Guidelines for Preparing Economic Analyses | December 2010 6-1
Chapter 6
Discounting Future Benefits
and Costs
D
iscounting renders benets and costs that occur in dierent time periods
comparable by expressing their values in present terms. In practice, it is
accomplished by multiplying the changes in future consumption (broadly
dened, including market and non-market goods and services) caused
by a policy by a discount factor. At a summary level, discounting reects
that people prefer consumption today to future consumption, and that invested capital is
productive and provides greater consumption in the future. Properly applied, discounting can
tell us how much future benets and costs are worth today.
Social discounting, the type of discounting discussed in this chapter, is discounting from
the broad society-as-a-whole point of view that is embodied in benet-cost analysis (BCA).
Private discounting, on the other hand, is discounting from the specic, limited perspective
of private individuals or rms. Implementing this distinction can be complex but it is an
important distinction to maintain because using a given private discount rate instead of a
social discount rate can bias results as part of a BCA.
is chapter addresses discounting over the relatively short term, what has become known
as intragenerational discounting, as well as discounting over much longer time horizons, or
intergenerational discounting. Intragenerational, or conventional, discounting applies to
contexts that may have decades-long time frames, but do not explicitly confront impacts on
unborn generations that may be beyond the private planning horizon of the current ones.
Intergenerational discounting, by contrast, addresses extremely long time horizons and the
impacts and preferences of generations to come. To some extent this distinction is a convenience
as there is no discrete point at which one moves from one context to another. However, the
relative importance of various issues can change as the time horizon lengthens.
Several sensitive issues surround the choice of discount rate. is chapter attempts to address
those most important for applied policy analysis. In addition to the sensitivity of the discount
rate to the choice of discounting approach, a topic discussed throughout this chapter,
these issues include: the distinction and potential confounding of eciency and equity
considerations (Section 6.3.2.1); the dierence between consumption and utility discount
rates (Sections 6.2.2.2 and 6.3.1); “prescriptive” vs. “descriptive” approaches to discount
rate selection (Section 6.3.1); and uncertainty about future economic growth and other
conditions (Sections 6.3.2.1 and 6.3.2.2).
6-2 Guidelines for Preparing Economic Analyses | December 2010
Chapter 6 Discounting Future Benefits and Costs
6.1 The Mechanics of
Future Costs and Benefits
Discounting reects: (1) the amount of time
between the present and the point at which these
changes occur; (2) the rate at which consumption
is expected to change over time in the absence
of the policy; (3) the rate at which the marginal
value of consumption diminishes with increased
consumption; and (4) the rate at which the future
utility from consumption is discounted with time.
Changes in these components or uncertainty
about them can lead to a discount rate that
changes over time, but for many analyses it may
be sucient to apply a xed discount rate or rates
without explicit consideration of the constituent
components or uncertainty.
1
ere are several methods for discounting future
values to the present, the most common of
which involve estimating net present values and
annualized values. An alternative is to estimate a
net future value.
6.1.1 Net Present Value (NPV)
e NPV of a projected stream of current and
future benets and costs relative to the analytic
baseline is estimated by multiplying the benets
and costs in each year by a time-dependent weight,
or discount factor, d, and adding all of the weighted
values as shown in the following equation:
NPV = NB
0
+ d
1
NB
1
+ d
2
NB
2
+
... + d
n–1
NB
n–1
+ d
n
NB
n
(1)
where NB
t
is the net dierence between benets
and costs (B
t
- C
t
) that accrue at the end of period
t. e discounting weights, d
t
, are given by:
d
t
=
(1
1
+ r)
t
(2)
where r is the discount rate. e nal period of the
policy’s future eects is designated as time n.
1 Note that accounting for changes in these components through
discounting is distinct from accounting for inflation, although observed
market rates reflect expected inflation. Both values (i.e., benefits and
costs) and the discount rate should be adjusted for inflation; therefore
most of the discussion in this chapter focuses on real discount rates
and values.
e NPV can be estimated using real or nominal
benets, costs, and discount rates. e analyst can
estimate the present value of costs and benets
separately and then compare them to arrive at net
present value.
It is important that the same discount rate be used
for both benets and costs because nearly any
policy can be justied by choosing a suciently
low discount rate for benets, by choosing
suciently high discount rates for costs, or by
choosing a suciently long time horizon. Likewise,
making suciently extreme opposite choices could
result in any policy being rejected.
When estimating the NPV, it is also important to
explicitly state how time periods are designated
and when, within each time period, costs and
benets accrue. Typically time periods are years,
but alternative time periods can be justied if
costs or benets accrue at irregular or non-annual
intervals. e preceding formula assumes that
t=0 designates the beginning of the rst period.
erefore, the net benets at time zero (NB
0
)
include a C
0
term that captures startup or one-time
costs such as capital costs that occur immediately
upon implementation of the policy. e formula
further assumes that no additional costs are
incurred until the end of the rst year of regulatory
compliance.
2
Any benets also accrue at the end of
each time period.
Figure 6.1 illustrates how net benets (measured
in dollars) are distributed over time. NB
1
is the
sum of benets and costs that may have been
spread evenly across the four quarters of the rst
year (NB
0i
through NB
0iv
) as shown in the bottom
part of the gure. ere may be a loss of precision
by “rounding” a policy’s eects in a given year to
the end or beginning of that year, but this is almost
always extremely small in the scope of an entire
economic analysis.
2 See U.S. EPA (1995c) for an example in which operating and monitoring
costs are assumed to be spread out evenly throughout each year of
compliance. While the exponential function in equation (2) is the most
accurate way of modeling the relationship between the present value
and a continuous stream of benefits and costs, simple adjustments to
the equations above can sometimes adapt them for use under alternative
assumptions about the distribution of monetary flows over time.
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Chapter 6 Discounting Future Benefits and Costs
6.1.2 Annualized Values
An annualized value is the amount one would have
to pay at the end of each time period t so that the
sum of all payments in present value terms equals
the original stream of values. Producing annualized
values of costs and benets is useful because it
converts the time varying stream of values to a
constant stream. Comparing annualized costs to
annualized benets is equivalent to comparing
the present values of costs and benets. Costs and
benets each may be annualized separately by
using a two-step procedure. While the formulas
below illustrate the estimation of annualized costs,
the formulas are identical for benets.
3
To annualize costs, the present value of costs
is calculated using the above formula for net
benets, except the stream of costs alone, not the
net benets, is used in the calculation. e exact
equation for annualizing depends on whether or
not there are any costs at time zero (i.e., at t=0).
Annualizing costs when there is no initial cost at t=0
is estimated using the following equation:
AC = PVC
*
r
*
(1 + r)
n
(1 + r)
n
– 1 (3)
where
AC = annualized cost accrued at the end of
each of n periods;
3 Variants of these formulas may be common in specific contexts. See,
for example, the Equivalent Uniform Annual Cost approach in EPA’s
Air Pollution Control Cost Manual (U.S. EPA 2002b).
PVC = present value of costs (estimated as in
equation 1, above);
r = the discount rate per period; and
n = the duration of the policy.
Annualizing costs when there is initial cost at t=0
is estimated using the following slightly dierent
equation:
AC = PVC
*
r
*
(1 + r)
n
(1 + r)
(n + 1)
– 1 (4)
Note that the numerator is the same in both
equations. e only dierence is the “n+1” term in
the denominator.
Annualization of costs is also useful when
evaluating non-monetized benets, such as
reductions in emissions or reductions in health
risks, when benets are constant over time.
e average cost-eectiveness of a policy or
policy option can be calculated by dividing the
annualized cost by the annual benet to produce
measures of program eectiveness, such as the cost
per ton of emissions avoided.
As mentioned above, the same formulas would
apply to estimating annualized benets.
6.1.3 Net Future Value
Instead of discounting all future values to the
present, it is possible to estimate value in some
future time period, for example, at the end of the
last year of the policy’s eects, n. e net future
value is estimated using the following equation:
NFV = d
0
NB
0
+ d
1
NB
1
+ d
2
NB
2
+ ... + d
n–1
NB
n–1
+ NB
n
(5)
NB
t
is the net dierence between benets
and costs (B
t
- C
t
) that accrue in year t and the
accumulation weights, d
t
, are given by
d
t
= (1 + r)
(n–t)
(6)
Year t 01 23
4n
...
...$NB
0
NB
1
NB
2
NB
3
NB
4
NB
n
TIME
Year t 0
1
$NB
0i
NB
0ii
NB
0iii
NB
0iv
TIME
Figure 6.1 - Distribution of Net Benefits
over Time
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Chapter 6 Discounting Future Benefits and Costs
where r is the discount rate. It should be noted
that the net present value and net future value can
be expressed relative to one another:
NPV =
(1
1
+ r)
n
(7)
6.1.4 Comparing the Methods
Each of the methods described above uses a
discount factor to translate values across time, so
the methods are not dierent ways to determine
the benets and costs of a policy, but rather are
dierent ways to express and compare these
costs and benets in a consistent manner. NPV
represents the present value of all costs and
benets, annualization represents the value
as spread smoothly through time, and NFV
represents their future value. For a given stream of
net benets, the NPV will be lower with higher
discount rates, the NFV will be higher with
higher discount rates, and the annualized value
may be higher or lower depending on the length
of time over which the values are annualized.
Still, rankings among regulatory alternatives are
unchanged across the methods.
Depending on the circumstances, one method
might have certain advantages over the others.
Discounting to the present to get a NPV is likely to
be the most informative procedure when analyzing
a policy that requires an immediate investment and
oers a stream of highly variable future benets.
However, annualizing the costs of two machines
with dierent service lives might reveal that the
one with the higher total cost actually has a lower
annual cost because of its longer lifetime.
Annualized values are sensitive to the
annualization period; for any given present value
the annualized value will be lower the longer the
annualization period. Analysts should be careful
when comparing annualized values from one
analysis to those from another.
e analysis, discussion, and conclusions presented
in this chapter apply to all methods of translating
costs, benets, and eects through time, even
though the focus is mostly on NPV estimates.
6.1.5 Sensitivity of Present Value
Estimates to the Discount Rate
e impact of discounting streams of benets and
costs depends on the nature and timing of benets
and costs. e discount rate is not likely to aect
the present value of the benets and costs for those
cases in which:
•
All eects occur in the same period
(discounting may be unnecessary or
superuous because net benets are positive or
negative regardless of the discount rate used);
•
Costs and benets are largely constant over
the relevant time frame (discounting costs and
benets will produce the same conclusion as
comparing a single year’s costs and benets);
and/or
•
Costs and benets of a policy occur
simultaneously and their relative values do
not change over time (whether the NPV is
positive does not depend on the discount
rate, although the discount rate can aect the
relative present value if a policy is compared
to another policy).
Discounting can, however, substantially aect
the NPV of costs and benets when there is a
signicant dierence in the timing of costs and
benets, such as with policies that require large
initial outlays or that have long delays before
benets are realized. Many of EPA’s policies t
these proles. Text Box 6.1 illustrates a case in
which discounting and the choice of the discount
rate have a signicant impact on a policy’s NPV.
6.1.6 Some Issues in Application
ere are several important analytic components
that need to be considered when discounting:
risk and valuation, placing eects in time, and the
length of the analysis.
6.1.6.1 Risk and Valuation
ere are two concepts that are oen
confounded when implementing social
discounting, but should be treated separately.
e rst is the future value of environmental
eects, which depends on many factors,
Guidelines for Preparing Economic Analyses | December 2010 6-5
Chapter 6 Discounting Future Benefits and Costs
including the availability of substitutes and the
level of wealth in the future. e second is the
role of risk in valuing benets and costs. For both
of these components, the process of determining
their values and then translating the values into
present terms are two conceptually distinct
procedures. Incorporating the riskiness of
future benets and costs into the social discount
rate not only imposes specic and generally
unwarranted assumptions, but it can also hide
important information from decision makers.
6.1.6.2 Placing Effects in Time
Placing eects properly in time is essential for
NPV calculations to characterize eciency
outcomes. Analyses should account for
implementation schedules and the resulting
changes in emissions or environmental quality,
including possible changes in behavior between
the announcement of policy and compliance.
Additionally, there may be a lag time between
changes in environmental quality and a
corresponding change in welfare. It is the change
in welfare that denes economic value, and
not the change in environmental quality itself.
Enumerating the time path of welfare changes is
essential for proper valuation and BCA.
6.1.6.3 Length of the Analysis
While there is little theoretical guidance on the time
horizon of economic analyses, a guiding principle
is that the time span should be sucient to capture
major welfare eects from policy alternatives.
is principle is consistent with the underlying
requirement that BCA reect the welfare outcomes
of those aected by the policy. Another way to view
this is to consider that the time horizon, T, of an
analysis should be chosen such that:
Σ
(B
t
– C
t
)e
–rt
≤ ε ,
t=T
(8)
where ε is a tolerable estimation error for the NPV
of the policy. at is, the time horizon should be
long enough that the net benets for all future
years (beyond the time horizon) are expected to
be negligible when discounted to the present. In
practice, however, it is not always obvious when
this will occur because it may be unclear whether
or when the policy will be renewed or retired
by policy makers, whether or when the policy
will become obsolete or “non-binding” due to
exogenous technological changes, how long the
capital investments or displacements caused by the
policy will persist, etc.
As a practical matter, reasonable alternatives for
the time span of the analysis may be based on
assumptions regarding:
•
e expected life of capital investments
required by or expected from the policy;
•
e point at which benets and costs reach a
steady state;
• Statutory or other requirements for the policy
or the analysis; and/or
•
e extent to which benets and costs are
separated by generations.
Suppose the benefits of a given program occur 30 years in the future and are valued (in real terms) at $5 billion
at that time. The rate at which the $5 billion future benefits is discounted can dramatically alter the economic
assessment of the policy: $5 billion 30 years in the future discounted at 1 percent is $3.71 billion, at 3 percent it
is worth $2.06 billion, at 7 percent it is worth $657 million, and at 10 percent it is worth only $287 million. In this
case, the range of discount rates generates over an order of magnitude of difference in the present value of benefits.
Longer time horizons will produce even more dramatic effects on a policy’s NPV (see Section 6.3 on intergenerational
discounting). For a given present value of costs, particularly the case where costs are incurred in the present and
therefore not affected by the discount rate, it is easy to see that the choice of the discount rate can determine whether
this policy is considered, on economic efficiency grounds, to offer society positive or negative net benefits.
Text Box 6.1 - Potential Effects of Discounting
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Chapter 6 Discounting Future Benefits and Costs
e choice should be explained and well-
documented. In no case should the time horizon
be arbitrary, and the analysis should highlight
the extent to which the sign of net benets or the
relative rankings of policy alternatives are sensitive
to the choice of time horizon.
6.2 Background and Rationales
for Social Discounting
e analytical and ethical foundation of the social
discounting literature rests on the traditional test
of a “potential” Pareto improvement in social
welfare; that is, the trade-o between the gains
to those who benet and the losses to those
who bear the costs. is framework casts the
consequences of government policies in terms of
individuals contemplating changes in their own
consumption (broadly dened) over time. Trade-
os (benets and costs) in this context reect the
preferences of those aected by the policy, and the
time dimension of those trade-os should reect
the intertemporal preferences of those aected.
us, social discounting should seek to mimic the
discounting practices of the aected individuals.
e literature on discounting oen uses a variety of
terms and frameworks to describe identical or very
similar key concepts. General themes throughout
this literature are the relationship between
consumption rates of interest and the rate of
return on private capital, the need for a social rate
of time preference for BCA, and the importance
of considering the opportunity cost of foregone
capital investments.
6.2.1 Consumption Rates of
Interest and Private Rates
of Return
In a perfect capital market with no distortions, the
return to savings (the consumption rate of interest)
equals the return on private sector investments.
erefore, if the government seeks to value costs
and benets in present day terms in the same way
as the aected individuals, it should also discount
using this single market rate of interest. In this
kind of “rst best” world, the market interest rate
would be an unambiguous choice for the social
discount rate.
Real-world complications, however, make the
issue much more complex. Among other things,
private sector returns are taxed (oen at multiple
levels), capital markets are not perfect, and capital
investments oen involve risks reected in market
interest rates. ese factors drive a wedge between
the social rate at which consumption can be traded
through time (the pre-tax rate of return to private
investments) and the rate at which individuals
can trade consumption over time (the post-tax
consumption rate of interest). Text Box 6.2
illustrates how these rates can dier.
A large body of economic literature analyzes the
implications for social discounting of divergences
between the social rate of return on private sector
investment and the consumption rate of interest.
Most of this literature is based on the evaluation of
public projects, but many of the insights still apply
to regulatory BCA. e dominant approaches
in this literature are briey outlined here. More
complete recent reviews can be found in Spackman
(2004) and Moore et al. (2004).
Suppose that the market rate of interest, net of inflation, is 5 percent, and that the taxes on capital income amount to
40 percent of the net return. In this case, private investments will yield 5 percent, of which 2 percent is paid in taxes
to the government, with individuals receiving the remaining 3 percent. From a social perspective, consumption can
be traded from the present to the future at a rate of 5 percent. But individuals effectively trade consumption through
time at a rate of 3 percent because they owe taxes on investment earnings. As a result, the consumption rate of
interest is 3 percent, which is substantially less than the 5 percent social rate of return on private sector investments
(also known as the social opportunity cost of private capital).
Text Box 6.2 - Social Rate and Consumption Rates of Interest
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Chapter 6 Discounting Future Benefits and Costs
6.2.2 Social Rate of
Time Preference
e goal of social discounting is to compare
benets and costs that occur at dierent times
based on the rate at which society is willing to
make such trade-os. If costs and benets can be
represented as changes in consumption proles
over time, then discounting should be based on
the rate at which society is willing to postpone
consumption today for consumption in the
future. us, the rate at which society is willing
to trade current for future consumption, or the
social rate of time preference, is the appropriate
discounting concept.
Generally a distinction is made between individual
rates of time preference and that of society as
a whole, which should inform public policy
decisions. e individual rate of time preference
includes factors such as the probability of death,
whereas society can be presumed to have a longer
planning horizon. Additionally, individuals
routinely are observed to have several dierent
types of savings, each possibly yielding dierent
returns, while simultaneously borrowing at
dierent rates of interest. For these and other
reasons, the social rate of time preference is
not directly observable and may not equal any
particular market rate.
6.2.2.1 Estimating a Social Rate of Time
Preference Using Risk-Free Assets
One common approach to estimating the social
rate of time preference is to approximate it from
the market rate of interest from long-term,
risk-free assets such as government bonds. e
rationale behind this approach is that this market
rate reects how individuals discount future
consumption, and government should value
policy-related consumption changes as individuals
do. In other words, the social rate of discount
should equal the consumption rate of interest (i.e.,
an individual’s marginal rate of time preference).
In principle, estimates of the consumption rate of
interest could be based on either aer-tax lending
or borrowing rates. Because individuals may be in
dierent marginal tax brackets, may have dierent
levels of assets, and may have dierent opportunities
to borrow and invest, the type of interest rate that
best reects marginal time preference will dier
among individuals. However, the fact that, on net,
individuals generally accumulate assets over their
working lives suggests that the aer-tax returns
on savings instruments generally available to the
public will provide a reasonable estimate of the
consumption rate of interest.
e historical rate of return, post-tax and
aer ination, is a useful measure because it is
relatively risk-free, and BCA should address risk
elsewhere in the analysis rather than through the
interest rate. Also, because these are longer-term
instruments, they provide more information on
how individuals value future benets over these
kinds of time frames.
6.2.2.2 Estimating a Social Rate
of Time Preference Using the
‘Ramsey’ Framework
A second option is to construct the social rate
of time preference in a framework originally
developed by Ramsey (1928) to reect: (1) the
value of additional consumption as income
changes; and (2) a “pure rate of time preference”
that weighs utility in one period directly against
utility in a later period. ese factors are combined
in the equation:
r =
g +
(9)
where (r) is the market interest rate, the rst term
is the elasticity of marginal utility (
) times the
consumption growth rate (g), and the second term
is pure rate of time preference (
). Estimating a
social rate of time preference in this framework
requires information on each of these arguments,
and while the rst two of these factors can be
derived from data,
is unobservable and must be
determined.
4
A more detailed discussion of the
Ramsey equation can be found in Section 6.3:
Intergenerational Social Discounting.
4 The Science Advisory Board (SAB) Council defines discounting based
on a Ramsey equation as the “demand-side” approach, noting that the
value judgments required for the pure social rate of time preference
make it an inherently subjective concept (U.S. EPA 2004c).
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Chapter 6 Discounting Future Benefits and Costs
6.2.3 Social Opportunity
Cost of Capital
e social opportunity cost of capital approach
recognizes that funds for government projects, or
those required to meet government regulations, have
an opportunity cost in terms of foregone investments
and therefore future consumption. When a regulation
displaces private investments society loses the total
pre-tax returns from those foregone investments. In
these cases, ignoring such capital displacements and
discounting costs and benets using a consumption
rate of interest (the post-tax rate of interest) does not
capture the fact that society loses the higher, social
(pre-tax) rate of return on foregone investments.
Private capital investments might be displaced
if, for example, public projects are nanced
with government debt or regulated rms cannot
pass through capital expenses, and the supply of
investment capital is relatively xed. e resulting
demand pressure in the investment market will
tend to raise interest rates and squeeze out private
investments that would otherwise have been
made.
5
Applicability of the social opportunity
cost of capital depends upon full crowding out of
private investments by environmental policies.
e social opportunity cost of capital can be
estimated by the pre-tax marginal rate of return on
private investments observed in the marketplace.
ere is some debate as to whether it is best to
use only corporate debt, only equity (e.g., returns
to stocks) or some combination of the two. In
practice, average returns that are likely to be higher
than the marginal return, are typically observed,
given that rms will make the most protable
investments rst; it is not clear how to estimate
marginal returns. ese rates also reect risks faced
in the private sector, which may not be relevant for
public sector evaluation.
5 Another justification for using the social opportunity cost of capital
argues that the government should not invest (or compel investment
through its policies) in any project that offers a rate of return less than
the social rate of return on private investments. While it is true that
social welfare will be improved if the government invests in projects
that have higher values rather than lower ones, it does not follow that
rates of return offered by these alternative projects define the level of
the social discount rate. If individuals discount future benefits using
the consumption rate of interest, the correct way to describe a project
with a rate of return greater than the consumption rate is to say that it
offers substantial present value net benefits.
6.2.4 Shadow Price of
Capital Approach
Under the shadow price of capital approach costs
are adjusted to reect the social costs of altered
private investments, but discounting for time
itself is accomplished using the social rate of
time preference that represents how society
trades and values consumption over time.
6
e
adjustment factor is referred to as the “shadow
price of capital.”
7
Many sources recognize this
method as the preferred analytic approach to social
discounting for public projects and policies.
8
e shadow price, or social value, of private capital
is intended to capture the fact that a unit of
private capital produces a stream of social returns
at a rate greater than that at which individuals
discount them. If the social rate of discount is the
consumption rate of interest, then the social value
of a $1 private sector investment will be greater
than $1. e investment produces a rate of return
for its owners equal to the post-tax consumption
rate of interest, plus a stream of tax revenues
(generally considered to be consumption) for the
government. Text Box 6.3 illustrates this idea of
the shadow price of capital.
If compliance with environmental policies
displaces private investments, the shadow price
of capital approach suggests rst adjusting the
project or policy cost upward by the shadow
price of capital, and then discounting all costs
and benets using a social rate of discount equal
to the social rate of time preference. e most
complete frameworks for the shadow price of
capital also note that while the costs of regulation
might displace private capital, the benets could
encourage additional private sector investments.
In principle, a full analysis of shadow price of
6 Because the consumption rate of interest is often used as a proxy for
the social rate of time preference, this method is sometimes known as
the “consumption rate of interest – shadow price of capital” approach.
However, as Lind (1982b) notes, what is really needed is the social rate
of time preference, so more general terminology is used. Discounting
based on the shadow price of capital is referred to as a “supply side”
approach by EPA’s SAB Council (U.S. EPA 2004c).
7 A “shadow price” can be viewed as a good’s opportunity cost, which
may not equal the market price. Lind (1982a) remains the seminal
source for this approach in the social discounting literature.
8 See OMB Circular A-4 (2003), Freeman (2003), and the report of EPA’s
Advisory Council on Clean Air Compliance Analysis (U.S. EPA 2004c).
Guidelines for Preparing Economic Analyses | December 2010 6-9
Chapter 6 Discounting Future Benefits and Costs
capital adjustments would treat costs and benets
symmetrically in this sense.
e rst step in applying this approach is
determining whether private investment ows
will be altered by a policy. Next, all of the altered
private investment ows (positive and negative)
are multiplied by the shadow price of capital
to convert them into consumption-equivalent
units. All ows of consumption and consumption
equivalents are then discounted using the social
rate of time preference. A simple illustration of this
method applied to the costs of a public project and
using the consumption rate of interest is shown in
Text Box 6.3.
9
9 An alternative approach for addressing the divergence between
the higher social rate of return on private investments and lower
consumption rate of interest is to set the social discount rate equal to a
weighted average of the two. The weights would equal the proportions
of project financing that displace private investment and consumption
respectively. This approach has enjoyed considerable popularity over
the years, but it is technically incorrect and can produce NPV results
substantially different from the shadow price of capital approach. (For
an example of these potential differences see Spackman 2004.)
6.2.4.1 Estimating the Shadow
Price of Capital
e shadow price of capital approach is data
intensive. It requires, among other things,
estimates of the social rate of time preference, the
social opportunity cost of capital, and estimates
of the extent to which regulatory costs displace
private investment and benets stimulate it. While
the rst two components can be estimated as
described earlier, information on regulatory eects
on capital formation is more dicult. As a result
empirical evidence for the shadow price of capital
is less concrete, making the approach dicult to
implement.
10
Whether or not this adjustment is necessary
appears to depend largely on whether the economy
in question is assumed to be open or closed, and
on the magnitude of the intervention or program
10 Depending on the magnitudes of the various factors, shadow prices
from about 1 to infinity can result (Lyon 1990). Lyon (1990) and Moore
et al. (2004) contain excellent reviews of how to calculate the shadow
price of capital and possible settings for the various parameters that
determine its magnitude.
To estimate the shadow price of capital, suppose that the consumption rate of interest is 3 percent, the pre-tax rate of
return on private investments is 5 percent, the net-of-tax earnings from these investments are consumed in each period,
and the investment exists in perpetuity (amortization payments from the gross returns of the investment are devoted to
preserving the value of the capital intact). A $1 private investment under these conditions will produce a stream of private
consumption of $.03 per year, and tax revenues of $.02 per year. Discounting the private post-tax stream of consumption
at the 3 percent consumption rate of interest yields a present value of $1. Discounting the stream of tax revenues at
the same rate yields a present value of about $.67. The social value of this $1 private investment – the shadow price of
capital – is thus $1.67, which is substantially greater than the $1 private value that individuals place on it.
To apply this shadow price of capital estimate, we need additional information about debt and tax financing as well as about
how investment and consumption are affected. Assume that increases in government debt displace private investments
dollar-for-dollar, and that increased taxes reduce individuals’ current consumption also on a one-for-one basis. Finally,
assume that the $1 current cost of a public project is financed 75 percent with government debt and 25 percent with current
taxes, and that this project produces a benefit 40 years from now that is estimated to be worth $5 in the future.
Using the shadow price of capital approach, first multiply 75 percent of the $1 current cost (which is the amount of
displaced private investment) by the shadow price of capital (assume this is the $1.67 figure from above). This yields
$1.2525; add to this the $.25 amount by which the project’s costs displace current consumption. The total social cost
is therefore $1.5025. This results in a net social present value of about $.03, which is the present value of the future
$5 benefit discounted at the 3 percent consumption rate of interest ($1.5328) minus the $1.5025 social cost.
Text Box 6.3 - Estimating and Applying the Shadow Price of Capital
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Chapter 6 Discounting Future Benefits and Costs
considered relative to the ow of investment
capital from abroad.
11
Some argue that early analyses implicitly assumed
that capital ows into the nation were either
nonexistent or very insensitive to interest rates,
known as the “closed economy” assumption.
12
Some empirical evidence suggests, however, that
international capital ows are quite large and are
sensitive to interest rate changes. In this case, the
supply of investment funds to the U.S. equity and
debt markets may be highly elastic (the “open
economy” assumption), thus private capital
displacement would be much less important than
previously thought.
Under this alternative view, it would be
inappropriate to assume that nancing a public
project through borrowing would result in dollar-
for-dollar crowding out of private investment. If
there is no crowding out of private investment,
then no adjustments using the shadow price of
capital are necessary; benets and costs should
be discounted using the social rate of time
preference alone. However, the literature to date
is not conclusive on the degree of crowding out.
ere is little detailed empirical evidence as to
the relationship between the nature and size of
projects and capital displacement. While the
approach is oen recognized as being technically
superior to simpler methods, it is dicult to
implement in practice.
6.2.5 Evaluating the Alternatives
e empirical literature for choosing a social
discount rate focuses largely on estimating the
consumption rate of interest at which individuals
translate consumption through time with
reasonable certainty. Some researchers have
explored other approaches that, while not detailed
here, are described briey in Text Box 6.4.
11 Studies suggesting that increased U.S. Government borrowing does
not crowd out U.S. private investment generally examine the impact
of changes in the level of government borrowing on interest rates. The
lack of a significant positive correlation of government borrowing and
interest rates is the foundation of this conclusion.
12 See Lind (1990) for this revision of the shadow price of capital
approach.
To estimate a consumption rate of interest that
includes low risk, historical rates of return on “safe”
assets (post-tax and aer ination), such as U.S.
Treasury securities, are normally used. Some may
use the rate of return to private savings. Recent
studies and reports have generally found government
borrowing rates in the range of around 2 percent to 4
percent.
13
Some studies have expanded this portfolio
to include other bonds, stocks, and even housing.
is generally raises the range of rates slightly. It
should be noted that these rates are realized rates
of return, not anticipated, and they are somewhat
sensitive to the choice of time period and the class of
assets considered.
14
Studies of the social discount rate
for the United Kingdom place the consumption rate
of interest at approximately 2 percent to 4 percent,
with the balance of the evidence pointing toward the
lower end of the range.
15
Others have constructed a social rate of
time preference by estimating the individual
arguments in the Ramsey equation. ese
estimates necessarily require judgments about
the pure rate of time preference. Moore et al.
(2004) and Boardman et al. (2006) estimate the
intragenerational rate to be 3.5 percent. Other
studies base the pure rate of time preference on
individual mortality risks in order to arrive at a
discount rate estimate. As noted earlier, this may
be useful for an individual, but is not generally
appropriate from a societal standpoint. e
Ramsey equation has been used more frequently
in the context of intergenerational discounting,
which is addressed in the next section.
13 OMB (2003) cites evidence of a 3.1 percent pre-tax rate for ten-year
U.S. Treasury notes. According to the U.S. Congressional Budget
Office (CBO) (2005), funds continuously reinvested in 10-year U.S.
Treasury bonds from 1789 to the present would have earned an
average inflation-adjusted return of slightly more than 3 percent a
year. Boardman et al. (2006) suggest 3.71 percent as the real rate
of return on ten-year U.S. Treasury notes. Newell and Pizer (2003)
find rates slightly less than 4 percent for thirty-year U.S. Treasury
securities. Nordhaus (2008) reports a real rate of return of 2.7 percent
for twenty-year U.S. Treasury securities. The CBO estimates the cost
of government borrowing to be 2 percent, a value used as the social
discount rate in their analyses (U.S. CBO 1998).
14 Ibbotson and Sinquefield (1984 and annual updates) provide historical
rates of return for various assets and for different holding periods.
15 Lind (1982b) offers some empirical estimates of the consumption
rate of interest. Pearce and Ulph (1994) provide estimates of the
consumption rate of interest for the United Kingdom. Lyon (1994)
provides estimates of the shadow price of capital under a variety of
assumptions.
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Chapter 6 Discounting Future Benefits and Costs
Some of the literature questions basic premises underlying the conventional social discounting analysis. For
example, some studies of individual financial and other decision-making contexts suggest that even a single
individual may appear to value and discount different actions, goods, and wealth components differently. This “mental
accounts” or “self-control” view suggests that individuals may evaluate one type of future consequence differently
from another type of future consequence. The discount rate an individual might apply to a given future benefit or
cost, as a result, may not be observable from market prices, interest rates, or other phenomena. This may be the case
if the future consequences in question are not tradable commodities. Some evidence from experimental economics
indicates that discount rates appear to be lower the larger the magnitude of the underlying effect being valued.
Experimental results have shown higher discount rates for gains than for losses, and show a tendency for discount
rates to decline as the length of time to the event increases. Further, individuals may have preferences about whether
sequences of environmental outcomes are generally improving or declining. Some experimental evidence suggests
that individuals tend to discount hyperbolically rather than exponentially, a structure that raises time-consistency
concerns. Approaches to social discounting based on alternative perspectives and ecological structures have also
been developed, but these have yet to be fully incorporated into the environmental economics literature.
16
e social opportunity cost of capital represents a
situation where investment is crowded out dollar-
for-dollar by the costs of environmental policies.
is is an unlikely outcome, but it can be useful for
sensitivity analysis and special cases. Estimates of
the social opportunity costs of capital are typically
in the 4.5 percent to 7 percent range depending
upon the type of data used.
17
e utility of the shadow price of capital approach
hinges on the magnitude of altered capital ows
from the environmental policy. If the policy will
substantially displace private investment then a
shadow price of capital adjustment is necessary
before discounting consumption and consumption
equivalents using the social rate of time preference.
e literature does not provide clear guidance
on the likelihood of this displacement, but it has
been suggested that if a policy is relatively small
17 OMB (2003) recommends a real, pre-tax opportunity cost of capital
of 7 percent and refers to Circular A-94 (1992) as the basis for this
conclusion. Moore et al. (2004) estimate a rate of 4.5 percent based on
AAA corporate bonds. In recent reviews of EPA’s plans to estimate the
costs and benefits of the Clean Air Act, the SAB Advisory Council (U.S.
EPA 2004c and U.S. EPA 2007b) recommends using a single central
rate of 5 percent as intermediate between 3 percent and 7 percent rates,
based generally on the consumption rate of interest and the cost of
capital, respectively.
and capital markets t an “open economy” model,
there is probably little displaced investment.
18
Changes in yearly U.S. government borrowing
during the past several decades have been in the
many billions of dollars. It may be reasonable to
conclude that EPA programs and policies costing
a fraction of these amounts are not likely to
result in signicant crowding out of U.S. private
investments. Primarily for these reasons, some
argue that for most environmental regulations it
is sucient to discount using a government bond
rate with some sensitivity analysis.
19
6.3 Intergenerational
Social Discounting
Policies designed to address long-term
environmental problems such as global climate
change, radioactive waste disposal, groundwater
pollution, or biodiversity will likely involve
signicant impacts on future generations. is
section focuses on social discounting in the context
of policies with very long time horizons involving
multiple generations, typically referred to in the
literature as intergenerational discounting.
18 Lind (1990) first suggested this.
19 See in particular Lesser and Zerbe (1994) and Moore et al. (2004).
Text Box 6.4 - Alternative Social Discounting Perspectives
16 See Thaler (1990) and Laibson (1998) for more information on
mental accounts; Guyse, Keller, and Eppell (2002) on preferences for
sequences; Gintis (2000) and Karp (2005) on hyperbolic discounting;
and Sumaila and Waters (2005) and Voinov and Farley (2007) for
additional treatments on discounting.
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Chapter 6 Discounting Future Benefits and Costs
Discounting over very long time horizons is
complicated by at least three factors: (1) the
“investment horizon” is longer than what is
reected in observed interest rates that are
used to guide private discounting decisions; (2)
future generations without a voice in the current
policy process are aected; and (3) compared to
intragenerational time horizons, intergenerational
investment horizons involve greater uncertainty.
Greater uncertainty implies rates lower than
those observed in the marketplace, regardless
of whether the estimated rates are measured in
private capital or consumption terms. Policies with
very long time horizons involve costs imposed
mainly on the current generation to achieve
benets that will accrue mainly to unborn, future
generations, making it important to consider how
to incorporate these benets into decision making.
ere is little agreement in the literature on the
precise approach for discounting over very long
time horizons.
is section presents a discussion of the
main issues associated with intergenerational
social discounting, starting with the Ramsey
discounting framework that underlies most of the
current literature on the subject. It then discusses
how the “conventional” discounting procedures
described so far in this chapter might need to
be modied when analyzing policies with very
long (“intergenerational”) time horizons. e
need for such modications arises from several
simplifying assumptions behind the conventional
discounting procedures described above. Such
conventional procedures will likely become less
realistic the longer is the relevant time horizon of
the policy. is discussion will focus on the social
discount rate itself. Other issues such as shadow
price of capital adjustments, while still relevant
under certain assumptions, will be only briey
touched upon.
Clearly, economics alone cannot provide
denitive guidance for selecting the “correct”
social welfare function or social rate of time
preference. In particular, the fundamental
choice of what moral perspective should guide
intergenerational social discounting — e.g., that
of a social planner who weighs the utilities of
present and future generations or those preferences
of the current generations regarding future
generations — cannot be made on economic
grounds alone. Nevertheless, economics can oer
important insights concerning discounting over
very long time horizons, the implications and
consequences of alternative discounting methods,
and the systematic consideration of uncertainty.
Economics can also provide some advice on the
appropriate and consistent use of the social welfare
function approach as a policy evaluation tool in an
intergenerational context.
6.3.1 The Ramsey Framework
A common approach to intergenerational
discounting is based upon methods economists
have used for many years in optimal growth
modeling. In this framework, the economy is
assumed to operate as if a “representative agent”
chooses a time path of consumption and savings
that maximizes the NPV of the ow of utility
from consumption over time.
20
Note that this
framework can be viewed in normative terms, as
a device to investigate how individuals should
consume and reinvest economic output over
time. Or it can be viewed in positive terms, as a
description (or “rst-order approximation”) of
how the economy actually works in practice. It is
a rst order approximation only from this positive
perspective because the framework typically
excludes numerous real-world departures from the
idealized assumptions of perfect competition and
full information that are required for a competitive
market system to produce a Pareto-optimal
allocation of resources. If the economy worked
exactly as described by optimal growth models —
i.e., there were no taxes, market failures, or other
distortions — the social discount rate as dened in
these models would be equal to the market interest
rate. And the market interest rate, in turn, would
be equal to the social rate of return on private
investments and the consumption rate of interest.
It is worth noting that the optimal growth
literature is only one strand of the substantial
20 Key literature on this topic includes Arrow et al. (1996a), Lind (1994),
Schelling (1995), Solow (1992), Manne (1994), Toth (1994), Sen
(1982), Dasgupta (1982), and Pearce and Ulph (1994).
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Chapter 6 Discounting Future Benefits and Costs
body of research and writing on intertemporal
social welfare. is literature extends from
the economics and ethics of interpersonal and
intergenerational wealth distribution to the
more specic environment-growth issues raised
in the “sustainability” literature, and even to the
appropriate form of the social welfare function,
e.g., utilitarianism, or Rawls’ maxi-min criterion.
As noted earlier, the basic model of optimal
economic growth, due to Ramsey (1928), implies
equivalence between the market interest rate (r),
and the elasticity of marginal utility (
) times the
consumption growth rate (g) plus the pure rate of
time preference (
):
r =
g +
(10)
e rst term,
g, reects the fact that the
marginal utility of consumption will change over
time as the level of consumption changes. e
second term,
, the pure rate of time preference,
measures the rate at which individuals discount
their own utility over time (taking a positive
view of the optimal growth framework) or the
rate at which society should discount utilities
over time (taking a normative view). Note
that if consumption grows over time — as
it has at a fairly steady rate at least since the
industrial revolution (Valdés 1999) — then
future generations will be richer than the
current generation. Due to the diminishing
marginal utility of consumption, increments to
consumption will be valued less in future periods
than they are today. In a growing economy,
changes in future consumption would be given a
lower weight (i.e., discounted at a positive rate)
than changes in present consumption under this
framework, even setting aside discounting due to
the pure rate of time preference (
).
ere are two primary approaches typically used in
the literature to specify the individual parameters
of the Ramsey equation: the “descriptive”
approach and the “prescriptive,” or more explicitly,
the normative approach. ese approaches
are illustrated in Text Box 6.5 for integrated
assessment models of climate change.
e descriptive approach attempts to derive
likely estimates of the underlying parameters
in the Ramsey equation. is approach argues
that economic models should be based on
actual behavior and that models should be able
to predict this behavior. By specifying a given
utility function and modeling the economy over
time one can obtain empirical estimates for the
marginal utility and for the change in growth rate.
While the pure rate of time preference cannot be
estimated directly, the other components of the
Ramsey equation can be estimated, allowing
to
be inferred.
Other economists take the prescriptive approach
and assign parameters to the Ramsey equation to
match what they believe to be ethically correct.
21
For instance, there has been a long debate, starting
with Ramsey himself, on whether the pure rate
of time preference should be greater than zero.
e main arguments against the prescriptive
approach are that: (1) people (individually and
societally) do not make decisions that match this
approach; and (2) using this approach would
lead to an over-investment in environmental
protection (e.g., climate change mitigation) at the
expense of investments that would actually make
future generations better o (and would make
intervening generations better o as well). ere
is also an argument that the very low discount rate
advocated by some adherents to the prescriptive
approach leads to unethical shortchanging of
current and close generations.
Other analyses have adopted at least aspects of
a prescriptive approach. For example, the Stern
Review (see Text Box 6.6) sets the pure rate of
time preference at a value of 0.1 percent and
the elasticity of marginal utility as 1.0. With an
assumed population growth rate of 1.3 percent,
the social discount rate is 1.4 percent. Guo et al.
(2006) evaluate the eects of uncertainty and
discounting on the social cost of carbon where
the social discount rate is constructed from the
Ramsey equation. A number of dierent discount
rate schedules are estimated depending on the
adopted parameters.
21 Arrow et al. (1996a).
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Chapter 6 Discounting Future Benefits and Costs
While use of the Ramsey discounting framework
is quite common and is based on an intuitive
description of the general problem of trading
o current and future consumption, it has some
limitations. In particular, it ignores dierences in
income within generations (at least in the basic
single representative agent version of the model).
Arrow (1996a) contains detailed discussion
of descriptive and prescriptive approaches to
discounting over long time horizons, including
examples of rates that emerge under various
assumptions about components of the Ramsey
equation.
6.3.2 Key Considerations
ere are a number of important ways in which
intergenerational social discounting diers from
intragenerational social discounting, essentially
due to the length of the time horizon. Over a very
long time horizon it is much more dicult, if not
impossible, for analysts to judge whether current
generation preferences also reect those of future
generations and how per capita consumption will
change over time. is section discusses eciency
and intergenerational equity concerns, and
uncertainty in this context.
6.3.2.1 Efficiency and
Intergenerational Equity
A principal problem with policies that span long
time horizons is that many of the people aected
are not yet alive. While the preferences of each
aected individual are knowable (if perhaps
unknown in practice) in an intragenerational
context, the preferences of future generations
in an intergenerational context are essentially
unknowable. is is not always a severe problem
for practical policy making, especially when
policies impose relatively modest costs and
benets, or when the costs and benets begin
immediately or in the not too distant future. Most
of the time, it suces to assume future generations
will have preferences much like those of present
generations.
e more serious challenge posed by long time
horizon situations arises primarily when costs
and benets of an action or inaction are very
large and are distributed asymmetrically over vast
expanses of time. e crux of the problem is that
future generations are not present to participate
in making the relevant social choices. Instead,
these decisions will be made only by existing
generations. In these cases social discounting can
no longer be thought of as a process of consulting
the preferences of all aected parties concerning
today’s valuation of eects they will experience in
future time periods.
Moreover, compounding interest over very long
time horizons can have profound impacts on
the intergenerational distribution of welfare. An
extremely large benet or cost realized far into the
future has essentially a present value of zero, even
when discounted at a low rate. But a modest sum
invested today at the same low interest rate can
The Ramsey approach has been most widely debated in the context of climate change. Most climate economists
adopt a descriptive approach to identify long-term real interest rates and likely estimates of the underlying parameters
in the Ramsey equation. William Nordhaus argues that economic models should be based on actual behavior and
that models should be able to predict this behavior. His Dynamic Integrated model of Climate and the Economy
(DICE), for example, uses interest rates, growth rates, etc., to calibrate the model to match actual historic levels
of investment, consumption, and other variables. In the most recent version of the DICE model (Nordhaus 2008),
he specifies the current rate of productivity growth to be 5.5 percent per year, the rate of time preference to be 1.5
percent per year, and the elasticity of marginal utility to be 2. In an earlier version (Nordhaus 1993) he estimates
the initial return on capital (and social discount) to be 6 percent, the rate of time preference to be 2 percent, and the
elasticity of marginal utility to be 3. Because the model predicts that economic and population growth will slow, the
social discount rate will decline.
Text Box 6.5 - Applying these Approaches to the Ramsey Equation
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Chapter 6 Discounting Future Benefits and Costs
grow to a staggering amount given enough time.
erefore, mechanically discounting very large
distant future eects of a policy without thinking
carefully about the implications is not advised.
22
For example, in the climate change context, Pearce
et al. (2003) show that decreasing the discount rate
from a constant 6 percent to a constant 4 percent
nearly doubles the estimate of the marginal benets
from carbon dioxide (CO
2
) emission reductions.
Weitzman (2001) shows that moving from a
constant 4 percent discount rate to a declining
discount rate approach nearly doubles the estimate
again. Newell and Pizer (2003) show that constant
discounting can substantially undervalue the
future given uncertainty in economic growth and
the overall investment environment. For example,
Newell and Pizer (2003) show that a constant
discount rate could undervalue net present benets
by 21 percent to 95 percent with an initial rate of
7 percent, and 440 percent to 700 percent with an
initial rate of 4 percent, depending upon the model
of interest rate uncertainty.
Using observed market interest rates for
intergenerational discounting in the representative
agent Ramsey framework essentially substitutes
the pure rate of time preference exhibited by
individuals for the weight placed on the utilities
of future generations relative to the current
generation (see OMB 2003 and Arrow et al.
1996). Many argue that the discount rate should
be below market rates — though not necessarily
zero — to: (1) correct for market distortions and
ineciencies in intergenerational transfers; and
(2) so that generations are treated equally based on
ethical principles (Arrow et al. 1996, and Portney
and Weyant 1999).
23
Intergenerational Transfers
e notion of Pareto compensation attempts to
identify the appropriate social discount rate in an
22 OMB’s Circular A-4 (2003) requires the use of constant 3 percent and
7 percent for both intra- and intergenerational discounting for benefit-
cost estimation of economically significant rules but allows for lower,
positive consumption discount rates, perhaps in the 1 percent to 3
percent range, if there are important intergenerational values.
23 Another issue is that there are no market rates for intergenerational
time periods.
intergenerational context by asking whether the
distribution of wealth across generations could
be adjusted to compensate the losers under an
environmental policy and still leave the winners
better o than they would have been absent the
policy. Whether winners could compensate losers
across generations hinges on the rate of interest
at which society (the United States presumably,
or perhaps the entire world) can transfer wealth
across hundreds of years. Some argue that in the
U.S. context, a good candidate for this rate is the
federal government’s borrowing rate. Some authors
also consider the infeasibility of intergenerational
transfers to be a fundamental problem for
discounting across generations.
24
Equal Treatment Across Generations
Environmental policies that aect distant future
generations can be considered to be altruistic
acts.
25
As such, some argue that they should be
valued by current generations in exactly the same
way as other acts of altruism are valued. Under this
logic, the relevant discount rate is not based on
an individual’s own consumption, but instead on
an individual’s valuation of the consumption (or
welfare) of someone else. ese altruistic values
can be estimated through either revealed or stated
preference methods.
At least some altruism is apparent from
international aid programs, private charitable
giving, and bequests within overlapping
generations of families. But the evidence suggests
that the importance of other people’s welfare to
an individual appears to grow weaker as temporal,
cultural, geographic, and other measures of
“distance” increase. e implied discount rates
survey respondents appear to apply in trading o
present and future lives also is relevant under this
approach. One such survey (Cropper, Aydede, and
Portney 1994) suggests that these rates are positive
on average, which is consistent with the rates
at which people discount monetary outcomes.
e rates decline as the time horizon involved
lengthens.
24 See Lind (1990) and a summary by Freeman (2003).
25 Schelling (1995), and Birdsall and Steer (1993) are good references for
these arguments.
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Chapter 6 Discounting Future Benefits and Costs
6.3.2.2 Uncertainty
A longer time horizon in an intergenerational
policy context also implies greater uncertainty
about the investment environment and economic
growth over time, and a greater potential for
environmental feedbacks to economic growth
(and consumption and welfare), which in turn
further increases uncertainty when attempting to
estimate the social discount rate.
is additional uncertainty has been shown to
imply eective discount rates lower than those
based on the observed average market interest
rates, regardless of whether or not the estimated
investment eects are predominantly measured as
private capital or consumption terms (Weitzman
1998, 2001; Newell and Pizer 2003; Groom et al.
2005; and Groom et al. 2007).
26
e rationale for
this conclusion is that consideration of uncertainty
in the discount rate should be based on the average
of discount factors (i.e., 1/(1+r)
t
) rather than the
standard discount rate (i.e., r). From the expected
discount factor over any period of time a constant,
certainty-equivalent discount rate that yields the
discount factor (for any given distribution of r)
can be inferred. Several methods for accounting
for uncertainty into intergenerational discounting
are discussed in more detail in the next section.
6.3.3 Evaluating Alternatives
ere is a wide range of options available to
the analyst for discounting intergenerational
costs and benets. Several of these are described
below, ordered from simplest to most analytically
complex. Which option is utilized in the analysis
is le to expert judgment, but should be based on
the likely consequences of undertaking a more
complex analysis for the bottom-line estimate of
expected net benets. is will be a function of the
proportion of the costs and benets occurring far
out on the time horizon and the separation of costs
and benets over the planning horizon. When
it is unclear which method should be utilized,
the analyst is encouraged to explore a variety of
approaches.
26 Gollier and Zeckhauser (2005) reach a similar result using a model
with decreasing absolute risk aversion.
6.3.3.1 Constant Discount Rate
One possible approach is to simply make no
distinction between intergenerational and
intragenerational social discounting. For example,
models of innitely-lived individuals suggest the
consumption rate of interest as the social discount
rate. Of course, individuals actually do not live long
enough to experience distant future consequences
of a policy and cannot report today the present
values they place on those eects. However, it
is equally sucient to view this assumption as
a proxy for family lineages in which the current
generation treats the welfare of all its future
generations identically with the current generation.
It is not so much that the individual lives forever
as that the family spans many generations (forever)
and that the current generation discounts
consumption of future generations at the same rate
as its own future consumption.
Models based on constant discount rates over
multiple generations essentially ignore potential
dierences in economic growth and income and/
or preferences for distant future generations. Since
economic growth is unlikely to be constant over
long time horizons, the assumption of a constant
discount rate is unrealistic. Interest rates are a
function of economic growth; thus, increasing
(declining) economic growth implies an increasing
(decreasing) discount rate.
A constant discount rate assumption also does not
adequately account for uncertainty. Uncertainty
regarding economic growth increases as one goes
further out in time, which implies increasing
uncertainty in the interest rate and a declining
certainty equivalent rate of return to capital
(Hansen 2006).
6.3.3.2 Step Functions
Some modelers and government analysts have
experimented with varying the discount rate with
the time horizon to reect non-constant economic
growth, intergeneration equity concerns, and/or
heterogeneity in future preferences. For instance,
in the United Kingdom the Treasury recommends
the use of a 3.5 percent discount rate for the rst
30 years followed by a declining rate over future
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Chapter 6 Discounting Future Benefits and Costs
time periods until it reaches 1 percent for 301 years
and beyond.
27
is method acknowledges that a
constant discount rate does not adequately reect
the reality of uctuating and uncertain growth
rates over long time horizons. However, application
of this method also raises several potential analytic
complications. First, there is no empirical evidence
to suggest the point(s) at which the discount rate
declines, so any year selected for a change in the
discount rate will be necessarily ad-hoc. Second,
this method can suer from a time inconsistency
problem. Time inconsistency means that an
optimal policy today may look sub-optimal in the
future when using a dierent discount rate and vice
versa. Some have argued that time inconsistency
is a relatively minor problem relative to other
conditions imposed (Heal 1998, Henderson and
Bateman 1995, and Spackman 2004).
6.3.3.3 Declining or Non-Constant
Discount Rate
Using a constant discount rate in BCA is
technically correct only if the rate of economic
growth will remain xed over the time horizon of
the analysis. If economic growth is changing over
time, then the discount rate, too, will uctuate.
In particular, one may assume that the growth
rate is declining systematically over time (perhaps
to reect some physical resource limits), which
will lead to a declining discount rate. is is
the approach taken in some models of climate
change.
28
In principle, any set of known changes
to income growth, the elasticity of marginal
utility of consumption, or the pure rate of time
preference will lead to a discount rate that changes
accordingly.
6.3.3.4 Uncertainty-Adjusted
Discounting
If there is uncertainty about the future growth rate,
then the correct procedure for discounting must
27 The guidance also requires a lower schedule of rates, starting with 3
percent for zero to 30 years, where the pure rate of time preference
in the Ramsey framework (the parameter
in our formulation) is
set to zero. For details see HM Treasury (2008) Intergenerational
wealth transfers and social discounting: Supplementary Green Book
Guidance.
28 See, for example, Nordhaus (2008).
account for this uncertainty in the calculation of
the expected NPV of the policy. Over the long
time horizon, both investment uncertainty and
risk will naturally increase, which results in a
decline in the imputed discount rate. If the time
horizon of the policy is very long, then eventually a
low discount rate will dominate the expected NPV
calculations for benets and costs far in the future
(Weitzman 1998).
Newell and Pizer (2003) expand on this
observation, using historical data on U.S.
interest rates and assumptions regarding their
future path to characterize uncertainty and
compute a certainty equivalent rate. In this
case, uncertainty in the individual components
of the Ramsey equation is not being modeled
explicitly. Their results illustrate that a constant
discount rate could substantially undervalue
net present benefits when compared to one
that accounts for uncertainty. For instance,
a constant discount rate of 7 percent could
undervalue net present benefits by between 21
percent and 95 percent depending on the way in
which uncertainty is modeled.
A key advantage of this treatment of the discount
rate over the step function and simple declining
rate discounting approaches is that the analyst is
not required to arbitrarily designate the discount
rate transitions over time, nor required to ignore
the eects of uncertainty in economic growth over
time. us, this approach is not subject to the time
inconsistency problems of some other approaches.
Another issue that has emerged about the use
of discount rates that decline over time due to
uncertainty is that they could generate inconsistent
policy rankings NPV versus NFV.
29
Because the
choice between NPV and NFV is arbitrary, such
an outcome would be problematic for applied
policy analysis. More recent work, however,
appears to resolve this seeming inconsistency,
conrming the original ndings and providing
sound conceptual rationale for the approach.
30
29 See Gollier (2004) for a technical characterization of this concern, and
Hepburn and Groom (2007) for additional exploration of the issues.
30 See Gollier and Weitzman (2009) provide a concise and clear
treatment. Freeman (2009) and Gollier (2009) also propose solutions.
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Chapter 6 Discounting Future Benefits and Costs
6.4 Recommendations
and Guidance
As summed up by Freeman (2003 p. 206),
“economists have not yet reached a consensus
on the appropriate answers” to all of the issues
surrounding intergenerational discounting. And
while there may be more agreement on matters
of principle for discounting in the context of
intragenerational policies, there is still some
disagreement on the magnitude of capital
displacement and therefore the importance of
accounting for the opportunity costs of capital
in practice.
31
e recommendations provided
here are intended as practical and plausible
default assumptions rather than comprehensive
and precise estimates of social discount rates
that must be applied without adjustment in all
situations. at is, these recommendations should
be used as a starting point for BCA, but if the
31 This chapter summarizes some key aspects from the core literature
on social discounting; it is not a detailed review of the vast and
varied social discounting literature. Excellent sources for additional
information are: Lind (1982a, b; 1990; 1994), Lyon (1990, 1994), Kolb
and Scheraga (1990), Scheraga (1990), Arrow et al. (1996), Pearce and
Turner (1990), Pearce and Ulph (1994), Groom et al. (2005), Cairns
(2006), Frederick et al. (2002), Moore et al. (2004), Spackman (2004),
and Portney and Weyant (1999).
In autumn 2006, the U.K. government released a detailed report titled The Economics of Climate Change: The Stern
Review, headed by Sir Nicholas Stern (2006). The report drew mainly on published studies and estimated that
damages from climate change could result in a 5 percent to 20 percent decline in global output by 2100. The report
found that costs to mitigate these impacts were significantly less (about 1 percent of GDP). Stern’s findings led him to
say that “climate change is the greatest and widest-ranging market failure ever seen,” and that “the benefits of strong
early action considerably outweigh the cost.” The Stern Review recommended that policies aimed towards sharp
reduction in GHG emissions should be enacted immediately.
While generally lauded for its thoroughness and use of current climate science, The Stern Review drew significant
criticism and discussion of how future benefits were calculated, namely targeting Stern’s assumptions about the
discount rate (Tol and Yohe 2006 and Nordhaus 2008). The Stern Review used the Ramsey discounting equation
(see Section 6.3.1), applying rates of 0.1 percent for the annual pure rate of time preference, 1.3 percent for the
annual growth rate, and a elasticity of marginal utility of consumption equal to 1. Combining these parameter values
reveals an estimated equilibrium real interest rate of 1.4 percent, a rate arguably lower than most returns to standard
investments, but not outside the range of values suggested in these Guidelines for intergenerational discount rates.
So why is the issue on the value of the discount rate so contentious? Perhaps the biggest concern is that climate
change is expected to cause significantly greater damages in the far future than it is today, and thus benefits are
sensitive to discounting assumptions. A low social discount rate means The Stern Review places a much larger
weight on the benefits of reducing climate change damages in 2050 or 2100 relative to the standard 3 percent or 7
percent commonly observed in market rates. Furthermore, Stern’s relatively low values of
and
imply that the
current generation should operate at a higher savings rate than what is observed, thus implying that society should
save more today to compensate losses incurred by future generations.
Why did Stern use these particular parameter values? First, he argues that the current generation has an ethical
obligation to place similar weights on the pure rate of time for future generations. Second, a marginal elasticity of
consumption of unity implies a relatively low inequality aversion, which reduces the transfer of benefits between the
rich and the poor relative to a higher elasticity. Finally, there are significant risks and uncertainties associated with
climate change, which could imply using a lower-than-market rate. Stern’s (2006) concluding remarks for using a
relatively low discount rate are clear, “However unpleasant the damages from climate change are likely to appear in the
future, any disregard for the future, simply because it is in the future, will suppress action to address climate change.”
Text Box 6.6 - What’s the Big Deal with The Stern Review?
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Chapter 6 Discounting Future Benefits and Costs
analysts can develop a more realistic model and
bring to bear more accurate empirical estimates
of the various factors that are most relevant to
the specic policy scenario under consideration,
then they should do so and provide the rationale
in the description of their methods. With this
caveat in mind, our default recommendations for
discounting are below.
•
Display the time paths of benets and
costs as they are projected to occur over
the time horizon of the policy, i.e., without
discounting.
•
e shadow price of capital approach
is the analytically preferred method for
discounting, but there is some disagreement
on the extent to which private capital is
displaced by EPA regulatory requirements.
EPA will undertake additional research and
analysis to investigate important aspects of
this issue, including the elasticity of capital
supply, and will update guidance accordingly.
In the interim analysts should conduct a
bounding exercise as follows:
•
Calculate the NPV using the consumption
rate of interest. is is appropriate for
situations where all costs and benets
occur as changes in consumption ows
rather than changes in capital stocks, i.e.,
capital displacement eects are negligible.
As of the date of this publication, current
estimates of the consumption rate of
interest, based on recent returns to
Government-backed securities, are close to
3 percent.
•
Also calculate the NPV using the rate of
return to private capital. is is appropriate
for situations where all costs and benets
occur as changes in capital stocks rather
than consumption ows. e OMB
estimates a rate of 7 percent for the
opportunity cost of private capital.
•
EPA intends to periodically review the
empirical basis for the consumption
discount rate and the rate of return to
private capital.
In most cases the results of applying the more
detailed “shadow price of capital” approach
will lie somewhere between the NPV
estimates ignoring the opportunity costs of
capital displacements and discounting all
costs and benets using these two alternative
discount rates.
•
If the policy has a long time horizon (more
than 50 years or so) where net benets vary
substantially over time (e.g., most benets
accrue to one generation and most costs
accrue to another) then the analysis should
use the consumption rate of interest as well
as additional approaches. ese approaches
include calculating the expected present
value of net benets using an estimated time-
declining schedule of discount factors (Newell
and Pizer 2003, Groom et al. 2007, and
Hepburn et al. 2009). is approach accounts
for discount rate uncertainty and variability,
which are known to have potentially large
eects on NPV estimates for policies with
long time horizons. If a time-declining
approach cannot be implemented, it is
possible to capture part of its empirical eect
by discounting at a constant rate somewhat
lower than those used in the conventional
case. For example, the current Interagency
guidance for valuing CO
2
emission reductions
includes treatment with certainty-equivalent
constant discount rates of 2.5 percent, 3
percent, and 5 percent. (See Text Box 7.1 for
more discussion of the Interagency guidance.)
Other more detailed alternatives, such as
constructing discounts rate from estimates
of the individual parameters in the Ramsey
equation, may merit inclusion in the analysis.
In any case, all alternatives should be fully
described, supported, and justied.
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Chapter 6 Discounting Future Benefits and Costs
When implementing any discounting approach
the following principles should be kept in mind:
•
In all cases social benets and costs should
be discounted in the same manner, although
private discount rates may be used to predict
behavior and to evaluate economic impacts.
•
e discount rate should reect marginal
rates of substitution between consumption
in dierent time periods and should not be
confounded with factors such as uncertainty
in benets and costs or the value of
environmental goods or other commodities
in the future (i.e., the “current price” in
future years).
•
e lag time between a change in regulation
and the resulting welfare impacts should
be accounted for in the economic analysis.
e monetary benets from the expected
future impacts should be discounted at the
same rate as other benets and costs in the
analysis. is includes changes in human
health, environmental conditions, ecosystem
services, etc.
