
on Utility Models and Prospect Theory 
Issue of 2021‒02‒22
nineteen papers chosen by 
By:  Mu Zhang 
Abstract:  Aggregating risks from multiple sources can be complex and demanding, and decision makers usually adopt heuristics to simplify the decision process. This paper axiomatizes two such heuristics, narrow bracketing and correlation neglect, by relaxing the standard independence axiom in the expected utility benchmark. Our representation theorem allows for either narrow bracketing, or correlation neglect, or both of them. The flexibility of our framework allows for applications in various setups. For example, we accommodate the experimental evidence in narrow bracketing and risk aversion over small gambles with background risk. In intertemporal choices, we show how our framework unifies three seemingly distinct models in the literature and introduce a new model that can satisfy many desirable normative properties in time preferences simultaneously, including indifference to temporal resolution of uncertainty, dynamic consistency and separation of time and risk preferences. One special class of the model shares the same predictions as Epstein and Zin (1989) in macroeconomics and finance applications, and is immune to the critique in Epstein, Farhi, and Strzalecki (2014). 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.07286&r=all 
By:  David McCarthy; Kalle Mikkola; Teruji Thomas 
Abstract:  A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multirepresentation that consists of realvalued, mixturepreserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixturepreserving multirepresentation when the dimension of the mixture space is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixturepreserving multirepresentation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixturepreserving multirepresentations that consist entirely of strictly increasing functions, and a uniqueness result. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.06898&r=all 
By:  Tapan Mitra (Cornell University); Santanu Roy (Southern Methodist University) 
Abstract:  In a general onesector model of stochastic growth where the marginal productivity of capital at zero is finite but can vary widely due to technology shocks, we derive explicitly the limiting optimal propensity to invest (the "slope" of the optimal policy function) at zero. We then derive an explicit condition that ensures it is optimal for capital stocks to regenerate with probability one if they are depleted to levels close enough to zero so that "long run" consumption is strictly positive with probability one. For a widely used class of utility and production functions, a strict violation of our regeneration condition implies almost sure global extinction of capital under the optimal policy. Risk aversion plays an important role in regeneration. Regeneration is likely to be optimal when the degree of risk aversion (near zero) is either high or low, while extinction may be optimal for intermediate levels of risk aversion. 
Keywords:  Stochastic Growth, Propensity to Invest, Optimal Policy Function, Regeneration, Conservation, Extinction, Risk Aversion. 
JEL:  C6 D9 O41 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:smu:ecowpa:2101&r=all 
By:  Kondor, Peter; Vayanos, Dimitri 
Abstract:  We develop a continuoustime model of liquidity provision in which hedgers can trade multiple risky assets with arbitrageurs. Arbitrageurs have constant relative riskaversion (CRRA) utility, while hedgers' asset demand is independent of wealth. An increase in hedgers' risk aversion can make arbitrageurs endogenously more riskaverse. Because arbitrageurs generate endogenous risk, an increase in their wealth or a reduction in their CRRA coefficient can raise risk premia despite Sharpe ratios declining. Arbitrageur wealth is a priced risk factor because assets held by arbitrageurs offer high expected returns but suffer the most when wealth drops. Aggregate illiquidity, which declines in wealth, captures that factor. 
Keywords:  liquidity risk; wealth effects; heterogeneous agents; intermediary asset pricing; endogenous risk; 336585 
JEL:  F3 G3 
Date:  2019–06–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:87520&r=all 
By:  Arnaud Reynaud (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Cécile Aubert (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  We conducted an artefactual field experiment in Vietnam to investigate whether and how experiencing a natural disaster affects individual attitudes toward risks. Using experimental and real household data, we show that households in villages affected by a flood in recent years exhibit more risk aversion, compared with individuals living in similar but unaffected villages. Interestingly, this result holds for the loss domain, but not the gain domain. In line with Prospect Theory, Vietnamese households distort probabilities. The distortion is related to aid received and social networks participation, but is unrelated to flood experience. 
Keywords:  Field experiment,Vietnam,Flood,Nonexpected utility,Risk preferences 
Date:  2020 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03050685&r=all 
By:  Laohakunakorn, Krittanai; Levy, Gilat; Razin, Ronny 
Abstract:  We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the firstprice and secondprice auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity. 
Keywords:  Ambiguity over correlation; Optimal auctions; Private and common value auctions 
JEL:  D44 D81 
Date:  2019–11–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:101410&r=all 
By:  Federico Echenique; Kota Saito; Taisuke Imai 
Abstract:  We propose a new measure of deviations from expected utility theory. For any positive number~$e$, we give a characterization of the datasets with a rationalization that is within~$e$ (in beliefs, utility, or perceived prices) of expected utility theory. The number~$e$ can then be used as a measure of how far the data is to expected utility theory. We apply our methodology to data from three largescale experiments. Many subjects in those experiments are consistent with utility maximization, but not with expected utility maximization. Our measure of distance to expected utility is correlated with subjects' demographic characteristics. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.06331&r=all 
By:  Belot, Michèle (Cornell University); Kircher, Philipp (Cornell University); Muller, Paul (Vrije Universiteit Amsterdam) 
Abstract:  We propose a simple method for eliciting individual time preferences without estimating utility functions even in settings where background consumption changes over time. It relies on lottery tickets with high rewards. In a standard intertemporal choice model high rewards decouple lottery choices from variation in background consumption. We validate our elicitation method experimentally on two student samples: one asked in December when their current budget is reduced by extraordinary expenditures for Christmas gifts; the other asked in February when no such extra constraints exist. We illustrate an application of our method with unemployed job seekers which naturally have income/consumption variation. 
Keywords:  time preferences, experimental elicitation, job search, hyperbolic discounting 
JEL:  D90 J64 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp14091&r=all 
By:  Benjamin Patrick Evans; Mikhail Prokopenko 
Abstract:  Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an informationtheoretic approach to the inference of agent decisions under Smithian competition. The model explicitly captures the boundedness of agents (limited in their informationprocessing capacity) as the cost of information acquisition for expanding their prior beliefs. The expansion is measured as the KullblackLeibler divergence between posterior decisions and prior beliefs. When information acquisition is free, the \textit{homo economicus} agent is recovered, while in cases when information acquisition becomes costly, agents instead revert to their prior beliefs. The maximum entropy principle is used to infer leastbiased decisions, based upon the notion of Smithian competition formalised within the Quantal Response Statistical Equilibrium framework. The incorporation of prior beliefs into such a framework allowed us to systematically explore the effects of prior beliefs on decisionmaking, in the presence of market feedback. We verified the proposed model using Australian housing market data, showing how the incorporation of prior knowledge alters the resulting agent decisions. Specifically, it allowed for the separation (and analysis) of past beliefs and utility maximisation behaviour of the agent. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.09180&r=all 
By:  Nicholas Moehle; Stephen Boyd 
Abstract:  The Merton problem is the wellknown stochastic control problem of choosing consumption over time, as well as an investment mix, to maximize expected constant relative risk aversion (CRRA) utility of consumption. Merton formulated the problem and provided an analytical solution in 1970; since then a number of extensions of the original formulation have been solved. In this note we identify a certainty equivalent problem, i.e., a deterministic optimal control problem with the same optimal value function and optimal policy, for the base Merton problem, as well as a number of extensions. When time is discretized, the certainty equivalent problem becomes a secondorder cone program (SOCP), readily formulated and solved using domain specific languages for convex optimization. This makes it a good starting point for model predictive control, a policy that can handle extensions that are either too cumbersome or impossible to handle exactly using standard dynamic programming methods. 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.10510&r=all 
By:  Hampus Engsner 
Abstract:  In this paper we explore ways of numerically computing recursive dynamic monetary risk measures and utility functions. Computationally, this problem suffers from the curse of dimensionality and nested simulations are unfeasible if there are more than two time steps. The approach considered in this paper is to use a Least Squares Monte Carlo (LSM) algorithm to tackle this problem, a method which has been primarily considered for valuing American derivatives, or more general stopping time problems, as these also give rise to backward recursions with corresponding challenges in terms of numerical computation. We give some overarching consistency results for the LSM algorithm in a general setting as well as explore numerically its performance for recursive CostofCapital valuation, a special case of a dynamic monetary utility function. 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2101.10947&r=all 
By:  Daniela Bellani (UniversitÃ di Bologna); Bruno Arpino (Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", UniversitÃ di Firenze) 
Abstract:  This article aims at contributing to the literature on fertility decision making process. The authors analyze an overlooked but potentially crucial factor, the preference for risk. A typology of fertility decision making process based on risk tolerance and attractiveness of parenthood is proposed. Empirically, the authors rely on a lottery question included in Italian longitudinal representative data. Results indicate that the most risk averse individuals have the highest probability to have a(n additional) child. This is consistent with the Hedger ideal type that considers children as an insurance. The most risk tolerant individuals, instead, in line with the Individualist type, seem to perceive fertility as incompatible with alternative risky and rewarding behaviors. This conflict results particularly strong for lowincome individuals. Our findings point to the importance of considering risk tolerance in fertility research to gain a more complete understanding of heterogeneity in fertility behaviors. 
Keywords:  fertility, risk aversion, risk preference 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:fir:econom:wp2021_02&r=all 
By:  PierreAndr\'e Chiappori; Alfred Galichon; Bernard Salani\'e 
Abstract:  In many economic contexts, agents from a same population team up to better exploit their human capital. In such contexts (often called "roommate matching problems"), stable matchings may fail to exist even when utility is transferable. We show that when each individual has a close substitute, a stable matching can be implemented with minimal policy intervention. Our results shed light on the stability of partnerships on the labor market. Moreover, they imply that the tools crafted in empirical studies of the marriage problem can easily be adapted to many roommate problems. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.06487&r=all 
By:  Yuhki Hosoya 
Abstract:  We present a necessary and sufficient condition for Alt's system to be represented by a concave utility function. This condition can be seen as an extension of Gossen's first law, and thus has an economic interpretation. Together with the above result, we present a rigorous proof of Alt's representation theorem on a Hausdorff, separable, and pathconnected topological space, and provide a necessary and sufficient condition for Alt's utility to be continuously differentiable. 
Date:  2021–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2102.07237&r=all 
By:  Schauf, Andrew; Oh, Poong 
Abstract:  When individuals extract benefits from multiple resources, the decision they face is twofold: besides choosing how much total effort to exert for extraction, they must also decide how to allocate this effort. We focus on the allocation aspect of this choice in an iterated game played on bipartite networks of agents and commonpool resources (CPRs) that degrade linearly in quality as extraction increases. When CPR users attempt to reallocate their extraction efforts among resources to maximize their own payoffs in the very next round (that is, myopically), collective wealth is increased. Using a heterogeneous meanfield approach, we estimate how these reallocations affect the payoffs of CPR users of different degrees within networks having different levels of degree heterogeneity. Focusing specifically on Nash equilibrium initial conditions, which represent the patterns of overexploitation that result from rational extraction, we find that networks with greater heterogeneity among CPR degrees show greater improvements over equilibrium due to reallocation. When the marginal utility of extraction diminishes, these reallocations also reduce wealth inequality. These findings emphasize that CPR users’ adaptive reallocations of effort—a behavior that previouslystudied network evolutionary game models typically disallow by construction—can serve to direct individuals’ self interest toward the collective good. 
Date:  2021–01–12 
URL:  http://d.repec.org/n?u=RePEc:osf:socarx:w2cxp&r=all 
By:  Matthew Adler (Duke University School of Law); Maddalena Ferranna (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); James K. Hammitt (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Nicolas Treick (TSE  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, GenPhySE, Université de Toulouse, INRAE, ENVT, 31326 CastanetTolosan, France) 
Abstract:  The social value of risk reduction (SVRR) is the marginal social value of reducing an individual's fatality risk, as measured by some social welfare function (SWF). This Article investigates SVRR, using a lifetime utility model in which individuals are differentiated by age, lifetime income profile, and lifetime risk profile. We consider both the utilitarian SWF and a "prioritarian" SWF, which applies a strictly increasing and strictly concave transformation to individual utility. We show that the prioritarian SVRR provides a rigorous basis in economic theory for the "fair innings" concept, proposed in the public health literature: as between an older individual and a similarly situated younger individual (one with the same income and risk profile), a risk reduction for the younger individual is accorded greater social weight even if the gains to expected lifetime utility are equal. The comparative statics of prioritarian and utilitarian SVRRs with respect to age, and to (past, present, and future) income and baseline survival probability, are significantly different from the conventional value per statistical life (VSL). Our empirical simulation based upon the U.S. population survival curve and income distribution shows that prioritarian SVRRs with a moderate degree of concavity in the transformation function conform to widely held views regarding lifesaving policies: the young should take priority but income should make no difference. 
Keywords:  value of statistical life (VSL),fair,innings,social value of risk reduction (SVRR),utilitarian,prioritarian,isk regulation,Social welfare function (SWF),benefitcost analysis (BCA) 
Date:  2021–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03097444&r=all 
By:  JeanPaul L'Huillier; Sanjay R. Singh; Donghoon Yoo (Department of Economics, University of California Davis) 
Abstract:  Diagnostic expectations have emerged as an important departure from rational expectations in macroeconomics and finance. We present a first treatment of diagnostic expectations in linear macroeconomic models. To this end, we establish a strong additivity property for diagnostic expectations. The solution method and stability properties are discussed in full generality. Under some conditions, diagnostic expectations generate higher volatility than rational expectations. We show that this is true in standard New Keynesian models, as in mediumscale DSGE models; in real business cycle models output and investment are characterized by dampening, instead. Finally, we discuss how the combination of diagnosticity with imperfect information can rationalize under and overreaction in macroeconomics. 
Keywords:  diagnostic expectations, macroeconomics, volatility, linear rational expectations, overshooting 
JEL:  E12 E32 E71 
Date:  2021–02–09 
URL:  http://d.repec.org/n?u=RePEc:cda:wpaper:339&r=all 
By:  Hetschko, Clemens; Knabe, Andreas; Schöb, Ronnie 
Abstract:  This chapter introduces identity utility to the study of (un)employment and (un)happiness. The concept is described in terms of an augmented utility function, the implications of which are assessed in light of the empirical literature on unemployment and wellbeing. Studies on unemployed persons' affective and cognitive wellbeing allow assessing the importance of the loss of identity utility relative to other nonmonetary consequences of joblessness, such as fewer social contacts and a lack of a structure in daily life. Unlike life satisfaction, unemployment leaves affective wellbeing mostly unaffected, which points to a major relevance of the loss of identity. This view is corroborated further by studies on the importance of the social norms to work and be selfreliant for the life satisfaction of the unemployed, as well as by studies showing the positive life satisfaction effect of retirement on unemployed workers. Based on this strong evidence for identity utility losses of unemployed persons, the notion of identity utility is used to explain heterogeneity in the effect of unemployment on life satisfaction. It is also linked to further consequences of unemployment, such as social exclusion and stigmatization. Moreover, this chapter uses identity utility to assess the likely effectiveness of labor market policies in alleviating the misery of the unemployed. Finally, research on work, happiness and identity is reconciled with a more standard economics view on labor supply based on studies examining the impact of working hours on workers' wellbeing. 
Keywords:  employment status,identity,subjective wellbeing,affective and cognitive wellbeing 
JEL:  D91 I31 J26 J60 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:zbw:glodps:783&r=all 
By:  Piper, Alan T. 
Abstract:  This study is an empirical investigation of the empty nest syndrome, commonly understood as a situation where there are feelings of loss or loneliness for mothers and/or fathers following the departure of the last child from the family home. This investigation makes use of rich, longitudinal, nationally representative German data to assess whether there is evidence for such a syndrome. Furthermore, the analysis considers the role of two key economic variables: consumption and leisure via the standard economic concept of utility maximisation. The analysis highlights a conflict between what economic theory predicts  more disposable income and a gain of leisure time  and the psychological (and cultural) notion of the lonely, sad empty nester. This conflict is an empirical question and here it is resolved via an assessment of the change in life satisfaction that is reported when parents become empty nesters. Importantly, this investigation also tracks what the last child leaving the household goes on to do: The found reduced life satisfaction seems to be wholly moderated if the last child leaves the nest for the purposes of education, but not if for purposes of employment. 
Keywords:  Life Satisfaction,Subjective Wellbeing,Empty Nest Syndrome,Family,Income,Consumption,Leisure 
JEL:  D64 I31 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:zbw:fubsbe:20214&r=all 