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on Utility Models and Prospect Theory |
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Issue of 2024‒06‒17
twenty papers chosen by |
| By: | Pawe{\l} Dziewulski; Joshua Lanier; John K. -H. Quah |
| Abstract: | Afriat's Theorem (1967) states that a dataset can be thought of as being generated by a consumer maximizing a continuous and increasing utility function if and only if it is free of revealed preference cycles containing a strict relation. The latter property is often known by its acronym, GARP (for generalized axiom of revealed preference). This paper surveys extensions and applications of Afriat's seminal result. We focus on those results where the consistency of a dataset with the maximization of a utility function satisfying some property can be characterized by a suitably modified version of GARP. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.08459&r= |
| By: | Richard T. Carson; Derrick H. Sun; Yixiao Sun |
| Abstract: | At the core of most random utility models (RUMs) is an individual agent with a random utility component following a largest extreme value Type I (LEVI) distribution. What if, instead, the random component follows its mirror image -- the smallest extreme value Type I (SEVI) distribution? Differences between these specifications, closely tied to the random component's skewness, can be quite profound. For the same preference parameters, the two RUMs, equivalent with only two choice alternatives, diverge progressively as the number of alternatives increases, resulting in substantially different estimates and predictions for key measures, such as elasticities and market shares. The LEVI model imposes the well-known independence-of-irrelevant-alternatives property, while SEVI does not. Instead, the SEVI choice probability for a particular option involves enumerating all subsets that contain this option. The SEVI model, though more complex to estimate, is shown to have computationally tractable closed-form choice probabilities. Much of the paper delves into explicating the properties of the SEVI model and exploring implications of the random component's skewness. Conceptually, the difference between the LEVI and SEVI models centers on whether information, known only to the agent, is more likely to increase or decrease the systematic utility parameterized using observed attributes. LEVI does the former; SEVI the latter. An immediate implication is that if choice is characterized by SEVI random components, then the observed choice is more likely to correspond to the systematic-utility-maximizing choice than if characterized by LEVI. Examining standard empirical examples from different applied areas, we find that the SEVI model outperforms the LEVI model, suggesting the relevance of its inclusion in applied researchers' toolkits. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.08222&r= |
| By: | Joshua Lanier; John K. -H. Quah |
| Abstract: | A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit index that is continuous and accurate, where the latter means that a perfect score is obtained if and only if a dataset can be rationalized by a well-behaved utility function. While many standard goodness-of-fit indices are inaccurate we show that these indices are (in a sense we make precise) essentially accurate. Goodness-of-fit indices are typically generated by loss functions and we find that standard loss functions usually do not yield a best-fitting utility function when they are minimized. Nonetheless, welfare comparisons can be made by working out a robust preference relation from the data. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.08464&r= |
| By: | Sendhil Mullainathan; Ashesh Rambachan |
| Abstract: | Machine learning algorithms can find predictive signals that researchers fail to notice; yet they are notoriously hard-to-interpret. How can we extract theoretical insights from these black boxes? History provides a clue. Facing a similar problem – how to extract theoretical insights from their intuitions – researchers often turned to “anomalies:” constructed examples that highlight flaws in an existing theory and spur the development of new ones. Canonical examples include the Allais paradox and the Kahneman-Tversky choice experiments for expected utility theory. We suggest anomalies can extract theoretical insights from black box predictive algorithms. We develop procedures to automatically generate anomalies for an existing theory when given a predictive algorithm. We cast anomaly generation as an adversarial game between a theory and a falsifier, the solutions to which are anomalies: instances where the black box algorithm predicts - were we to collect data - we would likely observe violations of the theory. As an illustration, we generate anomalies for expected utility theory using a large, publicly available dataset on real lottery choices. Based on an estimated neural network that predicts lottery choices, our procedures recover known anomalies and discover new ones for expected utility theory. In incentivized experiments, subjects violate expected utility theory on these algorithmically generated anomalies; moreover, the violation rates are similar to observed rates for the Allais paradox and Common ratio effect. |
| JEL: | B40 C1 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32422&r= |
| By: | Christopher P. Chambers; Federico Echenique; Takashi Hayashi |
| Abstract: | This paper studies manipulation of belief aggregation rules in the setting where the society first collects individual's probabilistic opinions and then solves a public portfolio choice problem with common utility based on the aggregate belief. First, we show that belief reporting in Nash equilibrium under the linear opinion pool and log utility is identified as the profile of state-contingent wealth shares in parimutuel equilibrium with risk-neutral preference. Then we characterize belief aggregation rules which are Nash-implementable. We provide a necessary and essentially sufficient condition for implementability, which is independent of the common risk attitude. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.01655&r= |
| By: | Yusuke Narita (Yale University); Haoge Chang; Kota Saito |
| Abstract: | We obtain a necessary and sufficient condition under which random-coefficient discrete choice models, such as mixed-logit models, are rich enough to approximate any nonparametric random utility models arbitrarily well across choice sets. The condition turns out to be the affine-independence of the set of characteristic vectors. When the condition fails, resulting in some random utility models that cannot be closely approximated, we identify preferences and substitution patterns that are challenging to approximate accurately. We also propose algorithms to quantify the magnitude of approximation errors. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2392&r= |
| By: | Adam Hallengreen (Department of Economics, University of Copenhagen); Thomas H. Joergensen (Department of Economics, University of Copenhagen); Annasofie M. Olesen (Department of Economics, University of Copenhagen) |
| Abstract: | The computational time required to solve and estimate dynamic economic models is one of the main constraints in empirical research. The Endogenous Grid Method (EGM) proposed by Carroll (2006) is known to offer impressive speed gains over more traditional stochastic dynamic programming methods, such as Value Function Iterations (VFI). However, existing EGM implementations implicitly require an analytical expression for the inverse marginal utility, which is not known in many interesting cases. We propose a simple and fast approach, which we refer to as the interpolated EGM (iEGM), that can be applied even when the inverse marginal utility is not known analytically. We show through two applications that the iEGM inherits the speed andaccuracy of the EGM and that our approach is an order of magnitude faster than traditionalapproaches. |
| Keywords: | Endogenous grid method, dynamic programming, numerical methods, limited commitment |
| JEL: | D13 D15 C61 C63 C78 |
| Date: | 2024–05–16 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kucebi:2411&r= |
| By: | Mika Akesaka; Ryo Mikami; Yoshiyasu Ono |
| Abstract: | This study theoretically considers household behavior with wealth preference and empirically investigates the validity of insatiable wealth preference using a nationally representative survey. With wealth preference, the marginal rate of substitution of asset holdings for consumption depends on the nominal interest rates of assets at each point in time. We focus on this property and find that the marginal utility of holding financial assets remains strictly positive as asset holdings increase and has a strictly positive lower bound, implying the insatiability of wealth preference. This property plays a crucial role in creating secular demand stagnation and expanding asset price bubbles. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1241r&r= |
| By: | Bolin, Kristian (Department of Economics, School of Business, Economics and Law, Göteborg University); Caputo, Mikael R (Dept. of Economics, Univ. of Central Florida) |
| Abstract: | An optimal control model of a consumer is developed that accounts for the consumption of many goods and services, the accumulation of wealth, a state variable that affects instantaneous preferences and wealth accumulation, and contains several canonical models as special cases. Formulas are provided for the feedback consumption functions in terms of certain partial derivatives of a consumer’s lifetime indirect utility function, thereby obviating the need to solve the necessary conditions of Pontryagin or the Hamilton-Jacobi-Bellman equation. The intrinsic qualitative properties of the optimal control model in differential form are derived, and an example of how to implement the results for econometric purposes is provided as well. |
| Keywords: | capital stock; feedback solutions; HJB equation; optimal control |
| JEL: | D15 I12 I18 |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:gunwpe:0843&r= |
| By: | Masamitsu Ohnishi; Makoto Shimoshimizu |
| Abstract: | This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders' execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class; it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.07184&r= |
| By: | Massimo Guidolin; Giacomo Leonetti; Manuela Pedio |
| Abstract: | Structured products in general, and investment certificates in particular, have gained increasing popularity among retail investors over the last decade, both in Europe and in the US. However, based on data on the ex-post realized gains of retail clients investing in certificates, the literature has generally concluded that the high demand of these products may be hard to rationalize within a portfolio optimization framework. In this paper, we investigate whether a rational, perfectly informed investor with standard constant relative risk aversion (CRRA) preferences who optimally allocates her wealth among risky and riskless assets can ex-ante expect to benefit from adding structured products to her portfolio. We show that the utility gains from investment certificates vary dramatically across alternative structures, investment horizons and levels of risk aversion. Therefore, a correct assessment of an investors’ risk tolerance and investment horizon is crucial when advising on the relevance of structured products. We also find that the optimal demand of investment certificates as well as their benefits depend heavily on the pricing model informing the portfolio assessment and that demand is considerably higher when the joint presence of jumps in returns and volatility were to go undetected. Therefore, the high demand of structured products can be explained by the use of asset pricing models that are excessively simplistic and ignore discontinuous dynamics. |
| Keywords: | Structured products, investment certificates, retail investors, asset allocation, models with jumps. |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:baf:cbafwp:cbafwp24222&r= |
| By: | Taha Choukhmane; Tim de Silva |
| Abstract: | We study the role of risk preferences and frictions in portfolio choice using variation in 401(k) default options. Patterns of active choice in response to different default funds imply that, absent participation frictions, 94% of investors prefer holding stocks, with an equity share of retirement wealth declining with age—patterns markedly different from observed allocations. We use this quasi-experiment to estimate a life cycle model and find a relative risk aversion of 2, EIS of 0.4, and $200 portfolio adjustment cost. Our results suggest that low levels of stock market participation in retirement accounts are due to participation frictions rather than non-standard preferences such as loss aversion. |
| JEL: | D14 D15 G0 G11 G40 G5 G51 J32 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:32476&r= |
| By: | Alfred Galichon; Antoine Jacquet |
| Abstract: | This chapter explores the role of substitutability in economic models, particularly in the context of optimal transport and matching models. In equilibrium models with substitutability, market-clearing prices can often be recovered using coordinate update methods such as Jacobi's algorithm. We provide a detailed mathematical analysis of models with substitutability through the lens of Z- and M-functions, in particular regarding their role in ensuring the convergence of Jacobi's algorithm. The chapter proceeds by studying matching models using substitutability, first focusing on models with (imperfectly) transferable utility, and then on models with non-transferable utility. In both cases, the text reviews theoretical implications as well as computational approaches (Sinkhorn, Gale--Shapley), and highlights a practical economic application. |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2405.07628&r= |
| By: | Attila Sarkany (Institute of Economic Studies, Charles University, Prague, Czech Republic & The Czech Academy of Sciences, IITA, Prague, Czech Republic); Lukas Janasek (Institute of Economic Studies, Charles University, Prague, Czech Republic & The Czech Academy of Sciences, IITA, Prague, Czech Republic); Jozef Barunik (Institute of Economic Studies, Charles University, Prague, Czech Republic & The Czech Academy of Sciences, IITA, Prague, Czech Republic) |
| Abstract: | We develop a novel approach to understand the dynamic diversification of decision makers with quantile preferences. Due to unavailability of analytical solutions to such complex problems, we suggest to approximate the behavior of agents with a Quantile Deep Reinforcement Learning (Q-DRL) algorithm. The research will provide a new level of understanding the behavior of economic agents with respect to preferences, captured by quantiles, without assuming a specific utility function or distribution of returns. Furthermore, we are challenging the traditional diversification methods as they proved to be insufficient due to heightened correlations and similar risk features between asset classes, and rather the research delves into risk factor investing as a solution and portfolio optimization based on them. |
| Keywords: | Portfolio Management, Quantile Deep Reinforcement Learning, Factor investing, Deep-Learning, Advantage-Actor-Critic |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:fau:wpaper:wp2024_21&r= |
| By: | Rösl, Gerhard |
| Abstract: | We create an alternative version of the present utility value formula to explicitly show that every store-of-value in the economy bears utility-interest (non-pecuniary income) for its holder regardless of possible interest earnings from financial markets. In addition, we generalize the well-known welfare measures of consumer and producer surplus as present value concepts and apply them not only for the production and usage of consumer goods and durables but also for money and other financial assets. This helps us, inter alia, to formalize the circumstances under which even a producer of legal tender might become insolvent. We also develop a new measure of seigniorage and demonstrate why the well-established concept of monetary seigniorage is flawed. Our framework also allows us to formulate the conditions for liability-issued money such as inside money and financial instruments such as debt certificates to become - somewhat paradoxically - net wealth of the society. |
| Keywords: | Welfare, money, seigniorage, net wealth |
| JEL: | D14 D60 E41 E50 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:imfswp:295241&r= |
| By: | Yuya Wakabayashi (JSPS Research Fellow (DC2), Graduate School of Economics, Osaka University); Ryosuke Sakai (School of Engineering, Tokyo Institute of Technology); Hiroki Shinozaki (Hitotsubashi Institute for Advanced Study, Hitotsubahi University) |
| Abstract: | We consider the single-object allocation problem with monetary transfers. Agents have hard budgets and their utility functions may exhibit income effects. We characterize truncated Vickrey rules with endogenous reserve prices by constrained efficiency or weak envy-freeness for equals, in addition to individual rationality, no subsidy for losers, and strategy-proofness. The same characterization result hold even if we replace weak envy freeness for equals with other fairness conditions; equal treatment of equals, envy-freeness, and anonymity in welfare. |
| Keywords: | Single-object allocation problem, Non-quasi-linear preference, Hard budget constraint, Efficiency, Fairness, Strategy-proofness, Vickrey rule with reserve prices |
| JEL: | D47 D63 D82 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:osp:wpaper:24e003&r= |
| By: | Swagata Bhattacharjee (Ashoka University); Srijita Ghosh (Ashoka University); Suraj Shekhar (Ashoka University) |
| Abstract: | We consider a static cheap talk model in an environment with either one or two experts whose biases are privately known by the experts themselves. Before the experts learn the state, they send a cheap talk message about their bias to the decision maker. Subsequently, the decision maker chooses one expert to get state relevant advice from. We ask two questions - One, is there an equilibrium where the experts’ bias is fully revealed? Two, is the bias revealing equilibrium welfare improving for the decision maker? We find that when there is only one expert, there is no bias revealing equilibrium. However, if there are two experts, there exists a bias revealing equilibrium, and under some conditions it gives the decision maker more utility than any equilibrium which is possible without bias revelation. This highlights a new channel through which sender competition can benefit the decision maker, through which sender competition can benefit the decision maker. |
| Keywords: | bias revelation; Cheap talk; multiple senders; uncertain bias |
| Date: | 2024–01–29 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:109&r= |
| By: | Chung-Han Hsieh; Yi-Shan Wong |
| Abstract: | This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which are deterministic and others are stochastic. The decision-maker's cumulative value is updated at each stage, reflecting the outcomes of the chosen alternatives. After formulating this as a stochastic control problem, we delineate the necessary optimality conditions for it. Two illustrative examples from optimal betting and inventory management are provided to support our theory. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.13371&r= |
| By: | Ylenia Brilli (Ca’ Foscari University of Venice and CHILD-Collegio Carlo Alberto); Simone Moriconi (IESEG School of Management, Univ. Lille, CNRS, UMR 9221 - LEM - Lille Economie Management, F-59000 Lille, France; CESIfo Munich; Institut Convergences Migrations) |
| Abstract: | This paper analyzes how culture affects the engagement of parents in child-rearing activities, and time allocations of parents inside the family. We use data from the World Value Survey to construct a country-specific measure of the value attached to obedience as a child quality, which we associate with the actual parenting behavior and time investments of firstand second-generation migrant parents in Australia. We show that migrant parents from countries in which obedience is more valued as an important child quality, are more likely to be warm and to enact discipline in their parent-child interactions. We also show that a higher value of obedience in the country of origin is associated with a shift of parental time from general care to playing activities, and from the weekdays to the weekends. These results are robust to a large set of sensitivity analyses, which account for omitted variable bias and selection. Finally, we provide evidence that this cultural value may feature a more egalitarian allocation of parenting vs. labor supply tasks at the household level, by increasing fathers’ parental time and mothers’ labor supply at the intensive margin. We interpret this as indirect evidence that fathers may have a greater marginal utility from parenting time than mothers, on average. |
| Keywords: | culture, parental investments, parenting, labor supply |
| JEL: | D10 J13 J15 J22 Z13 |
| Date: | 2024–05 |
| URL: | http://d.repec.org/n?u=RePEc:ies:wpaper:e202413&r= |
| By: | Ornella Tarola (University of Rome La Sapienza); Skerdilajda Zanaj (DEM, Université du Luxembourg) |
| Abstract: | In this paper, we propose a theoretical model of nationalism in consumption, aiming to uncover its effects on market outcomes and welfare. Nationalism is catalyzed by the perception of higher quality for domestic goods, which in turn provides a utility benefit. We construct a two-country setting of vertical product differentiation where consumers exchange consumption habits in social interactions, potentially spreading nationalism from one country to another. Consumers are heterogeneous with respect to their level of income. We demonstrate that in a globalized economy, in the realm of nationalism, intercountry meetings are mainly detrimental for firms producing high-quality goods and for low-income consumers. Our research highlights how the rising tension between nationalism and globalization manifests in consumption as a demarcation between those favoring a borderless world and its opponents who promote national attachment. The effects of these tensions are far from being evident. |
| Keywords: | Nationalism, Vertical Product Differentiation, Relative Preferences, Inter-country meetings |
| JEL: | A13 D91 L13 F52 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:24-03&r= |