Hyperbolic Discounting Model Research Articles

Present bias and its influence on financial behaviours amongst Indians

PurposePresent bias (PB) is a cognitive bias that stimulates the individual decision-maker to favour the present reward even over the higher reward in the future to avoid the uncertainty attached to the reward in an uncertain future. The article attempts to examine the prevalence of PB amongst Indians and the effect of such bias on savings and borrowings.Design/methodology/approachSecondary data on 47,132 respondents from the Financial Inclusion Insights, 2017 database was used in the study. The theory of self-control, which is captured by the widely accepted hyperbolic discounting model, was used to explore the presence of PB. Suitable statistical techniques and the binary probit regression model were employed to attain the objectives of the study.FindingsThe prevalence of PB was found amongst 8.2% of the sample respondents. The outcome of the study endorses the view of previous researchers that present-biased people tend to save less and borrow more.Originality/valueAlthough the exploration of the role of various cognitive biases on financial behaviour is gaining momentum in recent times, there is a dearth of studies exploring the prevalence of PB and its implication towards financial behaviour, especially in the context of the emerging economy of India. The study makes an original contribution in this regard by using a very rich dataset of 47,132 individuals in the Indian context for the first time.

Do time preferences predict diabetes outcomes? A combined survey and register-based study.

Identifying determinants of heterogeneity in health outcomes continues to be a focus in the health economic literature. In this study, we analyze whether time preferences predict health outcomes in individuals with type 1 diabetes (T1D) who use insulin pump therapy to manage their condition. We collect data on time preferences using a hypothetical matching task and estimate aggregate as well as individual-level discounting parameters using the exponential, hyperbolic, and quasi-hyperbolic discounting models. These parameters are then regressed against essential diabetes-related health outcomes obtained from registries and medical records, including glycemic control, kidney function, BMI, and number of hospital contacts. Our analyses indicate that all three discounting models fit the data equally well. Except for hospital contacts, we find robust evidence that impatience, as reflected by higher discounting, predicts worse health outcomes. Additionally, present bias is associated with worse kidney function. Our findings suggest that time preferences can explain some of the heterogeneity in health among individuals with T1D and call for increased attention on the role of time preferences in the design of disease management programs for individuals with chronic conditions.

The intertemporal choice study of individual water-saving irrigation construction under three water pricing and subsidy scenarios

The world is confronted with increasing droughts exacerbated by the inefficiency of irrigation, and water-saving irrigation (WSI) holds the potential to alleviate this dilemma. Since individual farmers are important participants in WSI, it is imperative to account for their decision preferences. In addition, previous research did not consider the decision reverse in the intertemporal choice of WSI construction. Recognizing the presence of bounded rationality, particularly in terms of time preference inconsistency, a hyperbolic discounting model is constructed. The implicit subsidy, explicit subsidy, and improved explicit subsidy scenarios are simulated to analyze the decision process of individual farmers in WSI construction. The proposed methods are applied to discuss the construction of WSI within the Taocheng District, Hebei Province. The results show that: (1) The participation and stability of individual WSI construction demonstrated an increase in both the explicit subsidy and improved explicit subsidy. (2) Compared with the implicit subsidy, there was a 29.6% decrease in the number of participants who chose not to engage in WSI construction at different intertemporal choice points in the explicit subsidy scenario, and the inconsistency of choice in different intertemporal choice points decreased from 70.4% to 31.4%. (3) In the improved explicit subsidy scenario, the inconsistency of choice in different intertemporal choice points will be further reduced to 22.5%. In order to promote WSI construction for water conservation, the policy implications of the subsidy mechanism are proposed in this paper.

Optimal Strategy for Corporate International Investment and Consumption Problem with Stochastic Hyperbolic Discounting

This study investigates the dynamics of a stochastic hyperbolic discounting model in a continuous-time framework to address the complexities associated with the corporate international investment consumption problem (CIICP). By formulating a dynamic programming equation based on the principles of dynamic programming, we seek to untangle the intricacies of CIICP by incorporating log utility. Our research provides valuable insights into the economic ramifications of the proposed model and presents a comprehensive analysis of numerical sensitivities. This investigation not only contributes to a deeper understanding of the CIICP phenomenon but also contributes to more informed decision-making within the field.

Can you change my generosity towards future others? The impact of observability on intertemporal pro‐social decisions

AbstractResearch has demonstrated that delays in realizing pro‐social decisions significantly influence pro‐social choices. However, the impact of time delay may vary by context. A key contextual factor is decision observability (i.e., the visibility of one's decision to others). Using a dictator game task with delayed rewards, the current study examined the effects of observability on intertemporal pro‐social choices. Subjects were randomly assigned to either an Anonymous group, where payment was private, or an Observable group, involving public payment. They had to decide between the selfish option (which only benefited the subject) and the generous option (sharing money with another person in a specific delay condition). Our data revealed that subjects were less eager to forgo money when time delay increased and showed more selfishness toward specific people, independent of decision observability. This pattern was aligned with a hyperbolic discounting model. Notably, observability mitigated the impact of time delay; subjects were more inclined to donate to temporally distant individuals when their decisions were observable instead of anonymous. In addition, we discuss the practical implications of observability for designing intertemporal donation appeals.

ПОВЕДЕНЧЕСКАЯ ЭКОНОМИКА: ИНТЕГРАЦИЯ И СИНЕРГИЯ ЭКОНОМИКИ И ПСИХОЛОГИИ

The article analyzes the scientific merits of behavioral economics, as one of the most promising and dynamically developing trends in modern science that is of great interest to researchers. Particular attention in the article is paid to the analysis of the scientific conclusions of Nobel laureate R. Thaler who is considered to be the most authoritative scientist in the field of behavioral economics. Scientific integration with psychology has enriched the methodology of economic research with many new scientific approaches, including experiment, which until the beginning of the 21st century was generally considered almost unacceptable in economic practice due to the irreversibility and unpredictability of its consequences. However, the use of experiment to study the psychological characteristics of people's behavior helped to understand the logic of many economic processes better, making them more predictable and controllable. The article concludes that the scientific developments of representatives of behavioral economics are important both for economic theory and for economic practice. They are implemented in predicting the dynamics of various markets, in optimizing socio-economic decisions based on the policy of ‘libertarian paternalism’. With their help, the widely used hyperbolic discounting model was developed, and another new branch of economics emerged — behavioral finance.

Non-exponential Reward Discounting in Reinforcement Learning

Reinforcement learning methods typically discount future rewards using an exponential scheme to achieve theoretical convergence guarantees. Studies from neuroscience, psychology, and economics suggest that human and animal behavior is better captured by the hyperbolic discounting model. Hyperbolic discounting has recently been studied in deep reinforcement learning and has shown promising results. However, this area of research is seemingly understudied, with most extant and continuing research using the standard exponential discounting formulation. My dissertation examines the effects of non-exponential discounting functions (such as hyperbolic) on an agent's learning and aims to investigate their impact on multi-agent systems and generalization tasks. A key objective of this study is to link the discounting rate to an agent's approximation of the underlying hazard rate of its environment through survival analysis.

Cultural differences in intertemporal decision making: A comparison between Chile and China.

A cross-cultural comparison is made of delay discounting in samples of participants from Chile and China. Comparisons are made based on previous literature that suggests that individuals from an Asian culture should be willing to postpone delayed rewards more than are individuals from a Latin American culture. To test the cross-cultural validity of a hyperbolic discounting model, the model was fitted to both data sets. Additionally, a self-enhancement measure was evaluated as a potential mediator between culture of origin and delay discounting. Seventy-eight college students from China and 120 college students from Chile, with similar demographic backgrounds, discounted hypothetical monetary outcomes using an adjusting-amount titration procedure. Additionally, participants completed a self-enhancement measure. Age, academic major, gender, and grade point average were controlled. Chilean participants discounted much more steeply than Chinese nationals did. No support was obtained for the mediation of self-enhancement between culture of origin and degree of delay discounting. In both samples, delay discounting was better described by a hyperboloid than an exponential function, the only exception being the $10,000 condition in which the medians for Chilean participants' present subjective value were equally well explained by a hyperboloid and an exponential function.

Dividend and corporate income taxation with present-biased consumers

Debates on the double taxation of dividends and corporate income have been long-standing. If double taxation were to be avoided, which type of tax policy would be more ideal? Conventional corporate theory based on microeconomic approaches does not yield a definitive answer, as either policy would distort firm investment and decrease firm value. Distinct from previous models, this paper addresses the double taxation issue in a macroeconomic context under a Laibson-type hyperbolic discounting model. In particular, this paper shows that in the hyperbolic economy, dividend taxes can improve consumer welfare, even though they decrease firm value. On the other hand, corporate income taxes negatively impact both consumers and firms. We also extend this result in an infinite-period steady-state model and show quantitative implications.

Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting

We prove existence of time consistent equilibria in a class of dynamic models with recursive payoffs and generalized discounting involving both behavioral and normative applications. Our generalized Bellman equation method identifies and separates both: recursive and strategic aspects of the equilibrium problem and allows to determine the sufficient assumptions on preferences and stochastic transition to establish existence. In particular we show existence of minimal state space stationary Markov equilibrium (a time-consistent equilibrium) in a deterministic model of consumption-saving with beta-delta discounting and its generalized versions involving non-additive payoffs, general form certainty equivalents, as well as stochastic semi-hyperbolic and hyperbolic discounting models (over possibly unbounded state and unbounded above reward space). We also provide an equilibrium approximation method for a hyperbolic discounting model.

Strategic Advice Provision in Repeated Human-Agent Interactions

This paper addresses the problem of automated advice provision in settings that involve repeated interactions between people and computer agents. This problem arises in many real world applications such as route selection systems and office assistants. To succeed in such settings agents must reason about how their actions in the present influence people's future actions. This work models such settings as a family of repeated bilateral games of incomplete information called ``choice selection processes'', in which players may share certain goals, but are essentially self-interested. The paper describes several possible models of human behavior that were inspired by behavioral economic theories of people's play in repeated interactions. These models were incorporated into several agent designs to repeatedly generate offers to people playing the game. These agents were evaluated in extensive empirical investigations including hundreds of subjects that interacted with computers in different choice selections processes. The results revealed that an agent that combined a hyperbolic discounting model of human behavior with a social utility function was able to outperform alternative agent designs, including an agent that approximated the optimal strategy using continuous MDPs and an agent using epsilon-greedy strategies to describe people's behavior. We show that this approach was able to generalize to new people as well as choice selection processes that were not used for training. Our results demonstrate that combining computational approaches with behavioral economics models of people in repeated interactions facilitates the design of advice provision strategies for a large class of real-world settings.

Strategic Advice Provision in Repeated Human-Agent Interactions (Abstract)

This paper addresses the problem of automated advice provision in settings that involve repeated interactions between people and computer agents. This problem arises in many real world applications such as route selection systems and office assistants. To succeed in such settings agents must reason about how their actions in the present influence people's future actions. The paper describes several possible models of human behavior that were inspired by behavioral economic theories of people's play in repeated interactions. These models were incorporated into several agent designs to repeatedly generate offers to people playing the game. These agents were evaluated in extensive empirical investigations including hundreds of subjects that interacted with computers in different choice selections processes. The results revealed that an agent that combined a hyperbolic discounting model of human behavior with a social utility function was able to outperform alternative agent designs. We show that this approach was able to generalize to new people as well as choice selection processes that were not used for training. Our results demonstrate that combining computational approaches with behavioral economics models of people in repeated interactions facilitates the design of advice provision strategies for a large class of real-world settings.

Temporal discounting in adolescents and adults with Tourette syndrome.

Tourette syndrome is a neurodevelopmental disorder associated with hyperactivity in dopaminergic networks. Dopaminergic hyperactivity in the basal ganglia has previously been linked to increased sensitivity to positive reinforcement and increases in choice impulsivity. In this study, we examine whether this extends to changes in temporal discounting, where impulsivity is operationalized as an increased preference for smaller-but-sooner over larger-but-later rewards. We assessed intertemporal choice in two studies including nineteen adolescents (age: mean[sd] = 14.21[±2.37], 13 male subjects) and twenty-five adult patients (age: mean[sd] = 29.88 [±9.03]; 19 male subjects) with Tourette syndrome and healthy age- and education matched controls. Computational modeling using exponential and hyperbolic discounting models via hierarchical Bayesian parameter estimation revealed reduced temporal discounting in adolescent patients, and no evidence for differences in adult patients. Results are discussed with respect to neural models of temporal discounting, dopaminergic alterations in Tourette syndrome and the developmental trajectory of temporal discounting. Specifically, adolescents might show attenuated discounting due to improved inhibitory functions that also affect choice impulsivity and/or the developmental trajectory of executive control functions. Future studies would benefit from a longitudinal approach to further elucidate the developmental trajectory of these effects.

Time-inconsistent discounting and the Friedman rule: roles of non-unitary discounting

Abstract We examine the optimality of the Friedman rule by considering recent development of behavioral economics. We construct a simple macroeconomic model where agents discount consumption and leisure at different rates. We also consider a standard exponential discounting model and a hyperbolic discounting model, by assuming that the same discounting applies to both consumption and leisure. Money is introduced via a cash-in-advance constraint. Although the three models are observationally equivalent, they provide different policy implications. The Friedman rule is optimal in the latter two models, while it is not optimal in the first model if agents discount consumption is at a higher rate than leisure.

A Mire of Discount Rates: Delaying Conservation Payment Schedules in a Choice Experiment

Studies on the public’s implicit discount rate in the willingness to pay for environmental amenities have mostly employed contingent valuation surveys. We investigate respondents’ time preferences using choice experiments with four payment schedules in a split-sample design in the context of mire conservation. We first examine preference and taste heterogeneity among respondents, finding them to a large extent independent of payment schedules. Next we use an endogenous approach to jointly estimate the implicit discount rates and preferences using choice experiments data. We explore exponential and hyperbolic discounting model specifications. We find insensitivity to the length of the payment period and support for hyperbolic discounting. Furthermore, we provide policy relevant valuation results concerning mire conservation.

Comparison of multiplicative and additive hyperbolic and hyperboloid discounting models in delayed lotteries involving gains and losses

Many day-to-day decisions may involve risky outcomes that occur at some delay after a decision has been made. We refer to such scenarios as delayed lotteries. Despite human choice often involves delayed lotteries, past research has primarily focused on decisions with delayed or risky outcomes. Comparatively, less research has explored how delay and probability interact to influence decisions. Within research on delayed lotteries, rigorous comparisons of models that describe choice from the discounting framework have not been conducted. We performed two experiments to determine how gain or loss outcomes are devalued when delayed and risky. Experiment 1 used delay and probability ranges similar to past research on delayed lotteries. Experiment 2 used individually calibrated delay and probability ranges. Ten discounting models were fit to the data using a genetic algorithm. Candidate models were derived from past research on discounting delayed or probabilistic outcomes. We found that participants' behavior was best described primarily by a three-parameter multiplicative model. Measures based on information criteria pointed to a solution in which only delay and probability were psychophysically scaled. Absolute measures based on residuals pointed to a solution in which amount, delay, and probability are simultaneously scaled. Our research suggests that separate scaling parameters for different discounting factors may not be necessary with delayed lotteries.

Time Consistent Equilibria in Dynamic Models With Recursive Payoffs and Behavioral Discounting

We prove existence of time consistent equilibria in a wide class of dynamic models with recursive payoffs and generalized discounting involving both behavioral and normative applications. Our generalized Bellman equation method identifies and separates both: recursive and strategic aspects of the equilibrium problem and allows to precisely determine the sufficient assumptions on preferences and stochastic transition to establish existence. In particular we show existence of minimal state space stationary Markov equilibrium (a time-consistent solution) in a deterministic model of consumption-saving with beta-delta discounting and its generalized versions involving magnitude effects, non-additive payoffs, semi-hyperbolic or hyperbolic discounting (over possibly unbounded state and unbounded above reward space). We also provide an equilibrium approximation method for a hyperbolic discounting model.

Variable time preference

We re-examine behavioral patterns of intertemporal choice with recognition that time preferences may be inherently variable, focusing in particular on the explanatory power of an exponential discounting model with variable discount factors – the variable exponential model. We provide analytical results showing that this model can generate systematically different choice patterns from an exponential discounting model with a fixed discount factor. The variable exponential model accounts for the common behavioral pattern of decreasing impatience, which is typically attributed to hyperbolic discounting. The variable exponential model also generates violations of strong stochastic transitivity in choices involving intertemporal dominance. We present the results of two experiments designed to evaluate the variable exponential model in terms of quantitative fit to individual-level choice data. Data from these experiments reveal that allowing for a variable discount factor significantly improves the fit of the exponential model, and that a variable exponential model provides a better account of individual-level choice probabilities than hyperbolic discounting models. In a third experiment we find evidence of strong stochastic transitivity violations when intertemporal dominance is involved, in accordance with the variable exponential model. Overall, our analytical and experimental results indicate that exponential discounting can explain intertemporal choice behavior that was supposed to be beyond its descriptive scope if the discount factor is permitted to vary at random. Our results also highlight the importance of allowing for different sources of randomness in choice modeling.

Hyperbolic Discounting and Its Consequences: Empirical Analysis on the Base of Surveys

During this cross-cultural research regarding time preferences the credibility of hyperbolic discounting model is examined. This paper is based on the comparison between the exponential discounting model and hyperbolic model and proposal of different modifications to the existing concepts. Different kind of anomalies, which bring up the necessity of the extension of the hyperbolic discounting model, are mentioned. This paper is aimed at exploring the discount model, the process of decisionmaking and the formation of the individuals’ subjective discount rate from the standpoint of behavioral economics by including in the model such psychological factors as cultural and economic environment and risk aversion. These supplements lead to more complex and credible discount model. The term of procrastination is considered as a direct implementation of hyperbolic discounting. Furthermore, the potential drawbacks occurred during the experimental part are highlighted and possible solutions are proposed. Empirical analysis is based on the surveys.

Prescription drug use under Medicare Part D: A linear model of nonlinear budget sets

Medicare Part D enrollees face a complicated decision: they dynamically choose prescription drug consumption in each period given difficult-to-find prices and a nonlinear budget set. We use Part D claims data to estimate a flexible model of consumption that accounts for nonlinear prices, dynamic responses, and salience. We use reduced form price responses from a linear regression of consumption on coverage range prices to compare performance under several models of behavior. We find small price elasticities, substantial myopia, and that salient characteristics impact consumption beyond their effect on prices. A hyperbolic discounting model with salience fits the data best.