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Individual laboratory-measured discount rates predict field behavior

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Abstract

We estimate discount rates of 555 subjects using a laboratory task and find that these individual discount rates predict inter-individual variation in field behaviors (e.g., exercise, BMI, smoking). The correlation between the discount rate and each field behavior is small: none exceeds 0.28 and many are near 0. However, the discount rate has at least as much predictive power as any variable in our dataset (e.g., sex, age, education). The correlation between the discount rate and field behavior rises when field behaviors are aggregated: these correlations range from 0.09–0.38. We present a model that explains why specific intertemporal choice behaviors are only weakly correlated with discount rates, even though discount rates robustly predict aggregates of intertemporal decisions.

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Notes

  1. Such small influences of specific personality traits is consistent with findings in both the psychological and economic literatures on individual differences, even for well-measured traits such as intelligence (e.g., Ross and Nisbett 1991; Richard et al. 2003; Swann and Selye 2005; Chabris et al. 1998; Barsky et al. 1997; see also Cutler and Glaeser 2005).

  2. Other studies with similar-size samples (e.g., de Wit et al. 2007) have been concerned with correlating discount rates with personality traits, intelligence, and other individual difference measures, rather than with field behaviors.

  3. There is also a nascent literature that relates different field measures of discounting. For example, Cutler and Glaeser (2005) argue that such relationships are weak because field behaviors that have intertemporal consequences have low intra-individual correlations. Scharff and Viscusi (2008) report evidence of field behaviors that have strong relationships at the group level. Our model (Section 3) reconciles these perspectives.

  4. Eighteen additional subjects were tested but were immediately excluded from data analysis for one or more of the following reasons: reported brain injury; reported mental illness; reported drug use; had difficulty understanding directions; was unable to complete the protocol; was previously tested.

  5. The BDI-II has high internal consistency among college students (0.93) and clinical populations (0.92) and adequate validity (Beck et al. 1996).

  6. Each subject brought a lunch, and was randomly assigned to eat that lunch either before or after completing the study (50% chance of being assigned to each condition). This variable was not considered in any of the analyses reported in this paper.

  7. Sixteen additional subjects were tested but were immediately excluded from data analysis for one or more of the following reasons: reporting brain injury, mental illness, or drug use; having difficulty understanding or following directions; not meeting eligibility criteria (such as not being a native English speaker); failing to complete the entire testing session; having data missing for one or more of the cognitive tasks (usually due to equipment failure or experimenter error).

  8. The Web study used a different screening questionnaire than the Weight and Cognition Studies. The Web screen did not ask about several of the exclusion criteria (e.g., mental illness) that were used in those studies.

  9. This criterion was also applied to the other two datasets, but no subjects in those studies were excluded.

  10. We do not use multi-parameter discount functions (e.g., Laibson 1997), because we want to study a discount function with only one free parameter, thereby simplifying the comparison between a person’s unique “discount rate” and their field behavior.

  11. We fix the variance to 1 so that our likelihood function is maximized at a unique value. Over half of the subjects in our dataset had consistent responses that could be rationalized by any \(\alpha \in \lbrack \alpha _{m},\alpha _{M}\rbrack\), for some α m  < α M  ∈ \(\mathbb{R}\). For these subjects, the model would not be identified with a free variance parameter.

  12. For a probit model, for example, Efron’s R 2 is simply \(R^{2}=1-\frac{\sum_{i=1}^{N}(y_{i}-\hat{\pi}_{i})^{2}}{\sum_{i=1}^{n}(y_{i}-\bar{y})^{2}}\), where y i are the observed values, \(\bar{y}\) is their average, and \( \hat{\pi}_{i}\) is the predicted probability.

  13. Scharff and Viscusi (2008) analyze data on workers’ wage-fatality risk tradeoffs and find that smokers’ discount rates are almost twice as high as those of non-smokers.

  14. While dieting is generally considered a health investment, one potential problem with this variable is that a person is more likely to go on a diet if he/she is overweight, which could be due to a high degree of impatience.

  15. We use OLS regressions because the R 2’s of the OLS regressions have a simple interpretation as the square of the correlation and fraction of variance explained. It is not clear what the probit or tobit counterpart should be. However, as Table 3 suggests, nonlinear regression models do not change the results significantly.

  16. Thus the coefficient vectors of the components are extracted as eigenvectors of the correlation (rather than covariance) matrix of the non-standardized variables.

  17. Wealth is measured in relative terms: “compared to your friends who are close to you in age” and “compared to other members of your family in your generation.”

  18. Cutler and Glaeser (2005) present a different but related framework. They make the identifying assumption that each of the domain general traits predicts all (relevant) behaviors with a uniform sign. Our evidence is inconsistent with their assumption. In the Weight study, for example, being female is associated positively with exercising less (r = 0.10) but associated negatively with smoking (r = − 0.18). Because of these considerations, the Cutler-Glaeser approach of using the correlation of two behaviors to derive an upper bound for the correlation between a behavior and a domain general trait (e.g. discounting) is not justified. Therefore, we do not use their framework.

  19. Note that because our studies used convenience samples rather than population samples, all of our variables likely have lower variance than they do in the larger population. However, this observation applies to both sides of our regressions and therefore may not bias our estimates. It is critical that more representative samples be studied in the future.

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Acknowledgements

We thank Kirill Babikov, Ananya Chakravarti, Lee Chung, Alison H. Delargy, Margaret E. Gerbasi, J. Richard Hackman, Jill M. Hooley, Steven E. Hyman, Thomas Jerde, Stephen M. Kosslyn, Melissa A. Liebert, Sarah Murphy, Jacob Sattelmair, Aerfen Whittle, and Anita W. Woolley for their advice, assistance, and support of this research. We acknowledge financial support by a NARSAD Young Investigator Award and DCI Postdoctoral Fellowship awarded to Christopher F. Chabris, an NSF ROLE grant to J. Richard Hackman and Stephen M. Kosslyn, and NIA (P01 AG005842, R01 AG021650) and NSF (0527516) grants to David I. Laibson.

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Correspondence to Christopher F. Chabris.

Appendices

Appendix 1a: Cognitive tests in cognition study

  1. (1)

    A 12-item short form (constructed and validated by Bors and Stokes 1998) of Raven’s Advanced Progressive Matrices, the generally accepted best measure of general fluid intelligence (Jensen 1998).

  2. (2)

    A computerized version of the mental rotation test developed by Shepard and Metzler (1971), in which, on each of 80 trials, subjects must compare two images and decide whether they depict the same three-dimensional object.

  3. (3)

    A six-minute 20-trial paper-and-pencil version of the same mental rotation task developed by Vandenberg and Kuse (1978).

  4. (4)

    A 3-back working memory task developed by Gray et al. (2003) in which subjects view a series of words at a rate of approximately one every three seconds and must decide whether each one is identical to the one presented three earlier in the sequence, which totals 128 trials.

  5. (5)

    A 144-trial version of the Multi-Source Interference Task developed by Bush et al. (2003), which is based on the classic Stroop inhibition test.

  6. (6)

    A test of categorical spatial relations encoding in which subjects must decide on each trial whether a briefly-presented dot is above or below a horizontal bar.

  7. (7)

    A test of coordinate spatial relations encoding, in which subjects see the same type of stimuli as in the previous task, but must decide whether the dot is inside or outside a distance of 8mm from the bar. This task and the categorical task described above each included 96 trials and was based on similar tasks created by Hellige and Michimata (1989).

  8. (8)

    The Verbal Fluency test from the Dellis-Kaplan Executive Function System, which provides a measure of how many different words the participant can generate within certain specified categories in a fixed amount of time. Performance on each task was scored as the percentage of trials answered correctly, except for Verbal Fluency, which was scored as the total number of words generated across six 1-min trials.

Appendix 1b: Cognitive tests in Web study

Tasks 1–9 are adapted from the MRAB (Shephard and Kosslyn 2005) and implemented in PsyScope-FL for online testing. Task 10 was designed specifically for this study, but is based on the first three trials of the Dellis-Kaplan verbal fluency task used in the Cognition Study.

  1. (1)

    Vigilance: measures ability to maintain attention over time (90 trials).

  2. (2)

    Three-Term Reasoning: measures verbal problem-solving ability in resolving standard three-term relational arguments (8 trials).

  3. (3)

    Divided Attention: measures ability to fixate simultaneously on two distinct stimuli or stimulus features (40 trials).

  4. (4)

    Mental Rotation: measures skill at spatial problem solving (32 trials).

  5. (5)

    Verbal Working Memory: measures ability to temporarily store and manipulate verbal information (60 trials).

  6. (6)

    Spatial Working Memory: measures capacity to temporarily store and manipulate spatial information (60 trials).

  7. (7)

    Filtering: measures capacity to focus on target information and ignore task-irrelevant information (84 trials).

  8. (8)

    Perceptual Reaction Time: measures speed of recognition and response to visual material (40 trials).

  9. (9)

    Cognitive Set-Switching: measures ability to sort stimuli according to specific criteria (24 trials).

  10. (10)

    Verbal Fluency: measures level of language skill and verbal processing (3 trials).

Appendix 2a: Health–related variables from the Weight study

Exercise

“Do you exercise regularly? Yes (1); No (0)” “About how many hours per week? 1–3 (3); 3–5; (2) 5+ (1)” “Overall intensity of workouts: Low (3); medium (2); high (1)”

Smoking

“Do you smoke? Yes (1); No (0)?” “About how many packs do you smoke per week?”

Dieting

“Are you currently following a specific diet plan? Yes (1); No (0)?”

Appendix 2b: Health–related variables from the Web study

Exercise

“How many hours per week are you physically active (for example, walking, working around the house, working out)?” “How many of those hours represent exercise primarily intended to improve or maintain your health or fitness?” “If you do any exercise primarily for health or fitness, how would you rate its intensity? Low (3); medium (2); high (1)”

Smoking

“Do you smoke (including cigarettes, cigars, pipes, or anything else)? Yes (1); No (0)” “If you smoke cigarettes, about how many packs do you smoke per week?”

Healthy food choices

“In a typical week, how often do you choose your food (the type and/or amount) with health and fitness concerns in mind? Every meal (1); most meals (2); some meals (3); few meals (4); no meals (5)”

Dental check-ups

“How often do you visit your dentist for a check-up? Two or more time a year (1); once per year (2); less than once per year (3); never (4)”

Prescription drug completion

“When your doctor gives you a prescription to fill at the drugstore (excluding birth control), do you follow it exactly (for example, by going to the drugstore, picking up the medication, taking all of the medication on schedule, and finishing the entire prescription)? Always (1); usually (2); sometimes (3); rarely (4)”

Flossing

“How often do you floss your teeth? At least once per day (1); Most days each week (2); Once or twice each week (3); Rarely or never (4)”

Overeating

“In a typical week, how often do you eat more than you think you should eat? Every meal (5); most meals (4); some meals (3); few meals (2); no meals (1)”

Appendix 2c: Finance-related variables from the Web study

Late credit card payments

“If you have any credit cards, over the past two years how many times were you charged a late fee for making a credit card payment after the deadline? Never (1) ; 1–2 times (2); 3–4 times (3); 5 or more times (4)”

Credit card bill

“If you have any credit cards, over the past two years, how often have you paid your credit card bill in full, as opposed to paying less than the full amount? (Paying in full means carrying no debt to the next month’s bill.) Never pay in full (5); rarely pay in full (4); pay in full about half of the time (3); usually pay in full (2); always pay in full (1)”

Percent saved

“Over the past three years, what percentage of your income have you saved? (Please include savings into retirement plans and any other form of savings that you do.)”

Gambling

“On average, how many days per month do you gamble money, including visiting casinos, buying lottery tickets, betting on sports, playing poker, etc? Never (1); sometimes but rarely (2); 2–5 days per month (3); 6–10 days per month (4); more than 10 days per month (5)”

Wealth accumulation (relative)

“Compared to your friends who are close to you in age, how much wealth have you accumulated? (Wealth includes retirement savings, stocks, bonds, and mutual funds you own, money in bank accounts, the value of your home minus the mortgage, etc.) More than all of my friends (1); more than most (2); about average (3); less than most (4); less than all (5)” “Compared to the other members of your family in your generation-brothers, sisters, and cousins close to your age-how much wealth have you accumulated? More than all (1); more than most (2); about average (3); less than most (4); less than all (5)”

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Chabris, C.F., Laibson, D., Morris, C.L. et al. Individual laboratory-measured discount rates predict field behavior. J Risk Uncertain 37, 237–269 (2008). https://doi.org/10.1007/s11166-008-9053-x

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