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on Utility Models and Prospect Theory |
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Issue of 2022‒03‒14
seventeen papers chosen by |
| By: | Xiaosheng Mu (Princeton University); Luciano Pomatto (Caltech); Philipp Strack (Yale University); Omer Tamuz (Caltech) |
| Abstract: | We show that under plausible levels of background risk, no theory of choice under risk can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) their preferences respect stochastic dominance, and (iii) they account for background risk. This impossibility result applies to expected utility theory, prospect theory, rank dependent utility and many other models. |
| Keywords: | risk, theories of choice |
| JEL: | D81 |
| Date: | 2021–08 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-26&r= |
| By: | Pham, Chau (University of Warwick) |
| Abstract: | This paper addresses two issues : the underinvestment in education and the povertytrap that ensues for poor households. In a setting where the end outcome is binary, aninvesting agent faces two levels of risk, one in the intermediate outcome - how muchhuman capital she obtains for a given amount of investment, and one inherent in theend outcome - whether she gets the high-paid job. We show that when human capital is inheritable, risk-averse agents are deterred from investing because their parentsare not sufficiently educated. Moreover, the U-shaped expected utility means theoptimal investment occurs at either corners. If this investment or underinvestment is sustained through generations, a separating equilibrium such that poor households do not invest while wealthier ones do emerges. The divergence in educational attainmenttranslates into a divergence in wealth between those who invest and those who do not.A simple calibration employing data from the NLSY97 demonstrates the existence ofthese equilibria at different levels of risk-aversion. |
| Keywords: | intergenerational human capital ; poverty trap ; risk-aversion ; underinvestment JEL Classification: I32 ; I24 ; C60 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wrkesp:28&r= |
| By: | Christoph Görtz; Mallory Yeromonahos |
| Abstract: | A large literature suggests that the expected equity risk premium is countercyclical. Using a variety of different measures for this risk premium, we document that it also exhibits growth asymmetry, i.e. the risk premium rises sharply in recessions and declines much more gradually during the following recoveries. We show that a model with recursive preferences, in which agents cannot perfectly observe the state of current productivity, can generate the observed asymmetry in the risk premium. Key for this result are endogenous fluctuations in uncertainty which induce procyclical variations in agent’s nowcast accuracy. In addition to matching moments of the risk premium, the model is also successful in generating the growth asymmetry in macroeconomic aggregates observed in the data, and in matching the cyclical relation between quantities and the risk premium. |
| Keywords: | Risk Premium, Business cycles, Bayesian Learning, Asymmetry, Uncertainty, Nowcasting. |
| JEL: | E2 E3 G1 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2021-101&r= |
| By: | Faruk R. Gul (Princeton University); Wolfgang Pesendorfer (Princeton University) |
| Abstract: | A collective choice problem is a finite set of social alternatives and a finite set of economic agents with vNM utility functions. We associate a public goods economy with each collective choice problem and establish the existence and efficiency of (equal income) Lindahl equilibrium allocations. We interpret collective choice problems as cooperative bargaining problems and define a set-valued solution concept, the equitable solution (ES).We provide axioms that characterize ES and show that ES contains the Nash bargaining solution. Our main result shows that the set of ES payoffs is the same a the set of Lindahl equilibrium payoffs. We consider two applications: in the first, we show that in a large class of matching problems without transfers the set of Lindahl equilibrium payoffs is the same as the set of (equal income) Walrasian equilibrium payoffs. In our second application, we show that in any discrete exchange economy without transfers every Walrasian equilibrium payoff is a Lindahl equilibrium payoff of the corresponding collective choice market. Moreover, for any cooperative bargaining problem, it is possible to define a set of commodities so that the resulting economy’s utility possibility set is that bargaining problem and the resulting economy’s set of Walrasian equilibrium payoffs is the same as the set of Lindahl equilibrium payoffs of the corresponding collective choice market. |
| Keywords: | collective choice |
| JEL: | D70 D71 |
| Date: | 2021–04 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-52&r= |
| By: | Peter A. Streufert (University of Western Ontario) |
| Abstract: | This paper introduces Gm, which is a category for extensive-form games. It also provides some applications. The category’s objects are games, which are understood to be sets of nodes which have been endowed with edges, information sets, actions, players, and utility functions. Its arrows are functions from source nodes to target nodes that preserve the additional structure. For instance, a game’s information-set collection is newly regarded as a topological basis for the game’s decision-node set, and thus a morphism’s continuity serves to preserve information sets. Given these definitions, a game monomorphism is characterized by the property of not mapping two source runs (plays) to the same target run. Further, a game isomorphism is characterized as a bijection whose restriction to decision nodes is a homeomorphism, whose induced player transformation is injective, and which strictly preserves the ordinal content of the utility functions. The category is then applied to some game-theoretic concepts beyond the definition of a game. A Selten subgame is characterized as a special kind of categorical subgame, and game isomorphisms are shown to preserve strategy sets, Nash equilibria, Selten subgames, subgame-perfect equilibria, perfect-information, and no-absentmindedness. Further, it is shown that the full sub-category for distinguished-action sequence games is essentially wide in the category of all games, and that the full subcategory of action-set games is essentially wide in the full subcategory for games with no-absentmindedness. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:uwo:uwowop:20212&r= |
| By: | Doruk Cetemen (Collegio Carlo Alberto); Felix Zhiyu Feng (University of Washington); Can Urgun (Princeton University) |
| Abstract: | This paper studies a continuous-time, finite-horizon contracting problem with renegotiation and dynamic inconsistency arising from non-exponential discounting. The problem is formulated as a dynamic game played among the agent, the principal and their respective future "selves", each with their own discount function. We identify the principal optimal renegotiation-proof contract as a Markov Perfect Equilibrium (MPE) of the game, prove such a MPE exists, and characterize the optimal contract via an extended Hamilton-Jacobi-Bellman system. We solve the optimal contract in closed-form when the discount functions of the selves are related by time difference, a property that is satisfied by common forms of non-exponential discounting such as quasi-hyperbolic discounting and anticipatory utility. In particular, quasi-hyperbolic discounting leads to a U-shaped action path and anticipatory utility leads to a humshaped path, both are qualitatively different from the monotonic action path that would arise under exponential discounting. |
| Keywords: | continuous-time contracting, dynamic inconsistency, renegotiation, extended HJB system, non-atomic games |
| JEL: | D82 D86 D91 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-58&r= |
| By: | Peter A. Streufert (University of Western Ontario) |
| Abstract: | This paper specifies an extensive form as a 5-ary relation (i.e. set of quintuples) which satisfies certain abstract axioms. Each quintuple is understood to list a player, a situation (e.g. information set), a decision node, an action, and a successor node. Accordingly, the axioms are understood to specify abstract relationships between players, situations, nodes, and actions. Such an extensive form is called a "5-form", and a "5-form game" is defined to be a 5-form together with utility functions. The paper's main result is to construct a bijection between (a) those 5-form games with information-set situations and (b) Gm games (Streufert 2021). In this sense, 5-form games equivalently formulate almost all extensive-form games. An application weakens the tree axiom in the presence of the other axioms, which leads to a convenient decomposition of 5-forms. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:uwo:uwowop:20213&r= |
| By: | Chiara Zanardello (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES)) |
| Abstract: | I investigate the operation of the academic market in Italy, mapping current scholars’ location choices. I build a new dataset of current professors, associating each scholar with a composite indicator of their quality. The analysis includes the quality of the university and the features of the city where the institution is located. I estimate the strength of different factors: gravity (distance), agglomeration (scholars are attracted to higher quality universities), selection (better scholars travel longer distances), and sorting (the better the scholar, the more the quality of universities is weighted). I find that all of these factors have an effect, and do not vary according to scholars’ gender. I find a greater expected utility for scholars in choosing private universities over public ones, through a consistent nesting procedure. Comparing these forces to historical trends in Italian academia, the sorting effect delineates a new momentum for the current academic market in Italy. |
| Keywords: | Human capital, Academic market, Universities, Scholars, Sorting, Italy |
| JEL: | I23 O15 N34 N33 |
| Date: | 2022–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvir:2022001&r= |
| By: | Xiaosheng Mu (Princeton University) |
| Abstract: | We study the outcome of a sequential choice procedure based on a potentially incomplete preference relation. A decision maker evaluates alternatives in a list and iteratively updates her choice by comparing the status quo to the next alternative. She favors the status quo whenever the two alternatives are incomparable according to her underlying preference. Developing a revealed preference approach, we characterize all choice functions that can arise from such a procedure, as well as all possible preferences that can rationalize given choices. |
| Keywords: | Choice from lists; Status quo bias; Revealed preference |
| JEL: | D11 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-35&r= |
| By: | David DESMARCHELIER |
| Abstract: | This paper develops a very simple model of endogenous growth à la Lucas (1988) in which a representative household has to choose between environmental preservation and human capital accumulation. After computing analytically all possible trajectories, we point out that one of them depicts an inverted U-shape relationship between human capital (production) and pollution (i.e. an Environmental Kuznets Curve). If the economy follows the EKC trajectory, then a steady state is reached in the long run, indicating the incompatibility between endogenous growth and the EKC. Moreover, this simple framework allows to compute explicitly the initial value of the control variable. It is then proved that the optimal trajectory is the balanced growth path, not the EKC. Finally, we show that endogenous growth is possible, whatever the effect of pollution on the marginal utility of consumption. |
| Keywords: | Endogenous growth, environmental Kuznets curve, human capital. |
| JEL: | C61 O44 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2022-03&r= |
| By: | Laurent Simula (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Alain Trannoy (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Considering optimal non-linear income tax problems when the social welfare function only depends on ranks as in Yaari (Econometrica 55(1):95–115, 1987) and weights agreeing with the Lorenz quasi-ordering, we extend the analysis of Simula and Trannoy (Am Econ J Econ Policy, 2021) in two directions. First, we establish conditions under which bunching does not occur in the social optimum. We find a sufficient condition on individual preferences, which appears as a reinforcement of the Spence-Mirrlees condition. In particular, the marginal dis-utility of gross income should be convex, but less convex the higher the productivity. We also show that, for all productivity distributions with a log-concave survival function, bunching is precluded under the maximin, Gini, and "illfare-ranked single-series Ginis". Second, we turn to a discrete population setting, and provide an "ABC" formula for optimal marginal tax rates, which is related to those for a continuum of types found in Simula and Trannoy (2021), but remain essentially distinct. |
| Keywords: | Rank dependence,Gini,Optimal Income Taxation,Bunching,Log-Concavity |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03550894&r= |
| By: | Xiaosheng Mu (Princeton University); Luciano Pomatto (Caltech); Philipp Strack (Yale University); Omer Tamuz (Caltech) |
| Abstract: | The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary, monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks. |
| Keywords: | statistics, decision-making |
| JEL: | D81 |
| Date: | 2021–07 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2021-36&r= |
| By: | Daniel Agness (UC Berkeley); Travis Baseler (University of Rochester); Sylvain Chassang (Princeton University); Pascaline Dupas (Stanford University); Erik Snowberg (UBC and University of Utah) |
| Abstract: | People’s value for their own time is a key input in evaluating public policies: evaluations should account for time taken away from work or leisure as a result of policy. Using rich choice data collected from farming households in western Kenya, we show that households exhibit non-transitive preferences consistent with behavioral features such as loss aversion and self-serving bias. As a result, neither market wages nor standard valuation techniques (such as the Becker-DeGroot-Marschak—BDM—mechanism of Becker et al., 1964) correctly measure participants’ value of time. Using a structural model, we identify the mix of behavioral features driving our choice data. We find that these features distort choices when exchanging cash either for time or for goods. Our model estimates suggest that valuing the time of the self-employed at 60% of the market wage is a reasonable rule of thumb. |
| Keywords: | value of time, non-transitivity, labor rationing, loss aversion, self-serving bias, Kenya |
| JEL: | D10 D19 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2022-2&r= |
| By: | Evans, George; Gibbs, Christopher; McGough, Bruce |
| Abstract: | We propose and experimentally test a model of boundedly rational and heterogeneous expectations that unifies adaptive learning, k-level reasoning, and replicator dynamics. Level-0 forecasts evolve over time via adaptive learning. Agents revise over time their depth of reasoning in response to forecast errors, observed and counterfactual. The unified model makes sharp predictions for when and how fast markets converge in Learning-to-Forecast Experiments, including novel predictions for individual and market behavior in response to announced events. The experimental results support these predictions. Our unified model is developed in a simple framework, but can clearly be extended to more general macroeconomic environments. |
| Keywords: | expectations; adaptive learning; level-k reasoning; behavioral macroeconomics; experiments |
| Date: | 2021–11 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2021-10&r= |
| By: | Brian Hill (HEC Paris - Recherche - Hors Laboratoire - HEC Paris - Ecole des Hautes Etudes Commerciales, CNRS - Centre National de la Recherche Scientifique, GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | A series of famous examples casts doubt on the standard, Bayesian account of belief and decision in situations of considerable uncertainty. They have spawned a significant literature in economics, and to a lesser extent philosophy. This chapter some of this literature, with an emphasis on the normative issue of rational decision. [Pre-print version: please see the book for the final version, and cite it.] |
| Date: | 2021–12–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03504015&r= |
| By: | Faruk Gul (Princeton University); Paulo Natenzon (Washington University in St. Louis); Wolfgang Pesendorfer (Princeton University) |
| Abstract: | We introduce random evolving lotteries to study preference for non-instrumental information. Each period, the agent enjoys a flow payoff from holding a lottery that will resolve at the terminal date. We provide a representation theorem for non-separable risk consumption preferences and use it to characterize information seeking and its opposite, information aversion. To address applications, we characterize peak-trough utilities that aggregate trajectories of flow utilities linearly but, in addition, put weight on the best (peak) and worst (trough) lotteries along each path. We identify conditions for the ostrich effect, decision makers’ tendency to prefer information after good news to information after bad news. Our model permits savoring (enjoying the gradual arrival of good and sudden arrival of bad news) and dread (disliking the gradual arrival of bad and sudden arrival of good news) and a preference for skewed information |
| Keywords: | Information; Lotteries; Lottery; Preference |
| JEL: | D11 D44 D83 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:pri:econom:2020-72&r= |
| By: | Mikael Juselius; Nikola Tarashev |
| Abstract: | A parsimonious extension of a well-known portfolio credit-risk model allows us to study a salient stylized fact – abrupt switches between high- and low-loss phases – from a risk-management perspective. As uncertainty about phase switches increases, expected losses decouple from unexpected losses, which reflect a high percentile of the loss distribution. Banks that ignore this decoupling have shortfalls of loss-absorbing resources, which is more detrimental if the portfolio is more diversified within a phase. Likewise, the risk-management benefits of improving phase-switch forecasts increase with diversification. The analysis of these findings leads us to an empirical method for comparing the degree of within-phase default clustering across portfolios. |
| Keywords: | expected loss provisioning, bank capital, unexpected losses, credit cycles, portfolio credit risk. |
| JEL: | G21 G28 G32 |
| Date: | 2022–01 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:995&r= |