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on Utility Models and Prospect Theory |
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Issue of 2024‒07‒08
fourteen papers chosen by |
| By: | Roy Allen |
| Abstract: | In a consideration set model, an individual maximizes utility among the considered alternatives. I relate a consideration set additive random utility model to classic discrete choice and the extended additive random utility model, in which utility can be $-\infty$ for infeasible alternatives. When observable utility shifters are bounded, all three models are observationally equivalent. Moreover, they have the same counterfactual bounds and welfare formulas for changes in utility shifters like price. For attention interventions, welfare cannot change in the full consideration model but is completely unbounded in the limited consideration model. The identified set for consideration set probabilities has a minimal width for any bounded support of shifters, but with unbounded support it is a point: identification "towards" infinity does not resemble identification "at" infinity. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.13945&r= |
| By: | Zongxia Liang; Qi Ye |
| Abstract: | This paper diverges from previous literature by considering the utility maximization problem in the context of investors having the freedom to actively acquire additional information to mitigate estimation risk. We derive closed-form value functions using CARA and CRRA utility functions and establish a criterion for valuing extra information through certainty equivalence, while also formulating its associated acquisition cost. By strategically employing variational methods, we explore the optimal acquisition of information, taking into account the trade-off between its value and cost. Our findings indicate that acquiring earlier information holds greater worth in eliminating estimation risk and achieving higher utility. Furthermore, we observe that investors with lower risk aversion are more inclined to pursue information acquisition. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.09339&r= |
| By: | Skjold, Benjamin; Steinkamp, Simon Richard; Connaughton, Colm; Hulme, Oliver J; Peters, Ole |
| Abstract: | Decision theories commonly assume that risk preferences can be expressed as utility functions, which vary from person to person but are stable over time. A recent model from ergodicity economics reveals that if people want their wealth to grow at the fastest rate they need to adjust their utility functions depending on the dynamics of their wealth. Here, we ask whether humans make such adjustments by exposing them to different wealth dynamics. We carried out an experiment in which participants made consequential risky decisions under two different conditions, additive and multiplicative wealth dynamics. We estimated risk aversion parameters separately in the two conditions for each participant, fitting isoelastic functions via hierarchical Bayesian models. In our pre-registered analyses, we found strong evidence for a change in utility function, namely an increase in the risk aversion parameter under the multiplicative condition, as predicted by ergodicity economics. Apart from evidence for a large effect of wealth dynamics, we also recover trait-like differences between participants that persist across the two conditions. Our study introduces a new experimental design and contains two independent replications between pilot data and a larger cohort. Together, these results provide evidence that human risk-taking behaviour is sensitive to the dynamical context in which decisions are made and that long-term wealth maximization is an important explanatory principle. |
| Date: | 2024–05–28 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:c96yd&r= |
| By: | Yang Liu; Zhenyu Shen |
| Abstract: | In hedge funds, convex compensation schemes are popular to stimulate a high-profit performance for portfolio managers. In economics, non-monotone risk aversion is proposed to argue that individuals may not be risk-averse when the wealth level is low. Combining these two ingredients, we study the optimal control strategy of the manager in incomplete markets. Generally, we propose a wide class of utility functions, the Piecewise Symmetric Asymptotic Hyperbolic Absolute Risk Aversion (PSAHARA) utility, to model the two ingredients, containing both non-concavity and non-differentiability as some abnormalities. Significantly, we derive an explicit optimal control for the family of PSAHARA utilities. This control is expressed into a unified four-term structure, featuring the asymptotic Merton term and the risk adjustment term. Furthermore, we provide a detailed asymptotic analysis and numerical illustration of the optimal portfolio. We obtain the following key insights: (i) A manager with the PSAHARA utility becomes extremely risk-seeking when his/her wealth level tends to zero; (ii) The optimal investment ratio tends to the Merton constant as the wealth level approaches infinity and the negative Merton constant when the wealth falls to negative infinity, implying that such a manager takes a risk-seeking investment as the wealth falls negatively low; (iii) The convex compensation still induces a great risk-taking behavior in the case that the preference is modeled by SAHARA utility. Finally, we conduct a real-data analysis of the U.S. stock market under the above model and conclude that the PSAHARA portfolio is very risk-seeking and leads to a high return and a high volatility (two-peak Sharpe ratio). |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.00435&r= |
| By: | Giulio Fella; Martin B. Holm; Thomas Michael Pugh |
| Abstract: | We use administrative data for Norway to estimate an incomplete-market life cycle model of retired singles and couples with a bequest motive, health-dependent utility, and uncertain longevity and health. We allow the parameters of the bequest utility to differ between households with and without offspring. Our estimates imply a very strong utility of residual wealth (bequest motive), in line with the estimates by Lockwood (2018). The bequest motive accounts for approximately three-quarters of aggregate wealth at age 85. More surprisingly, we estimate similar utility of residual wealth for households with and without offspring. that the utility of residual wealth represents forces beyond an altruistic bequest motive. |
| Keywords: | Economic models; Fiscal policy; Housing; Labour markets |
| JEL: | D11 D12 D14 E21 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:bca:bocawp:24-21&r= |
| By: | Wu, Keyu (University of Zurich); Fehr, Ernst (University of Zurich); Hofland, Sean (Lucerne School of Business); Schonger, Martin (Lucerne School of Business) |
| Abstract: | Ambiguous prospects are ubiquitous in social and economic life, but the psychological foundations of behavior under ambiguity are still not well understood. One of the most robust empirical regularities is the strong correlation between attitudes towards ambiguity and compound risk which suggests that compound risk aversion may provide a psychological foundation for ambiguity aversion. However, compound risk aversion and ambiguity aversion may also be independent psychological phenomena, but what would then explain their strong correlation? We tackle these questions by training a treatment group’s ability to reduce compound to simple risks, and analyzing how this affects their compound risk and ambiguity attitudes in comparison to a control group who is taught something unrelated to reducing compound risk. We find that aversion to compound risk disappears almost entirely in the treatment group, while the aversion towards both artificial and natural sources of ambiguity remain high and are basically unaffected by the teaching of how to reduce compound lotteries. Moreover, similar to previous studies, we observe a strong correlation between compound risk aversion and ambiguity aversion, but this correlation only exists in the control group while in the treatment group it is rather low and insignificant. These findings suggest that ambiguity attitudes are not a psychological relative, and derived from, attitudes towards compound risk, i.e., compound risk aversion and ambiguity aversion do not share the same psychological foundations. While compound risk aversion is primarily driven by a form of bounded rationality – the inability to reduce compound lotteries – ambiguity aversion is unrelated to this inability, suggesting that ambiguity aversion may be a genuine preference in its own right. |
| Keywords: | ambiguity aversion, compound risk aversion, bounded rationality, reduction of compound lotteries |
| JEL: | C91 D01 D91 |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17032&r= |
| By: | Elena Capatina (Australian National University, Acton Canberra, Australia); Gary Hansen (UCLA, Department of Economics, Los Angeles, USA); Minchung Hsu (National Graduate Institute for Policy Studies, Tokyo, Japan) |
| Abstract: | This paper compares the impact of long term care (LTC) risk on single and married households and studies the roles played by informal care (IC), consumption sharing within households, and Medicaid in insuring this risk. We develop a life-cycle model where individuals face survival and health risk, including the possibility of becoming highly disabled and needing LTC. Households are heterogeneous in various important dimensions including education, productivity, and the age difference between spouses. Health evolves stochastically. Agents make consumption-savings decisions in a framework featuring an LTC statedependent utility function. We find that household expenditures increase significantly when LTC becomes necessary, but married individuals are well insured against LTC risk due to IC. However, they still hold considerable assets due to the concern for the spouse who might become a widow/widower and can expect much higher LTC costs. IC significantly reduces precautionary savings for middle and high income groups, but interestingly, it encourages asset accumulation among low income groups because it reduces the probability of meanstested Medicaid LTC. |
| Keywords: | Long Term Care, Household Risk, Precautionary Savings, Medicaid, Informal Care |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:ngi:dpaper:23-14&r= |
| By: | Haoyang Cao; Zhengqi Wu; Renyuan Xu |
| Abstract: | This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages a continuous-time model that incorporates utility functions and a generic discounting scheme of a time-varying rate, tailored to each client's risk tolerance, valuation of daily consumption, and significant life goals. We address the resulting time inconsistency issue through state augmentation and the establishment of the dynamic programming principle and the verification theorem. Additionally, we provide sufficient conditions for the identifiability of client investment preferences. To complement our theoretical developments, we propose a learning algorithm based on maximum likelihood estimation within a discrete-time Markov Decision Process framework, augmented with entropy regularization. We prove that the log-likelihood function is locally concave, facilitating the fast convergence of our proposed algorithm. Practical effectiveness and efficiency are showcased through two numerical examples, including Merton's problem and an investment problem with unhedgeable risks. Our proposed framework not only advances financial technology by improving personalized investment advice but also contributes broadly to other fields such as healthcare, economics, and artificial intelligence, where understanding individual preferences is crucial. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.15975&r= |
| By: | Yasuhiro Nakamoto (Faculty of Informatics, Kansai University); Kazuo Mino (Institute of Economic Research, Kyoto University); Yunfang Hu (Graduate School of Economics, Kobe University) |
| Abstract: | This study integrates the dynamic 2×2×2 Hechscher-Ohlin model with the neoclassical growth model, considering heterogeneous households, to explore the relationship between preference structures, wealth distribution, and international trade in a unified setting. We demonstrate that if households have homothetic utility functions, the long-run trade pattern depends solely on the initial distribution of capital between two countries. Conversely, if preferences are non-homothetic, the initial distribution of wealth among households also influences long-run trade patterns. Numerical examples further examine the wealth distribution in each country, showing that the initially poor can catch up with the initially rich. |
| Keywords: | Dynamic Hecksher-Ohlin model, Non-homothetic preference, Heterogeneous households, Wealth distribution |
| JEL: | D31 E20 F11 F43 O41 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:kyo:wpaper:1105&r= |
| By: | Jian-Qiao Zhu; Haijiang Yan; Thomas L. Griffiths |
| Abstract: | The observed similarities in the behavior of humans and Large Language Models (LLMs) have prompted researchers to consider the potential of using LLMs as models of human cognition. However, several significant challenges must be addressed before LLMs can be legitimately regarded as cognitive models. For instance, LLMs are trained on far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the utility of LLMs as cognitive models. This approach involves (i) leveraging computationally equivalent tasks that both an LLM and a rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for an LLM to exhibit human-like behaviors. We apply this approach to decision-making -- specifically risky and intertemporal choice -- where the key computationally equivalent task is the arithmetic of expected value calculations. We show that an LLM pretrained on an ecologically valid arithmetic dataset, which we call Arithmetic-GPT, predicts human behavior better than many traditional cognitive models. Pretraining LLMs on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making. Our results also suggest that LLMs used as cognitive models should be carefully investigated via ablation studies of the pretraining data. |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2405.19313&r= |
| By: | Shumiao Ouyang; Hayong Yun; Xingjian Zheng |
| Abstract: | This study explores the risk preferences of Large Language Models (LLMs) and how the process of aligning them with human ethical standards influences their economic decision-making. By analyzing 30 LLMs, we uncover a broad range of inherent risk profiles ranging from risk-averse to risk-seeking. We then explore how different types of AI alignment, a process that ensures models act according to human values and that focuses on harmlessness, helpfulness, and honesty, alter these base risk preferences. Alignment significantly shifts LLMs towards risk aversion, with models that incorporate all three ethical dimensions exhibiting the most conservative investment behavior. Replicating a prior study that used LLMs to predict corporate investments from company earnings call transcripts, we demonstrate that although some alignment can improve the accuracy of investment forecasts, excessive alignment results in overly cautious predictions. These findings suggest that deploying excessively aligned LLMs in financial decision-making could lead to severe underinvestment. We underline the need for a nuanced approach that carefully balances the degree of ethical alignment with the specific requirements of economic domains when leveraging LLMs within finance. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.01168&r= |
| By: | Zhengyang Jiang |
| Abstract: | I propose a dynamic model of the reserve currency paradigm that centers on the liquidity demand for safe assets. In global recessions, the demand for the U.S. safe bond increases and raises its convenience yield, giving rise to a stronger dollar and a countercyclical seigniorage revenue. The seigniorage revenue raises the U.S. wealth and consumption shares in recessions, despite the U.S. suffering portfolio losses from its external positions. This asset demand channel also connects exchange rate dynamics to the marginal utility over bond holding, which provides new perspectives on exchange rate disconnect and on the relationship between exchange rates and capital flows. Under this safe-asset view, exorbitant privilege does not require exorbitant duty. |
| JEL: | E44 F32 G15 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32454&r= |
| By: | Giampaolo Bonomi |
| Abstract: | We study polarization in a probabilistic voting model with aggregate shocks and a decreasing marginal utility from office rents. In equilibrium, parties offer different policies, despite being rent-motivated and ex-ante identical from the point of view of voters. When candidates compete on a single policy issue, parties' equilibrium payoffs increase in voter polarization, even when the change is driven by the supporters of the opposite party becoming more extreme. With multiple policy issues, parties benefit if the society is split into two factions and the ideological cohesion within such factions increases. We connect our results to empirical evidence on polarizing political communication, party identity, and zero-sum thinking, and find that polarization could be reduced by intervening on the electoral rule. |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2405.20564&r= |
| By: | Laurence Jacquet; Etienne Lehmann |
| Abstract: | Policies that impact the production sector, such as intermediate goods taxation (e.g. taxing robots) and trade liberalization create winners and losers. When do we need to integrate pre-distribution concerns in the design of these production policies? Should we consider the endogenous changes of factor prices in tax formulas? We show that the answers to these two questions depend only on the features of the income tax system. More precisely, can the tax system distinguish incomes from each factor of production? Can it be reformed along the so-called “GE-replicating directions”, reproducing the impact of factor price adjustments on taxpayers’ utility? If the answer to either question, or both, is “no”, the design of production policies should also take into account its pre-distributive role and all formulas reveal novel, empirically implementable “GE multipliers”. These multipliers shape tax systems to correct for market failures as well as for the effects of price adjustments. In contrast, if the answer to both questions is “yes”, it is Pareto-improving to design production policies solely to enlarge production possibilities and the “GE multipliers” shape the income tax system only to account for market failures. We illustrate these insights with realistic tax systems and practical examples of production policies. |
| Keywords: | production efficiency, nonlinear income taxation, several income sources, endogenous prices |
| JEL: | H21 H22 H23 H24 L50 F13 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11130&r= |