Benefit Cost Analysis (BCA)
Overview and introduction to discounting
CHRIS MADDEN, www.grinningplanet.com
The advent of BCA
• growing impact of regulations on the economy (>
$200B/yr [1996])  need for reform  need for
economic analysis  BCA
• “…former presidents Carter, Reagan, and Bush
and President Clinton have all introduced formal
processes for reviewing economic implications
of major environmental, health, and safety
regulations.”
(Arrow et. al, 1996)
Federal impetus for BCA
– “direct(s) federal agencies to perform a…BCA…for
economically significant rules” >$100M annual effect
on the economy
• “OMB’s Circular A-4 (2003) provides guidance to
federal agencies on the development of
regulatory analysis of economically significant
rules as required by EO 12866.”
(EPA Guidelines, 2010)
BCA Roadmap
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•
Overview: theoretical foundations & steps
Aggregating over time: discounting
Uncertainty and risk
Politics and the role of BCA: usefulness, impact
and criticisms
Future lectures/discussions:
•
•
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Valuation of the environment (“the benefits”)
Measuring the costs of regulation
Application: Arsenic in drinking water.
Climate change
Overview
• BCA: estimating the net benefits of a
particular action/policy by estimating the
costs and benefits, usually (but not
always) with the goal of comparing
multiple alternatives on the criteria of (KaldorHicks) efficiency
– Sometimes also used to inform questions of
equity by differentiating net benefits by group
– Usually cast in monetary terms
Example: Lead in gasoline
• 1985 EPA "Regulatory Impact Analysis“
– Policy evaluated: sharp reduction of lead in gasoline
– This BCA: “(W)idely seen as a "Cadillac" among
benefit-cost analyses of proposed rules”
– Described in K&O p. 44-45
• Issue: significant research linking lead in blood to
– health and learning ability problems in children
– premature adult mortality from hypertension
• Note on approach: Benefits and costs measured as
incremental changes relative to the baseline (conforming
to the decision faced).
– NOT an attempt to measure the full value of the environment.
Farrow and Toman (1999)
(valve seats of older engines)
(e.g. some chronic health effects)
B2 < B 3
(annual)
BCA steps and good practice
(Farrow and Toman, 1999)
impacts
Discounting future values
• Discounting: a method of placing weights (usually < 1) on future
values (benefits and costs) to convert them into net present values so
that they can be combined to a single number in common units, the
“net present value”.
• Tells us how much future costs and benefits are worth today.
• “Present Value of Net Benefits” (PVNB), or “Net present value” (NPV):
present value of a stream of current and future benefits (PVB) minus
present value of a stream of current and future costs (PVC): EPA (2010)
• PVNB = NPV = PVB - PVC
• “Social rate of time preference” or “social discount rate” (r): a
parameter that determines the discounting weight (d) used to convert
a future value to a present value.
Why should we discount future payoffs
in B/C analysis?
Argument 1: “Time value of money” or the
“marginal productivity of investment”
– Public sector investments (e.g. in environmental
quality) should generate returns at or above the level
available in the private sector.
• E.g. business loan interest rate, rate of return in
the stock market
Why should we discount future payoffs
in B/C analysis?
Argument 2: human decisions often reflect a “pure
rate of time preference”
Why should we discount future payoffs
in B/C analysis?
Argument 2: human decisions often reflect a “pure
rate of time preference”
– Reflects how individuals themselves think about
payoffs over time.
– A discount rate based on the preference to receive
payoffs sooner rather than later due factors like
impatience and/or an uncertainty as to whether an
individual will be able to receive the future benefit.
– E.g., I will give you $100 in 1 year: What would you
be willing to accept today in lieu of this promise?
Discounting is applied
AFTER inflation is
already addressed by
converting values from
nominal to real.
Nominal
($ of the day)
Buying
power in
1982
$ 10
($1982)
Real
(in $ units of a
reference year)
Buying
power in
2014
$ 24.53
(in $2014)
In a BCA analysis, benefits and
costs from each year are stated
in the same real units, e.g. in
2014 dollars.
Why do discount rates matter?
Higher discount rates:
• favor more rapid depletion of
nonrenewables and lower stock levels of
renewables (Conrad, J.M. Resource Economics. 1999.)
• can make investments to improve
environmental quality relatively less
attractive compared to those in the private
sector (Conrad, J.M. Resource Economics. 1999.)
Why do discount rates matter? II
• increase the probability of a negative PVNB for projects
with high immediate costs and delayed benefits
(typical feature of investments in environmental quality—
recall Excel demo)
• r = 6%  4%
– almost doubles the estimate of the MB from CO2
emission reductions (Pearce et al. 2003)
• r = 4%  declining discount rate approach
– nearly doubles the estimate again (Weitzman, 2001)
Dynamic BCA: streams of benefits and costs
• Discounting allows us to sum up net benefits over time
into one number with common units:
“present value” of net benefits (PVNB)
• Dynamic efficiency rule of thumb: maximize PVNB,
• Frequently we will ask a simpler question:
• Policy A, yes or no? (Is the PVNB of Policy A greater than
zero?)
• Policy A or B? (Which policy has the greater PVNB?)
PVNB calculation example
Goulder and Stavins (2002) “An eye on the future”
• Simplified climate policy question
Should we implement a GHG control policy with
– Immediate cost: $4B
– One-time benefit in 100 years: $800B
– Discount rate: 5%
– What’s the PVNB?
• Example D: What is the PVNB given a discount rate, r = 0.05 and:
– NBt = 6, t = 1,…,15
and then
NBt = 20, t = 16,…,∞.
t=1
t=16
∞
PVNBt=1:15
t=1
PVNBt=16:∞
t=1
t=16
t=16
∞
∞
PVNBt=16:∞
t=1
t=16
∞
PVNBt=1:∞ =
PVNBt=1:15 + PVNBt=16:∞
Alternative decision criteria for
long-run policy questions
1. Efficiency: What option provides the greatest PVNB (if
question is go/no-go, is the PVNB > 0)?
2. Alternative: responsibility under considerations of
intergenerational equity (distribution)
• We should judge intergenerational fairness by direct examination
(not via an artificially deflated discount rate).
Estimating a social discount rate
One approach: Estimate the long-run,
after-tax, risk-free return to investment
• 7%: approx. the real return to investment in large companies (1926–
1990) (Newell and Pizer, 2004)
• But personal taxes (up to 50%) mean that return to investors, the
consumption rate of interest, is closer to 4%.
– And this 4% return includes a premium for risk (firms may fail).
– To separate the issue of risk from this analysis, consider relatively safe
government bonds: 4% nominal return2% after taxes.
• “The appropriate rate …. in the United States is generally taken to
be around a 3% real, riskless rate.” (Kopp et. al, 1997)
Federal guidelines
• U.S. OMB 2003 :
– provide estimates of PVNB using discount rates of 3% and 7%
– 3%: consumption rate of interest (i.e. after tax return on
investments)
– 7%: OMB estimate of the opportunity cost of capital
• see: http://www.whitehouse.gov/omb/circulars_a004_a-4/
• “Many economists believe that this…range…is too high”
(Fraas and Lutter, 2011)
Problems with discounting: Lack of
consensus on choosing an appropriate
discount rate
Q: What discount rate
do you favor for
discounting long-term
environmental
projects?
Respondents-over
2,000 Ph.D. level
economists
Weitzman, M. L. (2001). “Gamma discounting.” American Economic Review 91, 260-271.
Image: http://www.dbj.jp/ricf/en/research/symposium199511.html
Caveats
“The most critical single problem with discounting future benefits and
costs is that no consensus now exists, or for that matter has ever
existed, about what actual rate of interest to use.”
• The considerations on which a discount rates are based “are
fundamentally matters of judgment or opinion, on which fully
informed and fully rational individuals might be expected to differ.”
(Weitzman, 2001, p. 260)
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• “We should have less confidence in a project for which
– the sign of the PVNB is highly sensitive to
• the discount rate or to
• small changes in projected future benefits and costs,
compared with a project with a PVNB that is not very
sensitive to these elements.” (Goulder and Stavins 2002, p. 674)
Caveats II
• The justification for a pure rate of time
preference is based on the choices
individuals make about payoffs in their
own lifetime.
• Some economists argue that at the
societal level there is no good ethical
argument for using a pure rate of time
preference other than zero.
– Especially, across generations.
Uncertainty
• Uncertainty: future outcomes are not know with
certainty (they are not “deterministic”)
– Risk: probability measure is known (can be
crude).
• E.g. if outcome is determined by flipping a coin, we know the
probability of “heads”
– Ambiguity: probability measure is unknown.
• E.g. …don’t know the true probability of heads, or even if the
process is like flipping a coin.
Expected value
• What number do we use for BCA when we don’t know exactly what
will happen (i.e. under uncertainty)?
• Expected value (aka “mean”) of a random variable:
– The integral of the random variable with respect to its probability
measure.
– Discrete random variables:
• the probability-weighted sum of the possible values.
• If we were to observe an infinite sequence of independent draws of
the random variable, the average should converge to the expected
value.
• Possible confusion
– NOT the mode (most probable value).
– “Value” in “expected value” doesn’t refer to “economic” or “monetary” value.
Ross (2007), Hamming (1991)
Working with uncertainty: Expected value
• Expected value of a “random variable”
– A cheerful example:
• Let X represent the annual number of deaths that occur from a
hazardous chemical at a landfill. Ahead of time this number is
unknown.
– E(X) = the expected value of X
= the sum of each possible value X can take, weighted by the
probability it will occur
= X1*Pr(X1) +
, Xi
X2*Pr(X2) + …. + XN*Pr(XN)
, Pr(Xi)
X1 =
X2 =
.
.
XN=X5=
0.27
Expected value:
Who wants to be a millionaire?!
• Suppose you’ve already won
$64K.
• You are facing a tough
question for $125K.
• Your choices
$125K
– 1) Quit and walk away with $64K
– 2) Try to answer the question. If
you get it right you win $125K; if
you get it wrong you get $0.
• What is the best choice?
– What option provides the
greatest “expected value of NB”
or ENB?
h/t: Shuzo Takahashi, UND
Expected value:
Who wants to be a millionaire?!
• What are the ENB (expected net
ben.) of your two choices?
$125K
– 1) Quit and walk away with $64K
ENB(quit) = 1*64 = 64 (only 1 possibility)
– 2) Try to answer the question. If you
get it right you win $125K; if you get it
wrong you get $0.
ENB(answer) = Pr(correct)*125 +
Pr(wrong)*0
Suppose Pr(correct) = 0.52.

Pr(wrong) = 1-Pr(correct) = 0.48.
Then ENB(answer) = 0.52*125 + 0.48 *0
= $65K
$65K=ENB(answer) > ENB(quit)=$64K
h/t: Shuzo Takahashi, UND
Federal guidance in A-4
• “Your analysis should provide sufficient information for decision
makers to grasp the degree of scientific uncertainty and the
robustness of estimated probabilities, benefits, and costs to changes
in key assumptions” (U.S. OMB 2003, p. 40).
– because of the potential compounding of high-end or low-end
assumptions in developing benefits estimates, the analyst,
decision makers, and the public cannot know without a
quantitative uncertainty analysis whether the estimates provided
by an RIA are within the ballpark of likely effects
• “…virtually no (regulatory impact analyses) provided a full
characterization of uncertainty” (Fraas and Lutter, 2011).
“How to Lie with Benefit-Cost Analysis”
where to look to critique an analysis
• Fiddle with the definition of baselines so that benefits of regulation
are enlarged or costs are diminished (e.g. 2008 lead standard)
• Omit impacts or costs that do not support your cause
• Use upper- or lower-bound estimates of benefits or costs.
• Omit alternatives that you don't wish to see implemented.
• Limit the monetization of benefits to make it difficult to compare
benefits to costs.
• Use discounting assumptions that distort benefits or costs.
Six (“required”) summary
slides to review outside of
class:
Summary of theoretical foundations of BCA
Basics:
• Benefits: increases in human well-being
(utility).
• Costs: reductions in human well-being.
• For a project or policy to qualify on costbenefit grounds:
– Versus the status quo: its social benefits must
exceed its social costs (NB>0).
– Versus a set of alternatives: it must have the
highest net benefits (be most efficient)
(Pearce et al. 2006, Ch. 2)
Summary of theoretical foundations of BCA
Scope and aggregation
• “Society” is simply the aggregation of individuals.
• Geographical boundary: often national (but can be local or int’l)
• Aggregating benefits across different social groups or nations can
involve summing willingness to pay/accept (WTP, WTA), either
1. regardless of the circumstances of the beneficiaries or losers
OR
2. with higher weights to disadvantaged or low income groups
• [Rationale: marginal utilities of income will vary, being higher
for the low income group]
(Pearce et al. 2006, Ch. 2)
Summary of theoretical foundations of BCA
• Time
– Aggregating over time involves discounting
• Establishing the weight placed on future benefits and costs relative to today
– Discounted future benefits and costs are known as “present values”
– Inflation should be accounted for (convert nominal values to real values
with respect to a reference year) before discounting is applied.
• Valuation
– The notions of WTP and WTA are firmly grounded in the theory of
welfare economics
•
(Correspond to economic notions of compensating and equivalent variations)
– WTP and WTA can diverge, sometimes substantially, and with WTA > WTP.
(Pearce et al. 2006, Ch. 2)
Two sides of the BCA coin:
"….benefit-cost analysis has a solid
methodological footing and provides a valuable
performance measure for an important
governmental function, improving the well-being of
society.
...
However, benefit-cost analysis requires analytical
judgments which, if done poorly, can obfuscate an
issue or worse, provide a refuge for scoundrels
in the policy debate.“
Farrow and Toman (1999)
The consensus view of economists on BCA:
Exceptionally useful for policy analysis, but (1) not
always essential, and (2) not sufficient on it’s own-other types of analysis are important.
“Although …benefit–cost analysis
• should not be viewed as either necessary or sufficient for
…public policy,
• it can provide an exceptionally useful framework for
– consistently organizing disparate information,
• …greatly improve the process and, hence, the outcome
of policy analysis.”
Arrow KJ, Cropper ML, Eads GC, Hahn RW, Lave LB, Noll RG, Portney PR, Russell M, Schmalensee R, Smith VK, et al. Is there a role for benefit-cost analysis in
environmental, health, and safety regulation? Science 272:221-222 (1996).
How BCA can improve policy
Hahn & Dudley (2007)
• Efficiency: help decision makers select policies with positive net
social benefits
• Equity: identify the likely winners and losers as a result of a policy
• Uncertainty: evaluate the impact of uncertainty on the net benefits of
different policies,
• Learning: assess the potential value of new information
(Stokey and Zeckhauser 1978; Raiffa, 1970)
• Ignorance: can also help identify key deficiencies in our
understanding
• Sensitivity: show how sensitive the results are to different
assumptions
(Viscusi and Hamilton, 1999)
Optional additional material
Criticism: theoretical foundations
• The extent to which CBA rests on robust theoretical
foundations as portrayed by the Kaldor-Hicks
compensation test.
• The fact that the underlying “social welfare function” in
CBA is one of an arbitrarily large number of such
functions on which consensus is unlikely to be achieved.
• The extent to which one can make an ethical case for
letting individuals’ preferences be the (main) determining
factor in guiding social decision rules.
(Pearce et al. 2006, Ch. 2)
Dilbert on discounting:
Uncertainty and decision-making
• Descriptive (“positive”) application:
NRC (Chp. 6, 2004)
– Under deterministic outcomes: individuals
seek to maximize their utility
– Under uncertainty: maximize their expected
utility
• A sum of utility at each possible outcome weighted
by the probability that outcome will occur
• Prescriptive (“normative”) application
– Advocate decision which maximizes expected
utility or expected net benefits.
Estimating a social discount rate
Option 2: Ramsey Framework
Ramsey (1928) optimal growth model equation:
Economy operates as if a “representative agent” selects
consumption and savings to max NPV of the stream of
utility from consumption over time.
• r = ρ + ƞg
• r: real return to capital, long-run equilibrium
• ρ: pure rate of time preference
“time discount rate”, due to “impatience”
• ƞ: elasticity of marginal utility w.r.t. consumption
• g: average growth in consumption per capita
Estimating a social discount rate
Option 2: Ramsey Framework
•
r: real return to capital, long-run equilibrium; ρ: pure rate of time preference;
ƞ: elasticity of marginal utility w.r.t. consumption;
g: average growth in consumption per capita
1. Descriptive approach/Nordhaus & the DICE model
• Use economic data to estimate parameters:
• Nordhaus (2008):
• r = ρ + ƞg = 0.04 (average over the next century (Nordhaus, 2008, 10))
–
5.5% over first 50 years (61).
• Economic growth and population growth will slow, rate will fall over time.
2. Prescriptive approach/Stern & the Stern Review (2006)
• Argument: No ethical reason to discount future generations due to a
pure rate of time preference except for the possibility that we might not
be here at all (ρ reflects only ann. prob. of extinction). 1.3% growth
assumed.
• r = ρ + ƞg = 0.001 + 1*0.013 = 0.014