Heterogeneous risk and time preferences

J Risk Uncertain (2016) 53:1–28 DOI 10.1007/s11166-016-9243-x Heterogeneous risk and time preferences Alina Ferecatu1 · Ayse Önçüler2 Published online: 14 November 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract Assessing individuals’ time and risk preferences is crucial in domains such as health-related decisions (e.g., dieting, addictions), environmentally-friendly practices, and saving opportunities. We propose a new method to jointly elicit and estimate risk attitudes and intertemporal choices. We use a novel individual level estimation procedure based on a hierarchical Bayes methodology, which can integrate different functional forms for discounting and risk attitudes. This method provides individual level estimates, and allows us to explore the heterogeneity in the data. In addition, we report a negative correlation between risk and time preferences, implying that risk-seeking individuals are less patient and less willing to defer consumption. Keywords Risk and time · Risk preferences · Intertemporal choice · Joint elicitation · Hierarchical Bayes · Heterogeneity JEL Classifications D81 · D90 · C11 Electronic supplementary material The online version of this article (doi:10.1007/s11166-016-9243-x) contains supplementary material, which is available to authorized users.  Alina Ferecatu Ayse Önçüler 1 Rotterdam School of Management, Erasmus University, Burgemeester Oudlaan 50, 3062PA, Rotterdam, The Netherlands 2 ESSEC Business School, 1 Avenue Bernard Hirsch, 95000, Cergy, France 2 J Risk Uncertain (2016) 53:1–28 1 Introduction When making decisions in an intertemporal setting, individuals are known to heavily discount future outcomes and to have a strong preference for immediate gains (Loewenstein and Prelec 1992; Frederick et al. 2002). Understanding individuals’ intertemporal decisions and designing tools to improve their decision making process has been a major research concern, with individual welfare and public policy implications. Are people myopic about health decisions such as following better diets, quitting smoking, or exercising? Do public policy makers respond appropriately to the threat of global warming, a decision involving a tradeoff between short term expenses and long run rewards? Chesson and Viscusi (2003) analyze the joint influence of time and uncertainty and conclude that people may have difficulties choosing the optimal precautionary measures to prevent climate change, a long term hazard, due to both ambiguity in the probability of global warming phenomena and also due to the ambiguity in the timing of global warming consequences. This suggests that a joint model of risk and time preferences is necessary to assess decision makers’ tradeoffs between outcomes at different points in time. The current study proposes a methodology that jointly elicits and estimates risk and time preferences at the individual level. We elicit risk attitudes and intertemporal choices following Holt and Laury’s (2002) risk aversion experimental procedure and Coller and Williams’s (1999) time discounting methodology involving price lists. We embed a constant relative risk aversion specification in an exponential discounting model, following Andersen et al. (2008). Our main contribution is methodological. We add a layer of flexibility to the estimation method through a hierarchical Bayes methodology, which allows us to recover individual level estimates and assess the heterogeneity in intertemporal choices and risk attitudes. Hierarchical Bayes modeling is a validated alternative to maximum likelihood estimation (Rossi et al. 2005; Toubia et al. 2013). The flexibility of the method in dealing with highly non-linear model specifications represents an important benefit. Such individual level estimates can be used in simulation studies to assess the effectiveness of changes in public policy decisions. To our knowledge, this is the first study that uses hierarchical Bayes modeling to jointly estimate risk and time preferences and to analyze the heterogeneity in the data. Our results suggest that individuals are generally risk-averse, with a mean constant relative risk aversion coefficient of 0.515; their discount rates are in line with previous findings on joint elicitation (mean discount rate of 12%). The methodology is general and can be adapted to different functional forms. To test the robustness of our results, we estimate time preferences by using an exponential model, a hyperbolic model proposed by Mazur (1987), another hyperbolic specification by Prelec (2004), and a mixture model that allows a part of the population to behave as exponential discounters, and the remaining part as hyperbolic discounters. Our study provides evidence that controlling for the curvature of the risk aversion leads to lower estimated discount rates in experiments with hypothetical stakes. We conduct a clustering study and find three types of decision makers based on their risk and time preferences: J Risk Uncertain (2016) 53:1–28 3 a high patience type (risk-averse, low discounting), a moderate patience type (with average risk and time preferences), and a low patience cluster (risk-seeking, high discounting). This result suggests that regulators could design policy interventions specifically aimed at people with various degrees of patience. The increased reliability of our estimates also allows us to revisit the issue of the correlation between risk and time preferences. We find evidence that risk-seeking people are more impatient and require higher interest rates to postpone consumption. The remainder of the paper is organized as follows. In the next section, we present a brief literature review on joint elicitation and estimation of risk and time preferences. The experimental procedure for the joint elicitation of risk and time preferences is introduced in Section 3. In Section 4, we introduce our empirical model and present the estimation methodology involving a hierarchical Bayes approach. In Section 5, we report the results from our Bayesian estimation and further investigate the heterogeneity of risk and time preferences via individual differences and clusters of decision makers. The paper concludes with a discussion and the implications of our findings. 2 Existing literature Recent developments in the intertemporal choice literature include a joint elicitation of risk and time preferences (Andersen et al. 2008; Laury et al. 2012; Andreoni and Sprenger 2012a; Toubia et al. 2013). This stream of literature emerged based on the conjecture that eliciting time preferences while assuming risk neutrality leads to an overestimation of discount rates. Using multiple price lists, Andersen et al. (2008) jointly elicit subjects’ risk attitudes and intertemporal choices and show that discount rates are significantly lower than those reported in previous studies and more in line with market rates (10.1% on average). (...truncated)