Experimental elicitation of ambiguity attitude using the random incentive system

Abstract

We demonstrate how the standard usage of the random incentive system in ambiguity experiments eliciting certainty and probability equivalents might not be incentive compatible if the decision-maker is ambiguity averse. We propose a slight modification of the procedure in which the randomization takes place before decisions are made and the state is realized, and prove that if subjects evaluate the experimental environment in that way (first-risk, second-uncertainty), incentive compatibility may be restored.

Randomize at Your Own Risk: On the Observability of Ambiguity Aversion

“…Consequently, integration predicts that SAA subjects will not be . This point is very closely related to Raiffa's (1961) argument and has recently been made by Bade (2015, first version 2011); Kuzmics (2017, first version 2012); Baillon, Halevy, and Li (2022, first version 2013); Azrieli, Chambers, and Healy (2018, first version 2014) and Oechssler and Roomets (2014).…”

“…We were genuinely surprised by the absence of a difference between the After and Before treatments. In a previously‐circulating theoretical paper (Baillon, Halevy, and Li (2022)), we conjectured that more subjects would exhibit ambiguity aversion in the Before treatment, especially if the difference between the two treatments was very salient. In other words, we expected (integrating) subjects to exhibit Statewise Monotonicity rather than Reversal of Order.…”

“…With this procedure, it was maximally salient that the random incentives determining which choice problem matters for payment preceded the resolution of uncertainty concerning the draws from the bags. This implementation followed our proposal in Baillon, Halevy, and Li (2022), which was previously implemented in Epstein and Halevy (2019). After and After‐6 treatment: Once all subjects were done with the experiment, the implementer drew a chip from each bag and announced the color of each chip.…”

“…In other words, they first evaluate the bets (with their ambiguity preferences) and then consider the randomization over the subjective values they assigned to the bets. Hence, Statewise Monotonicity directly implies incentive compatibility in the Before treatment (Baillon, Halevy, and Li (2022), Azrieli, Chambers, and Healy (2018)) and under this property, SAA subjects should be . Note that SAA subjects cannot satisfy both Reversal of Order and Statewise Monotonicity because it would lead to contradictions (violations of transitivity or stochastic dominance).…”

“…The interplay between risk and ambiguity poses a very practical challenge of the mere observation of ambiguity attitudes. Despite ample theoretical arguments suggesting that the usage of RIS makes it impossible to observe ambiguity aversion (Bade (2015, first version 2011); Kuzmics (2017, first version 2012); Baillon, Halevy, and Li (2022, first version 2013); Oechssler and Roomets (2014); Azrieli, Chambers, and Healy (2018, first version 2014)), most (but not all) of the experimental literature continues to use RIS to measure ambiguity attitudes, with varying degrees of success (Trautmann and van de Kuilen (2015)), suggesting that isolation may take place, at least in some cases. These issues highlight important tradeoffs involved in the design of experiments that measure behavioral preferences more broadly.…”