nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2023‒04‒24
thirteen papers chosen by
Alexander Harin
Modern University for the Humanities

  1. Optimal consumption with labor income and borrowing constraints for recursive preferences By Dirk Becherer; Wilfried Kuissi-Kamdem; Olivier Menoukeu-Pamen
  2. Optimal Investment in Defined Contribution Pension Schemes with Forward Utility Preferences By Kenneth Tsz Hin Ng; Wing Fung Chong
  3. Investigation of the Convex Time Budget Experiment by Parameter Recovery Simulation By Keigo Inukai; Yuta Shimodaira; Kohei Shiozawa
  4. Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learning By Ruitu Xu; Yifei Min; Tianhao Wang; Zhaoran Wang; Michael I. Jordan; Zhuoran Yang
  5. Longevity, Health and Housing Risks Management in Retirement By Pierre-Carl Michaud; Pascal St-Amour
  6. Nash equilibria for relative investors with (non)linear price impact By Nicole B\"auerle; Tamara G\"oll
  7. How Do Political Institutions Affect Sustainability? By C.Y. Cyrus Chu; Meng-Yu Liang
  8. When do privatizations have popular support? A voting model By Rim Lahmandi-Ayed; Didier Laussel
  9. A "Potentially Better" α−MaxMin Axiomatisation of Temporally-Biased Multiple Discounts By Jean-Pierre Drugeon; Thai Ha-Huy
  10. Measuring Stochastic Rationality By Efe A. Ok; Gerelt Tserenjigmid
  11. Strategic Ambiguity in Global Games By Takashi Ui
  12. Are academic achievement and preferences in Math and Japanese associated with Prosociality? By Endo Naoki
  13. Bernard Mandeville: Wealth beyond Vice and Virtue By Jimena Hurtado

  1. By: Dirk Becherer (Institute of Mathematics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany); Wilfried Kuissi-Kamdem (Department of Mathematics, University of Rwanda, Kigali 4285, Rwanda); Olivier Menoukeu-Pamen (Institute of Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom)
    Abstract: We study the optimal consumption and investment problem for an investor with liquidity constraints who has isoelastic recursive Epstein-Zin utility preferences and receives a stochastic stream of income. We characterize the optimal consumption strategy as well as the terminal wealth for recursive utility under dynamic liquidity constraints, which prevent the investor to borrow against his stochastic future income. Using duality and backward SDE methods in a possibly non-Markovian diffusion model for the financial market, this gives rise to an interplay of singular control and optimal stopping problems. Our analysis extends to more general liquidity constraints.
    Keywords: Liquidity constraints, Optimal consumption, Stochastic income, Epstein-Zin recursive utility, Duality, Optimal stopping, Singular control, Reflected BSDE
    Date: 2023–03–07
  2. By: Kenneth Tsz Hin Ng; Wing Fung Chong
    Abstract: Optimal investment strategies of an individual worker during the accumulation phase in the defined contribution pension scheme have been well studied in the literature. Most of them adopted the classical backward model and approach, but any pre-specifications of retirement time, preferences, and market environment models do not often hold in such a prolonged horizon of the pension scheme. Pre-commitment to ensure the time-consistency of an optimal investment strategy derived from the backward model and approach leads the supposedly optimal strategy to be sub-optimal in the actual realizations. This paper revisits the optimal investment problem for the worker during the accumulation phase in the defined contribution pension scheme, via the forward preferences which resolve the pre-specification issues in the backward model and approach. Stochastic partial differential equation representation for the worker's forward preferences is illustrated. This paper constructs two of the forward utility preferences and solves the corresponding optimal investment strategies, in the cases of initial power and exponential utility functions.
    Date: 2023–03
  3. By: Keigo Inukai; Yuta Shimodaira; Kohei Shiozawa
    Abstract: The convex time budget (CTB) method is a widely used experimental technique for eliciting an individual’s time preference in intertemporal choice problems. This paper investigates the accuracy of the estimation of the discount factor parameter and the present bias parameter in the quasi-hyperbolic discounting utility function for the CTB experiment. In this paper, we use a simulation technique called “parameter recovery.” We found that the precision of present bias parameter estimation is poor within the scope of previously reported parameter estimates, making it difficult to detect the effect of present bias. Our results recommend against using a combination of the CTB experimental task and the quasi-hyperbolic discounting utility model to explore the effect of present bias. This paper contributes to addressing the replicability issue in experimental economics and highlights the importance of auditing the accuracy of parameter estimates before conducting an experiment.
    Date: 2022–08
  4. By: Ruitu Xu; Yifei Min; Tianhao Wang; Zhaoran Wang; Michael I. Jordan; Zhuoran Yang
    Abstract: We study a heterogeneous agent macroeconomic model with an infinite number of households and firms competing in a labor market. Each household earns income and engages in consumption at each time step while aiming to maximize a concave utility subject to the underlying market conditions. The households aim to find the optimal saving strategy that maximizes their discounted cumulative utility given the market condition, while the firms determine the market conditions through maximizing corporate profit based on the household population behavior. The model captures a wide range of applications in macroeconomic studies, and we propose a data-driven reinforcement learning framework that finds the regularized competitive equilibrium of the model. The proposed algorithm enjoys theoretical guarantees in converging to the equilibrium of the market at a sub-linear rate.
    Date: 2023–02
  5. By: Pierre-Carl Michaud; Pascal St-Amour
    Abstract: Annuities, long-term care insurance and reverse mortgages remain unpopular to manage longevity, medical and housing price risks after retirement. We analyze low demand using a life-cycle model structurally estimated with a unique stated-preference survey experiment of Canadian households. Low risk aversion, substitution between housing and consumption and low marginal utility when in poor health explain most of the reduced demand. Bequests motives are found to be a luxury good and play a limited role. The remaining disinterest is explained by information frictions and behavioural status-quo biases. We find evidence of strong spousal co-insurance motives motivating LTCI and of responsiveness to bundling with a near doubling of demand for annuities when reverse mortgages can be used to annuitize, instead of consuming home equity. Les rentes, l'assurance soins de longue durée (ASLD) et les prêts hypothécaires inversés restent impopulaires pour gérer les risques de longévité, les risques médicaux et les risques liés au prix du logement après la retraite. Nous analysons la faible demande à l'aide d'un modèle de cycle de vie estimé de manière structurelle avec une expérience par enquête unique de préférences déclarées auprès de ménages canadiens. Une faible aversion pour le risque, la substitution entre le logement et la consommation et une faible utilité marginale en cas de mauvaise santé expliquent principalement la faible demande. Les motifs de legs s'avèrent être un bien de luxe et ne jouent qu'un rôle limité. Le désintérêt restant s'explique par des frictions informationnelles et des biais comportementaux (inertie). Nous trouvons des preuves de l'existence d'une forte motivation de coassurance entre conjoints, qui motive l'achat d'ASLD; et de réactivité à l'offre groupée, avec un quasi-doublement de la demande de rentes lorsque les prêts hypothécaires inversés peuvent être utilisés pour constituer des rentes, au lieu de consommer la valeur nette du logement.
    Keywords: retirement wealth, insurance, health risk, housing risk, patrimoine retraite, assurance, risque santé, risque logement
    JEL: J14 G52 G53
    Date: 2023–03–13
  6. By: Nicole B\"auerle; Tamara G\"oll
    Abstract: We consider the strategic interaction of $n$ investors who are able to influence a stock price process and at the same time measure their utilities relative to the other investors. Our main aim is to find Nash equilibrium investment strategies in this setting in a financial market driven by a Brownian motion and investigate the influence the price impact has on the equilibrium. We consider both CRRA and CARA utility functions. Our findings show that the problem is well-posed as long as the price impact is at most linear. Moreover, numerical results reveal that the investors behave very aggressively when the price impact is beyond a critical parameter.
    Date: 2023–03
  7. By: C.Y. Cyrus Chu (Institute of Economics, Academia Sinica, Taipei, Taiwan); Meng-Yu Liang (Institute of Economics, Academia Sinica, Taipei, Taiwan)
    Abstract: In capturing the famous collapsing case of Easter Island, we set up a model where the society’s ruler has to allocate resources between consumption goods and statue construction. Since the incumbent rulers may be addicted to the glory or pleasure of statue erection, their utility function may be alienated from that of the citizens. We analyze how sustainability may differ under democracy and autocracy regimes. We prove that when the discount factor is small (large), the democracy regime is more sustainable (both regimes are equally sustainable). When the discount factor is somewhere in between, citizens’attitude toward state accountability plays a critical role. When citizens are “weak”, the threat of replacing a reckless ruler under democracy is not credible. We identify a narrow parameter range in which an autocrat has a strong self-discipline to prevent an environmental collapse, whereas the democracy regime performs worse.
    Date: 2023–04
  8. By: Rim Lahmandi-Ayed (UR MASE - Modélisation et Analyse Statistique et Economique - ESSAIT - Ecole Supérieure de la Statistique et de l'Analyse de l'Information - Université de Carthage - University of Carthage); Didier Laussel (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We consider a general equilibrium model with vertical preferences, where workers and consumers are differentiated respectively by their sensitivity to effort and their intensity of preference for quality. We consider a public monopoly, i.e. which is owned equally by all individuals. The question is under which conditions the firm will be privatized and at which rate/price. The decisions are taken through majority vote in a plurality system. When the firm is controlled by the State, the price is determined through a vote among all the population. Otherwise, the price is the one which maximizes the profit. We prove that, when the maximum disutility of working in the firm is higher than the maximum utility of consuming its output, privatization may emerge as a possible choice of the majority, even if no hypothesis is made on the efficiency of a private management relative to a public one.
    Keywords: Democracy, General equilibrium, Privatization, Vertical preferences, Majority vote, Public monopoly
    Date: 2022–05
  9. By: Jean-Pierre Drugeon (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Thai Ha-Huy (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay)
    Abstract: This article introduces an axiomatic approach of utilities streams based upon three preference relations, namely the close future order, the distant future order, and the main order. Assuming all these preferences to be bi-separable, the article derives a unanimous representation for weights over periods. The analysis of two categories of a \emph{potentially better} property allows for the establishment of \textit{MaxMin}, \textit{MaxMax}, and $\alpha-$\textit{MaxMin} representations. This is followed by the presentation of a multiple discounts rates version of $T^{*}$-temporally biased, generalizing quasi-hyperbolic discounting for the close future order. A similar analysis for the distant future is also performed, where it is proved that Banach limits can be considered as the distant future counterpart of exponential discounting in the evaluation of the close future.
    Keywords: Axiomatisation, Multiple Discounts, α−MaxMin Citeria, Temporal Biases, Banach Limits
    Date: 2023–03–02
  10. By: Efe A. Ok; Gerelt Tserenjigmid
    Abstract: We develop a partial ordering approach toward comparing stochastic choice functions on the basis of their rationality. We do this by assigning to any stochastic choice function a one-parameter class of deterministic choice correspondences, and then checking for the rationality (in the standard sense of revealed preference) of these correspondences for each parameter value. Similar to the classical notion of deterministic rationality, our rationality ordering detects violations of (stochastic) transitivity as well as inconsistencies between choices from nested menus. We obtain an easy-to-use characterization of this ordering, and then use that characterization to introduce an index of stochastic rationality. We apply our ordering and index to some well-known stochastic choice models and provide an empirical application using a famous experiment by Amos Tversky.
    Date: 2023–03
  11. By: Takashi Ui
    Abstract: In games with incomplete and ambiguous information, rational behavior depends not only on fundamental ambiguity (ambiguity about states) but also on strategic ambiguity (ambiguity about others' actions). We study the impact of strategic ambiguity in global games. Ambiguous-quality information makes more players choose an action yielding a constant payoff, whereas (unambiguous) low-quality information makes more players choose an ex-ante best response to the uniform belief over the opponents' actions. If the ex-ante best-response action yields a constant payoff, sufficiently ambiguous-quality information induces a unique equilibrium, whereas sufficiently low-quality information generates multiple equilibria. In applications to financial crises, we demonstrate that news of more ambiguous quality triggers a debt rollover crisis, whereas news of less ambiguous quality triggers a currency crisis.
    Date: 2023–03
  12. By: Endo Naoki (Graduate School of Economics, Keio University (Graduate student))
    Abstract: Research surrounding prosociality, defined as the ability to promote behaviors that enhance the utility of others, has been one of the most interesting studies in recent years. This is because prosociality is widely defined as one of the non-cognitive abilities, and non-cognitive abilities are attracting attention as abilities that affect socioeconomic characteristics such as children's future education and income (JJ. Heckman, 2006; Elango et al., 2005). There is a high level of interdisciplinary interest in how such prosociality develops and improves. In particular, several existing studies in the field of educational economics have reported a relationship between academic achievement in core subjects and prosociality in countries other than Japan, such as the United States (Wantzel, 1993; Keung, 2003; Penner et al. 2005; Caprara et al. 2015; Maria et al., 2018; Alpona, 2020). These previous studies adopted the mechanism of the influence of prosociality on academic achievement as a theoretical framework but given that prosociality requires the ability to understand others, it is possible that there is a mechanism by which academic achievement influences prosociality. Since one of the goals of Japanese language education in Japan is to enhance the ability to understand others through text reading, it is thought that academic ability in the Japanese language has a sufficient influence on prosociality. However, there have been no studies examining the relationship between academic achievement and prosociality using data from Japan. Also, there are no studies that examine how preference for major subjects is related to the development and improvement of prosociality. Even if academic ability is high, preference for a subject is considered to be an important factor in whether or not the ability learned from that subject is put into practice. Therefore, it is thought that preference for each subject, as well as academic ability, is related to prosociality. Similarly, there is no study that analyzes how the relationship between academic ability, preference, and prosociality changes over a wide range of grades from lower to upper grades. Because the ability to understand others increases with age, we would expect a stronger relationship between academic achievement and prosociality to emerge with increasing age. Therefore, in order to investigate the relationship between academic achievement and preference for Japanese and mathematics and prosociality in Japan, and how these relationships change with increasing age, I conducted regression analysis using JCPS data for grades 1 through 3 (7-15 years old). The results showed that most of the significant relationships between academic achievement and preference for Japanese and arithmetic (mathematics) and prosociality were observed to be positive. On the other hand, significant negative relationships were reported between academic achievement in math (mathematics) and prosociality, which consisted of the question item "be kind to younger children, " in the 5th and 1st grades of elementary school and 1st grade of junior high school. This can be attributed to the fact that children who were sufficiently rationalized by math did not choose prosocial behavior as a means of maximizing their utility, since they could not expect anything in return from younger children. In addition, the independent variable that was most significantly related to each prosociality in each grade was the preference for the Japanese, and a significant positive relationship was found in all analyses. In the multiple regression analysis that included the independent variables of academic ability in reading comprehension and preference for the Japanese, which are considered to have a strong positive relationship with the ability to understand others, with each prosociality as the dependent variable, the other academic ability variables were not significant or contrary to expectations, were significant with a negative coefficient. The multiple regression results suggest that the single regression analysis in this paper, which included only the academic achievement variable and not the preference for the national language, and the results in the previous literature have turned the academic achievement variable into a proxy variable for the preference for the national language. There are three major contributions of this study to prosociality: First, it was the first empirical analysis of the relationship between prosociality and academic achievement in Japan, and compared the results with those of other countries. Although the results of the analysis of the relationship between academic achievement and prosociality in Japan were not significantly different from those of other countries, some of the results of this study suggest that children may choose prosocial behaviors to maximize their own utility, not based on social preferences. Second, this is the first empirical analysis and discussion of the relationship between preference for major subjects and prosociality. The most positive relationship between prosociality and preference for the Japanese language was found in all the analyses conducted at each grade level. Third, the empirical analysis showed differences in the development of prosociality between the subjects and their preferences through the analysis of each grade. The third is that the empirical analysis showed differences in the development of prosociality between subjects and preferences through analysis at each grade level. No special differences were found in the relationship between preference for each subject and prosociality as age increased. Rather, the results showed an increase in non-significant results for academic achievement and prosociality. This result is contrary to the original expectation of this study, and suggests that the academic achievement variable is positively related to the ability to understand others, which is necessary for prosociality, but it is also positively related to tendencies that inhibit prosocial behavior, such as calculated behavior. Therefore, as students move up through the grades and as calculation ability becomes more important, it tends to lose its relationship with prosocial behavior. Future research should explore whether prosociality changes when academic performance changes, and whether the relationship between academic performance and prosociality tends to strengthen with age, even for children younger than first grade.
    Keywords: prosociality, academic achievement, preference, ability to understand others, Perspective-Taking, Personality, Genetics
    JEL: H53 I20 J24
    Date: 2023–03–16
  13. By: Jimena Hurtado
    Abstract: Bernard Mandeville denounced the moral philosophy of his times, its theoretical and practical dimensions, as elitist and contrary to human nature. The explanations and recommendations derived from this moral philosophy, according to Mandeville, were inadequate to understand and govern commercial society. Mandeville scrutinized existing theories about human nature, confronted them with what he presented as facts and unraveled their contradictions. This leads to Mandeville's challenge: accepting things as they are or assuming the responsibility of transformation. This is the challenge I explore in this paper. We can continue to live in a highly unequal society based on pride and shame or we can create incentives that will lead to a different calculation of passions in line with a Utilitarian criterion.
    Keywords: Bernard Mandeville, moral philosophy, Utilitarianism.
    JEL: A13 B11 B31
    Date: 2023–03–22

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