Schedule - Parallel Session 7 - Ambiguity: Theory and Applications 2
IMC Auditorium - 09:00 - 10:30Estimating a Structural Model of Smooth Ambiguity Aversion: a Joint Maximum Likelihood Approach
Hong Il Yoo; Morten Igel Lau; Jimmy Martinéz-Correa
Abstract
Several theories address decision making under ambiguity (e.g., Machina and Siniscalchi, 2014 and references therein). Ambiguity refers to cases where the true probability distribution of outcomes is unknown to the decision maker, and “risk” refers to cases where it is known. Most popular models of ambiguity aversion assume that the decision maker has multiple prior beliefs regarding the true distribution of outcomes from an uncertain event, and acts from a set of multiple subjective probability distributions instead of one distribution. The smooth ambiguity aversion model (SAAM) of Klibanoff et al. (2005) has attracted a lot of attention, for its intuitive appeal and analytic tractability. But only a few studies have estimated this model structurally (e.g. Conte and Hey, 2013) despite the growing interest in structural estimation of other ambiguity aversion models that consider a particular subset of prior beliefs (Hey et al. 2010, Hey and Pace 2014, Kothiyal et al. 2014, and Stahl 2014). The SAAM assumes that the decision maker forms a second-order probability distribution over the full set of prior beliefs. S/he first evaluates the expected utility from each belief, and then forms a subjective probability distribution over expected utilities from the full set of beliefs. Estimating the SAAM requires disentangling ambiguity aversion from other latent parameters that influence decision making under ambiguity, and may be confounded with ambiguity aversion. These include the measures of “risk” aversion, and the subjective second-order probability distribution. We develop an empirical approach that can, together with the experimental design of Abdellaoui et al. (2015), identify ambiguity aversion and other latent parameters of the SAAM. Their design features a series of decision tasks involving simple risk, compound risk (with variation in complexity), and ambiguity. Our approach builds on the joint maximum likelihood approach to disentangle risk and time preferences (Andersen et al., 2008). Since the different types of tasks are better (or uniquely) suited to identifying different latent parameters in the SAAM, the joint use of those tasks allows one to estimate the model under less restrictive assumptions than previously made. For example, one can avoid equating ambiguity aversion with compound risk aversion, and also avoid experimentally induced second-order probability distributions. We use maximum simulated likelihood to allow for unobservable preference heterogeneity. Our preliminary results using the dataset of Abdellaoui et al. (2015) look plausible and promising. When ambiguity entails complete lack of information on the true outcome distribution, the average decision maker behaves as if s/he assigns almost identical second-order probabilities to all outcomes in the decision task. S/he also is averse to ambiguity and high complexity compound risk, and is less averse to simple risk and other types of compound risks.
Discounting Future Gains and Losses of Time
Cedric Gutierrez; Mohammed Abdellaoui; Emmanuel Kemel
Abstract
In many decisions, saving or losing time, now or in the future, is as relevant as saving or losing money now or in the future. Benefits of projects such as automation solutions for high-speed production lines or enlarging expressways are economically justified by the value of time saved. It is however usual to assess the economic value of such saved/lost time by discounting the corresponding monetary values over time rather than discounting the very values of time over time. While intertemporal choice of money has been studied extensively, very few studies have analyzed the way people discount time, despite the fact that it is a scarce and valuable resource. We investigate this issue in a laboratory experiment where consequences are measured in units of time and real incentives are implemented in gains and losses. We created a concrete scenario in order to facilitate subjects’ understanding of the concepts of gains and losses of time, and to give them a common reference point from which gains and losses of time were defined. We used this scenario for the implementation of real incentives. We also measured intertemporal decisions with monetary consequences, as a benchmark. We estimated all the components of the discounted utility model using maximum likelihood. We took a descriptive perspective and allowed for discount rates to vary over time. We also measured utility of time and money in order to disentangle attitudes towards delays from attitudes towards outcomes. Finally, we used mixed modeling in order to take into account heterogeneity in intertemporal preferences. We find that subjects discount more gains of time than gains of money. This difference between time and money is reversed for losses: people discount less losses of time than losses of money. Moreover, we observe that subjects are more likely to exhibit non-constant discount rates for time than for money in both gain and loss domains. Analyses also show that there is a significant correlation between impatience towards money and impatience towards time: subjects who are impatient for money also tend to be impatient for time. Finally, mixed modeling analyses show that there is more heterogeneity in discounting behavior for time consequences than for monetary consequences. As a conclusion, we find that people do not discount time as they discount money. The paper also reveals the complexity and diversity of intertemporal preferences.
Trust and Ambiguity
Chen Li
Abstract
The decision to trust others is of an ambiguous nature: it is difficult to assess the chance that one’s trust will be reciprocated. Therefore, people’s decision to trust is not only driven by their beliefs about others’ trustworthiness, but also by their preferences for this source of social ambiguity. In this study, we used an experimental design that allowed for separate investigation of how these two factors may drive people’s decision to trust. In our experiment, subjects first made a trustor decision in a trust game with their randomly assigned partner. We then elicited their ambiguity attitude using the method introduced by Baillon et al. (2015), which allowed for a separation between the additive part of people’s subjective beliefs and the non-additive part due to distortions by their ambiguity attitudes. Finally subjects made a trustee decision in the same trust game with the same partner. We found that, people who decided to trust believed that their trust were more likely to be reciprocated by their partners than those who did not. Moreover, people who trusted were also less ambiguity averse. Sapienza et al. (2013), argued that trust has two components: a belief-based one and a preference-based one. Our findings provided direct supporting evidence to this argument. Also, people who decided to trust were those who were more trustworthy themselves when making the trustee decision; and more trustworthy people believed that their partners were more likely to be trustworthy than those who were less trustworthy. This finding is consistent with the finding on “false consensus” (Ross et al. 1977), which implies that people tend to overestimate the proportion of others who would think (behave) like them.
It Is the Monotonicity Axiom!
Berend Roorda; Reinoud Joosten
Abstract
We identify the monotonicity axiom as a problematic cornerstone of normative theory on decision making, and propose sequential consistency as an alternative, weaker axiom, that is still strong enough to induce uniqueness of updates, yet sufficiently flexible to rationalize the Allais and Ellsberg preferences. It is generally believed that the monotonicity property is an indispensable feature of a normative preference ordering. Phrased as `if A is better than B in all states tomorrow, it must be better now’, its intuitive appeal is immediate. We also take it for granted, in case A and B are acts, or lotteries, that actually pay out in each state tomorrow. In other words, we adopt monotonicity in real monetary outcomes. Its extension to the general case, however, with A and B not yet resolved in tomorrow’s states, is less innocent than this phrasing suggests. At closer inspection, the word `better’ comes in two different forms: better if it comes to obtaining (often the tacit assumption), and better if it comes to the opposite perspective (returning, delivering, writing). We argue that the discrepancy between both perspectives, also referred to as endowment, or the gap between willingness to pay and accept, or the bid-ask spread, is inherent in most common preference orderings in the first place, rather than the effect of additional psychological phenomena. Now this undermines the seemingly absolutely compelling nature of the monotonicity axiom (see [2] for an elaborate discussion). Inspired by [1-3], we propose an alternative axiomatic framework for complete continuous preference orderings on finite state acts, in which the standard (conditional) monotonicity axiom is replaced by the much weaker axiom of sequential consistency ([2], mainly Def 4.1 and axioms A1-6). This extra flexibility gives room to combine uniqueness of updates, consequentialism, and dynamic choice consistency in a such a way that it accommodates the Allais and Ellsberg preferences without giving up a normative claim.
References
[1] B. Roorda and J.M. Schumacher (2015) Weakly Time Consistent Convex Risk Measures and their Dual Representations. To appear in Finance \& Stochastics, Open Access. DOI: 10.1007/s00780-015-0285-8
[2] B. Roorda and R.A.M.G. Joosten (2015). Dynamically Consistent Non-Expected Utility Preferences with Tuned Risk Aversion. Working paper
[3] B. Roorda and R.A.M.G. Joosten (2014). Tuned Risk Aversion as Interpretation of Non-Expected Utility Preferences. Presented at the FUR 2014 Rotterdam conference. Reworked to new working paper [2].