1. 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 11 th 2010

2. Co-Authors Dave KrantzKatherine ThompsonElke Weber

3. The Discounting Bandwagon

4. Incidence of discounting at BDRM 2010 10% (7 out of 69 talks)

5. 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

6. (figure courtesy of Olivola & Wang, 2009)

7. Matching Choice: Multiple Staircase Choice: Titration

8. So, what are matching, titration, and multiple staircase?

9. 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

10. Choice: Titration Please choose which option you prefer in each pair: 1. Receive $300 immediately ORReceive $250 ten years from now 2. Receive $300 immediately ORReceive $475 ten years from now 3. Receive $300 immediately ORReceive $900 ten years from now...

11. Choice: Multiple Staircase Dynamic version of titration Funnels into the indifference point Adapted from psychophysics (Gracely et al, 1988)

12. 1. Receive $300 immediately ORReceive $7,700 ten years from now

13. 2. Receive $300 immediately ORReceive $1,750 ten years from now

14. 3. Receive $300 immediately ORReceive $6,500 ten years from now

15. ...

16. *Multiple* Staircase? Several different staircases are interleaved, to reduce order effects or false consistency

17. Matching! Multiple Staircase! Titration!

18. Questions How do they differ in discount rates?...for novel and complex scenarios? How well do they predict consequential intertemporal choices?

19. Participants 316 US residents, recruited and run online mean age = 41 (SD = 14) paid $8, plus lottery

20. 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

21. 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...

22. Financial Gain Questions Receive $300 immediately ORReceive $7,700 ten years from now

23. 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=.35.00.10.20.30.40.50.60 matchingmultiple-stairstitration discount rate gain loss

24. Why does this happen?

25. 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

26. 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 $230

27. 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 $410 $250$390 $250$370 $250$350 $250$330 $250$310 $250$290 $250$270 $250 $230 80% 16%

28. Anchoring effects Obviously range matters Order also matters (Ariely et al, 2003)

29. 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

30. Titration Scale: Two Orders interaction: F(1,76)=4.8, p<.05

31. But matching is not immune to anchoring either...

32. 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=.2.00.10.20.30.40.50.60.70.80.90 1.00 matchingmatching, after m- staircase matching, after titration discount rate gain loss

33. Matching! Multiple Staircase! Titration! Minimal Anchoring

34. Matching! Multiple Staircase! Titration! Part 2: Easy to Use?

35. 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...

36. 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...

37. 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 -.20 -.10.00.10.20.30.40.50 matchingmultiple-stairstitration discount rate gain loss

38. Matching! Multiple Staircase! Titration! Easily Usable

39. Matching! Multiple Staircase! Titration! Part 3: Predicting Consequential Intertemporal Choices

40. Consequential Choice $100 now, or $200 next year? Logistic regressions, using 1-year discount rates to predict choosing the future $200: betap-value (2-tailed) r2r2 matching-0.7.07.04 m-staircase-0.4.11.05 titration-0.5<.01.18

41. Life Choice Do you smoke? Y/N Logistic regressions, using 1-year discount rates to predict smoking: betap-value (1-tailed) r2r2 matching0.05.43.00 m-staircase0.10.35.00 titration0.29.04.05 (consistent with Chabris et al, 2008; Reimers et al, 2009)

42. Matching! Multiple Staircase! Titration! Predicts Consequential Intertemporal Choices

43. Conclusions Dynamic, multiple-staircase method not any better than simple titration Order and range of choice options matters for discount rates, too

44. Summary Minimal anchoring Unlimited range Quick Easy for participants to answer Predicts consequential choices Matching Titration

45. 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)

46. Special Thanks To... NSF grant SES-0820496 PAM lab & CRED lab The Center for Decision Sciences

47. Thank You!

48. 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, & 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.

49. Extra Slides

50. Timing M-Staircase participants took 380s longer than titration participants (54s longer per timescale)

51. 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

52. 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

53. Median Indifference Points: $300 gain 1-year10-years50-years matching5002,30010,000 m-staircase5554,36799,794 titration3632,52565,000

54. Median Indifference Points: $300 loss 1-year10-years50-years matching3405701,300 m-staircase3381,4032,817 titration3636881,325

55. Mean Indifference Points: $300 gain 1-year10-years50-years matching565404779,354 m-staircase3,18911,62670,606 titration5,71722,02363,250

56. Mean Indifference Points: $300 loss 1-year10-years50-years matching4281,27212,975 m-staircase7035,76710,768 titration5,1893,17012,227

57. Median Indifference Points: air gain now1-year10-years50-years matching1,000 1,5001,000 m- staircase 5,1623,71730241 titration3,6501,450563395

58. Median Indifference Points: air loss now1-year10-years50-years matching500 250 m- staircase 5,1615,1292,5811,230 titration3,6501,450

59. Mean Indifference Points: air gain now1-year10-years50-years matching 67,661122,51514,616,9054,446,030 m- staircase 27,56621,6416,9142,930 titration 19,58414,29812,31313,278

60. Mean Indifference Points: air loss now1-year10-years50-years matching 1,2351,2571,8144,019* m- staircase 18,95719,07712,75512,222 titration 30,73427,68122,93020,790 With 1 outlier removed. Otherwise, it would be 119 billion.

66. Correlations of indifference points delayrhop m-staircase w/ matching1 year.42<.01 m-staircase w/ matching10 years.59<.01 m-staircase w/ matching50 years.3<.01 titration w/ matching1 year.49<.01 titration w/ matching10 years.66<.01 titration w/ matching50 years.26<.01