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on Utility Models and Prospect Theory |
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Issue of 2024‒08‒12
thirteen papers chosen by |
| By: | Fabian Herweg; Svenja Hippel; Daniel Müller; Fabio Römeis |
| Abstract: | We investigate whether violations of canonical axioms of choice under risk are mistakes or a manifestation of true preferences. First, we elicit axiom and gamble preferences and then allow subjects to revise their potentially conflicting preferences. Among the behavioral patterns that allow for a clear-cut interpretation on the decision level, we find that roughly 70% of axiom viola-tions are intentional whereas only 30% are mistakes. On the subject level we can clearly categorize almost half of our subjects. Among those, roughly 24%are rational expected utility maximizers, 24% make occasional mistakes, and 52% refute the normative value of these axioms. |
| Keywords: | axiomatic rationality, choice under risk, context-dependent preferences, mistakes, regret theory |
| JEL: | C91 D01 D81 D91 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11166 |
| By: | Romain Gauchon (ISFA - Institut de Science Financière et d'Assurances); Karim Barigou (ISFA - Institut de Science Financière et d'Assurances) |
| Abstract: | Expected utility is an influential theory to study rational choice among risky assets. For each investment, an economic agent expects to receive a random payoff and therefore maximizes its expected utility. To the best of our knowledge, there exists no general procedure to take the derivative of the expected utility as a function of the investment without heavy assumptions on the underlying processes. This article considers expected utility maximization when payoffs are modeled by a family of random variables increasing with investment for the convolution order such as Poisson, Gamma or Exponential distributions. For several common utility functions, with the help of fractional calculus, we manage to obtain closed-form formulas for the expected utility derivative. The paper also provides two economic applications: production of competitive firms and investment in prevention. |
| Keywords: | Convolution order, Expected utility, Fractional calculus, Prevention |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-03295594 |
| By: | Bahman Angoshtari; Xiang Yu; Fengyi Yuan |
| Abstract: | This paper studies a loss-averse version of the multiplicative habit formation preference and the corresponding optimal investment and consumption strategies over an infinite horizon. The agent's consumption preference is depicted by a general S-shaped utility function of her consumption-to-habit ratio. By considering the concave envelope of the S-shaped utility and the associated dual value function, we provide a thorough analysis of the HJB equation for the concavified problem via studying a related nonlinear free boundary problem. Based on established properties of the solution to this free boundary problem, we obtain the optimal consumption and investment policies in feedback form. Some new and technical verification arguments are developed to cope with generality of the utility function. The equivalence between the original problem and the concavified problem readily follows from the structure of the feedback policies. We also discuss some quantitative properties of the optimal policies under several commonly used S-shaped utilities, complemented by illustrative numerical examples and their financial implications. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.20063 |
| By: | Yuan Gu; Chao Hung Chan |
| Abstract: | This paper proposes a model of decision-making under uncertainty in which an agent is constrained in her cognitive ability to consider complex acts. We identify the complexity of an act according to the corresponding partition of state space. The agent ranks acts according to the expected utility net of complexity cost. A key feature of this model is that the agent is able to update her complexity cost function after the arrival of new information. The main result characterizes axiomatically an updating rule for complexity cost function, the Minimal Complexity Aversion representation. According to this rule, the agent measures the complexity cost of an act conditional on the new information by using the cost of another act that gives exactly the same partition of the event but with the lowest ex-ante cost. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.18463 |
| By: | Mark Whitmeyer |
| Abstract: | We begin by formulating and characterizing a dominance criterion for prize sequences: $x$ dominates $y$ if any impatient agent prefers $x$ to $y$. With this in hand, we define a notion of comparative patience. Alice is more patient than Bob if Alice's normalized discounted utility gain by going from any $y$ to any dominating $x$ is less than Bob's discounted utility gain from such an improvement. We provide a full characterization of this relation in terms of the agents' discount rules. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.02323 |
| By: | James A. Roumasset (Department of Economics, University of Hawaii at Manoa) |
| Abstract: | Assertions of pervasive inefficiency in the behavior and organization of developing agriculture are found to be based on unsound methodologies. Models apparently based on expected utility theory are theoretically flawed and use highly restrictive assumptions that make them largely irrelevant for explaining actual decisions. When a more appropriate model is applied to the case of the green revolution in the Philippines, the hypothesis that loss aversion impedes adoption of new technology is rejected. Common assertions about the inefficiency of agricultural institutions are also found wanting. The risk-bearing theory share- tenancy, which is thought to imply high agency costs associated with effort shirking, cannot explain observed tenant shares. Once the disadvantages of fixed-lease contracts are recognized, sharing is plausibly second-best efficient. The purported inefficiency implied by the inverse relationship between farm size and yield per hectare also dissipates once the endogeneity of farm size is accounted for. In as much as efficiency can explain the stylized facts of behavior and organization in developing agriculture, policy recommendations based on misplaced exogeneity should be viewed with considerable skepticism. |
| Keywords: | Loss-aversion, uncertainty, share tenancy, developing agriculture, nature of the firm |
| JEL: | D01 G22 J43 O12 Q12 Q15 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:hai:wpaper:202403 |
| By: | Oliver, Adam |
| Abstract: | In a previously published article, I reported some tests of prospect theory's reflection effect over outcomes defined by money and life years gained from treatment. Those results suggested qualified support for the reflection effect over money outcomes and strong support over longevity outcomes. This article reruns those tests while accounting for the intensity of individual risk attitudes, and, overall, show consistency with the reflection effect. However, I argue that these results do not necessarily offer support for the explanatory power of prospect theory. Rather, the results may be driven by evolved responses to circumstances that provoke perceptions of scarcity and abundance. Therefore, from an ecological perspective, behavioral patterns such as those that are consistent with the reflection effect, which, by extension, tend to be considered as erroneous or biased by most behavioral economists because they conflict with the postulates of rational choice theory, may not be unreasonable. Recognizing as such is important when considering how behavioral insights ought to inform public policy design and implementation. |
| Keywords: | expected utility theory; prospect theory; reflection effect; risk intensity; risk sensitivity theory |
| JEL: | B21 C12 C91 |
| Date: | 2024–01–01 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:123966 |
| By: | Brian McFadden |
| Abstract: | A mechanism is described that addresses the fundamental trade off between media producers who want to increase reach and consumers who provide attention based on the rate of utility received, and where overreach negatively impacts that rate. An optimal solution can be achieved when the media source considers the impact of overreach in a cost function used in determining the optimal distribution of content to maximize individual consumer utility and participation. The result is a Nash equilibrium between producer and consumer that is also Pareto efficient. Comparison with the literature on Recommender systems highlights the advantages of the mechanism.The review suggests advancements over that literature including identifying an optimal content volume for the consumer and improvements for handling multiple objectives A practical algorithm to generate the optimal distribution for each consumer is provided. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.16212 |
| By: | Cremer, Helmuth (Toulouse School of Economics); Lozachmeur, Jean-Marie (Toulouse School of Economics) |
| Abstract: | We study the design of nonlinear reimbursement rules for expenses on secondary preventive and on therapeutic care. With some probability individuals are healthy and do not need any therapeutic health care. Otherwise they become ill and the severity of their disease is realized and identifies their ex post type. Preventive care is determined ex ante, that is before the health status is determined while curative care is chosen ex post. Insurance benefits depend on preventive and curative care in a possibly nonlinear way, and marginal benefits can be positive or negative. In the first best, achieved when health status is ex post publicly observable, insurance benefits are flat (lump sum payments) and do not depend on expenditures. When the severity of the disease is not observable, so that there is ex post moral hazard, this solution is not incentive compatible (for more healthy individuals). The optimal insurance then implies benefits that increase with both types of care. This is because health expenditures reduce informational rents and they are upward distorted. This relaxes the incentive constraint because less healthy individuals value care more than healthy individuals. Even though preventive care is chosen ex ante, when there is no asymmetry of information, it does have an impact on the incentive constraint and thus on informational rents. This is due to two concurring effects. First, prevention is more e§ective for the more severely ill. Second, these individuals also have a lower marginal utility of income so that a given level of expenditure on preventive care has less impact on their utility. Finally, when individuals misperceive the benefits of preventive care, our results remain valid, but there is now an extra corrective (Pigouvian) term in the expression for the marginal reimbursement of preventive care. |
| Keywords: | ex post moral hazard, health insurance, secondary prevention |
| JEL: | I11 I13 I18 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17090 |
| By: | Atulya Jain; Vianney Perchet |
| Abstract: | How should an expert send forecasts to maximize her utility subject to passing a calibration test? We consider a dynamic game where an expert sends probabilistic forecasts to a decision maker. The decision maker uses a calibration test based on past outcomes to verify the expert's forecasts. We characterize the optimal forecasting strategy by reducing the dynamic game to a static persuasion problem. A distribution of forecasts is implementable by a calibrated strategy if and only if it is a mean-preserving contraction of the distribution of conditionals (honest forecasts). We characterize the value of information by comparing what an informed and uninformed expert can attain. Moreover, we consider a decision maker who uses regret minimization, instead of the calibration test, to take actions. We show that the expert can achieve the same payoff against a regret minimizer as under the calibration test, and in some instances, she can achieve strictly more. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.15680 |
| By: | Jeremias Lenzi |
| Abstract: | Voting mechanisms are widely accepted and used methods for decentralized decision-making. Ensuring the acceptance of the voting mechanism's outcome is a crucial characteristic of robust voting systems. Consider this scenario: A group of individuals wants to choose an option from a set of alternatives without requiring an identification or proof-of-personhood system. Moreover, they want to implement utilitarianism as their selection criteria. In such a case, players could submit votes multiple times using dummy accounts, commonly known as a Sybil attack (SA), which presents a challenge for decentralized organizations. Is there a voting mechanism that always prevents players from benefiting by casting votes multiple times (SA-proof) while also selecting the alternative that maximizes the added valuations of all players (efficient)? One-person-one-vote is neither SA-proof nor efficient. Coin voting is SA-proof but not efficient. Quadratic voting is efficient but not SA-proof. This study uses Bayesian mechanism design to propose a solution. The mechanism's structure is as follows: Players make wealth deposits to indicate the strength of their preference for each alternative. Each player then receives an amount based on their deposit and the voting outcome. The proposed mechanism relies on two main concepts: 1) Transfers are influenced by the outcome in a way that each player's optimal action depends only on individual preferences and the number of alternatives; 2) A player who votes through multiple accounts slightly reduces the expected utility of all players more than the individual benefit gained. This study demonstrates that if players are risk-neutral and each player has private information about their preferences and beliefs, then the mechanism is SA-proof and efficient. This research provides new insights into the design of more robust decentralized decision-making mechanisms. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.01844 |
| By: | Enrique Estefania-Salazar; Michael Carter; Eva Iglesias; Álvaro Escribano |
| Abstract: | Despite its promise to help low-wealth households manage climate risk, index insurance remains hampered by downside basis risk, meaning that an insured party suffers a loss, but receives no payment because the insurance index fails to register a loss. While efforts to reduce basis risk focus on the creation of indices that better predict losses, this paper focuses on the creation of statistically rigorous insurance zones that minimize downside basis risk. In contrast to our approach, most existing index insurance contracts use statistically ad hoc administrative boundaries to demarcate insurance zones. To improve on this practice, we develop a machine learning algorithm that forms zones to maximizes lower tail dependence within the zone. After exploring the logic for using lower tail dependence, we apply our algorithm to the long-running index-based livestock insurance contract in Northern Kenya. We show that compared to the currently employed administrative insurance areas, our algorithm creates an insurance contract that increases the expected utility value of the insurance by 60-200% even when keeping the number of zones the same. Optimizing the number of zones using our method can further increase the economic value of index insurance to its beneficiaries. |
| JEL: | G22 O13 O16 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32618 |
| By: | Axelle Ferriere; Philipp Grübener; Dominik Sachs |
| Abstract: | Over the last decades, the United States has experienced a large increase in, both, income inequality and living standards. The workhorse models of optimal income taxation call for more redistribution as inequality rises. By contrast, living standards play no role for taxes and transfers in these homothetic environments. This paper incorporates living standards into the optimal income tax problem by means of non-homothetic preferences. In a Mirrlees setup, we show that rising living standards alter both sides of the equity-efficiency trade-off. As an economy becomes richer, non-homotheticities imply a fall in the dispersion of marginal utilities, which weakens distributional concerns but has ambiguous effects on efficiency concerns. In a dynamic incomplete-market setup calibrated to the United States in 1950 and 2010, we quantify this new channel. Rising living standards dampen by at least 25% the desired increase in redistribution due to rising inequality. |
| Keywords: | taxation, growth, non-homothetic preferences, redistribution |
| JEL: | E62 H21 H31 O23 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11141 |