|
on Utility Models and Prospect Theory |
| By: | Thibault Gajdos (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I], Ecole d'économie de Paris - Paris School of Economics - [Université Panthéon-Sorbonne - Paris I]); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I], Ecole d'économie de Paris - Paris School of Economics - [Université Panthéon-Sorbonne - Paris I]); Jean-Christophe Vergnaud (CES - Centre d'économie de la Sorbonne - [CNRS : UMR8174] - [Université Panthéon-Sorbonne - Paris I], Ecole d'économie de Paris - Paris School of Economics - [Université Panthéon-Sorbonne - Paris I]); Takashi Hayashi (Department of Economics, University of Texas at Austin - [University of Texas at Austin]) |
| Abstract: | This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability-possibility set, that is, a set $P$ of probability measures on the state space. The decision maker is told that the true probability law lies in $P$ and is assumed to rank pairs of the form $(P,f) $ where $f$ is an act mapping states into outcomes. The<br />key representation result delivers maxmin expected utility where the min operator ranges over a set of probability priors --just as in the maxmin expected utility (MEU) representation result of \cite{GILB/SCHM/89}. However, unlike the MEU representation, the representation here also delivers a mapping, $\varphi$, which links the probability-possibility set, describing the available<br />information, to the set of revealed priors. The mapping $\varphi$ is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability-possibility set.<br />This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability-possibility set, i.e. , $\varphi$ is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed<br />probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the ``mean value'' of the probability-possibility set, and (ii) shrinking the probability-possibility set toward the mean value to a degree determined by preferences. |
| Keywords: | precise information, imprecision aversion, multiple priors, Steiner point. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00177378_v1&r=upt |
| By: | De Borger B.; Mogens F. |
| Abstract: | We consider binary choices on the trade-off between money and travel time, and formulate a model of reference-dependent preferences based on a linear reference-free utility function. Reference-dependence is captured by value functions that are centered at the reference. The model predicts a particular relationship between four commonly used valuation measures (willingness to pay (WTP), willingness to accept (WTA), equivalent gain (EG) and equivalent loss (EL)), and is has directly testable implications. Moreover, we show that the model allows recovering the underlying reference-free value of time. Based on a large survey data set, we estimate an econometric version of the model, allowing for both observed and unobserved heterogeneity. We find strong supporting evidence for reference-dependence in a series of tests of high statistical power. The gap between WTP and WTA is found to exceed a factor four. Loss aversion plays an important role in explaining responses; moreover, drivers are more loss averse in the time dimension than the cost dimension. We further find evidence of asymmetrically diminishing sensitivity. Finally, we show that the fraction of ´mistakes`, in the sense that participants are observed to sometimes select dominated options, varies systematically in a way consistent with the model of reference-dependence. |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:ant:wpaper:2006034&r=upt |
| By: | Frederik Lundtofte (Swiss Institute of Banking and Finance, University of St-Gallen) |
| Abstract: | This paper analyzes the expected life-time utility and the hedging demands in an exchange only, representative agent general equilibrium under incomplete information. We derive an expression for the investor’s expected life-time utility, and analyze his hedging demands for intertemporal changes in the unobservable stochastic growth of the endowment process and the changing quality of information regarding these changes. The hedging demands consist of two components, which could work in opposite directions so that a conservative consumer may end up having positive hedging demands. Our results are qualitatively different from those within constant growth equilibria. |
| Keywords: | learning, incomplete information, equilibrium, hedging demands |
| JEL: | C13 G11 G12 |
| Date: | 2003–11 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0623&r=upt |
| By: | Pascal St-Amour (HEC University of Lausanne, HEC University of Montreal and Swiss Finance Institute) |
| Abstract: | Reference–dependent preference models assume that agents derive utility from deviations of consumption from benchmark levels, rather than from consumption levels. These references can be either backward-looking (as explicit in the Habit literature) or forward-looking (as implicitly suggested by Prospect Theory). For both cases, we specify and estimate a fully structural multi-variate Brownian system in optimal consumption, portfolio and wealth using aggregate household financial and real estate wealth data. Our results reveal that references are (i) strongly relevant, (ii) state-dependent, and (iii) that the data is more consistent with the backwardthan the forward-looking reference model. |
| Keywords: | Portfolio choice, Reference–dependent utility, Habit, Prospect, Estimation of diffusion processes |
| JEL: | G11 G12 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0709&r=upt |
| By: | Enrico De Giorgi (University of Lugano); Thierry Post (Erasmus University Rotterdam) |
| Abstract: | This study develops a framework for dealing with stochastic reference points and endogenously selecting the reference point in reference-dependent choice theories that accounts for the joint probability distribution of the prospects and the reference point. Without accounting for the dependence structure, the endogenous reference point can deviate from the decision-maker’s optimum. Accounting for dependence, reference dependence affects choice behavior only if the reference point is (in part or in whole) exogenously fixed. In an application to well-known US investment benchmark data, investors invest in riskless T-bills rather than stocks if we ignore the dependence structure, while investing in small value stocks is optimal when we account for dependence. |
| Keywords: | Reference-dependent preferences, loss aversion, prospect theory, dependence structure |
| JEL: | D81 C23 C91 C93 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0714&r=upt |
| By: | Jack Stecher; Radhika Lunawat; Kira Pronin; John Dickhaut |
| Abstract: | What is a rational decision-maker supposed to do when facing an unfamiliar problem, where there is uncertainty but no basis for making probabilistic assessments? One answer is to use a form of expected utility theory, and assume that agents assign their own subjective probabilities to each element of the (presumably known) state space. In contrast, this paper presents a model in which agents do not form subjective probabilities over the elements of the state space, but nonetheless use new information to update their beliefs about what the elements of the state space are. This model is shown to lead to different predictions about trading behavior in a simple asset market under uncertainty. A controlled laboratory experiment tests the predictions of this model against those of expected utility theory and against the hypothesis that subjects act na¨ıvely and non-strategically. The results suggest that a lack of subjective probabilities does not imply irrational or unpredictable behavior, but instead allows individuals to use both what they know and knowledge of what they do not know in their decision making. <P>Comment un décideur rationnel est-il censé réagir face à un problème qui ne lui est pas familier lorsqu’il existe une certaine incertitude, et en l’absence d’une base sur laquelle effectuer des estimations probabilistes? Une solution consiste à utiliser une forme de la théorie de l’utilité espérée et de présumer que les agents attribuent leurs propres probabilités subjectives à chaque élément de la représentation d’état (sans doute connue). Par contraste, notre article présente un modèle où les agents ne forment pas de probabilités subjectives sur les éléments de la représentation d’état, mais utilisent de nouveaux renseignements afin de mettre à jour leurs croyances sur les éléments formant la représentation d’état. Le comportement des échanges avec ce modèle dans un marché d’actifs simple et incertain nous mène à des prédictions différentes. En utilisant une expérience contrôlée en laboratoire, nous avons vérifié les prédictions de ce modèle contre celles de la théorie de l’utilité espérée et contre l’hypothèse que les sujets agissent avec naïveté et sans recourir à une stratégie. Les résultats suggèrent qu’un manque de probabilités subjectives n’implique pas un comportement irrationnel ou imprévisible, mais permet plutôt aux individus d’utiliser autant l’information qu’ils possèdent que la connaissance de l’information qu’ils ne possèdent pas dans leur prise de décision. |
| Keywords: | Uncertainty; non-expected utility; incomplete preferences; ambiguity., Incertitude, utilité non espérée, préférences incomplètes, ambiguïté. |
| JEL: | M41 D80 D82 D83 |
| Date: | 2007–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2007s-21&r=upt |
| By: | Adam, Klaus; Marcet, Albert; Nicolini, Juan Pablo |
| Abstract: | Introducing bounded rationality into a standard consumption based asset pricing model with a representative agent and time separable preferences strongly improves empirical performance. Learning causes momentum and mean reversion of returns and thereby excess volatility, persistence of price-dividend ratios, long-horizon return predictability and a risk premium, as in the habit model of Campbell and Cochrane (1999), but for lower risk aversion. This is obtained, even though we restrict consideration to learning schemes that imply only small deviations from full rationality. The findings are robust to the particular learning rule used and the value chosen for the single free parameter introduced by learning, provided agents forecast future stock prices using past information on prices. |
| Keywords: | asset pricing puzzles; consumption-based asset pricing; learning |
| JEL: | D84 G12 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6518&r=upt |
| By: | Enrico De Giorgi (University of Lugano and Swiss Finance Institute); Thorsten Hens (University of Zurich); Marc Oliver Rieger (University of Zurich) |
| Abstract: | The paper shows that financial market equilibria need not exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. The reason is an infinite short-selling problem. But even when a short-sell constraint is added, non-existence can occur due to discontinuities in agents demand functions. Existence of equilibria is established when short-sales constraints are imposed and there is also a continuum of agents in the market. |
| Keywords: | Cumulative prospect theory, general equilibrium model, non-convex preferences, continuum of agents |
| JEL: | G11 D81 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0721&r=upt |
| By: | Boaz Moselle (The Brattle Group); François Degeorge (University of Lugano and Swiss Finance Institute); Richard Zeckhauser (Harvard University, Kennedy School of Government) |
| Abstract: | We analyze the risk levels chosen by agents who have private information regarding their quality, and whose performance will be judged and rewarded by outsiders. Assume that risk choice is observable. Even risk-neutral agents will choose risk strategically to enhance their expected reputation. We show that conspicuous conservatism is to be expected: agents of different qualities choose levels below those that would be chosen if quality were observable. This happens because bad agents must cloak their identity by choosing the same risk level as good agents, and good agents are more likely to distinguish themselves if they reduce the risk level. Our results contrast starkly with those for the case when risk choice cannot be observed. |
| Keywords: | risk choice, signaling, conservatism |
| JEL: | D81 D82 G30 |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0715&r=upt |
| By: | Anke Gerber (University of Zurich and Swiss Banking Institute); Kirsten I.M. Rohde (Erasmus University, Department of Applied Economics, The Netherlands) |
| Abstract: | This paper argues that observations of non-stationary choice behavior need not necessarily imply specific properties of the individual’s discount function. As we show, the observed “anomalies” in intertemporal choice can alternatively be explained by an individual’s perception of the risk that is involved whenever an outcome is to be received in the future. This risk may concern the size of the actual outcome or the endowment consumption stream to which the outcome is added. Both types of uncertainty naturally appear in the context of intertemporal choice and both are difficult to control in experiments. We show how relative degrees of changes in risk over time can predict choices. |
| Keywords: | Hyperbolic Discounting, Decreasing Impatience, Increasing impatience, Risk, Magnitude Effect, Gain-Loss Asymmetry |
| JEL: | D91 D81 |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0712&r=upt |
| By: | Elvio Accinelli (UASLP, Facultad de Economía, San Luis Potosí, México); Leobardo Plata (UASLP, Facultad de Economía, San Luis Potosí, México); Martín Puchet (UNAM, Facultad de Economía, México D.F.) |
| Abstract: | In this paper we show that in a pure exchange economy it is possible to improve the social welfare along an e±cient path. This path will be called the Negishi map. Moving the relative weights of the agent in a social welfare utility function, we obtain an e±cient path of allocations and social weights, such that along this path the social welfare level change. Moving along this path it is possible to reach a maximum social welfare. The e±cient allocation maximizing the social welfare is characterized by the fact that the individual utilities have the same value. This level will be called the Negishi number of the economy. Such allocation is not necessarily an allocation corre- sponding to a walrasian equilibrium so, the participation of a benevolent policy maker can have sense. We introduce a de¯nition of developed economy. Finally, the relations between changes in utilities and changes in social weights is analized. |
| Keywords: | Negishi approach, Negishi map, social welfare |
| JEL: | D6 D51 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:ude:wpaper:0807&r=upt |
| By: | Reichling, Felix |
| Abstract: | I develop an equilibrium matching model in which workers have preferences over consumption and hours of work and are able to self-insure against unemployment risks by accumulating precautionary wealth. Wages and working hours are the outcomes of Nash bargaining between workers and firms. I focus on an unemployment insurance (UI) system with constant benefits of indefinite duration financed through a constant labor income tax. Low-wealth individuals work unusually long hours to quickly accumulate precautionary wealth. The Frisch elasticity of labor supply governs a worker’s utility cost of supplying labor and hence the cost of accumulating precautionary wealth. A lower elasticity implies a higher utility cost of adjusting hours. I take Frisch elasticities from recent research using household data and find that the optimal level of UI benefits is between 34 and 40 percent of average compensation. The potential welfare gains from moving from current 34 percent to the optimal policy are as large as 0.13 percent of lifetime consumption. The optimal replacement rate is decreasing in the Frisch elasticity of labor supply. |
| Keywords: | Unemployment insurance; Labor supply; Matching equilibrium; Self-insurance |
| JEL: | J22 H00 J65 E24 |
| Date: | 2006–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5362&r=upt |