Transcript How to measure discount rates? An experimental

How to measure discount
rates?
An experimental comparison of
three methods
David Hardisty, Katherine Thompson, Dave Krantz, & Elke Weber
Columbia University
2010 Behavioral Decision Research in Management Conference
June 11th 2010
Co-Authors
Katherine Thompson
Dave Krantz
Elke Weber
discount* papers / psycholog* papers
The Discounting Bandwagon
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
1980
1985
1990
1995
2000
2005
Incidence of discounting at BDRM
2010
10%
(7 out of 69 talks)
What is Discounting?
• We discount the value of future events
• Example: with a 10% discount rate, $100
delayed one year is worth the same as
$90 today
• Multiple factors determine discounting
behavior
(figure courtesy of Olivola & Wang, 2009)
Matching
Choice:
Multiple Staircase
Choice:
Titration
So, what are matching, titration,
and multiple staircase?
Matching
Please fill in the amount that would make
the following two options equally attractive:
A. Receive $300 immediately
B. Receive $____ ten years from now
Choice: Titration
Please choose which option you prefer in each
pair:
1. Receive $300
immediately
2. Receive $300
immediately
OR
3. Receive $300
immediately
OR
OR
...
Receive $250 ten
years from now
Receive $475 ten
years from now
Receive $900 ten
years from now
Choice: Multiple Staircase
• Dynamic version of titration
• Funnels into the indifference point
• Adapted from psychophysics (Gracely et
al, 1988)
1.
Receive $300
immediately
OR
Receive $7,700
ten years from
now
2.
Receive $300
immediately
OR
Receive $1,750
ten years from
now
3.
Receive $300
immediately
OR
Receive $6,500
ten years from
now
...
*Multiple* Staircase?
• Several different staircases are
interleaved, to reduce order effects or
false consistency
Matching!
Multiple
Staircase!
Titration!
Questions
• How do they differ in discount rates?
• ...for novel and complex scenarios?
• How well do they predict consequential
intertemporal choices?
Participants
• 316 US residents, recruited and run online
• mean age = 41 (SD = 14)
• paid $8, plus lottery
Methods Overview
• 3 x 2 x 3 x 2 mixed design
• 3: between subjects: matching (n=154),
titration (n=82), or staircase (n=80)
• 2: between subjects: gain or loss
• 3: within subjects: delay of 1, 10, or 50
years
• 2: within subjects: financial or air quality
Financial Gain Scenario
Imagine the city you live in has a budget
surplus that it is planning to pay out as
rebates of $300 for each citizen. The city is
also considering investing the surplus in
fixed-interest endowment funds that will
mature at different possible times in the
future. Investing in a fund would allow the
city to offer rebates of a different amount, to
be paid when the fund matures...
Financial Gain Questions
Receive $300
immediately
OR
Receive $7,700
ten years from
now
Mean Discount Rates
.60
discount rate
.50
.40
gain
loss
.30
.20
.10
.00
matching
multiple-stairs
titration
method: F(2,307)=9.3, p<.001; sign: F(1,307)=13.7, p<.001; interaction: F(2,307)=1.1, p=.35
Why does this happen?
Titration Scale
Note: staircases used the same range as titration
$300
$300
$300
$300
$85,000
$45,000
$23,500
$12,000
$300
$300
$300
$6,400
$3,300
$1,750
$300
$900
$300
$300
$475
$250
Titration Scale from Hardisty &
Weber (2009), Study 2
$250
$250
$250
$250
$410
$390
$370
$350
$250
$250
$250
$330
$310
$290
$250
$270
$250
$250
$250
$230
1-year discount rate for present
study vs Hardisty & Weber (2009)
$300
$85,000
$250
$410
$300
$45,000
$250
$390
$300
$23,500
$250
$370
$300
$12,000
$250
$350
$300
$6,400
$250
$330
$300
$3,300
$250
$310
$300
$1,750
$250
$290
$300
$900
$250
$270
$300
$475
$250
$250
$300
$250
$250
$230
80%
16%
Anchoring effects
• Obviously range matters
• Order also matters (Ariely et al, 2003)
Titration Scale: Two Orders
$300
$85,000
$300
$250
$300
$45,000
$300
$475
$300
$23,500
$300
$900
$300
$12,000
$300
$1,750
$300
$6,400
$300
$3,300
$300
$3,300
$300
$6,400
$300
$1,750
$300
$12,000
$300
$900
$300
$23,500
$300
$475
$300
$45,000
$300
$250
$300
$85,000
Titration Scale: Two Orders
.70
mean discount rate
.60
.50
.40
high first
low first
.30
.20
.10
.00
gain
loss
interaction: F(1,76)=4.8, p<.05
But matching is not immune to
anchoring either...
discount rate
Order Effects: On Matching
1.00
.90
.80
.70
.60
.50
.40
.30
.20
.10
.00
gain
loss
matching
matching, after mstaircase
matching, after
titration
method: F(2,304)=22.1, p<.001; sign: F(1,304)=35.1, p<.001; interaction: F(2,304)=1.6, p=.2
Minimal Anchoring
Matching!
Multiple
Staircase!
Titration!
Part 2:
Easy to Use?
Matching!
Multiple
Staircase!
Titration!
Air Quality Gain Scenario
Imagine the current air quality (measured by
number and size of particulates) in your area
is neither particularly good nor especially
bad. The local government has a budget
surplus that it will either return to the citizens
as rebates, or spend to enact various policy
and infrastructure changes that will lead to a
permanent improvement in air quality. Once
the changes are put into place, the air will
feel surprisingly clean and fresh...
Air Quality Gain Questions
Please fill in the amount that would make the
following options equally attractive:
A. Improved air quality starting now
B. Receive $____ immediately
A. Improved air quality starting one year from now
B. Receive $____ immediately
...
Air Quality Discount Rates
.50
discount rate
.40
.30
.20
gain
loss
.10
.00
-.10
-.20
matching
multiple-stairs
titration
method: F(2,304)=14.3, p<.001; sign: F(1,304)=3.7, p=.06; interaction: F(2,304)=4.1, p<.05
Easily Usable
Matching!
Multiple
Staircase!
Titration!
Part 3:
Predicting Consequential
Intertemporal Choices
Matching!
Multiple
Staircase!
Titration!
Consequential Choice
•$100 now, or $200 next year?
Logistic regressions, using 1-year discount rates
to predict choosing the future $200:
beta
r2
matching
-0.7
p-value
(2-tailed)
.07
m-staircase
-0.4
.11
.05
titration
-0.5
<.01
.18
.04
Life Choice
•Do you smoke? Y/N
Logistic regressions, using 1-year discount rates
to predict smoking:
beta
r2
matching
0.05
p-value
(1-tailed)
.43
m-staircase
0.10
.35
.00
titration
0.29
.04
.05
(consistent with Chabris et al, 2008; Reimers et al, 2009)
.00
Predicts Consequential
Intertemporal Choices
Matching!
Multiple
Staircase!
Titration!
Conclusions
• Dynamic, multiple-staircase method not
any better than simple titration
• Order and range of choice options matters
for discount rates, too
Summary
Matching
• Minimal anchoring
• Unlimited range
• Quick
Titration
• Easy for participants
to answer
• Predicts
consequential choices
Other cool elicitation methods
• Evaluating sequences of outcomes
(Chapman, 1996; Guyse, 2002)
• Intertemporal allocation (Frederick, 2008)
• Patience auction (Olivola & Wang, 2009)
• Ask directly for discount rates (Read et al,
working paper)
Special Thanks To...
• NSF grant SES-0820496
• PAM lab & CRED lab
• The Center for Decision Sciences
Thank You!
References
Ariely, D., Loewenstein, G., & Prelec, D. (2003). “Coherent arbitrariness”: Stable demand curves
without stable preferences. The quarterly journal of economics, 118, 73-105.
Chabris, C. F., Laibson, D., Morris, C. L., Schuldt, J. P. & Taubinsky, D. T. (2008). Individual laboratorymeasured discount rates predict field behavior. Journal of Risk and Uncertainty, 37, 237.
Chapman, G. B. (1996). Expectations and preferences for sequences of health and money.
Organizational behavior and decision processes, 67, 59-75.
Frederick, S., Loewenstein, & O’Donoghue, T. (2002). Time discounting and time preference: A critical
review. Journal of Economic Literature, 40, 351-401.
Frederick, S., & Loewenstein, G. (2008). Conflicting motives in evaluations of sequences. Journal of
Risk and Uncertainty, 37, 221-235.
Guyse, J. L., Keller, L. R., & Eppel, T. (2002). Valuing environmental outcomes: Preferences for
constant or improving sequences. Organizational behavior and decision processes, 87, 253-277.
Hardisty, D. J. & Weber, E. U. (2009). Discounting future green: money versus the environment.
Journal of experimental psychology: General, 138, 239-340.
Read, D., Airoldi, M., & Loewe, G. (working paper). Intertemporal tradeoffs priced in interest rates and
amounts: A study of method variance.
Reimers, S., Maylor, E. A., Stewart, N., & Chater, N. (2009). Associations between a one-shot delay
discounting measure and age, income, education and real-world impulsive behavior. Personality
and individual differences, 47, 973-978.
Olivola, C., & Wang, S. (2009). Patience auctions: Novel mechanisms for eliciting discount rates and
the impact of time vs. money framing. Presented at the Center for Decision Sciences.
Extra Slides
Timing
• M-Staircase participants took 380s longer
than titration participants (54s longer per
timescale)
Consequential Choice
• $100 now, or $200 next year?
Nonparametric correlation between 1-year financial
indifference point and choosing the future $200:
p-value
matching
Spearman’s
rho
-.174
m-staircase
-.384
<.001
titration
-.374
<.001
<.05
Consequential Choice
• Do you smoke?
Nonparametric correlation between 1-year financial
indifference point and smoking:
Spearman’s
rho
matching
.06
2-tailed
p-value
.44
m-staircase
.14
.22
Titration
.16
.15
Median Indifference Points: $300
gain
1-year
10-years
50-years
500
2,300
10,000
m-staircase 555
4,367
99,794
titration
2,525
65,000
matching
363
Median Indifference Points: $300
loss
1-year
10-years
50-years
340
570
1,300
m-staircase 338
1,403
2,817
titration
688
1,325
matching
363
Mean Indifference Points: $300
gain
1-year
10-years
50-years
565
4047
79,354
m-staircase 3,189
11,626
70,606
titration
22,023
63,250
matching
5,717
Mean Indifference Points: $300
loss
1-year
10-years
50-years
428
1,272
12,975
m-staircase 703
5,767
10,768
titration
3,170
12,227
matching
5,189
Median Indifference Points: air gain
now
1-year
10-years 50-years
matching 1,000
1,000
1,500
1,000
m5,162
staircase
3,717
302
41
titration
1,450
563
395
3,650
Median Indifference Points: air loss
now
1-year
10-years 50-years
matching 500
500
500
250
m5,161
staircase
5,129
2,581
1,230
titration
1,450
1,450
1,450
3,650
Mean Indifference Points: air gain
now
1-year
10-years
matching 67,661
122,515
14,616,905 4,446,030
27,566
mstaircase
21,641
6,914
2,930
19,584
14,298
12,313
13,278
titration
50-years
Mean Indifference Points: air loss
now
1-year
10-years 50-years
matching 1,235
1,257
1,814
4,019*
18,957
mstaircase
19,077
12,755
12,222
30,734
27,681
22,930
20,790
titration
With 1 outlier removed. Otherwise, it would be 119 billion.
Correlations of indifference points
delay
rho
p
m-staircase w/ matching
1 year
.42
<.01
m-staircase w/ matching
10 years .59
<.01
m-staircase w/ matching
50 years .3
<.01
titration w/ matching
1 year
.49
<.01
titration w/ matching
10 years .66
<.01
titration w/ matching
50 years .26
<.01