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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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