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on Utility Models and Prospect Theory |
| By: | Chiaki Hara (Institute of Economic Research, Kyoto University) |
| Abstract: | A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumerfs discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates. |
| Keywords: | Complete monotonicity, discount factor, discount rate, representative consumer, expected utility, time additivity, relative risk aversion, Bernsteinfs theorem. |
| JEL: | D51 D53 D61 D81 D91 E43 G12 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:636&r=upt |
| By: | Shin-ichi Fukuda (Faculty of Economics, University of Tokyo) |
| Abstract: | This paper explores how Knightian uncertainty affects dynamic properties in a model of economic growth. The decision-making theory in the analysis is that of expected utility under a non-additive probability measure, that is, the Choquet expected utility model of preference. We apply this decision theory to an overlapping-generations model where producers face uncertainty in their technologies. When the producer has aversion to uncertainty, the firm's profit function may not be differentiable. The firm's decision to invest and hire labor therefore becomes rigid for some measurable rage of real interest rate. In the dynamic equilibrium, the existence of the firm level rigidity causes discontinuity in the wage function, which makes multiple equilibria more likely outcome under log utility and Cobb-Douglass production functions. We show that even if aversion to uncertainty is small, "poverty trap" can arise for a wide range of parameter values. |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2007cf502&r=upt |
| By: | Helga Fehr-Duda (Institute of Economic Research, Swiss Federal Institute of Technology Zurich); Adrian Bruhin (Socioeconomic Institute, University of Zurich); Thomas Epper (Institute of Economic Research, Swiss Federal Institute of Technology Zurich); Renate Schubert (Institute of Economic Research, Swiss Federal Institute of Technology Zurich) |
| Abstract: | It has long been recognized that relative risk aversion over gains increases with stake size. The evidence for losses is mixed, however. Based on experimental data on choices over real gains and losses in China, we find that average behavior under losses is not sensitive to stake size. In the gain domain, increasing relative risk aversion can be attributed to a significant change in probability weights: The probability weighting curve for high gains lies significantly closer to the rational, i.e. linear, weighting line than the curve for low gains. A finite mixture regression analysis of heterogeneity shows that the majority of subjects weight low-gain probabilities much more optimistically than high-gain probabilities. A minority of near rational types do not react to rising stakes at all. Our results question the validity of rank-dependent theories of choice. |
| Keywords: | Risk Aversion, Stake-Size Effect, Prospect Theory, Latent Heterogeneity |
| JEL: | D81 C91 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:soz:wpaper:0708&r=upt |
| By: | Selima Benmansour (DRM - Dauphine Recherches en Management - [CNRS : UMR7088] - [Université Paris Dauphine - Paris IX]); Elyès Jouini (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - [CNRS : UMR7534] - [Université Paris Dauphine - Paris IX]); Clotilde Napp (DRM - Dauphine Recherches en Management - [CNRS : UMR7088] - [Université Paris Dauphine - Paris IX], CREST - Centre de Recherche en Économie et Statistique - [INSEE] - [ École Nationale de la Statistique et de l'Administration Économique]); Jean-Michel Marin (INRIA Futurs - A3 - [INRIA] - [Université Paris Sud - Paris XI]); Christian Robert (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - [CNRS : UMR7534] - [Université Paris Dauphine - Paris IX]) |
| Abstract: | Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance.This quantity is of particular importance since it characterizes the consensus belief in risk-taking situations with heterogeneous beliefs. Its estimation leads to a nontrivial statistical problem. We start from a large lottery survey (1536 individuals). We assume that individuals have true unobservable characteristics and that their answers in the survey are noisy realizations of these characteristics. We adopt a Bayesian approach for the statistical analysis of this problem and use an hybrid MCMC approximation method to numerically estimate the distributions of the unobservable characteristics. We obtain that individuals are on average pessimistic and that<br />pessimism and risk tolerance are positively correlated. As a consequence, we conclude that the<br />consensus belief is biased towards pessimism. |
| Keywords: | Bayesian estimation, MCMC scheme, importance sampling, pessimism, risk tolerance, risk aversion, consensus belief. |
| Date: | 2007–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00163678_v1&r=upt |
| By: | Mark Huggett; Gustavo Ventura; Amir Yaron (Department of Economics, Georgetown University) |
| Abstract: | Is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime? We answer this question within a model that features idiosyncratic shocks to human capital, estimated directly from data, as well as heterogeneity in ability to learn, initial human capital, and initial wealth { features which are chosen to match observed properties of earnings dynamics by cohorts. We find that as of age 20, differences in initial conditions account for more of the variation in lifetime utility, lifetime earnings and lifetime wealth than do differences in shocks received over the lifetime. Among initial conditions, variation in initial human capital is substantially more important than variation in learning ability or initial wealth for determining how an agent fares in life. An increase in an agent's human capital affects expected lifetime utility by raising an agent's expected earnings pro¯le, whereas an increase in learning ability affects expected utility by producing a steeper expected earnings profile. Classification-JEL Codes: E21, D3, D91. |
| Keywords: | Lifetime Inequality, Human Capital, Idiosyncratic Risk |
| Date: | 2007–07–04 |
| URL: | http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~07-07-04&r=upt |
| By: | Rosalie Viney (CHERE, University of Technology, Sydney); Elizabeth Savage (CHERE, University of Technology, Sydney) |
| Abstract: | This paper investigates the nature of the utility function for health care, defined over the probability of survival, survival duration, health state and cost of treatment. A discrete choice experiment, involving treatment choice for a hypothetical health condition is used to test restrictions on preferences in the QALY model. We find that preferences do not conform to expected utility, and there are significant interactions between health state and survival duration. Individual characteristics are significant, implying substantial differences in valuations of health states across the population. The results suggest the QALY approach distorts valuations of health outcomes. |
| Keywords: | Discrete choice experiment, Qalys, preferences, health state valuation |
| JEL: | I19 |
| URL: | http://d.repec.org/n?u=RePEc:her:chewps:2006/10&r=upt |
| By: | Kentaro Nakajima (Graduate School of Economics, University of Tokyo); Takatoshi Tabuchi (Faculty of Economics, University of Tokyo) |
| Abstract: | The examination of long-term Japanese data on interregional migration revealed three stylized facts of migration behavior. Based on the facts, we formulated an operational model and estimated interregional utility differentials. We found that the interregional utility differentials have been converging until the late 1970s. We showed that the utility estimates are highly correlated with per capita real income. We also applied the model to interregional migration in the United States and Canada as well as the interindustry movement in Japan and confirmed the model's validity. |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2007cf496&r=upt |
| By: | Andreas Ortmann (Center for Economic Research and Graduate Education, Charles University, and Economics Institute, Academy of Sciences of the Czech Republic (CERGE-EI).); Alexandra Prokosheva (Center for Economic Research and Graduate Education, Charles University, and Economics Institute, Academy of Sciences of the Czech Republic (CERGE-EI).); Ondrej Rydval (Max-Planck-Institute of Economics (Strategic Interaction Group), Jena, Germany); Ralph Hertwig (University of Basel, Switzerland) |
| Abstract: | Gneezy, List and Wu [Q. J. Econ. 121 (2006) 1283-1309] document that lotteries are often valued less than the lotteries’ worst outcomes. We show how to undo this result. |
| Keywords: | Risky choice, framing, experiments, task ambiguity, subject confusion |
| JEL: | C81 C91 C93 D83 |
| Date: | 2007–07–18 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2007-038&r=upt |
| By: | Helga Fehr (Institute of Economic Research, Swiss Federal Institute of Technology Zurich); Thomas Epper (Institute of Economic Research, Swiss Federal Institute of Technology Zurich); Adrian Bruhin (Socioeconomic Institute, University of Zurich); Renate Schubert (Institute of Economic Research, Swiss Federal Institute of Technology Zurich) |
| Abstract: | When valuing risky prospects, people tend to overweight small probabilities and to underweight large probabilities. Nonlinear probability weighting has proven to be a robust empirical phenomenon and has been integrated in decision models, such as cumulative prospect theory. Based on a laboratory experiment with real monetary incentives, we show that incidental emotional states, such as preexisting good mood, have a significant effect on the shape of the probability weighting function, albeit only for women. Women in a better than normal mood tend to exhibit mood-congruent behavior, i.e. they weight probabilities of gains and losses relatively more optimistically. Men’s probability weights are not responsive to mood state. We find that the application of a mechanical decision criterion, such as the maximization of expected value, immunizes men against effects of incidental emotions. 40% of the male participants indeed report applying expected values as decision criterion. Only a negligible number of women do so. |
| Keywords: | prospect theory, probability weighting function, risk taking behavior, incidental emotions, rationality |
| JEL: | D81 C91 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:soz:wpaper:0703&r=upt |
| By: | Theresa Fahrenberger (Center of Economic Research (CER-ETH) at ETH Zurich); Hans Gersbach (Center of Economic Research (CER-ETH) at ETH Zurich) |
| Abstract: | In this paper we propose minority voting as a scheme that can partially protect individuals from the risk of repeated exploitation. We consider a committee that meets twice to decide about projects where the first-period project may have a long-lasting impact. In the first period a simple open majority voting scheme takes place. Voting splits the committee into three groups: voting winners, voting losers, and absentees. Under minority voting only voting losers keep the voting right in the second period. We show that as soon as absolute risk aversion exceeds a threshold value minority voting is superior to repeated application of the simple majority rule. |
| Keywords: | voting, minority, durable decision, risk aversion, tyranny of majority rules |
| JEL: | D7 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:eth:wpswif:07-70&r=upt |
| By: | Adrian Bruhin (Socioeconomic Institute, University of ZurichAuthor-Name: Helga Fehr; Institute of Economic Research, Swiss Federal Institute of Technology Zurich); Thomas Epper (Institute of Economic Research, Swiss Federal Institute of Technology Zurich) |
| Abstract: | It has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture regression model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two distinct types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from rational probability weighting consistent with prospect theory. 20% of the subjects weight probabilities linearly and behave essentially as expected value maximizers. Moreover, the individuals are assigned to one of these two groups with probabilities of close to one resulting in a low measure of entropy. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling. |
| Keywords: | individual risk taking behavior, latent heterogeneity, finite mixture regression models |
| JEL: | D81 C49 |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:soz:wpaper:0705&r=upt |
| By: | Kaynar, B.; Birbil, S.I.; Frenk, J.B.G. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University) |
| Abstract: | In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted. |
| Keywords: | Elliptical distributions;Linear loss functions;Value-at-risk;Conditional value-at-risk;Portfolio optimization;Disutility; |
| Date: | 2007–05–24 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureri:300011262&r=upt |
| By: | Troy Davig |
| Abstract: | This paper assesses the implications for optimal discretionary monetary policy if the slope of the Phillips curve changes. The paper first derives a ‘switching’ Phillips curve from the optimal pricing decision of a monopolistic firm that faces a changing cost of price adjustment. Two states exists, a state with a high cost of price adjustment that generates a ‘flat’ Phillips curve and a low-cost state that generates a relatively ‘steep’ curve. The second aspect of the paper constructs a utility-based welfare criterion. A novel feature of this criterion is that it has a relative weight on output gap deviations that is state dependent, so it changes with the cost of price adjustment. Optimal monetary policy is computed subject to the switching-Phillips curve under both ad-hoc and utility-based welfare criteria. The utility-based criterion instructs monetary policy to disregard the slope of the Phillips curve and keep its systematic actions constant across different states. This stands in contrast to the prescription coming under the ad-hoc criterion, which advises monetary policy to change its systematic behavior according to the slope of the Phillips curve. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedkrw:rwp07-04&r=upt |
| By: | Nadja Silberhorn; Yasemin Boztug; Lutz Hildebrandt |
| Abstract: | The paper discusses the nested logit model for choices between a set of mutually exclusive alternatives (e.g. brand choice, strategy decisions, modes of transportation, etc.). Due to the ability of the nested logit model to allow and account for similarities between pairs of alternatives, the model has become very popular for the empirical analysis of choice decisions. However the fact that there are two different specifications of the nested logit model (with different outcomes) has not received adequate attention. The utility maximization nested logit (UMNL) model and the non-normalized nested logit (NNNL) model have different properties, influencing the estimation results in a different manner. This paper introduces distinct specifications of the nested logit model and indicates particularities arising from model estimation. The effects of using various software packages on the estimation results of a nested logit model are shown using simulated data sets for an artificial decision situation. |
| Keywords: | nested logit model, utility maximization nested logit, nonnormalized nested logit, simulation study |
| JEL: | C13 C31 C87 M31 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2007-046&r=upt |
| By: | Stéphane Loisel (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - [Université Claude Bernard - Lyon I]); Didier Rullière (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - [Université Claude Bernard - Lyon I]) |
| Abstract: | In a classical risk model under constant interest force, we study the probability that the surplus of an insurance company reaches an upper barrier before a lower barrier. We define this probability as win-first probability. Borrowing ideas from life-insurance theory, hazard rates of the maximum of the surplus before ruin, regarded as a remaining future lifetime random variable, are studied, and provide an original derivation of the win-first probability. We propose an algorithm to efficiently compute this risk-return indicator and its derivatives in the general case, as well as bounds of these quantities. The efficiency of the proposed algorithm is compared with adaptations of other existing methods, and its interest is illustrated by the computation of the expected amount of dividends paid until ruin in a risk model with a dividend barrier strategy. |
| Keywords: | Ruin probability; hazard rate; upper absorbing barrier; constant interest force; risk-return indicator; win-first probability |
| Date: | 2007–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:hal-00165791_v1&r=upt |
| By: | Itzhak Gilboa (Tel-Aviv University, HEC, and Cowles Foundation, Yale University); Andrew Postlewaite (Department of Economics, University of Pennsylvania); David Schmeidler (Tel-Aviv University and Ohio State University) |
| Abstract: | Economic modeling assumes, for the most part, that agents are Bayesian, that is, that they entertain probabilistic beliefs, objective or subjective, regarding any event in question. We argue that the formation of such beliefs calls for a deeper examination and for explicit modeling. Models of belief formation may enhance our understanding of the probabilistic beliefs when these exist, and may also help up characterize situations in which entertaining such beliefs is neither realistic nor necessarily rational. |
| Keywords: | Decision making, Bayesian, Behavioral Economics |
| JEL: | B4 D8 |
| Date: | 2007–08–02 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:07-023&r=upt |
| By: | James Mitchell; Martin Weale |
| Abstract: | This paper assesses the accuracy of individuals’ expectations of their financial circumstances, as reported in the British Household Panel Survey, as predictors of outcomes and identifies what factors influence their reliability. Bivariate ordered probit models, appropriately identified, are estimated to draw out the differential effect of information on expectations and realisations. Rationality is then tested and we seek to explain deviations of realisations from expectations at a micro-economic level, possibly with reference to macroeconomic shocks. A bivariate regime-switching ordered probit model, distinguishing between states of rationality and irrationality, is then estimated to try and explain departures from rationality and identify whether certain individual characteristics are associated with rational behaviour. |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:nsr:niesrd:287&r=upt |
| By: | Stéphane Loisel (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - [Université Claude Bernard - Lyon I]) |
| Abstract: | We consider a main insurance company with K subcompanies (or lines of busi- ness). The joint evolution of the surpluses of these lines of business is modeled by a Markov-modulated multivariate compound Poisson model with Poisson common shocks, modified by interactions between the lines of business and paiement of divi- dends. We assume that the financial situation of the subcompanies has an impact on the other companies, for example because they have part of their surplus invested in one another. If a line of business is in the red, the others have to pay a penalty, which is traduced by a decrease of the premium received by unit of time, or by a lost of dividends for the shareholders if the other line of business is "doing well". Conversely, a line of business with a high surplus level may increase the premium by unit of time of the others as they receive part of the dividends. In this paper, we focus on a particular line of business, and provide an approximation for expected time to ruin, and the expected amounts of dividends paid to the shareholders, and used to pay penalty due to insolvency of some subcompany. The method is to discretize claim amounts and to approximate the multidimensional surplus process of the subcompanies with a continuous time Markov process with finite state space. A technique of Frostig (2005) and Kella and Whitt (1992) enables us to get approximates, which are shown to converge to the desired values. It is possible to compare the behavior of the main company with and without the other subcompanies, which could provide a tool to help making consortium building decision. |
| Keywords: | multi-risk model; ruin theory; dividends; lines of business; Markovian environment; common shock |
| Date: | 2007–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:hal-00165776_v1&r=upt |
| By: | Karen A. Kopecky (The University of Western Ontario) |
| Abstract: | In each of the following chapters, macro models are developed to explore the impact of technological progress on the household. Chapter 1 focuses on the impact of technological progress in transportation on suburbanization. In this chapter, a model of a city is developed in which agents choose both whether or not to own a car, and where to live. Focusing on the period 1910 to 1970, the model is calibrated to match the fall in automobile prices, the rise in real incomes, and the rise in the cost of commuting by public transportation relative to commuting by car. Under the baseline calibration the model predicts both a rise in car-ownership and decentralization. In Chapter 2, a model with leisure production and endogenous retirement is used to explain the declining labor-force participation rates of elderly males. Using the Health and Retirement Study, the model is calibrated to cross-sectional data on the labor-force participation rates of elderly US males by age and their average drop in market consumption in the year 2000. Running the calibrated model for the period 1850 to 2000, a prediction of the evolution of the cross-section is obtained and compared with data. The model is able to predict both the increase in retirement since 1850 and the observed drop in market consumption at the moment of retirement. The increase in retirement is driven by rising real wages and a falling price of leisure goods over time. Finally, in Chapter 3, the welfare gain from technological progress in personal computer production is measured by constructing a simple model of computer demand. The innovation of the model is in the agent's utility function. Preferences are defined such that the marginal utility of zero computer consumption is finite. Thus the model can predict the zero demand for computers observed in the data and generate a finite welfare gain from their introduction into the market. The model is calibrated using data on computer expenditures. The model suggests that the welfare gain from technological progress in personal computers is approximately 4 percent of total consumption expenditure. |
| Keywords: | technological progress, suburbanization, population density gradient, retirement leisure goods, computers, welfare gain |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:eag:disser:4&r=upt |