how to measure discount rates? an experimental comparison of three methods david hardisty, katherine...
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How to measure discount rates?
An experimental comparison of three methods
David Hardisty, Katherine Thompson, Dave Krantz, & Elke WeberColumbia University2010 Behavioral Decision Research in Management ConferenceJune 11th 2010
Co-Authors
Dave KrantzKatherine Thompson Elke Weber
The Discounting Bandwagon
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1980 1985 1990 1995 2000 2005
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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
OR Receive $250 ten years from now
2. Receive $300 immediately
OR Receive $475 ten years from now
3. Receive $300 immediately
OR 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! MultipleStaircase!
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
method: F(2,307)=9.3, p<.001; sign: F(1,307)=13.7, p<.001; interaction: F(2,307)=1.1, p=.35
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matching multiple-stairs titration
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Why does this happen?
Titration Scale Note: staircases used the same range as titration
$300 $85,000
$300 $45,000
$300 $23,500
$300 $12,000
$300 $6,400
$300 $3,300
$300 $1,750
$300 $900
$300 $475
$300 $250
Titration Scale from Hardisty & Weber (2009), Study 2
$250 $410
$250 $390
$250 $370
$250 $350
$250 $330
$250 $310
$250 $290
$250 $270
$250 $250
$250 $230
1-year discount rate for present study vs Hardisty & Weber (2009)
$300 $85,000
$300 $45,000
$300 $23,500
$300 $12,000
$300 $6,400
$300 $3,300
$300 $1,750
$300 $900
$300 $475
$300 $250
$250 $410
$250 $390
$250 $370
$250 $350
$250 $330
$250 $310
$250 $290
$250 $270
$250 $250
$250 $230
80% 16%
Anchoring effects
• Obviously range matters• Order also matters (Ariely et al, 2003)
Titration Scale: Two Orders
$300 $250
$300 $475
$300 $900
$300 $1,750
$300 $3,300
$300 $6,400
$300 $12,000
$300 $23,500
$300 $45,000
$300 $85,000
$300 $85,000
$300 $45,000
$300 $23,500
$300 $12,000
$300 $6,400
$300 $3,300
$300 $1,750
$300 $900
$300 $475
$300 $250
Titration Scale: Two Orders
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gain loss
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high firstlow first
interaction: F(1,76)=4.8, p<.05
But matching is not immune to anchoring either...
Order Effects: On Matching
method: F(2,304)=22.1, p<.001; sign: F(1,304)=35.1, p<.001; interaction: F(2,304)=1.6, p=.2
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matching matching, after m-staircase
matching, aftertitration
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Matching! MultipleStaircase!
Titration!
Minimal Anchoring
Matching! MultipleStaircase!
Titration!
Part 2:Easy to Use?
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 nowB. Receive $____ immediately
A. Improved air quality starting one year from nowB. Receive $____ immediately
...
Air Quality Discount Rates
method: F(2,304)=14.3, p<.001; sign: F(1,304)=3.7, p=.06; interaction: F(2,304)=4.1, p<.05
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matching multiple-stairs titration
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Matching! MultipleStaircase!
Titration!
Easily Usable
Matching! MultipleStaircase!
Titration!
Part 3:Predicting Consequential
Intertemporal Choices
Consequential Choice
•$100 now, or $200 next year?
Logistic regressions, using 1-year discount rates to predict choosing the future $200:
beta p-value(2-tailed)
r2
matching -0.7 .07 .04
m-staircase -0.4 .11 .05
titration -0.5 <.01 .18
Life Choice•Do you smoke? Y/N
Logistic regressions, using 1-year discount rates to predict smoking:
beta p-value(1-tailed)
r2
matching 0.05 .43 .00
m-staircase 0.10 .35 .00
titration 0.29 .04 .05
(consistent with Chabris et al, 2008; Reimers et al, 2009)
Matching! MultipleStaircase!
Titration!
Predicts Consequential Intertemporal Choices
Conclusions
• Dynamic, multiple-staircase method not any better than simple titration
• Order and range of choice options matters for discount rates, too
Summary
• Minimal anchoring• Unlimited range• Quick
• Easy for participants to answer
• Predicts consequential choices
Matching Titration
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!
ReferencesAriely, 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
laboratory-measured 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:
Spearman’s rho
p-value
matching -.174 <.05
m-staircase -.384 <.001
titration -.374 <.001
Consequential Choice• Do you smoke?
Nonparametric correlation between 1-year financial indifference point and smoking:
Spearman’s rho
2-tailed
p-value
matching .06 .44
m-staircase .14 .22
Titration .16 .15
Median Indifference Points: $300 gain
1-year 10-years 50-years
matching 500 2,300 10,000
m-staircase 555 4,367 99,794
titration 363 2,525 65,000
Median Indifference Points: $300 loss
1-year 10-years 50-years
matching 340 570 1,300
m-staircase 338 1,403 2,817
titration 363 688 1,325
Mean Indifference Points: $300 gain
1-year 10-years 50-years
matching 565 4047 79,354
m-staircase 3,189 11,626 70,606
titration 5,717 22,023 63,250
Mean Indifference Points: $300 loss
1-year 10-years 50-years
matching 428 1,272 12,975
m-staircase 703 5,767 10,768
titration 5,189 3,170 12,227
Median Indifference Points: air gain
now 1-year 10-years 50-years
matching 1,000 1,000 1,500 1,000
m-staircase
5,162 3,717 302 41
titration 3,650 1,450 563 395
Median Indifference Points: air loss
now 1-year 10-years 50-years
matching 500 500 500 250
m-staircase
5,161 5,129 2,581 1,230
titration 3,650 1,450 1,450 1,450
Mean Indifference Points: air gain
now 1-year 10-years 50-years
matching 67,661 122,515 14,616,905 4,446,030
m-staircase
27,566 21,641 6,914 2,930
titration 19,584 14,298 12,313 13,278
Mean Indifference Points: air loss
now 1-year 10-years 50-years
matching 1,235 1,257 1,814 4,019*
m-staircase
18,957 19,077 12,755 12,222
titration 30,734 27,681 22,930 20,790
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