Testing theories of financial decision making

Abstract

We describe the observable content of some of the most widely used models of decision under uncertainty: models of translation invariant preferences. In particular, we characterize the models of variational, maxmin, constant absolute risk aversion, and constant relative risk aversion utilities. In each case we present a revealed preference axiom that is satisfied by a dataset if and only if the dataset is consistent with the corresponding utility representation. We test our axioms using data from an experiment on financial decisions.revealed preference | translation invariance | homotheticity | uncertainty T his paper is an investigation of the testable implications of models of decision under uncertainty. We carry out this investigation in financial markets, one of the most common environments in which human subjects face uncertainty.Risk is uncertainty that can be objectively quantified probabilistically. A gambler in a casino faces risk: He may calculate the probability that a roulette wheel stops on the number 7, or that a die lands on 5. Most scientists, in contrast, face the more general concept of uncertainty and study subjects who face uncertainty. Scientists conduct or analyze experiments with outcomes that they do not know, and for which no probabilities are objectively given.Of course, the scientist or the subject may have a subjective judgment of how likely different events are. Such judgments may even have a probabilistic expression, but the uncertainty is not resolved by means of a mechanical device for which probabilities can be objectively calculated. Moreover, this fact may cause subjects to display uncertainty aversion, a tendency to prefer risky bets over uncertain ones. Uncertainty aversion was famously documented by David Ellsberg (1), and the theories we treat in our paper are in part designed to describe uncertainty aversion.In uncertain situations, human subjects choose among uncertain prospects. These are functions specifying an "outcome" for each element of a given set of "states of the world." Think of an insurance contract that pays off a given sum only if some accident occurs. The set of states of the world is the binary set that codifies whether an accident has occurred, and the outcome is the payoff. In financial markets, the uncertain prospects correspond to financial assets, whereas the state of the worlds describe the relevant economic fundamentals, and the outcomes monetary payoffs.* A long tradition in decision theory develops models of how humans make decisions under uncertainty. A crucial idea in this development is that of translation invariance. Translation invariance means that if two uncertain prospects are transformed in the same way, by adding to each prospect a given, fixed, monetary payment, then the subject's preference between the two prospects should be preserved. For example, if the subject prefers insurance contract A over B, then the preference should be maintained after the price of each insurance contract has been raised by the same amount. A related idea is ...

Revealed Preferences over Risk and Uncertainty

“…A natural follow-up to Afriat's contribution is to characterize those datasets which are rationalizable by more specialized utility functions. Among these papers are those which characterize state price and contingent consumption demand observations that are consistent with the EU model 10 and (in more recent papers) some of its generalizations: these include Varian (1983aVarian ( , b, 1988; Green and Srivastava (1986); Diewert (2012); Bayer et al 2013; Echenique and Saito (2015); Chambers, Liu, and Martinez (2016); and Chambers, Echenique, and Saito (2016). 11 The principal difference between our results and this literature is that we do not rely on the sufficiency of first-order conditions.…”

“…12 Our results do depend on the realization in each state being one-dimensional (which can be interpreted as a monetary payoff, but not a bundle of goods). This case is the one most often considered in applications and experiments and is also the assumption in a number of recent papers, including Kubler, Selden, and Wei (2014); Echenique and Saito (2015); and Chambers, Echenique, and Saito (2016). The papers by Varian (1983a, b); Green and Srivastava (1986); Bayer et al (2013); and Chambers, Liu, and Martinez (2016) allow for multidimensional realizations.…”

Costly information acquisition

“…3 See also Brown and Calsamiglia (2007) and Chambers, Echenique and Saito (2016) for variants of this condition in an explicit revealed preference framework.…”

“…The GACI condition rules out the possibility of cycles in ex-ante payoff across different decision problems. Using this condition, we invoke a version of Afriat's theorem (see Chambers and Echenique (2016)).…”

Ever since Allais

“…(2013), Kubler, Selden, andWei (2014, 2017), Echenique and Saito (2015), Chambers, Liu, and Martinez (2016), Chambers, Echenique, and Saito (2016), Nishimura, Ok, and Quah (2017, Echenique, Imai, andSaito (2019, 2021), Polisson, Quah, andRenou (2020), andde Clippel andRozen (2021). We compare our approach and contribution to existing work along four dimensions-methods, measures, tests, and power.…”