nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2019‒12‒09
seventeen papers chosen by
Alexander Harin
Modern University for the Humanities

  1. Revealed Preference Analysis of Expected Utility Maximization under Prize-Probability Trade-Offs By Laurens Cherchye; Thomas Demuynck; Bram De Rock; Mikhail Freer
  2. Risk-sensitive preferences and age-dependent risk aversion By Phitawat Poonpolkul
  3. Time lotteries and stochastic impatience By DeJarnette, Patrick; Dillenberger, David; Gottlieb, Daniel; Ortoleva, Pietro
  4. Speculative Trading, Prospect Theory and Transaction Costs By Alex S. L. Tse; Harry Zheng
  5. Choquet utility depending on the state of nature By Issouf Abdou; Philibert Andriamanantena; Mamy Raoul Ravelomanana; Rivo Rakotozafy
  6. The Qualitative Expectations Hypothesis: Model Ambiguity, Consistent Representations of Market Forecasts, and Sentiment By Roman Frydman; Soren Johansen; Anders Rahbek; Morten Tabor
  7. Fair Innings? The Utilitarian and Prioritarian Value of Risk Reduction over a Whole Lifetime By Adler, Matthew; Ferranna, Maddalena; Hammitt, James K.; Treich, Nicolas
  8. Incorporating Conditional Morality into Economic Decisions By Masclet, David; Dickinson, David L.
  9. Incorporating Conditional Morality into Economic Decisions By David Masclet; David L. Dickinson
  10. Proportionality and the Limits of Welfarism By Dominik Peters; Piotr Skowron
  11. Guarantees in Fair Division: beyond Divide & Choose and Moving Knifes By Anna bogomolnaia; Herve Moulin; Richard Stong
  12. The Knightian Uncertainty Hypothesis: Unforeseeable Change and Muth`s Consistency Constraint in Modeling Aggregate Outcomes By Roman Frydman; Soren Johansen; Anders Rahbek; Morten Tabor
  13. The Financing Dilemma Supporting a Project By Mullat, Joseph
  14. Modeling UK Mortgage Demand Using Online Searches By Jaroslav Pavlicek; Ladislav Kristoufek
  15. Betting on the Lord: Lotteries and Religiosity in Haiti By Auriol, Emmanuelle; Delissaint, Diego; Fourati, Maleke; Miquel-Florensa, Josepa; Seabright, Paul
  16. Collectivised Pension Investment with Homogeneous Epstein-Zin Preferences By John Armstrong; Cristin Buescu
  17. Labor Contracts, Gift-Exchange and Reference Wages: Your Gift Need Not Be Mine! By Hernán Bejarano; Brice Corgnet; Joaquín Gómez-Miñambres

  1. By: Laurens Cherchye; Thomas Demuynck; Bram De Rock; Mikhail Freer
    Abstract: We provide a revealed preference characterization of expected utility maximization in binary lotteries with prize-probability trade-offs. This characterization applies to a wide variety of decision problems, including first price auctions, crowdfunding games, posted price mechanisms and principal agent problems. We start by characterizing optimizing behavior when the empirical analyst exactly knows either the probability function of winning or the decision maker’s utility function. Subsequently, we provide a statistical test for the case where the utility function is unknown and the probability function has to be estimated. Finally, we consider the situation with both the probability function and utility function unknown. We show that expected utility maximization has empirical content when these functions satisfy log-concavity assumptions. We demonstrate the empirical usefulness of our theoretical findings through an application to an experimental data set.
    Keywords: expected utility maximization; prize-probability trade offs; revealed preference characterization; testable implication; experiemental data
    JEL: D00
    Date: 2019–11
  2. By: Phitawat Poonpolkul
    Abstract: People in different age groups have shown to differ in their degrees of risk aversion. This study investigates the macroeconomic implications of population aging when households are assumed to be increasingly risk-averse in future utility when they age. The model incorporates risk-sensitive preferences used in Hansen & Sargent (1995), which is the only recursive preferences that can separate risk aversion and intertemporal elasticity of substitution while being monotonic, into a 16-generation discrete-time OLG model with undiversifiable income risk. Compared to a time-additive counterpart, risk-sensitive preferences capture precautionary saving motive that exacerbates adverse responses of aggregate macroeconomic variables under a population aging scenario through demographic re-weighting and life-cycle redistribution channels. Varying risk aversion also allows households to internalize future uncertainties when evaluating their welfare impacts of demographic change, resulting in non-monotonic welfare dynamics with higher welfare loss under a high-risk environment and vice versa. Risk-sensitive preferences with age-dependent risk aversion can play an important role in optimal policy settings by introducing uncertainties into the welfare impact analysis, while taking into account more realistic risk-taking behavior of different age cohorts.
    Keywords: Demographic change, risk-sensitive preferences, overlapping-generation model, precautionary savings, risk aversion
    JEL: D52 E21 E60
    Date: 2019–11
  3. By: DeJarnette, Patrick; Dillenberger, David; Gottlieb, Daniel; Ortoleva, Pietro
    Abstract: We study preferences over lotteries in which both the prize and the payment date are uncertain. In particular, a time lottery is one in which the prize is fixed but the date is random. With Expected Discounted Utility, individuals must be risk seeking over time lotteries (RSTL). In an incentivized experiment, however, we find that almost all subjects violate this property. Our main contributions are theoretical. We first show that within a very broad class of models, which includes many forms of non-Expected Utility and time discounting, it is impossible to accommodate even a single violation of RSTL without also violating a property we termed Stochastic Impatience, a risky counterpart of standard Impatience. We then offer two positive results. If one wishes to maintain Stochastic Impatience, violations of RSTL can be accommodated by keeping Independence within periods while relaxing it across periods. If, instead, one is willing to forego Stochastic Impatience, violations of RSTL can be accommodated with a simple generalization of Expected Discounted Utility, obtained by imposing only the behavioral postulates of Discounted Utility and Expected Utility.
    Keywords: Time Lotteries; Stochastic Impatience; Risk and Time preferences; Expected Discounted Utility
    JEL: C91 C81 D90
    Date: 2019–11–13
  4. By: Alex S. L. Tse; Harry Zheng
    Abstract: A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset as to maximize the expected utility of the round-trip profit net of transaction costs. The optimization problem is formulated as a sequential optimal stopping problem and we provide a complete characterization of the solution. Depending on the preference and market parameters as well as the initial price of the asset, the optimal strategy can be "buy and hold", "buy low sell high", "buy high sell higher" or "no trading". Transaction costs do not necessarily curb speculative trading. For example, while a large proportional transaction cost on sale can unambiguously suppress trading participation, introducing a fixed market entry fee will indeed encourage trading when the asset price level is high.
    Date: 2019–11
  5. By: Issouf Abdou (Université des Comores); Philibert Andriamanantena (Université de Fianarantsoa [Fianarantsoa]); Mamy Raoul Ravelomanana; Rivo Rakotozafy (Université de Fianarantsoa [Fianarantsoa])
    Abstract: This article, which is part of the general framework of mathematics applied to economics, is a decision-making model in total ignorance. Such an environment is characterized by the absence of a law of distribution of the states of nature allowing having good forecasts or anticipations. Based primarily on the integral of Choquet, this model allows aggregating the different states of nature in order to make a better decision. This integral of Choquet imposes itself with respect to the complexity of the environment and also by its relevance of aggregation of the interactive or conflicting criteria. The present model is a combination of the Schmeidler model and the Brice Mayag algorithm for the determination of Choquet 2-additive capacity. It fits into the framework of subjective models and provides an appropriate response to the Ellsberg paradox.
    Abstract: Cet article qui s'inscrit dans le cadre général des mathématiques appliquées à l'économie est un modèle de prise de décision dans l'ignorance totale. Un tel environnement est caractérisé par l'absence d'une loi de distribution des états de la nature permettant d'avoir des bonnes prévisions ou anticipations. Se basant principalement sur l'intégrale de Choquet, ce modèle permet d'agréger les différents états de la nature afin de prendre une meilleure décision. Cette intégrale de Choquet s'impose par rapport à la complexité de l'environnement et aussi par son caractère pertinent d'agrégation des critères interactifs ou conflictuels. Le présent modèle est une combinaison du modèle de Schmeidler et de l'algorithme de Brice Mayag pour la détermination de la capacité 2-additive de Choquet. Il s'inscrit dans le cadre des modèles subjectifs et apporte une réponse appropriée au paradoxe d'Ellsberg.
    Keywords: Intégrale de Choquet,Utilité,Préférences Subjectives,Incertitude,Mesure floue,Uncertainty,Subjective Preferences,Utility,Choquet Integral,Fuzzy measure
    Date: 2019–11–04
  6. By: Roman Frydman (New York University); Soren Johansen (University of Copenhagen); Anders Rahbek (University of Copenhagen); Morten Tabor (University of Copenhagen)
    Abstract: We introduce the Qualitative Expectations Hypothesis (QEH) as a new approach to modeling macroeconomic and Financial outcomes. Building on John Muth`s seminal insight underpinning the Rational Expectations Hypothesis (REH), QEH represents the market`s forecasts to be consistent with the predictions of an economist`s model. However, by assuming that outcomes lie within stochastic intervals, QEH, unlike REH, recognizes the ambiguity faced by an economist and market participants alike. Moreover, QEH leaves the model open to ambiguity by not specifying a mechanism determining specific values that outcomes take within these intervals. In order to examine a QEH model`s empirical relevance, we formulate and estimate its statistical analog based on simulated data. We show that the proposed statistical model adequately represents an illustrative sample from the QEH model. We also illustrate how estimates of the statistical model`s parameters can be used to assess the QEH model`s qualitative implications.
    Keywords: Asset-Price Movements, Model Ambiguity, Models with Time-Varying Parameters, REH, Behavioral Finance, GAS Models
    JEL: D84 C65 G02 G12 C51
  7. By: Adler, Matthew; Ferranna, Maddalena; Hammitt, James K.; Treich, Nicolas
    Abstract: The social value of risk reduction (SVRRi) is the marginal social value of reducing an individual’s fatality risk, as measured by some social welfare function (SWF). This Article investigates SVRR, using a lifetime utility model in which individuals are differentiated by age, lifetime income profile, and lifetime risk profile. We consider both the utilitarian SWF and a “prioritarian” SWF, which applies a strictly increasing and concave transformation to individual utility. We show that the prioritarian SVRR provides a rigorous basis in economic theory for the “fair innings” concept, proposed in the public health literature: as between an older individual and a similarly situated younger individual (one with the same income and risk profile), a risk reduction for the younger individual is accorded greater social weight even if the gains to expected lifetime utility are equal. The comparative statics of prioritarian and utilitarian SVRRs with respect to age, and to (past, present, and future) income and baseline survival probability, are significantly different from the conventional value per statistical life (VSL). Our empirical simulation based upon the U.S. population survival curve and income distribution shows that prioritarian SVRRs with a moderate degree of concavity in the transformation function conform to lay moral judgments regarding lifesaving policies: the young should take priority but income should make no difference.
    Keywords: Social welfare function (SWF); benefit-cost analysis (BCA); value of statistical life (VSL); fair innings; social value of risk reduction (SVRR); utilitaria; prioritarian; risk regulation
    Date: 2019–11
  8. By: Masclet, David (University of Rennes); Dickinson, David L. (Appalachian State University)
    Abstract: We present a framework that incorporates both moral motivations and fairness considerations into utility. The main idea is that individuals face a preference trade-off between their material individual interest and their desire to follow moral norms. In our model, we assume that moral motivation is conditional and may be influenced by others' actions. Specifically, in our framework moral obligation is a combination of two main components: an autonomous component and a social influence component that captures the influence of others. Our framework is able to explain many stylized results in the literature and to improve theories of economic behavior.
    Keywords: fairness, ethical decision making, moral motivation, behavioral economics
    JEL: B3 D6 D9
    Date: 2019–11
  9. By: David Masclet; David L. Dickinson
    Abstract: We present a framework that incorporates both moral motivations and fairness considerations into utility. The main idea is that individuals face a preference trade-off between their material individual interest and their desire to follow moral norms. In our model, we assume that moral motivation is conditional and may be influenced by others’ actions. Specifically, in our framework moral obligation is a combination of two main components: an autonomous component and a social influence component that captures the influence of others. Our framework is able to explain many stylized results in the literature and to improve theories of economic behavior. Key Words: Fairness, Ethical Decision Making, Moral Motivation, Behavioral Economics
    JEL: B3 D6 D9
    Date: 2019
  10. By: Dominik Peters; Piotr Skowron
    Abstract: We study two influential voting rules proposed in the 1890s by Phragm\'en and Thiele, which elect a committee or parliament of k candidates which proportionally represents the voters. Voters provide their preferences by approving an arbitrary number of candidates. Previous work has proposed proportionality axioms satisfied by Thiele's rule (now known as Proportional Approval Voting, PAV) but not by Phragm\'en's rule. By proposing two new proportionality axioms (laminar proportionality and priceability) satisfied by Phragm\'en but not Thiele, we show that the two rules achieve two distinct forms of proportional representation. Phragm\'en's rule ensures that all voters have a similar amount of influence on the committee, and Thiele's rule ensures a fair utility distribution. Thiele's rule is a welfarist voting rule (one that maximizes a function of voter utilities). We show that no welfarist rule can satisfy our new axioms, and we prove that no such rule can satisfy the core. Conversely, some welfarist fairness properties cannot be guaranteed by Phragm\'en-type rules. This formalizes the difference between the two types of proportionality. We then introduce an attractive committee rule which satisfies a property intermediate between the core and extended justified representation (EJR). It satisfies laminar proportionality, priceability, and is computable in polynomial time. We show that our new rule provides a logarithmic approximation to the core. On the other hand, PAV provides a factor-2 approximation to the core, and this factor is optimal for rules that are fair in the sense of the Pigou--Dalton principle.
    Date: 2019–11
  11. By: Anna bogomolnaia; Herve Moulin; Richard Stong
    Abstract: Divide and Choose among two agents, and the Diminishing Share (DS) and Moving Knife (MK) algorithms among many, elicit parsimonious information to guarantee to each a Fair Share, worth at least 1/n-th of the whole manna. Our n-person Divide and Choose (D&C) rule, unlike DS and MK, works if the manna has subjectively good and bad parts. If utilities are additive over indivisible items, it implements the canonical "Fair Share up to one item" approximation. The D&C rule also offers one interpretation of the Fair Share when utilities are neither additive nor monotonic . Under a mild continuity assumption, it guarantees to each agent her minMax utility: that of her best share in the worst possible partition. This is lower than her Maxmin utility: that of her worst share in the best possible partition. When the manna is unanimously good, or unanimously bad, better guarantees than minMax are feasible. Our Bid & Choose rules fix an additive benchmark measure of shares, and ask agents to bid the smallest size of a share they find acceptable. The resulting Guarantee is between the minMax and Maxmin utilities
    Date: 2019–11
  12. By: Roman Frydman (New York University); Soren Johansen (University of Copenhagen); Anders Rahbek (University of Copenhagen); Morten Tabor (University of Copenhagen)
    Abstract: This paper introduces the Knightian Uncertainty Hypothesis (KUH), a new approach to macroeconomics and finance theory. KUH rests on a novel mathematical framework that characterizes both measurable and Knightian uncertainty about economic outcomes. Relying on this framework and John Muth`s pathbreaking hypothesis, KUH represents participants`forecasts to be consistent with both uncertainties. KUH thus enables models of aggregate outcomes that 1) are premised on market participants` rationality, and 2) yet accord a role to both fundamental and psychological (and other non-fundamental) factors in driving outcomes. The paper also suggests how a KUH model`s quantitative predictions can be confronted with time series data.
    Keywords: Unforeseeable Change; Knightian Uncertainty; Muth`s Hypothesis; Model Ambiguity; REH; Behavioral Finance
    JEL: C02 C51 E00 D84 E00
  13. By: Mullat, Joseph
    Abstract: In this note, we will deal with one of the simplest cases of player-formed coalitions, all of which can be considered as “outstanding” in terms of bounded rationality. Bounded rationality is the idea that rational decision making of people is limited by people’s irrational nature. We focused on special coalitions, called "Kernels", that have an advantage over the remaining, due to yielding higher contribution of each individual participant.
    Keywords: coalition, game, contribution, donation, monotonic, project
    JEL: C51 C53 C71
    Date: 2019–11–11
  14. By: Jaroslav Pavlicek (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Opletalova 26, 110 00, Prague, Czech Republic); Ladislav Kristoufek (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Opletalova 26, 110 00, Prague, Czech Republic)
    Abstract: The internet has become the primary source of information for most of the population in modern economies, and as such, it provides an enormous amount of readily available data. Among these are the data on the internet search queries, which have been shown to improve forecasting models for various economic and financial series. In the aftermath of the global financial crisis, modeling and forecasting mortgage demand and subsequent approvals have become a central issue in the banking sector as well as for governments and regulators. Here, we provide new insights into the dynamics of the UK mortgage market, specifically the demand for mortgages measured by new mortgage approvals, and whether or how models of this market can be improved by incorporating the online searches of potential mortgage applicants. Because online searches are expected to be one of the last steps before a customer’s actual application for a large share of the population, intuitive utility is an appealing approach. We compare two baseline models – an autoregressive model and a structural model with relevant macroeconomic variables – with their extensions utilizing online searches on Google. We find that the extended models better explain the number of new mortgage approvals and markedly improve their nowcasting and forecasting performance.
    Keywords: Mortgage, online data, Google Trends, forecasting
    JEL: C22 C52 C53 C82 E27 E51
    Date: 2019–07
  15. By: Auriol, Emmanuelle; Delissaint, Diego; Fourati, Maleke; Miquel-Florensa, Josepa; Seabright, Paul
    Abstract: We conducted an experimental study in Haiti testing for the relationship between religious belief and individual risk taking behavior. 774 subjects played lotteries in a standard neutral protocol and subsequently with reduced endowments but in the presence of religious images of Catholic, Protestant and Voodoo tradition. Subjects chose between paying to play a lottery with an image of their choice, and saving their money to play with no image. Those who chose the former are dened as image buyers and those who chose the latter as non-buyers. Image buyers, who tend to be less educated, more rural, and to exhibit greater religiosity, bet more than non-buyers in all games. In addition, in the presence of religious images all participants took more risk, and buyer took more risk when playing in the presence of their chosen images than when playing with other images. We develop a theoretical model calibrated with our experimental data to explore the channels through which religious images might aect risk-taking. Our results suggest that the presence of images tends to increase individuals' subjective probability of winning the lottery, and that subjects therefore believe in a god who intervenes actively in the world in response to their requests.
    Keywords: Risk preferences; Religion; Field Experiment
    JEL: C93 D81 Z12
    Date: 2019–11
  16. By: John Armstrong; Cristin Buescu
    Abstract: In a collectivised pension fund, investors agree that any money remaining in the fund when they die can be shared among the survivors. We compute analytically the optimal investment-consumption strategy for a fund of $n$ identical investors with homogeneous Epstein--Zin preferences, investing in the Black--Scholes market in continuous time but consuming in discrete time. Our result holds for arbitrary mortality distributions. We also compute the optimal strategy for an infinite fund of investors, and prove the convergence of the optimal strategy as $n\to \infty$. The proof of convergence shows that effective strategies for inhomogeneous funds can be obtained using the optimal strategies found in this paper for homogeneous funds, using the results of [2]. We find that a constant consumption strategy is suboptimal even for infinite collectives investing in markets where assets provide no return so long as investors are "satisfaction risk-averse." This suggests that annuities and defined benefit investments will always be suboptimal investments. We present numerical results examining the importance of the fund size, $n$, and the market parameters.
    Date: 2019–11
  17. By: Hernán Bejarano (CIDE - Centro de inversitgacion y docencia economicas); Brice Corgnet (emlyon business school, GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Joaquín Gómez-Miñambres (Chapman University)
    Abstract: We extend Akerlof's (1982) gift-exchange model to the case in which reference wages respond to changes in the work environment such as those related to unemployment benefits or workers' productivity levels. Our model shows that these changes spur disagreements between workers and employers regarding the value of the reference wage. These disagreements tend to weaken the gift-exchange relationship thus reducing production levels and wages. We find support for these predictions in a controlled, yet realistic, workplace environment. Our work also sheds light on several stylized facts regarding employment relationships such as the increased intensity of labor conflicts when economic conditions are unstable.
    Keywords: Gift-exchange,incentives,self-serving biases,reference-dependent utility,laboratory experiments,labor conflicts
    Date: 2019–11–18

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