Models of Risk Preferences: Descriptive and Normative Challenges: Volume 22

Behavioral economics poses a challenge for the welfare evaluation of choices, particularly those that involve risk. It demands that we recognize that the descriptive account of behavior toward those choices might not be the ones we were all taught, and still teach, and that subjective risk perceptions might not accord with expert assessments of probabilities. In addition to these challenges, we are faced with the need to jettison naive notions of revealed preferences, according to which every choice by a subject expresses her objective function, as behavioral evidence forces us to confront pervasive inconsistencies and noise in a typical individual’s choice data. A principled account of errant choice must be built into models used for identification and estimation. These challenges demand close attention to the methodological claims often used to justify policy interventions. They also require, we argue, closer attention by economists to relevant contributions from cognitive science. We propose that a quantitative application of the “intentional stance” of Dennett provides a coherent, attractive and general approach to behavioral welfare economics.

The author presents new estimates of the probability weighting functions found in rank-dependent theories of choice under risk. These estimates are unusual in two senses. First, they are free of functional form assumptions about both utility and weighting functions, and they are entirely based on binary discrete choices and not on matching or valuation tasks, though they depend on assumptions concerning the nature of probabilistic choice under risk. Second, estimated weighting functions contradict widely held priors of an inverse-s shape with fixed point well in the interior of the (0,1) interval: Instead the author usually finds populations dominated by “optimists” who uniformly overweight best outcomes in risky options. The choice pairs used here mostly do not provoke similarity-based simplifications. In a third experiment, the author shows that the presence of choice pairs that provoke similarity-based computational shortcuts does indeed flatten estimated probability weighting functions.

We take Cumulative Prospect Theory (CPT) seriously by rigorously estimating structural models using the full set of CPT parameters. Much of the literature only estimates a subset of CPT parameters, or more simply assumes CPT parameter values from prior studies. Our data are from laboratory experiments with undergraduate students and MBA students facing substantial real incentives and losses. We also estimate structural models from Expected Utility Theory (EUT), Dual Theory (DT), Rank-Dependent Utility (RDU), and Disappointment Aversion (DA) for comparison. Our major finding is that a majority of individuals in our sample locally asset integrate. That is, they see a loss frame for what it is, a frame, and behave as if they evaluate the net payment rather than the gross loss when one is presented to them. This finding is devastating to the direct application of CPT to these data for those subjects. Support for CPT is greater when losses are covered out of an earned endowment rather than house money, but RDU is still the best single characterization of individual and pooled choices. Defenders of the CPT model claim, correctly, that the CPT model exists “because the data says it should.” In other words, the CPT model was borne from a wide range of stylized facts culled from parts of the cognitive psychology literature. If one is to take the CPT model seriously and rigorously then it needs to do a much better job of explaining the data than we see here.

We evaluate the hypothesis of temporal stability in risk preferences using two recent data sets from longitudinal lab experiments. Both experiments included a combination of decision tasks that allows one to identify a full set of structural parameters characterizing risk preferences under Cumulative Prospect Theory (CPT), including loss aversion. We consider temporal stability in those structural parameters at both population and individual levels. The population-level stability pertains to whether the distribution of risk preferences across individuals in the subject population remains stable over time. The individual-level stability pertains to within-individual correlation in risk preferences over time. We embed the CPT structure in a random coefficient model that allows us to evaluate temporal stability at both levels in a coherent manner, without having to switch between different sets of models to draw inferences at a specific level.

Risk preferences play a critical role in almost every facet of economic activity. Experimental economists have sought to infer the risk preferences of subjects from choice behavior over lotteries. To help mitigate the influence of observable, and unobservable, heterogeneity in their samples, risk preferences have been estimated at the level of the individual subject. Recent work has detailed the lack of statistical power in descriptively classifying individual subjects as conforming to Expected Utility Theory (EUT) or Rank Dependent Utility (RDU). I discuss the normative consequences of this lack of power and provide some suggestions to improve the accuracy of normative inferences about individual-level choice behavior.