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on Utility Models and Prospect Theory |
| By: | Nobuki Mochida (The University of Tokyo) |
| Abstract: | In economics, uncertainty is distinguished into two types: risk, which can be evaluated in terms of probability, and ambiguity, in which the probability is unknown. In decision making under risk, the rational course of action is to make a choice that maximizes expected utility, which is the utility of an event weighted by its probability. On the other hand, under ambiguity, where the probability is unknown, how should decisions be made? We first introduce the Minimax Regret, a decision-making criterion under ambiguity where probabilities are unknown but the interval is known. As a concrete example, consider two slot machines: one existing and one new. The winning probability of the former is known, while the winning probability of the latter is unknown, with only the interval provided. In this case, the optimal strategy according to the Minimax Regret criterion would be to randomly pull each of the two slot machines with a certain probability. Next, when utility is measured by a long-term metric, the interval of uncertainty for this metric decreases over time. To address this, we introduce the Adaptive Minimax Regret (AMR) approach, which maximizes utility by updating the probabilities according to the Minimax Regret criterion based on the information available at each point in time. Simulation testing on the case of the existing and new slot machines mentioned earlier showed that AMR produced high performance comparable to bandit algorithms. As an application of AMR in marketing, we propose sequential campaign strategies and probabilistic A/B testing aimed at maximizing the average customer lifetime (utility) of the target audience. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:tky:fseres:2024cf1232 |
| By: | Miller, Anne |
| Abstract: | Two propositions are required to introduce separate needs into utility theory. Firstly, the shape of the utility function must represent the different stages of fulfilment of a need as experienced by a consumer: deprivation, subsistence, sufficiency, satiation, surfeit. The second proposes weak separability for the utilities of commodities fulfilling the same need, and strong separability for different needs. A utility function, formed from the addition of two leaning-S-shaped, bounded cardinal utilities with satiation at infinity, is used to create an indifference curve map. Functional forms for the leisure-consumption choice are derived and their diagrams drawn – labour supply, consumption demand and their Engels curves. The main outcomes are: * Concave- and convex-to-the-origin indifference curves, (the former defining ‘dysfunctional poverty), are separated by a straight-line indifference curve, BA, (the slope of which is defined by relative-intensities-of-need), identifiable as an absolute poverty line. It leads to disequilibrium in the derived functional forms. * Each commodity responds as superior, inferior and even Giffen, in different areas of the convex-to-the-origin indifference curves. Their boundaries are reflected in envelope curves in the derived functional form diagrams. * An individual’s labour supply responses vary markedly according to three levels of unearned consumption/income, representing dysfunctional poverty (involuntary unemployment), functional poverty (working, but deprived of either leisure or consumption) and sufficiency. * The reservation wage is a U-shaped function of endowments of unearned consumption. The functional form’s parameters have meaningful psychological interpretations. The concept of separate needs in utility offers a new dimension in labour supply theory. |
| Keywords: | leaning-S-shaped utility, additive utilities, absolute poverty line, disequilibrium, Giffen good, envelope curve, involuntary unemployment, functional poverty, reservation wage |
| JEL: | D11 J22 |
| Date: | 2024–08–02 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121671 |
| By: | Astebro, Thomas B. (HEC Paris); Fossen, Frank M. (University of Nevada, Reno); Gutierrez, Cédric (Bocconi University) |
| Abstract: | Entrepreneurship scholars are interested in understanding and describing how entrepreneurs make decisions under uncertainty, where the probabilities of outcomes are not known but perceived, resulting in ambiguous probabilities. In this context, ambiguity refers to the lack of precise and objective probability assessments and the presence of subjective judgments regarding potential outcomes. In this chapter, we discuss the development of thought on how entrepreneurs perceive and react to uncertainty from Frank Knight (1921) to the present day. Recognizing that entrepreneurs face uncertainty rather than risk and are unlikely to have estimates of all probabilities for all potential outcomes, it becomes difficult to accept Expected Utility Theory (EUT), developed by Savage (1951) and von Neumann and Morgenstern (1953), as a relevant model for entrepreneurial decision-making. We examine a range of decision theories, ranking them in an order starting from EUT and proceeding to the most structure-free models of entrepreneurial choice, allowing for comparisons and contrasts of the main components and underlying concepts as they apply to entrepreneurial decision making. |
| Keywords: | entrepreneurship, uncertainty, ambiguity, decision theory, Bayesian Entrepreneurship |
| JEL: | L26 J24 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17231 |
| By: | Peter P. Caradonna; Christopher Turansick |
| Abstract: | We characterize those ex-ante restrictions on the random utility model which lead to identification. We first identify a simple class of perturbations which transfer mass from a suitable pair of preferences to the pair formed by swapping certain compatible lower contour sets. We show that two distributions over preferences are behaviorally equivalent if and only if they can be obtained from each other by a finite sequence of such transformations. Using this, we obtain specialized characterizations of which restrictions on the support of a random utility model yield identification, as well as of the extreme points of the set of distributions rationalizing a given data set. Finally, when a model depends smoothly on some set of parameters, we show that under mild topological assumptions, identification is characterized by a straightforward, local test. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06547 |
| By: | Dirk Krueger; Fulin Li; Harald Uhlig |
| Abstract: | This paper characterizes the transition dynamics of a continuous-time neoclassical production economy with capital accumulation in which households face idiosyncratic income risk and cannot commit to repay their debt. Therefore, even though a full set of contingent claims that pay out conditional on the realization of idiosyncratic shocks is available, the equilibrium features imperfect insurance and a non-degenerate cross-sectional consumption distribution. When household labor productivity takes two values, one of which is zero, and the utility function is logarithmic, we characterize the entire transition dynamics induced by unexpected technology shocks, including the evolution of the consumption distribution, in closed form. Thus, the model constitutes an analytically tractable alternative to the standard incomplete markets general equilibrium Aiyagari (1994) model by retaining its physical environment, but replacing the incomplete asset markets structure with one in which limits to consumption insurance emerge endogenously due to limited commitment. |
| JEL: | D11 E21 G22 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32880 |
| By: | Sasaki, Hiroaki; Mizutani, Aya |
| Abstract: | This study presents a three-sector growth model that consists of manufacturing, private services, and public services, and examines the relationship between sectoral compositions and the tax rate. We identify an optimal tax rate that maximizes instantaneous utility. The optimal tax rate increases as manufacturing productivity increases, though it converges to a certain level that is less than unity. |
| Keywords: | public services; cost disease; optimal tax rate; growth disease |
| JEL: | H21 H40 H50 O14 O41 |
| Date: | 2024–08–12 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121693 |
| By: | Appelbaum, Elie; Anam, Mahmudul; Chiang, Shin-Hwan |
| Abstract: | Using a simple duopolistic trade model with demand uncertainty and an identical traded product, we show that we can view trade in goods as implicit exports/imports of risk and risk aversion. Specifically, we show that a relatively “risk-aversion abundant” country is more likely to be a net importer of the product – hence an importer of low risk-aversion. Similarly, a “relatively high-risk abundant” country is more likely to be the net exporter of the product - hence an importer of low risk. We also show that market correlations and differences in risk aversion and risk are sources of implicit risk-sharing and diversification gains from trade. Consequently, the relatively high-risk or high-risk-aversion country always gains from trade, whereas the other country will most likely gain unless markets are highly positively correlated. Furthermore, we re-examine the (Brander-Spencer) strategic export subsidy game in the context of uncertainty and find that because both efficient risk management and rent shifting need to be considered, contrary to conventional wisdom, the equilibrium policy regime may be an export tax rather than a subsidy. |
| Keywords: | Patterns of Trade; Gains from Trade; Risk;Risk Aversion; Exports; Subsidies. |
| JEL: | D81 F12 F13 F15 |
| Date: | 2024–07–28 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:121605 |
| By: | Peter Caradonna; Christopher P. Chambers |
| Abstract: | We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces, constant relative/absolute risk and ambiguity aversion axioms, stationarity for dated rewards or consumption streams, separability, and many others. We provide necessary and sufficient conditions for invariant rationalizability via a novel approach which relies on tools from the theoretical computer science literature on automated theorem proving. We also establish a generalization of the Dushnik-Miller theorem, which we use to give a complete description of the out-of-sample predictions generated by the data under any such collection of axioms. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.04573 |
| By: | Benami, Elinor; Carter, Michael R.; Hobbs, Andrew; Jin, Zhenong; Kirchner, Ella |
| Abstract: | Agricultural index insurance seeks to protect producers against negative shocks that are common across a prespecified area, i.e., an index insurance zone. Often, administrative boundaries are used to delineate such index insurance zones. However, administrative boundaries may not reflect relevant variations in yield over space, which can be costly for policyholders as well as the public, especially since agricultural insurance is often heavily subsidized. Increased availability of finely resolved geospatial data on agronomic conditions coupled with machine learning approaches to identify similarities promises the ability to reduce losses associated with index insurance by identifying more homogeneous zones. In this work, we examine the changes in welfare impacts of a hypothetical area-yield index insurance when redrawing zone boundaries on the basis of relevant observed agronomic conditions. Drawing upon crop cut data from over 10, 000 maize fields in Kenya from 2016-2020 combined with satellite-based estimates of agronomic conditions, we examine the changes in expected utility to assess the value of data-driven and administrative insurance zones. When keeping the number of insurance zones equal to the number of administrative zones, we find that data-driven zones may offer only slightly higher risk reduction value than administrative zones. If no set number of zones are prespecified, the data-driven approach offers a flexible approach to identify an optimal number of zones that balances costs and performance. This approach can help inform program design as well as impact evaluations, as it further sheds light on trade-offs between the costs of ground sampling and zone size that can inform how to design and evaluate new programs in resource-constrained environments for maximum impact. |
| Keywords: | Agricultural Finance, International Development, Risk and Uncertainty |
| Date: | 2024–08–27 |
| URL: | https://d.repec.org/n?u=RePEc:ags:cfcp15:344685 |
| By: | Bach Dong-Xuan; Philippe Bich |
| Abstract: | People often face trade-offs between costs and benefits occurring at various points in time. The predominant discounting approach is to use the exponential form. Central to this approach is the discount rate, a unique parameter that converts a future value into its present equivalent. However, a universally accepted discount rate remains a matter of ongoing debate and lacks consensus. This paper provides a robust solution for resolving conflicts in discount rates, which recommends considering all discount rates but aims to assign varying degrees of importance to these rates. Moreover, a considerable number of economists support a theory that suggests equal consideration of future and present utilities. In response to this debate, we introduce a general criterion capable of accommodating situations where it is feasible not to discount future utilities. This criterion encompasses and extends various existing criteria in the literature. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.05632 |