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on Utility Models and Prospect Theory |
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Issue of 2022‒05‒02
ten papers chosen by |
| By: | Nail Kashaev; Victor H. Aguiar |
| Abstract: | We study a dynamic generalization of stochastic rationality in consumer behavior, the Dynamic Random Utility Model (DRUM). Under DRUM, a consumer draws a utility function from a stochastic utility process and maximizes this utility subject to her budget constraint in each time period. Utility is random, with unrestricted correlation across time periods and unrestricted heterogeneity in a cross-section. We provide a revealed preference characterization of DRUM when we observe a panel of choices from budgets. This characterization is amenable to statistical testing. Our result unifies Afriat's (1967) theorem that works with time-series data and the static random utility framework of McFadden-Richter (1990) that works with cross-sections of choice. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.07220&r= |
| By: | Glötzl, Erhard |
| Abstract: | In economics balance identities as e.g. C+K'-Y(L,K)=0 must always apply. Therefore, they are called constraints. This means that variables C,K,L cannot change independently of each other. In general equilibrium theory (GE) the solution for the equilibrium is obtained as an optimisation under the above or similar constraints. The standard method for modelling dynamics in macroeconomics are Dynamic Stochastic General Equilibrium (DSGE) models. Dynamics in DSGE models result from the maximisation of an intertemporal utility function that results in the Euler-Lagrange equations. The Euler-Lagrange equations are differential equations that determine the dynamics of the system. In Glötzl, Glötzl, und Richters (2019) we have introduced an alternative method to model dynamics, which constitutes a natural extension of GE theory. This approach is based on the standard method for modelling dynamics under constraints in physics. We therefore call models of this type "General Constrained Dynamic (GCD)" models. In Glötzl (2022b) this modelling method is described for non-intertemporal utility functions in macroeconomics. Since intertemporal utility functions are, however, essential for many economic models, this paper sets out to extend the GCD modelling framework to intertemporal GCD models, referred to as IGCD models in the following. This paper sets out to define the principles of formulating IGCD models and show how IGCD can be understood as a generalisation and alternative to DSGE models. |
| Keywords: | macroeconomic models, intertemporal utility function, constraint dynamics, GCD, DSGE, out-of-equilibrium dynamics, Lagrangian mechanics, stock flow consistent, SFC |
| JEL: | A12 B13 B41 B59 C02 C30 C54 C60 E10 |
| Date: | 2022–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112387&r= |
| By: | Yuhki Hosoya |
| Abstract: | We study a calculation method for utility function from a candidate of a demand function that is not differentiable but locally Lipschitz. Using this method, we obtain two new necessary and sufficient condition for a candidate of a demand function to be a demand function. First is the symmetry and negative semi-definiteness of the Slutsky matrix, and second is the global existence of a unique concave solution for some partial differential equation. Moreover, we present under several assumptions, the upper semi-continuous weak order that corresponds to the demand function is unique, and this weak order is represented by our calculated utility function. We also provide applications of these results to econometric theory. First, we show that under several requirements, if a sequence of demand functions converges to some function with respect to a metric corresponds to the topology of compact convergence, then the limit function is also a demand function. Second, the space of demand functions that have uniform Lipschitz constant on any compact set is complete under the above metric. Third, under some additional requirement, the mapping from a demand function into a utility function we calculate becomes continuous. This implies that a consistent estimation method for the demand function immediately defines a consistent estimation method for the utility function by using our calculation method. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.04770&r= |
| By: | Yevhen Havrylenko; Maria Hinken; Rudi Zagst |
| Abstract: | Equity-linked insurance products often have capital guarantees. Common investment strategies ensuring these guarantees are challenged nowadays by low interest rates. Thus, we study an alternative strategy when an insurance company shares financial risk with a reinsurance company. We model this situation as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the utilities of both parties. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.04053&r= |
| By: | Xin Zhang |
| Abstract: | In behavioral finance, aversion affects investors' judgment of future uncertainty when profit and loss occur. Considering investors' aversion to loss and risk, and the ambiguous uncertainty characterizing asset returns, we construct a distributional robust portfolio model (DRP) under the condition that the distribution of risky asset returns is unknown. Specifically, our objective is to find an optimal portfolio of assets that maximizes the worst-case utility level on the Wasserstein ball, which is centered on the empirical distribution of sample returns and the radius of the ball quantifies the investor's ambiguity level. The model is also formulated as a mixed-integer quadratic programming problem with cardinality constraints. In addition, we propose a hybrid algorithm to improve the efficiency of the solution and make it more suitable for large-scale problems. The distributional robust portfolio model considering aversion is empirically tested for superior performance in asset allocation, and we also compare common asset allocation strategies to further enhance the credibility of the portfolio. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.13999&r= |
| By: | Daniel Agness; Travis Baseler; Sylvain Chassang; Pascaline Dupas; Erik Snowberg |
| 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 |
| JEL: | C93 D03 D61 D91 J22 O12 Q12 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9567&r= |
| By: | Glötzl, Erhard |
| Abstract: | In economics balance identities as e.g. C+K'-Y(L,K) = 0 must always apply. Therefore, they are called constraints. This means that variables C,K,L cannot change independently of each other. In the general equilibrium theory (GE) the solution for the equilibrium is obtained as an optimisation under the above or similar constraints. The standard method for modelling dynamics in macroeconomics is DSGE. Dynamics in DSGE models result from the maximisation of an intertemporal utility function that results in the Euler-Lagrange equations. The Euler-Lagrange equations are differential equations that determine the dynamics of the system. In Glötzl, Glötzl, und Richters (2019) we have introduced an alternative method to model dynamics, which is a natural extension of GE theory. It is based on the standard method in physics for modelling dynamics under constraints. We therefore call models of this type "General Constrained Dynamic (GCD)" models. In this paper we apply this method to macroeconomic models of increasing complexity. The target of this labour is primarily to show the methodology of GCD models in principle and why and how it can be useful to analyse the macroeconomy with this method. Concrete economic statements play only a subordinate role. All calculations, even for GCD models of any complexity, can be easily performed with the open-source program GCDconfigurator. |
| Keywords: | Stephen Smale, Problem 8, macroeconomic models, constraint dynamics, GCD, DSGE, out-of-equilibrium dynamics, Lagrangian mechanics, stock flow consistent, SFC |
| JEL: | A12 B13 B41 B59 C02 C30 C54 C60 E10 |
| Date: | 2022–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112385&r= |
| By: | Gerard Cornelis van der Meijden; Cees A. Withagen; Hassan Benchekroun |
| Abstract: | Inspired by empirical evidence from the oil market, we build a model of an oligopoly facing a fringe as well as competition from renewable resources. We explore different subclasses of HARA utility functions (Cobb-Douglas, power and quadratic utility) to check the robustness of results found in the previous literature. For isoelastic demand, we characterize the equilibrium extraction rates of the fringe and the oligopolists. There always exists a phase of simultaneous supply of the oligopolists and the fringe, implying an inefficient order of use of resources since the oligopolists have smaller unit extraction costs and carbon emissions than the fringe. We calibrate our model to the oil market to quantify this sequence effect. In our benchmark calibration, we find for the three HARA subclasses that the sequence effect is responsible for almost all of the welfare loss compared to the first-best. It becomes smaller as market power decreases. Furthermore, we show that climate damage and Green Paradox effects depend non-monotonically on the degree of market power. |
| Keywords: | oligopoly-fringe, climate policy, non-renewable resource, Herfindahl rule, limit pricing, oligopoly, HARA preferences |
| JEL: | Q31 Q42 Q54 Q58 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9585&r= |
| By: | Shota Ichihashi; Byung-Cheol Kim |
| Abstract: | We study competition for consumer attention, in which platforms can sacrifice service quality for attention. A platform can choose the “addictiveness” of its service. A more addictive platform yields consumers a lower utility of participation but a higher marginal utility of allocating attention. We provide conditions under which increased competition can harm consumers by encouraging platforms to offer low-quality services. In particular, if attention is scarce, increased competition reduces the quality of services because business stealing incentives induce platforms to increase addictiveness. Restricting consumers’ platform usage may decrease addictiveness and improve consumer welfare. A platform’s ability to charge for its service can also decrease addictiveness. |
| Keywords: | Economic models |
| JEL: | D40 L51 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:22-16&r= |
| By: | Kombarov, Sayan |
| Abstract: | The thesis of this paper is mathematical formulation of the laws of Economics with application of the principle of Least Action of classical mechanics. This paper is proposed as the rigorous mathematical approach to Economics provided by the fundamental principle of the physical science – the Principle of Least Action. This approach introduces the principle of Action into main-stream economics and allows to reconcile the main principles Austrian School of Economics with the laws of market, such Say’s law, marginal value and interest rate theory, with the modern results of mathematical economics, such as Capital Asset Pricing Model (CAPM), game theory and behavioral economics. This principle is well known in classical mechanics as the law of conservation of action that governs any system as a whole and all its components. It led to the revolution in physics, as it allows to derive the laws of Newtonian and quantum mechanics and probability. Ludwig von Mises defined Economics is the science of Human Action. Action is introduced into Economics by the founder of Austrian School of Economic, Carl Menger. Production or acquisition of any goods, services and assets are results of purposeful acts in the form of expenditure of work and energy in the form of flow of money and material resources. Humans take them to achieve certain desired goals with given resources and time. Any economic good and service, financial, productive, or real estate asset is the result of such action. |
| Keywords: | Human Action, Say's law of markets, Principle of least action, Energy of money circulation, velocity of money, gold, exchange, value of use, law of diminishing value, marginal value, value of use, normal distribution, interest rate theory, GDP, Game theory, CAMP, The Prospect Theory |
| JEL: | A10 A12 A13 A20 C20 C22 C25 C52 C55 C58 C61 C62 C65 C70 C72 D00 D01 D03 D4 D40 D46 D50 D51 D53 D80 D83 D84 D86 D90 F0 G0 G01 G02 G11 G12 G14 |
| Date: | 2021–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:112474&r= |