How to measure discount rates? An experimental comparison

How to measure discount rates? An experimental comparison

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 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! 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 $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 $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 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) 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 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, & ODonoghue, 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: Spearmans

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: Spearmans 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 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 titration 14,298 12,313 13,278 19,584 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 titration 27,681 22,930 20,790 30,734

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

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