Completing Incomplete Revealed Preference Under Limited Attention

This paper discusses how to improve the identification of the preference of a decision‐maker (DM) with limited attention proposed by Masatlioglu, Nakajima and Ozbay (2012). in “Revealed Attention”. Their identification method relies on choice reversals so the obtained revealed preference is often incomplete. We propose three approaches to address this problem. The first one is accommodating a model‐free approach, which respects the DM's choice in making a welfare analysis, as long as it does not contradict the revealed preference of Masatlioglu et al. The second approach incorporates the DM's exogenously obtained attention/inattention information into the model of Masatlioglu et al. The third approach is to take framings that influence the DM's attention into effect for the identification.     

A class of incomplete and ambiguity averse preferences

This paper characterizes models of ambiguous beliefs in the absence of the completeness axiom. We axiomatize multiple-selves versions of some of the most important examples of complete and ambiguity averse preferences, and characterize when those incomplete preferences are ambiguity averse.     

Rational choice with status quo bias

Motivated by the empirical findings concerning the importance of one's current situation on her choice behavior, the main objective of this paper is to propose a rational choice theory that allows for the presence of a status quo bias, and that incorporates the standard choice theory as a special case. We follow a revealed preference approach, and obtain two nested models of rational choice that allow phenomena like the status quo bias and the endowment effect, and that are applicable in any choice situation to which the standard (static) choice model applies.     

Small worlds: Modeling attitudes toward sources of uncertainty

We introduce the concept of a conditional small world event domain—an extension of Savage's [The Foundations of Statistics, Wiley, New York, 1954] notion of a ‘small world’—as a self-contained collection of comparable events. Under weak behavioral conditions we demonstrate probabilistic sophistication in any small world event domain without relying on monotonicity or continuity. Probabilistic sophistication within, though not necessarily across, small worlds provides a foundation for modeling a decision maker that has source-dependent risk attitudes. This also helps formalize the idea of source preference and suggests an interpretation of ambiguity aversion, often associated with Ellsberg-type behavior, in terms of comparative risk aversion across small worlds.     

Expected utility theory without the completeness axiom

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.     

Risk taking with additive and multiplicative background risks

We examine the effects of background risks on optimal portfolio choice. Examples of background risks include uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. While some of these risks are additive and have been amply studied, others are multiplicative in nature and have received far less attention. The simultaneous effect of both additive and multiplicative risks has hitherto not received attention and can explain some paradoxical choice behavior. We rationalize such behavior and show how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor.     

Dynamic price competition

We consider the model of price competition for a single buyer among many sellers in a dynamic environment. The surplus from each trade is allowed to depend on the path of previous purchases, and as a result, the model captures phenomena such as learning by doing and habit formation in consumption.We characterize Markovian equilibria for finite and infinite horizon versions of the model and show that the stationary infinite horizon version of the model possesses an efficient equilibrium where all the sellers receive an equilibrium payoff equal to their marginal contribution to the social welfare.     

Dynamic common agency

A general model of dynamic common agency with symmetric information is considered. The set of truthful Markov perfect equilibrium payoffs is characterized and the efficiency properties of the equilibria are established. A condition for the uniqueness of equilibrium payoffs is derived for the static and the dynamic game. The payoff is unique if and only if the payoff of each principal coincides with his marginal contribution to the social value of the game. The dynamic model is applied to a game of agenda setting.     

Observational equivalence and nonequivalence of subjective and robust mean–variance preferences

We identify the conditions where robust mean–variance preferences, which capture ambiguity aversion, are observationally nonequivalent to subjective mean–variance preferences. Conversely, we also provide an example showing that observational equivalence holds regardless of the degree of ambiguity aversion.     

Optimal annuitization, uncertain survival probabilities, and maxmin preferences

We consider a life-cycle model with bequest motives, and assume that the individual does not know his/her survival probability and has maxmin utility preferences; we show that it is optimal not to annuitize but to purchase pure life insurance policies instead.     

Moment conditions for Almost Stochastic Dominance

This study establishes necessary conditions for Almost Stochastic Dominance criteria of various orders. These conditions take the form of restrictions on algebraic combinations of moments of the probability distributions in question. The relevant set of conditions depends on the relevant order of ASD but not on the critical value for the admissible violation area. These conditions can help to reduce the information requirement and computational burden in practical applications. A numerical example and an empirical application to historical stock market data illustrate the moment conditions. The first four moment conditions in particular seem appealing for many applications.     

A subjective model of experimentation

Typically an experiment is defined by a set of possible signals and a likelihood function, and both are specified exogenously—they are taken to be observable by the analyst. This paper renders them subjective by showing that they may be derived from suitable choice behavior. This is done in the context of an axiomatic representation theorem for preference on a suitable domain.     

Dynamic variational preferences

We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60-66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.     

“Fair go” for all? Wealth and Risk Aversion of Australian Households*

A mean‐variance framework is applied to Australian household financial portfolios in order to provide estimates of relative risk aversion in the economy. Controlling for various socio‐economic characteristics, we explore whether risk aversion heterogeneity is a function of wealth heterogeneity. In contrast to most studies, we find evidence of very high risk aversion amongst the majority of households of poor households but vastly lower risk aversion amongst the high percentiles in the wealth distribution. Applying a first differences model across three survey waves spanning 2002 to 2010, we find that risk tolerance increases significantly with wealth. Risk tolerance is positively associated with mortgage payments, but rental payments have no relationship. In addition, we found no evidence that holding a university education has any discernible impact on risk aversion. Lastly, we present some preliminary findings as to the impact of financial advice on observed risk aversion. Financial advice is found to accentuating risk aversion, particularly amongst the wealthiest households. The findings have potential implications for the distribution of wealth in Australia that has received renewed interest recently.     

Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.     

Saving rates and portfolio choice with subsistence consumption

We analytically show that a common across rich/poor individuals Stone-Geary utility function with subsistence consumption in the context of a simple two-asset portfolio-choice model is capable of qualitatively and quantitatively explaining: (i) the higher saving rates of the rich, (ii) the higher fraction of personal wealth held in risky assets by the rich, and (iii) the higher volatility of consumption of the wealthier. On the contrary, time-variant “keeping-up-with-the-Joneses” weighted average consumption which plays the role of moving benchmark subsistence consumption gives the same portfolio composition and saving rates across the rich and the poor, failing to reconcile the model with what micro data say.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

Increasing workload in a stochastic environment

We show that a steeply increasing workload before a deadline is compatible with time-consistent preferences. The key departure from the literature is that we consider a stochastic environment where success of effort is not guaranteed.     

Price discrimination via information provision

We study price discrimination where different prices are offered as a bundle with different levels of information about a product. The seller’s price discrimination induces high valuation buyers to purchase a good without information and low valuation buyers to purchase with information. Our analysis highlights several interesting results about price discrimination: (i) the seller’s choice of information provision is the combination of full information and no information, (ii) products can be cheaper without information provision than with information provision, (iii) as a result of price discrimination, prices can be more dispersed as buyers’ valuations become largely similar, and (iv) the high valuation buyers purchase a damaged good and may earn negative surplus. Furthermore, we investigate under which circumstances price discrimination is more profitable than uniform pricing. We show that a decline in transportation costs which facilitate price discrimination can be welfare reducing.     

Models of Capital Requirements in Static and Dynamic Settings

The aim of this paper is twofold. First, we generalize the notion of capital requirement, originally formulated in a regulatory framework, in order to unify other apparently diverse financial concepts. Second, we stress the interpretation of a capital requirement as a measure of risk, providing a link with the theory of coherent risk measures. We define a capital requirement as the minimal initial cost of a hedging action that makes the original position acceptable. Three basic elements are involved in such a methodology: a system of prices, a class of permitted hedging actions and a criterion of acceptability. Our approach is very general, because we construct capital requirements on vector spaces. However, we will give some concrete applications related, in particular, to the availability of a financial market, to the presence of different business units in an institution or to the fact that pay-offs are spread over different dates.