
on Utility Models and Prospect Theory 
Issue of 2020‒05‒11
nineteen papers chosen by 
By:  Jose Apesteguia; Miguel Ángel Ballester 
Abstract:  We study random utility models in which heterogeneity of preferences is modeled using an ordered collection of utilities, or types. The paper shows that these models are particularly amenable when combined with domains in which the alternatives of each decision problem are ordered by the structure of the types. We enhance their applicability by: (i) working with arbitrary domains composed of such decision problems, i.e., we do not need to assume any particularly rich data domain, and (ii) making no parametric assumption, i.e., we do not need to formulate any particular assumption on the distribution over the collection of types. We characterize the model by way of two simple properties and show the applicability of our result in settings involving decisions under risk. We also propose a goodnessoffit measure for the model and prove the strong consistency of extremum estimators defined upon it. We conclude by applying the model to a dataset on lottery choices. 
Keywords:  Random utility model; ordered typedependent utilities; arbitrary domains; nonparametric; goodnessoffit; extremum estimators; decision under risk. 
JEL:  C00 D00 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:upf:upfgen:1719&r=all 
By:  Bontemps, Christophe; Bougherara, Douadia; Nauges, Céline 
Abstract:  Even if there exists an extensive literature on the modeling of farmers’ behavior under risk, actual measurements of the quantitative impact of risk aversion on input use are rare. In this article we use simulated data to quantify the impact of risk aversion on the optimal quantity of input and farmers’ welfare when production risk depends on how much of the input is used. The assumptions made on the technology and form of farmers’ risk preferences were chosen such that they are fairly representative of crop farming conditions in the US and Western Europe. In our benchmark scenario featuring a traditional expected utility model we find that less than 4% of the optimal pesticide expenditure is driven by risk aversion and that risk induces a decrease in welfare that varies from ‐1.5% to ‐3.0% for individuals with moderate to normal risk aversion. We find a stronger impact of risk aversion on quantities of input used when farmers’ risk preferences are modeled under the cumulative prospect theory framework. When the reference point is set at the median or maximum profit, and for some levels of the parameters that describe behavior toward losses, the quantity of input used that is driven by risk preferences represents up to 19% of the pesticide expenditure. 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:124232&r=all 
By:  Simone CerreiaVioglio; Fabio Maccheroni; Massimo Marinacci 
Abstract:  We provide two characterizations, one axiomatic and the other neurocomputational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation, where pt (a; A) is the probability that alternative a is selected from the set A of feasible alternatives if t is the time available to decide, is a time dependent noise parameter measuring the unit cost of information, u is a time independent utility function, and is an alternativespecific bias that determines the initial choice probabilities and possibly reáects prior information. Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when is constant). Our neurocomputational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behavior. Jointly, the two approaches provide a thorough understanding of softmaximization in terms of internal causes (neurophysiological mechanisms) and external e§ects (testable implications). Keywords: Discrete Choice Analysis, Drift Di§usion Model, Heteroscedastic Extreme Value Models, Luce Model, Metropolis Algorithm, Multinomial Logit Model, Quantal Response Equilib ium, Rational Inattention 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:663&r=all 
By:  Yehuda John Levy; Andre Veiga 
Abstract:  We assume a fixed number of symmetric firms, competition in prices, constant returns to scale and frictionless consumer choices. Consumers differ in their preferences and profitability (e.g., due to heterogeneous risk aversion and loss probabilities), which creates adverse selection. Firms can offer multiple contracts to screen individuals, in equilibrium and in any deviation. We show that equilibrium profits vanish if each consumer has a unique optimizing bundle at equilibrium prices or, more generally, if there exists a linear ordering over of contracts that dictates the preferences of firms whenever consumers are indifferent between multiple optimal contracts. For instance, equilibrium profits vanish if the marginal rate of substitution of quality for price is sharper for profit than for utility. In particular, profit also vanishes if utility equals the sum of (negative) profit, and a surplus (eg, due to risk aversion). We provide examples of economies where there exists an equilibrium with strictly positive profit and show that these examples are robust (hold for an open set of economies). 
Keywords:  Perfect Competition, Equilibrium, Screening 
JEL:  D41 C62 D82 G22 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:gla:glaewp:202002&r=all 
By:  John Dagpunar 
Abstract:  In this paper I extend the work of Bernhardt and Donnelly (2019) dealing with modern explicit tontines, as a way of providing income under a specified bequest motive, from a defined contribution pension pot. A key feature of the present paper is that it relaxes the assumption of fixed proportions invested in tontine and bequest accounts. In making the bequest proportion an additional control function I obtain, hitherto unavailable, closedform solutions for the fractional consumption rate, wealth, bequest amount, and bequest proportion under a constant relative risk averse utility. I show that the optimal bequest proportion is the product of the optimum fractional consumption rate and an exponentiated bequest parameter. Typical scenarios are explored using UK Office of National Statistics life tables, showing the behaviour of these characteristics under varying degrees of constant relative risk aversion. 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2005.00715&r=all 
By:  Niko Suhonen; Jani Saastamoinen; David Forrest; Tuomo Kainulainen 
Abstract:  Gambling is often regarded as a lower form of pleasure with an elitist perception of gamblers as being either ignorant or exhibiting poor mathematical skills. Gambling also poses a challenge to the notion of rational decisionmaking because individuals take on wagers which are losing bets by expectation. From the paternalistic perspective, gambling may be attributed to poor decisiontaking resulting from cognitive failures and biases. From the liberal perspective, however, it is possible to account for gambling within the framework of rational choice by appealing to risk preferences or by a utility of gambling itself. This paper examines how a person’s cognitive ability (IQ) predicts his betting behaviour. We combine three individuallevel data sets from Finland, including online horse bets from the betting monopoly, cognitive ability test scores from the Finnish Defence Forces and administrative registry data on Finnish citizens. Our results show that intelligence is a positive predictor of participation, gambling consumption and success in gambling. Moreover, we find that gamblers are unlikely to exhibit poor mathematical skills because mathematical intelligence drives this result. Our results suggest that a one standard deviation increase in mathematical IQ from the mean increases the probability of participation in betting by more than a third, the bettor’s annual amount wagered by a half and his annual losses by 40%. Overall, our results are consistent with gambling being consumption of entertainment, which intelligent individuals enjoy. This is consistent with the liberal perspective on gambling. 
Keywords:  gambling, horse betting, intelligence, mathematical intelligence, consumption, performance 
JEL:  D12 D91 L83 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:liv:livedp:202012&r=all 
By:  Masayuki Sawada; Kohei Kawaguchi 
Abstract:  We propose an estimation procedure for discrete choice models of differentiated products with possibly highdimensional product attributes. In our model, highdimensional attributes can be determinants of both mean and variance of the indirect utility of a product. The key restriction in our model is that the highdimensional attributes affect the variance of indirect utilities only through finitely many indices. In a framework of the randomcoefficients logit model, we show a bound on the error rate of a $l_1$regularized minimum distance estimator and prove the asymptotic linearity of the debiased estimator. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2004.08791&r=all 
By:  Ikuto Aiba (Graduate School of Economics, The University of Tokyo); Yasuhiro Sato (Faculty of Economics, The University of Tokyo) 
Abstract:  We explore the theoretical properties of public good provision under the complementarity between safety and private/public good consumption. The presence of the mobile worker generates fiscal externality, making the equilibrium ineffcient. The direction of ineffciency is determined by three factors: the characteristics of the utility function, the difference in income between the immobile and mobile workers, and the immobile workerâ€™s marginal utility of hosting another mobile worker. We show that the complementarity between safety and private good consumption plays a crucial role in determining the impacts of the third factor whereas the complementarity between safety and public good does not. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2020cf1150&r=all 
By:  Dalia Ibrahim (FiQuant  Chaire de finance quantitative  CentraleSupélec  Ecole Centrale Paris); Frédéric Abergel (FiQuant  Chaire de finance quantitative  CentraleSupélec  Ecole Centrale Paris, MICS  Mathématiques et Informatique pour la Complexité et les Systèmes  CentraleSupélec) 
Abstract:  This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled by a stochastic differential equations. Using the change of measure techniques, the partial observation context can be transformed into a full information context such that coefficients depend only on past history of observed prices (filter processes). Adapting the stochastic nonlinear filtering, we show that under some assumptions on the model coefficients, the estimation of the filters depend on a priori models for the trend and the stochastic volatility. Moreover, these filters satisfy a stochastic partial differential equations named "KushnerStratonovich equations". Using the martingale duality approach in this partially observed incomplete model, we can characterize the value function and the optimal portfolio. The main result here is that the dual value function associated to the martingale approach can be expressed, via the dynamic programming approach, in terms of the solution to a semilinear partial differential equation which depends also on the filters estimate and the volatility. We illustrate our results with some examples of stochastic volatility models popular in the financial literature. 
Keywords:  Martingale duality method,Utility maximization,KushnerStratonovich equations,Stochastic volatility,Nonlinear filtering,Partial information,Semilinear partial differential equation 
Date:  2018–06 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal01018869&r=all 
By:  Dingqian Sun 
Abstract:  We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth. Based on the work [9] with an additional stochastic payoff function, we characterize the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equation (BSDE for short) with unbounded terminal condition. In regard to discrete problem, we get the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provide some useful prior estimates about the solutions with the help of auxiliary forwardbackward SDE system and Malliavin calculus. Finally, we obtain the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2004.14627&r=all 
By:  Brian Jabarian 
Abstract:  In their article, "Egalitarianism under Severe Uncertainty", (Philosophy and Public Affairs, 2018), Thomas Rowe and Alex Voorhoeve elegantly develop a theory of distributive justice, called "pluralist egalitarianism", for cases under maximal uncertainty. In this pr\'ecis for our PEA Soup Discussion, I firstly sketch their views and arguments. I then discuss their main scenarios. Finally, I suggest several objections against their view, proposing a twostage ambiguity thought experiment. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2004.08892&r=all 
By:  Matthias Stefan; Jürgen Huber; Michael Kirchler; Matthias Stefan; Markus Walzl 
Abstract:  Rankings are prevalent information and incentive tools in labor markets with strong competition for talent. In a dynamic model of multitasking and an accompanying experiment with financial professionals, we identify hidden ranking costs when performance in one task is incentivized and ranked while another prosocial task is not: (i) a ranking influences behavior if individuals lag behind: they spend more total effort and substitute effort in the prosocial task with effort in the ranked task; (ii) those ahead in the ranking spend less total effort and lower relative effort in the ranked task. Implications for incentive schemes are discussed. 
Keywords:  multitasking decision problem, rank incentives, framed field experiment, finance professionals 
JEL:  C93 D02 D91 
Date:  2020–06 
URL:  http://d.repec.org/n?u=RePEc:inn:wpaper:202006&r=all 
By:  Firpo, Sergio (Insper, São Paulo); Galvao, Antonio F. (University of Arizona); Kobus, Martyna (Institute of Economics, Polish Academy of Sciences); Parker, Thomas (University of Waterloo); RosaDias, Pedro (Imperial College London) 
Abstract:  In this paper we develop theoretical criteria and econometric methods to rank policy interventions in terms of welfare when individuals are lossaverse. The new criterion for "loss aversionsensitive dominance" defines a weak partial ordering of the distributions of policyinduced gains and losses. It applies to the class of welfare functions which model individual preferences with nondecreasing and lossaverse attitudes towards changes in outcomes. We also develop new statistical methods to test loss aversionsensitive dominance in practice, using nonparametric plugin estimates. We establish the limiting distributions of uniform test statistics by showing that they are directionally differentiable. This implies that inference can be conducted by a special resampling procedure. Since pointidentification of the distribution of policyinduced gains and losses may require very strong assumptions, we also extend comparison criteria, test statistics, and resampling procedures to a partiallyidentified case. Finally, we illustrate our methods with an empirical application to welfare comparison of two income support programs. 
Keywords:  welfare, loss aversion, policy evaluation, stochastic ordering, directional differentiability 
JEL:  C12 C14 I30 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp13176&r=all 
By:  Ole Peters; Alexander Adamou; Mark Kirstein; Yonatan Berman 
Abstract:  Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and probabilities inferred from real people's decisions (the same parameters estimated empirically). The inferred probabilities are called "decision weights." It is considered a robust experimental finding that decision weights are higher than probabilities for rare events, and (necessarily, through normalisation) lower than probabilities for common events. Typically this is presented as a cognitive bias, i.e. an error of judgement by the person. Here we point out that the same observation can be described differently: broadly speaking, probability weighting means that a decision maker has greater uncertainty about the world than the observer. We offer a plausible mechanism whereby such differences in uncertainty arise naturally: when a decision maker must estimate probabilities as frequencies in a time series while the observer knows them a priori. This suggests an alternative presentation of probability weighting as a principled response by a decision maker to uncertainties unaccounted for in an observer's model. 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2005.00056&r=all 
By:  Jakob Egholt Sï¿½gaard (CEBI, Department of Economics, University of Copenhagen) 
Abstract:  Using Danish administrative data, I investigate the magnitude and nature of optimization frictions in the labor market of Danish students. Danish students face a unique institutional setting that makes it possible to distinguish between different types of frictions and estimate their effect on individual utility. I find that frictions significantly affect observed labor market outcomes. In particular, the empirical evidence points to inattention as the dominant type of friction. In contrast, my findings appear inconsistent with real adjustment costs, price misperception and gradual learning. Overall, optimization frictions reduce the utility of individuals by approximately 23 percent of disposable income. 
Keywords:  Optimization frictions; labor supply; bunching; inattention; student labor markets 
JEL:  H21 H24 J22 
Date:  2019–01–17 
URL:  http://d.repec.org/n?u=RePEc:kud:kucebi:1901&r=all 
By:  Roy Gernhardt; Bjorn Persson 
Abstract:  This paper identifies for the first time the mathematical equivalence between economic networks of CobbDouglas agents and Artificial Neural Networks. It explores two implications of this equivalence under general conditions. First, a burgeoning literature has established that network propagation can transform microeconomic perturbations into large aggregate shocks. Neural network equivalence amplifies the magnitude and complexity of this phenomenon. Second, if economic agents adjust their production and utility functions in optimal response to local conditions, market pricing is a sufficient and robust channel for information feedback leading to global, macroscale learning at the level of the economy as a whole. 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2005.00510&r=all 
By:  Jesper R.V. Soerensen (Department of Economics, University of Copenhagen, Denmark); Mogens Fosgerau (Department of Economics, University of Copenhagen, Denmark) 
Abstract:  We study the additive random utility model of discrete choice under minimal assumptions. We make no assumptions regarding the distribution of random utility components or the functional form of systematic utility components. Exploiting the power of convex analysis, we are nevertheless able to generalize a range of important results. We characterize demand with a generalized WilliamsDalyZachary theorem. A similarly generalized version of HotzMiller inversion yields constructive partial identification of systematic utilities. Estimators based on our partial identification result remain well defined in the presence of zeros in demand. We also provide necessary and sufficient conditions for point identification. 
Keywords:  Additive random utility model; Discrete choice; Convex duality; Demand inversion; Partial identification 
JEL:  C25 C6 D11 
Date:  2020–12–17 
URL:  http://d.repec.org/n?u=RePEc:kud:kuiedp:2001&r=all 
By:  Scott R. Baker (Northwestern University, Kellogg School of Management, Department of Finance); Brian Baugh (University of Nebraska at Lincoln); Lorenz Kueng (University of Lugano  Faculty of Economics; Swiss Finance Institute; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR); Northwestern University  Kellogg School of Management) 
Abstract:  How households shift spending across firms in response to income fluctuations is an important source of risk to individual firms. Using transactionlevel data, we study how households interact with the universe of retailers following changes in income. We find that increases in income, both within and across households, result in substitution towards retailers in a category that are higher quality, smaller, more profitable, and have higher labor intensity, R&D intensity, and equity betas. While not all shifts are economically large, they do not average out across retailers. Thus, retailer choice has implications for key financial and macroeconomic outcomes such as aggregate profitability and labor demand. 
Keywords:  choice, retailer substitution, customer base, transactional data 
JEL:  D10 D22 L11 
Date:  2020–04 
URL:  http://d.repec.org/n?u=RePEc:chf:rpseri:rp2029&r=all 
By:  Michael C. Nwogugu 
Abstract:  While Indices, Index tracking funds and ETFs have grown in popularity during then last ten years, there are many structural problems inherent in Index calculation methodologies and the legal/economic structure of ETFs. These problems raise actionable issues of Suitability and fraud under US securities laws, because most Indices and ETFs are misleading, have substantial tracking errors and dont reflect what they are supposed to track. This article contributes to the existing literature by: a) introducing and characterizing the errors and Biases inherent in riskadjusted index weighting methods and the associated adverse effects; b) showing how these biases/effects inherent in Index calculation methods reduce social welfare, and can form the basis for harmful arbitrage activities. 
Date:  2020–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2005.01708&r=all 