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Individual decision-making experiments with risk and intertemporal choice

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Abstract

Many decisions require tradeoffs over time and in the presence of risk. To examine interactions between risk and intertemporal effects we developed a laboratory experiment. In the experiment, subjects choose between payoffs that take place at different points in time. We find that very few subjects are consistently risk averse or risk loving. Instead, we find that subjects are less patient in the presence of risk. We also find that increased risk decreases subjects’ patience levels. However, we do not find evidence that the effect of risk on the intertemporal decision depends on the length of the temporal delay.

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Notes

  1. Holt and Davis (1993) provide a summary of experimental studies of individual decision making with risk.

  2. A few experimental studies have examined dynamic (as opposed to intertemporal) decision making under uncertainty (see, for example, Cubitt et al. (2003)). These experiments focus on sequential decisions, rather than decisions that include a time delay.

  3. In addition to preferences regarding the timing of payments, subjects might also have preferences regarding when the uncertainty is resolved. Chew and Ho (1994) report evidence that subjects prefer to delay resolution in hypothetical survey questions about tax refunds and payments. Alternatively, Wu (1999) presents a theoretical model that separately captures the disutility of delayed consumption and the disutility of delayed uncertainty resolution. Our experimental design does not allow us to make this distinction since the resolution of risk is delayed in all cases. We chose this design because, as Wu notes, “delayed resolution is the norm for many important decisions (p. 161).”

  4. Actual payment dates (e.g., October 21) were used in the experiment rather than delays (e.g., 2 weeks). Read et al. (2005) present evidence that discount rates are lower when dates, rather than delays, are used to describe future payments.

  5. This aspect of the experimental design follows the design used by Coller et al. (2003).

  6. See Smith (1969) and Ford and Ghose (1995) for examples of Ellsberg experiments without a time component.

  7. For the 14 and 28 day designs we used two different sets of payoff structures because we wanted to make sure that our results were robust to different payment choices. For example, in the 14.1 treatment subjects were never given a choice between $20 and $21 or between $20 and $25. In the 14.2 treatment, subjects were offered these choices (but not others). As discussed in the results section, we did not find any statistically significant differences between the 14.1 and 14.2 treatments and between the 28.1 and 28.2 treatments, so we chose to not conduct a second 56 day treatment.

  8. We used an on-line survey instrument developed by Charles Holt to collect the data. Subjects were tracked by an identification number that was linked to the subject’s computer location but not to the subject’s identity. See http://veconlab.econ.virginia.edu/guide.php for a discussion of the on-line instrument.

  9. Goeree et al. (2002) discuss how a series of decisions made by a subject can be analyzed as multiple one-shot games when subjects are presented with all of the decisions at once and do not receive feedback about the outcomes of their decisions.

  10. Randomly selecting one of the scenarios to “play” is a common practice and has been shown by Camerer (1989) and Starmer and Sugden (1991) to provide approximately the same results as when subjects only make one decision. Thus it allows the experimenter to collect additional data at no increased cost and to minimize wealth effects. Furthermore, it minimizes any possible order effects since subjects only receive feedback about the outcome of one decision.

  11. Statistical significance was evaluated using two-tail Fisher Exact Probability test.

  12. More specifically, for a given value of the Option B payment, there are no statistically significant differences in the frequency with which Option B is chosen between the 14.1 and 14.2 treatments and the 28.1 and 28.2 treatments according to a two-tail Fisher Exact Probability test at the 95% confidence level.

  13. According to a t-test with a 90% confidence level.

  14. We use a random effects model rather than a fixed effects model because several of the variables of interest do not vary for a given subject (e.g., the length of the temporal delay) and fixed effects models cannot include such variables. Additionally, we would not be able to include any observations from subjects that always choose the same option because the fixed effect would perfectly predict the outcome for those subjects.

  15. The xtprobit command uses a Gauss–Hermite quadrature procedure to evaluate the log-likelihood function. (See Butler and Moffitt (1982) for a discussion of this model.) For all of the regressions reported, we estimated the model using 100 quadrature points and used the quadchk command in Stata to confirm that the quadrature was stable.

  16. The correlation coefficient between the two variables is 0.92.

  17. More specifically, \(\rho = \frac{{\sigma _\upsilon ^2 }}{{\sigma _\upsilon ^2 + 1}}\) where \(\sigma _\upsilon ^2 \) is the subject-specific variance.

  18. No subjects chose Option A for all 25 scenarios.

  19. Subjects that always choose Option B also exhibit behavior that is consistent with certainty equivalence. However, there are alternative explanations for their behavior such as a low discount rate.

  20. For the 75:25 lottery, we calculated the standard deviation for the following set of values {$16, $16, $16, $32}.

  21. However, for one scenario the difference was statistically significant at the 90% confidence level.

  22. For the scenario in question, Option A was a 75:25 lottery between $48 and $96 for the High Payoff treatment and between $16 and $32 for the 14.2 treatment. Option B was a 50:50 lottery between $60 and $72 for the High Payoff treatment and between $20 and $24 for the 14.2 treatment. Nine out of 32 subjects chose Option A in the High Payoff treatment while only two out of 35 subjects chose Option A in the 14.1 treatment.

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Author information

Authors and Affiliations

  1. Department of Economics, College of William and Mary, Williamsburg, VA, 23187, USA

    Lisa R. Anderson & Sarah L. Stafford

Authors
  1. Lisa R. Anderson
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  2. Sarah L. Stafford
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Corresponding author

Correspondence to Lisa R. Anderson.

Additional information

Financial support from the National Science Foundation (SES-0344732) is gratefully acknowledged.

Appendix A: Sample instructions

Appendix A: Sample instructions

This is an experiment in the economics of decision making. At the end of the session today, you will each receive $5 in cash for showing up. In addition, you will earn more money based on your decisions. Specifically, you will be making choices between two options, such as those represented as “Option A” and “Option B” in Scenario 1 below.

  1. 1.

    Scenario 1. Please choose between the following options:

    • ○ Option A: on October 21 receive $20

    • ○ Option B: on November 4 receive $22

    Notice that you will choose to receive your additional earnings for the decision making phase of this experiment on one of two possible payment days. Option A is always payable on October 21 and Option B is always payable on November 4. The payment sessions are always during the same time period and on the same day of the week as the session you are currently attending. The payment session will require only 15 min of your time.

    In some cases, such as Scenario 2 below, you will be choosing between lotteries and the money prizes will be determined by drawing colored balls from a container. For example, in Scenario 2 below, if you choose Option A, you will return on October 21 and you will have a 50 in 100 chance of earning $18 and a 50 in 100 chance of earning $22. Specifically, we will draw one ball from a container with 50 Gold balls and 50 Purple balls. Similarly, if you choose Option B you will return on November 4 and will have a 50 in 100 chance of earning $20 and a 50 in 100 chance of earning $24.

  2. 2.

    Scenario 2. Please choose between the following options:

    • ○ Option A: on October 21 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on November 4 receive $20 if a Red ball is drawn (50 out of 100) OR receive $24 if a Navy ball is drawn (50 out of 100)

    Even though you will make 25 decisions, only one of these will end up being used. The selection of the scenario for which you will be paid will be determined at the end of the experiment today by drawing a numbered bingo ball from a container. The container has 25 balls numbered 1 through 25, so no decision is any more likely to be used than any other. You will not know before making your decisions which scenario will be selected, so please think about each one carefully. At the completion of the session today, we will present you with your $5 show up fee and a payment certificate that you must bring with you to your payment session. If you are unable to return on your payment day, you may send someone in your place. However, it is essential that you (or the person you send in your place) bring the certificate to your payment session.

1.1 Summary

  1. Step 1:

    Making Decisions: On the computer screen in front of you, you will see a list with 25 scenarios and five follow up questions. Make your choice by clicking on the buttons on the left, option A or option B, for each of the 30 questions. You may make these choices in any order and change them as much as you wish until you press the “Submit” button at the bottom of the screen.

  2. Step 2:

    The Relevant Scenario: Once everyone has submitted answers to all 30 questions, one of the 25 scenarios will be selected at random by drawing a numbered ball from a container, and the Option that you chose for that particular scenario will be recorded on a payment certificate. Please think about each decision carefully, since each of the 25 scenarios is equally likely to end up being the one that is used to determine payoffs. Notice that the five follow-up questions at the end are not relevant for your earnings.

  3. Step 3:

    Determining the Payoff: If you chose Option A for the scenario selected for payment, you will report to Morton 305 on October 21 with your payment certificate. If you chose Option B for the scenario selected, you will report to Morton 305 on November 4 with your payment certificate. If your payment involves a lottery, we will conduct the lottery on the day you return by drawing colored balls from a container. The scenario chosen today (in Step 2) will inform you whether or not your payoff involves a lottery and, if so, the colors and proportions of balls in the container and the payoff associated with each color. You will be paid in cash on your payment day. Each payment certificate has been personally guaranteed by both Professor Anderson and Professor Stafford of the William and Mary Economics Department.

Are there any questions?

1.2 Sample Questionnaire

Welcome statement: Please answer all 30 questions, then wait quietly at your desk until everyone has finished.

  1. 1.

    (Scenario 1) Scenario 1. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $22

  2. 2.

    (Scenario 2) Scenario 2. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $24

  3. 3.

    (Scenario 3) Scenario 3. Please choose between the following options:

    • ○ on November 19 receive $20

    • ○ Option B: on December 3 receive $26

  4. 4.

    (Scenario 4) Scenario 4. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $28

  5. 5.

    (Scenario 5) Scenario 5. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $30

  6. 6.

    (Scenario 6) Scenario 6. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $20 if a Red ball is drawn (50 out of 100) OR receive $24 if a Navy ball is drawn (50 out of 100)

  7. 7.

    (Scenario 7) Scenario 7. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $16 if a Pink ball is drawn (50 out of 100) OR receive $28 if a Yellow ball is drawn (50 out of 100)

  8. 8.

    (Scenario 8) Scenario 8. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $22 if a Purple ball is drawn (50 out of 100) OR receive $26 if a Black ball is drawn (50 out of 100)

  9. 9.

    (Scenario 9) Scenario 9. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $24 if a Navy ball is drawn (50 out of 100) OR receive $28 if a Yellow ball is drawn (50 out of 100)

  10. 10.

    (Scenario 10) Scenario 10. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $20 if a Red ball is drawn (75 out of 100) OR receive $28 if a Yellow ball is drawn (25 out of 100)

  11. 11.

    (Scenario 11) Scenario 11. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $20 if a Red ball is drawn (75 out of 100) OR receive $36 if a White ball is drawn (25 out of 100)

  12. 12.

    (Scenario 12) Scenario 12. Please choose between the following options:

    • ○ Option A: on November 19 receive $20]

    • ○ Option B: on December 3 receive $16 if a Pink ball is drawn (25 out of 100) OR receive $20 if a Red ball is drawn (25 out of 100) OR receive $26 if a Black ball is drawn (50 out of 100)

  13. 13.

    (Scenario 13) Scenario 13. Please choose between the following options:

    • ○ Option A: on November 19 receive $20

    • ○ Option B: on December 3 receive $16 if a Pink ball is drawn (50 out of 100) OR receive $28 if a Yellow ball is drawn (25 out of 100) OR receive $36 if a White ball is drawn (25 out of 100)

  14. 14.

    (Scenario 14) Scenario 14. Please choose between the following options:

    • ○ Option A: on November 19 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $22

  15. 15.

    (Scenario 15) Scenario 15. Please choose between the following options:

    • ○ Option A: on November 19 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $24

  16. 16.

    (Scenario 16) Scenario 16. Please choose between the following options:

    • ○ Option A: on November 19 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $26

  17. 17.

    (Scenario 17) Scenario 17. Please choose between the following options:

    • ○ Option A: on November 19 receive $16 if a Pink ball is drawn (75 out of 100) OR receive $32 if an Orange ball is drawn (25 out of 100)

    • ○ Option B: on December 3 receive $24

  18. 18.

    (Scenario 18) Scenario 18. Please choose between the following options:

    • ○ Option A: on November 19 receive $12 if a Clear ball is drawn (50 out of 100) OR receive $24 if a Navy ball is drawn (25 out of 100) OR receive $32 if an Orange ball is drawn (25 out of 100)

    • ○ Option B: on December 3 receive $24

  19. 19.

    (Scenario 19) Scenario 19. Please choose between the following options:

    • ○ Option A: on November 19 receive $12 if a Clear ball is drawn (25 out of 100) OR receive $20 if a Red ball is drawn (25 out of 100) OR receive $24 if a Navy ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $22

  20. 20.

    (Scenario 20) Scenario 20. Please choose between the following options:

    • ○ Option A: on November 19 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $20 if a Red ball is drawn (50 out of 100) OR receive $24 if a Navy ball is drawn (50 out of 100)

  21. 21.

    (Scenario 21) Scenario 21. Please choose between the following options:

    • ○ Option A: on November 19 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $22 if a Purple ball is drawn (50 out of 100) OR receive $26 if a Black ball is drawn (50 out of 100)

  22. 22.

    (Scenario 22) Scenario 22. Please choose between the following options:

    • ○ Option A: on November 19 receive $18 if a Gold ball is drawn (50 out of 100) OR receive $22 if a Purple ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $20 if a Red ball is drawn (75 out of 100) OR receive $36 if a White ball is drawn (25 out of 100)

  23. 23.

    (Scenario 23) Scenario 23. Please choose between the following options:

    • ○ Option A: on November 19 receive $16 if a Pink ball is drawn (75 out of 100) OR receive $32 if an Orange ball is drawn (25 out of 100)

    • ○ Option B: on December 3 receive $20 if a Red ball is drawn (50 out of 100) OR receive $24 if a Navy ball is drawn (50 out of 100)

  24. 24.

    (Scenario 24) Scenario 24. Please choose between the following options:

    • ○ Option A: on November 19 receive $12 if a Clear ball is drawn (25 out of 100) OR receive $20 if a Red ball is drawn (25 out of 100) OR receive $24 if a Navy ball is drawn (50 out of 100)

    • ○ Option B: on December 3 receive $16 if a Pink ball is drawn (25 out of 100) OR receive $20 if a Red ball is drawn (25 out of 100) OR receive $26 if a Black ball is drawn (50 out of 100)

  25. 25.

    (Scenario 25) Scenario 25. Please choose between the following options:

    • ○ Option A: on November 19 receive $12 if a Clear ball is drawn (50 out of 100) OR receive $24 if a Navy ball is drawn (25 out of 100) OR receive $32 if an Orange ball is drawn (25 out of 100)

    • ○ Option B: on December 3 receive $16 if a Pink ball is drawn (50 out of 100) OR receive $28 if a Yellow ball is drawn (25 out of 100) OR receive $36 if a White ball is drawn (25 out of 100)

  26. 26.

    (Follow-up Question 1) Follow-up Question 1: Are you

    • ○ Male

    • ○ Female

  27. 27.

    (Follow-up Question 2) Follow-up Question 2: Have you smoked a cigarette in the past week?

    • ○ Yes

    • ○ No

  28. 28.

    (Follow-up Question 3) Follow-up Question 3: Do you currently have a credit card?

    • ○ Yes

    • ○ No

  29. 29.

    (Follow-up Question 4) Follow-up Question 4: Are you financing any of your college education through loans?

    • ○ Yes

    • ○ No

  30. 30.

    (Follow-up Question 5) Follow-up Question 5: What area does your major (or intended major) fall under?

    • ○ Business or Economics

    • ○ Humanities (e.g. English, Philosophy, Modern Languages, Religion, Art, Classics, etc.)

    • ○ Social Science (e.g. Anthropology, Government, Public Policy, Sociology, Psychology, etc.)

    • ○ Science (e.g. Biology, Chemistry, Physics, Geology, etc.)

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Anderson, L.R., Stafford, S.L. Individual decision-making experiments with risk and intertemporal choice. J Risk Uncertain 38, 51–72 (2009). https://doi.org/10.1007/s11166-008-9059-4

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