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Risk and time preferences interaction: An experimental measurement

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Abstract

We experimentally characterize and measure the interaction between risk and time preferences. Our results indicate that risk and time preferences are intertwined. We find that decision makers are insensitive to time delay for small probabilities of gains, but become progressively more sensitive to time delay as the probability of gain increases. We compare the fit of existing decision models that capture risk and time preferences. Our results indicate that the models which allow for probability-time interaction and capture magnitude effect fit the data better. We also show that accounting for risk-time preferences interaction leads to lower estimated discount rates.

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Notes

  1. Prelec and Loewenstein (1991) showed that there are many parallels between the impacts of risk and time preferences on decision making.

  2. The model is based on the axiomatic system developed by Chew and Epstein (1990) that extends non-expected utility to temporal prospects.

  3. Magnitude effect implies that people are more patient when discounting larger outcomes.

  4. Andreoni and Sprenger (2012) focus on common ratio property as applied to intertemporal risk and show that different alternatives to DEU cannot explain the observed choices. In contrast, our study does not focus on a specific property but explores in more general how risk and time preferences interact with each other by estimating different decision models and comparing them.

  5. Noussair and Wu (2006), Abdellaoui et al. (2011b) focus on the time of uncertainty resolution (by fixing the time of payment), we focus on the time of payment (by fixing the time of uncertainty resolution).

  6. Similar approach has been followed by other studies (Andreoni & Sprenger, 2012; Abdellaoui et al., 2019) to avoid time of uncertainty resolution from affecting the preferences (Kreps & Porteus, 1978).

  7. We use the terms “time of payment” and “time delay” interchangeably. All models discussed in the section focus on the present value of the prospect, therefore time of payment corresponds to time delay.

  8. For prospect \(L_{2},\) this can be inferred by substituting \(w_{t}=\delta ^{t}p\) into the more general form of Eq. (1) described above.

  9. Note that, although, RSU agrees with PTT when evaluating value (or certainty equivalent) of a single outcome prospect, range effects may intervene in RSU when comparing two single outcome prospects.

  10. The sooner payment was not paid immediately but tomorrow, to ensure the transaction costs were similar for both the choices.

  11. We used colored coins as a substitute for the colored balls that were used in the experimental stimuli

  12. If the subject was chosen to receive real incentive, then one of the questions was randomly selected. For that specific question, one of the choices in the choice list was randomly selected and the uncertainty (if any) was resolved immediately by picking a coin from a box consisting of different colored coins. The subjects were paid on the specific date based on their choices and the resolved uncertainty.

  13. The results are for forty four subjects. For three subjects, the algorithm did not converge.

  14. We estimate the RSU model by assuming \(S(t)=pe^{-rt}\).

  15. The parameters of RSU are also elicited for an alternate specification of the discount rate \(r_{x}=r_{0}\left[ 1+\frac{M}{x}\right]\) in Table 14, Appendix C.

  16. We also estimated the hyperbolic discounted rank dependent utility (HDRDU) model, but the estimated AIC was higher than the DRDU model.

  17. In fact, when we consider all 44 prospects and estimate the WTU model, the K parameter is negative indicating the dependence of utility on time of payment.

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Acknowledgements

We thank Manel Baucells, Enrico Diecidue, Matthias Seifert, Konstantinos Stouras for their helpful comments on this draft of the paper. We also thank Mohammed Abdellaoui, Ehud Lehrer, and Bob Nau for their helpful comments during the different stages of the project. We acknowledge the help rendered by INSEAD Sorbonne lab research assistants Hoai Huong Ngo and Jean-Yves Mariette with the data collection. We also gratefully acknowledge support from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement 290255 and HEC Paris.

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Authors and Affiliations

  1. IE Business School, Madrid, Spain

    Jeeva Somasundaram

  2. S3 Labs, HEC Paris, Paris, France

    Vincent Eli

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  1. Jeeva Somasundaram
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Correspondence to Jeeva Somasundaram.

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Somasundaram, J., Eli, V. Risk and time preferences interaction: An experimental measurement. J Risk Uncertain 65, 215–238 (2022). https://doi.org/10.1007/s11166-022-09394-9

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