Social Discount Rate
12-706 / 19-702
Admin Issues
Pipeline case study writeup - due Monday
Format expectations:
Framing of problem (see p. 7!),
Answer/justify with preliminary calculations
Don’t just estimate the answer!
Do not need to submit an excel printout, but
feel free to paste a table into a document
Length: Less than 2 pages.
Real and Nominal Values
 Nominal: ‘current’ or historical data
 Real: ‘constant’ or adjusted data
Use deflator or price index for real
 Generally “Real” has had inflation/price changes factored
in and nominal has not
 For investment problems:
If B&C in real dollars, use real disc rate
If B&C in nominal dollars, use nominal rate
Both methods will give the same answer
Similar to Real/Nominal :
Foreign Exchange Rates / PPP
Big Mac handout
Common Definition of inputs
Should be able to compare cost across
countries
Interesting results? Why?
What are limitations?
Is it worth to spend $1 million today to
save a life 10 years from now?
How about spending $1 million today so
that your grandchildren can have a
lifestyle similar to yours?
RFF Discounting Handout
How much do/should we care about
people born after we die?
Ethically, no one’s interests should count
more than another’s: “Equal Standing”
Social Discount Rate
 Rate used to make investment decisions for society
 Most people tend to prefer current, rather than future,
consumption
Marginal rate of time preference (MRTP)
 Face opportunity cost (of foregone interest) when we
spend not save
Marginal rate of investment return
Intergenerational effects
We have tended to discuss only short
term investment analyses (e.g. 5 yrs)
Economists agree that discounting should
be done for public projects
Do not agree on positive discount rate
Climate Change
Discussions ongoing about how best to manage
global CO2 emissions to limit effects of global
change.
Should we sacrifice short-run economic growth
to do something to improve environment and
leave resources for the future?
Two Questions
What duty do we have to make sacrifices
for future generations?
If we sacrifice, what is the optimal policy
to maximize benefit?
So we should compare global change
proposals with alternatives
Perhaps higher R&D spending on science or
medicine would have higher benefits!
Government Discount Rates
US Government Office of Management and
Budget (OMB) Circular A-94
http://www.whitehouse.gov/omb/circulars/a09
4/a094.html
Discusses how to do BCA and related
performance studies
What discount, inflation, etc. rates to use
Basically says “use this rate, but do sensitivity
analysis with nearby rates”
OMB Circular A-94, Appendix C
 Provides the current suggested values to use for federal
government analyses
http://www.whitehouse.gov/omb/circulars/a094/a94_appxc.html
Revised yearly, usually “good until January of the next year”
How would the government decide its discount rates?
What is the government’s MARR?
Historic Nominal Interest
Rates (from OMB A-94)
2005
2006
3.7
4.7
4.1
4.8
4.4
4.9
4.6
5.0
5.2
5.2
Real Discount Rates (from A-94)
2005
2006
1.7
2.5
2.0
2.6
2.3
2.7
2.5
2.8
3.1
3.0
What do people think
Cropper et al surveyed 3000 homes
Asked about saving lives in the future
Found a 4% discount rate for lives 100 years
from now
Hume’s Law
Discounting issues are normative vs.
positive battles
Hume noted that facts alone cannot tell
us what we should do
Any recommendation embodies ethics and
judgment
E.g. focusing on ‘highest NPV’ implies net
benefits is only goal for society
Some Issues Arise
Equal standing does not imply different
generations have equal claims to present
resources!
Harsanyi says only do so if their marginal
gain is higher than our loss
If future generations will be better off than us
anyway
Then we might have no reason to make additional
sacrifices
There might be ‘special standing’ in addition to
‘equal standing’
Immediate relatives vs. distant relatives
Different discount rates over time
Why do we care so much about future and ignore some
present needs (poverty)
A Few More Questions
Current government discount rates are
‘effectively zero’
What does this mean for projects and
project selection decisions?
What does it say about intergenerational
effects?
What are implications of zero or negative
discount rates?
Comprehensive Everglades
Restoration Project
Comprehensive project to restore natural
water flow to the Florida Everglades.
Enhance water supply to South Florida
region.
Provide continuous flood protection.
See more info at
http://www.evergladesplan.org/
Indian River Lagoon-South (IRLS)
 Part of Everglades Restoration Project.
 Total Cost of $1.21 billion.
 Annual Benefits of $159 million after project is
completed in 2015.
 Find NPV of first 25 years of project.
IRLS Cash Schedule
$159 per year
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
$0.425
16
17
18
19
20
21
22
23
$2.043
$12.62
All values are in millions
$447.3
$748.3
24
25
NPV of Project
$0
3%
7%
20%
-$100
NPV of Project (Millions)
-$200
-$300
-$400
-$500
-$600
-$700
Discount Rate
What would NPV be if we used a negative discount rate?
NPV of Project
$1,000
$800
$600
NPV of Project (Millions)
$400
$200
$0
3%
7%
20%
-$200
-$400
-$600
-$800
Discount Rate
0%
-1%
Which is the right discount rate?
What are implications of each?
Show of Hands Example
Choice #1:
$50 today or $100 paid 1 year from now?
Why?
Choice #2:
$50 to be paid in 5 years or $100 in 6 years?
Why?
Hyperbolic Discounting
Behavioral economics:
We generally prefer smaller, sooner payoffs
to larger, later payoffs when the smaller
payoffs would be imminent;
When same payoffs are distant in time, we
tend to prefer the larger, even though the time
lag (e.g., 1 year) would be the same
Hyperbolic Discounting
Our “preferences” follow a hyperbolic curve
rather than the conventional, exponential curve
that would produce consistent choice over time
We are time inconsistent (we don’t perceive the
same tradeoff values today vs. in 5+ years)
Recall: Continuous P=F * e-in
P=F /(1+kn)
Where k is still the steepness of our tradeoff
Hyperbolic versus standard
1200
800
600
400
200
time
F-standard
F-hyperbolic
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
Present Value
1000
Hyperbolic DiscountingImplications
If we actually have hyperbolic preferences
What do our discount rates look like?
How would that affect our preferences for
social projects, especially those with long
time horizons?
Time inconsistency known in advance
Next Up:
Friday’s review: more discounting
Loans, taxes, etc.
Monday
Pipeline Case
Sensitivity Analysis