
and
1, … , , and they differ only by age; that is, all individuals share the
0 in order to focus on the extent of heterogeneity
. We assume further that
in the pure rate of time preference owing to life expectancy alone. This implies, using equation
(1) subscripting for time and superscripting for the individual, that each individual ’s
0 is
demographically determined discount rate at
1
This makes immediately clear that as
discounting of the future. Moreover, as
.
→ 0 it follows that
→ 0 and
→ 1 it follows that
→ ∞ and
0 → 1, implying no
0 → 0, implying
complete discounting of the future.
0 is given by
The age profile of the population in year
,…,
. We make the
further simplifying assumption that the age distribution is stable through time, which means that
the growth rate is identical for all ages in the population. While this assumption is common in
demography (Casewell 2001) and used to study human capital (Arrow, Dasgupta, and Mumford
2014, UNU-IHDP and UNEP 2014), we test and discuss this assumption in the results section.
The assumption greatly simplifies our analysis here because current population structures are
sufficient for providing estimates, eliminating the need for demographic projections, although
the approach could be extended to account for demographic shifts.
Although the effective discount rates derived for individuals are based entirely on the
demographics associated with life expectancy, aggregating them into a social UDR requires
normative judgments. Any aggregation requires some sort of weighting across individuals of
different ages, and there is a literature on aggregating individuals’ time preferences into a
planner’s objective function.7 In this paper, we are agnostic about how such weighting should
occur, but employ two aggregation rules because of their simplicity and frequent application.
Our first approach is to estimate a social UDR based on the mean discount rate in the
population. Of course, one justification for using the mean is that the social UDR represents the
discount rate of a representative individual. This is simply
7
See the recent paper by Millner and Heal (2014) and the references cited therein.
6
̅
1
,
where the assumption of a stable population structure means that we need only consider life
expectancies at time
0. The intuition for why we need only consider one point in time is that
while individuals’ discount rates change as they age, the fraction of the population at each age
remains constant. Thus, the population’s social UDR does not change over time.
Our second approach is to estimate the social UDR using the discount rate of the median
individual such that
Median
,…,
.
While this approach provides a useful point of comparison, it can also be justified as consistent
with demographic principles of majority rule. In what follows, we estimate the different social
UDRs for nearly all countries of the world, in addition to the world as a whole.
3. Estimation of Social Utility Discount Rates
We obtain demographic data from the World Health Organization’s (WHO) 2012 life
tables. 8 The tables report vital statistics binned in ages 0, 1-4, and then in 5-year increments. The
important variables for our purposes are the number of individuals and the life expectancy in
each bin. We treat the number of individuals in each bin identically. We assume that individuals
know their age specific life expectancy at age (Smith, Taylor, and Sloan 2001), but are uncertain
about their own specific survival. Based on the available data, let
|
denote the expected
number of years left to live for someone at age , which we now treat as the binned age classes
and drop subscripts for time. Then for individuals in each age class, we assume survival from
year to year is independently and identically distributed such that survival is a series of Bernoulli
. It follows that an individual’s probably of
trials, with mortality probability at a given age
survival as time passes is geometrically distributed. This means that the geometric distribution
describes probabilistically the number of periods passing until the individual’s death. We thus
have the relationship whereby mean of the geometric distribution is the inverse of the expect
number of periods until death—that is,
|
. Using this relationship and equation (2),
8
Global Health Observatory Data Repository, Life Tables by Country 1990-2013 (webpage on the Internet).
Geneva: World Health Organization; 2013. http://apps.who.int/gho/data/node.main.692?lang=en> [cited November
2015]
7
we are able to estimate a demographically based discount rate for all individuals in each age
class. We then calculate social UDRs for all countries using the mean and median aggregation
rules described in equations (3) and (4). We also calculate corresponding UDRs for the world as
a whole using data on the population structure of all countries combined.
3.1 Country-Specific Results
We find substantial country-specific heterogeneity in social UDRs. We report the results
for every country in Appendix Table 1 and summarize the general pattern in Figure 1. When
using the mean aggregation (top panel), country-specific social UDRs mostly vary between 2 and
4 percent. When using the median aggregation, the social UDRs are generally lower and range
between 1.5 and 3 percent. The distribution of social UDRs is left skewed, and developed
countries generally have higher social UDRs than developing countries.
The variation in social UDRs is driven by two offsetting and yet related effects. The first
is countries with longer life expectancies will have lower social UDRs, all else equal. These tend
to be countries with greater incomes and better access to medical care. These same countries,
however, also tend to have older populations, and this is the second effect that pushes towards a
higher social UDR, all else equal. It follows that two countries may have the same social UDR
but for very different reasons. One may be a developed country with long life expectancy and an
older population, while the other may be a developing country with shorter life expectancy and a
younger population.9 These offsetting effects illustrate the importance of age distribution when
using life expectancy to estimate a social UDR.
We further illustrate the role of demographic structure by showing how country-specific
UDRs differ based on the fraction of a country’s population over the age of 65 and life
expectancy at birth. For all countries, Figure 2 plots life expectancy against the fraction of the
population over the age of 65, and the points are colored according to the size of the country’s
social UDR based on the mean aggregation. The figure shows how countries with lower life
expectancies at birth—e.g., those less than 65 years of age—have little variation in the social
UDR, and the magnitudes are relatively low (below the world estimate discussed below). This is
because these same countries tend to have very young populations, in large part because they
have shorter life expectancies. Focusing instead on the countries with life expectancies at birth
9
NOTE: We should pull out a few specific examples to illustrate this point.
8
greater than 65 years of age indicates the importance of the age distribution as captures by the
fraction over the age of 65. Among these countries, increases in the fraction from 2 to 10 percent
in of the population over 65 results yields substantial differences in the social UDR. These
results provide one slice through the data that underscore the importance of demographic
structure on the social UDR.
3.2. Global Results
We follow the same procedures described above to estimate social UDRs for the world.
The estimates are based on demographic information for the world constructed from the WHO’s
country-specific life tables. This approach effectively treats all people of the world as a single
population as described above. Using the mean aggregation, we estimate a global, social UDR of
2.9 percent, which is very close that that used in previous research (e.g., Nordhaus and Yang
(1996)). Using the median aggregation lowers the estimate to 2.0 percent. While both rates are
substantially greater than zero, it is useful to emphasize that the aggregation rule plays an
important role. We focus on the mean and median, but alternative normative judgments will
produce different results. For example, if only the utility of newborns are taken into account, the
social UDR would be close to zero. In contrast, accounting for only the elderly would produce a
social UDR that easily exceeds 100 percent. This range emphasizes the importance of normative
judgments implicit in the aggregation rule across a population, be it a country or the world as a
whole. Indeed, the estimates that we report in this subsection treat the people of the world as a
single population, but alternative estimates are possible whereby social UDRs are estimated for
each country and then aggregated based on country-weights. Alternatives to consider include the
mean and median social UDR across countries, which differ from our approach here, which
essentially represent population-weighted mean and median estimates across countries.
4. Relation to Social (Consumption) Discount Rates
The primary focus of our analysis is on deriving demographically based estimate of the
social UDR. But this is only one component of deriving the overall social (consumption)
discount rate that is used for intertemporal economic evaluation of long-term or intergenerational
projects. In this context, the overall social discount rate most commonly employed is based on
the Ramsey rule:
9
,
where
is the UDR that we seek to inform with our analysis. The other term is the product of the
elasticity of the marginal utility of consumption , and the rate of growth in consumption .
While there exists a literature on whether the social discount rate should be constant or declining
(see Arrow et al. 2014), we assume a constant rate here for the illustrative purpose of placing our
results in the larger context of deriving the overall social discount rate.
We use the following procedures to obtain estimates of the other parameters in the
Ramsey equation. Our estimate of the elasticity of the marginal utility of consumption is based
on the expert opinion survey conducted by Drupp et al. (2015). This implies a single value of
1.35 for our purposes. For estimates of the growth rate in consumption, we use the
International Monetary Fund’s mean 20-year projection for real per capita GPD growth in each
country.10This provides different estimates of
for each country. We then combine these
estimates with our estimates of the social UDR to derive overall social discount rates for all
countries. We use the mean aggregation for the UDR to be consistent with our use of GDP per
capita.
We estimate an overall social discount rate for the world of 6.8 percent. As a point of
reference, the U.S. Office of Management and Budget recommends using discount rates that
range between 3 and 7 percent for social regulatory impact analysis (OMB 2003). Using our
procedure to estimate a social discount rate for the United States in particular, we find a rate of
6.0 percent.11 We report the results for all countries in the last column of Appendix Table 1.
There is a large degree of heterogeneity across countries owing to variation in our estimates of
the social UDR and differences in the forecasted rate of grown in countries. To determine the
extent to which heterogeneity is social discount rate is driven by heterogeneity in the social
UDRs, we plot the former against the latter in Figure 4 for all countries. There appears to be no
systematic pattern, suggesting that estimates of the social UDR are not explaining a substantial
share of the heterogeneity in the social discount rates.12 This is not surprising because the very
10
https://www.imf.org/external/pubs/ft/weo/2015/01/weodata/index.aspx (Derived from NGDPRPC indicator)
NOTE: We should provide more details about exactly how we derived this calculation and how it compares to the
way others calibrate parameters in the Ramsey equation in the broader macro literature.
11
Although we focus on the mean aggregation rule, a potential alternative using the median for the United States
may be of interest. Given the near zero rate of median income growth in the United States (DeNavas-Walt and
Proctor 2015), a social discount rate based on the median aggregation would be close to 2.3 percent, which is close
to the OMB’s lower bound.
12
Some countries have negative social discount rates as a result of negative per capita GDP growth projections. 10
different demographic patterns can lead to the same UDR, and it is unlikely that demographic
patterns can be used to explain GDP growth.
5. Tests of Some Assumptions
Our estimates of the social UDRs have been based on the WHO life tables that provide
statistics in binned age classes. But for some countries, e.g., the United States, more detailed life
tables are available such as the U.S. Social Security life tables. The Social Security Life Table
treats every birth year as distinct (e.g., age 0,1,2,3,…). For the United States, therefore, we can
therefore explore the sensitivity of our results to the level of detail captured in the life tables.
Using the data available for every year of life, we estimate social UDRs of 4.1 and 2.4 percent
for the mean and median aggregation rules, respectively. These are comparable to the previous
U.S. estimates of 3.3 and 2.3 percent using the WHO life tables. The mean rate differ by 0.8
percentage points, and the median rate differs by only 0.1 percentage point. The mean rates are
more sensitive to the older end of the age distribution, and the US Social Security Administration
is much more detailed for the extreme elderly.
We also explore the empirical basis for our assumption of a stable population structure.
We do this by estimating country specific UDRs based on the WHO life tables for 1990, 2000,
and 2012 for all countries in existence in 1990. Then to evaluation whether they vary to large
degree, we illustrate the standard deviations of the estimates in Figure 5. The top panel maps the
standard deviations for the mean aggregation, and the bottom panel does so for the median
aggregation. We find that for most countries the UDRs are quite stable over this period. The
mean standard deviation for mean and median aggregated social UDRs is less than 0.25
percentage points (0.20 and 0.14 percent, respectively). Moreover, more than 78 percent of
countries’ standard deviations for the mean aggregation are less than a quarter of a percentage
point, and the same holds for more than 88 percent of the countries regarding the median
aggregation. The countries that do not have relatively stable rates experienced war, major
political-economic change (e.g., fall of socialism in central and eastern Europe), or rapid
development associated with major political or economic reforms and institutional change (e.g.,
Chili and China).
6. Discussion and Conclusion
11
Using age structure and life expectancy at age, we construct utility discount rates within
the range, but slightly greater than the central tendency measure, that economists generally
discuss as reasonable. However, difference in the aggregation approach can lead to difference is
in the UDR that are on the order of 1 percentage point, which is quite substantial. Moreover, in
comparison with statements of economists (Drupp et al. 2015; Weitzman 2001) it likely some
economists are making various adjustments when stating the pure rate of time preference for a
representative agent. Indeed, it is interesting that Drupp et al. (2015) find the older economists
suggest high social utility discount rates. While they provide a few hypotheses, this result is not
surprising if personal preferences are creeping into survey responses. Moreover, when combined
with per capita GDP growth rate forecasts, our approach produces consumption discount rates in
the range generally considered appropriate for business as usual consumption rates and rates
observed in markets.
Ramsey’s discounting rule remains the cornerstone of models of economic dynamics.
Ethical arguments by economists often conclude that when applying the Ramsey rule the UDR,
, should be equal to or near equal to zero (Ramsey 1928; Pearce and Ulph 1995; Asheim 2010;
Kula 1997; Stern 2007).13 Ramsey developed, what in modern terminology, would be referred to
as a representative agent model. The discounting literature is replete with references to such a
representative agent in the Ramsey framework (e.g., Dasgupta 2008; Weitzman 2009).
Ramsey’s work has provided great insight into how to discount, but Ramsey’s simplifying
assumption of an infinitely lived representative agent, often interpreted as a sequence of nonoverlapping generations, provides little guidance on parameterizing his discounting rule.
Ramsey’s assumption of an infinitely lived representative agent is fully consistent with our
approach when all individuals have zero mortality risk. But, this can hardly represent any
conceivable aggregation of agents alive today. The representative agent must die.
Global climate change motivated the recent debates about discount rates, but
infrastructure, conservation, and public investments of all types are evaluated using a social
discount rate. The choice of appropriate discount rates for long lived public projects is
complicated, and it is more complicated when these projects span countries, as in the case of
climate change.
13
Kula (1997) reviews debates about discounting among classical economists and early neo-classical economists. 12
A core reason to worry about computing a utility discount rate or a consumption rate
constructively, i.e., from the utility discount rate, is in models with endogenous growth or per
capita consumption. In these cases the utility discount rate anchors the analysis. Such analyses
are essential for the economics of climate change. While our results lend support to Nordhaus’s
(2007) aggregate results. It is the regional and country level analysis and comparison that are
critical. It is quite possible that when our country specific UDRs are used in place of a single
UDR for all countries (e.g., Nordhaus and Yang 1996) the country level and aggregate results
could be substantially different from analysis where the UDR is the same for all countries.
Therefore, we hope the Supplemental Table with results for all countries is a useful resource for
economists conducting such analyses.
An interesting question emerges if the policy being evaluated will meaningfully impact
the life expectance or demographic structure, making
endogenious. Disease, addressable with
healthcare investment, continue to be a major concern, especially in developing countries
(Chakraborty, Papageorgiou, and Sebastian 2010). The practical implication is that the
assumption a stable age distribution and UDR is probably much more tenable for developed
countries. However, empirically our approach to calculating UDRs yields fairly stable estimates
even for much of the developing world, at least for the last 30 years. This suggests that
endogenous demographic change may be more on interesting academic problem that a practical
policy concern.
Within country heterogeneity is important for establishing social UDRs, but the use of
social discount rates across countries is also not straight forward. Our work suggests that
countries with young populations, which are overwhelming poorer, would place greater weight
on future utility than countries with older populations, which are generally richer. Such younger
countries may argue for the world to place greater weight on future utility provided by public,
non-market goods. However, there does not appear to be a relationship between the rank
ordering of UDRs and consumption discount rates. Though it is possible that poorer, less stable
countries may have greater consumption rates, perhaps because they have expectations of higher
growth rates of income or incur greater risk (perhaps as a result of poorly functioning
institutions). This could result in a situation where countries with generally younger populations,
which are generally poorer and subject to risk, articulate a desire for greater weight on the future,
e.g., more global climate mitigation, conservation, and provision of other public goods, but
13
prefer to consume at high rates today relative to older (wealthier) countries. While older
wealthier countries may be willing to forgo a greater amount of present consumption, but simply
value future utility less since a larger fraction of their populations will not enjoy that future. This paper is certainly not the final word on discounting. Rather, we hope it is useful
starting point. A starting point that leads to a more data-driven approach to establishing UDRs,
which are critical for considering intertemporal allocation decisions.
14
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Figure 1: Mean (top) and median (bottom) country-specific social utility discount rates
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Figure 2: Mean country-specific social utility discount rates by fraction of population over the
age of 65 and life expectancy at birth
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Figure 3: Country-specific social (consumption) discount rates
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Figure 4: Social (consumption) discount rate against social utility discount rate for all countries
using the mean aggregation rule
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Figure 5: Standard deviation of mean (top) and median (bottom) social utility discount rates
from 1990-2012 for Countries That Existed Prior to 1990
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Appendix Table 1: Country-specific social utility discount rates and consumption discount rates
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Appendix Table 1: (Continued)
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