Hyperbolic Discounting Research Articles

Digital Addiction in Teenagers: Tackling it With an App Based on Behavioral Economics

In recent years, smartphone usage has increased rapidly, especially in teenagers. The excessive screen time can lead to digital addiction which means people use technology to a point where they cannot stop, even though they recognize the negative consequences associated with it. In behavioral economics, there are two ways of classifying all decisions we make in life: rational and irrational. A rational decision would be one that gives us the most utility or satisfaction. Because humans are imperfect, we constantly make irrational decisions, such as using our phone too much even though we know that it is not the best use of our time. There is an explanation in behavioral economics behind this though. There are theories such as hyperbolic discounting and present bias that say humans value things more that are in the present time. I am recommending the use of an app in order to lower teens' screen time. This app would have numerous features such as goal setting, points/rewards, and a leaderboard that directly counteract this irrational behavior.

Hyperbolic discounting in an intergenerational model with altruistic parents

Hyperbolic utility discounting has emerged as a leading alternative to exponential discounting because it can explain time-inconsistent behaviors. Intuitively, hyperbolic discounting should play a crucial role in intergenerational models characterized by intertemporal trade-offs. In this paper, we incorporate hyperbolic discounting into a dynamic model in which parents are altruistic towards their children. Agents live for four periods and choose levels of consumption, fertility, investment in their children’s human capital, and bequests to maximize discounted utility. In the steady state, hyperbolic discounting decreases fertility, increases human capital investment, and shifts consumption towards younger ages. These effects are more pronounced in the time-consistent problem (in which agents cannot commit to a course of action) than in the commitment problem, which can be interpreted as realized and intended actions, respectively. The preference-based discrepancy between intended fertility and realized fertility has important implications for the empirical literature that compares the two.

Theory-based residual neural networks: A synergy of discrete choice models and deep neural networks

Researchers often treat data-driven and theory-driven models as two disparate or even conflicting methods in travel behavior analysis. However, the two methods are highly complementary because data-driven methods are more predictive but less interpretable and robust, while theory-driven methods are more interpretable and robust but less predictive. Using their complementary nature, this study designs a theory-based residual neural network (TB-ResNet) framework, which synergizes discrete choice models (DCMs) and deep neural networks (DNNs) based on their shared utility interpretation. The TB-ResNet framework is simple, as it uses a (δ, 1-δ) weighting to take advantage of DCMs’ simplicity and DNNs’ richness, and to prevent underfitting from the DCMs and overfitting from the DNNs. This framework is also flexible: three instances of TB-ResNets are designed based on multinomial logit model (MNL-ResNets), prospect theory (PT-ResNets), and hyperbolic discounting (HD-ResNets), which are tested on three data sets. Compared to pure DCMs, the TB-ResNets provide greater prediction accuracy and reveal a richer set of behavioral mechanisms owing to the utility function augmented by the DNN component in the TB-ResNets. Compared to pure DNNs, the TB-ResNets can modestly improve prediction and significantly improve interpretation and robustness, because the DCM component in the TB-ResNets stabilizes the utility functions and input gradients. Overall, this study demonstrates that it is both feasible and desirable to synergize DCMs and DNNs by combining their utility specifications under a TB-ResNet framework. Although some limitations remain, this TB-ResNet framework is an important first step to create mutual benefits between DCMs and DNNs for travel behavior modeling, with joint improvement in prediction, interpretation, and robustness.

Hyperbolic discounting and the time‐consistent solution of three canonical environmental problems

AbstractIn this paper I propose a time‐consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time‐consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time‐consistent hyperbolic discounting. This result is also confirmed for open‐access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.

Hyperbolic Discounting and the Time-Consistent Solution of Three Canonical Environmental Problems

In this paper I propose a time-consistent method of discounting hyperbolically that contains the discount rate implied by Gamma discounting as a special case. I apply the discounting method to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, (iii) economic growth and pollution. I then compare results with those for conventional exponential discounting using the normalization that both methods provide the same present value of an infinite constant flow. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the Modified Green Golden Rule.

The Origins of Behavioural Public Policy

The Origins of Behavioural Public Policy

Non-parametric Analysis of Time-Inconsistent Preferences

AbstractThis article provides a revealed preference characterisation of quasi-hyperbolic discounting which is designed to be applied to readily available expenditure surveys. We describe necessary and sufficient conditions for the leading forms of the model and also study the consequences of the restrictions on preferences popularly used in empirical lifecycle consumption models. Using data from a household consumption panel dataset, we explore the prevalence of time-inconsistent behaviour. The quasi-hyperbolic model provides a significantly more successful account of behaviour than the alternatives considered. We estimate the joint distribution of time preferences and the distribution of discount functions at various time horizons.

Quasi-Hyperbolic Present Bias: A Meta-Analysis

Quasi-hyperbolic discounting is one of the most well-known and widely-used models to capture self-control problems in the economics literature. The underlying assumption of this model is that agents have a toward current consumption such that all future rewards are downweighed relative to rewards in the present (in addition to standard exponential discounting for the length of delay). We report a meta-analytic dataset of estimates of the present bias parameter β based on searches of all major research databases (62 papers with 81 estimates in total). We find that the literature shows that people are on average present biased for both monetary rewards (β = 0.82, 95% confidence interval of [0.74, 0.90]) and nonmonetary rewards (β = 0.66, 95% confidence interval of [0.51, 0.85]) but that substantial heterogeneity exists across studies. The source of this heterogeneity comes from the subject pool, elicitation methodology, geographical location, payment method, mode of data collection (e.g. laboratory or field), and reward type. There is evidence of selective reporting and publication bias in the direction of overestimating the strength of present-bias (making β estimates smaller), but present bias still exists after correcting for these issues (for money β = 0.87 with 95% confidence interval of [0.82, 0.92] after correcting for selective reporting).

Computing Time-Consistent Equilibria: A Perturbation Approach

Time-consistency is a key feature of many important policy problems, such as those relating to optimal fiscal policy and optimal monetary policy. It is also important for private-sector decision-making through mechanisms such as quasi-hyperbolic discounting. These problems are generally solved using some form of projection method. The difficultly with projection methods is that their computational complexity increases rapidly with the number of state variables, limiting the sophistication of the models that can be solved. This paper develops a perturbation method for solving models with time-inconsistency that enables larger models to be more readily solved and analyzed. The method operates on a model’s (generalized) Euler equations; it does not require forming a quadratic approximation to household welfare and it does not require that the model’s steady state be efficient. We apply the method to several models featuring time-inconsistency and show that it exhibits good accuracy.

Quasi-hyperbolic Present Bias: A Meta-analysis

Quasi-hyperbolic discounting is one of the most well-known and widely-used models to capture selfcontrol problems in the economics literature. The underlying assumption of this model is that agents have a “present bias” toward current consumption such that all future rewards are downweighed relative to rewards in the present (in addition to standard exponential discounting for the length of delay). We report a meta-analytic dataset of estimates of the present bias parameter 𝛽 based on searches of all major research databases (62 papers with 81 estimates in total). We find that the literature shows that people are on average present biased for both monetary rewards (𝛽 = 0.82%-|-| confidence interval of [0.74, 0.90]) and non- monetary rewards (𝛽 = 0.66, 95% confidence interval of [0.51, 0.85]) but that substantial heterogeneity exists across studies. The source of this heterogeneity comes from the subject pool, elicitation methodology, geographical location, payment method, mode of data collection (e.g. laboratory or field), and reward type. There is evidence of selective reporting and publication bias in the direction of overestimating the strength of present-bias (making 𝛽 estimates smaller), but present bias still exists after correcting for these issues (for money 𝛽 = 0.87 with 95% confidence interval of [0.82, 0.92] after correcting for selective reporting).

Identification of Intertemporal Preferences From Choice Set Variation

The paper provides conditions to identify the discount factor(s) and utility function in a infinite-horizon dynamic discrete choice model variation in choice sets over time. We show that if current choices or states are informative about the choice set the agent will face in the future, then the discount factor and utility are identified without any strong normalization. These identification results hold in both the exponential discounting model and, if the choice set provides a form of pre-commitment, the quasi-hyperbolic discounting model. Identifying the discount factor and utility allows us to identify the counterfactual policies which often are the objects of interest in dynamic discrete-choice analysis, but which are not generally identified.

On the Rationale for Repeated U.S. Consumer Bankruptcy Filings

A theoretical model of U.S. consumer behavior is developed which allows the consumer to file for bankruptcy protection at different points, and on multiple occasions, over her lifespan. The model allows for conspicuous consumption, hyperbolic discounting, and random budget shocks. Findings suggest that individuals who file for bankruptcy protection multiple times may be better or worse off than those who file only once. However, repeat filers present with much more skewed consumption patterns, and evidence of much higher overspending at the time of filing, than individuals who have never filed for bankruptcy or who file for the first time. Keywords: consumer bankruptcy, financial epidemiology, conspicuous consumption

Are Delay and Interval Effects the Same Anomaly in the Context of Intertemporal Choice in Finance?

Traditionally, the interval and delay effects have been identified and considered as the same anomaly in the context of intertemporal choice, when individuals or groups of individuals make their decisions about reward preferences. This has supposed that most studies on this topic have been focused on the delay effect and, consequently, that the discount functions provided by the existing literature have considered only this effect. This is the case of hyperbolic discounting, which has been used to describe the delay, but not the interval effect. Therefore, the main objective of this paper is to carry out a detailed analysis of both anomalies, which will allow us to mathematically relate them, thus finding their analogies and differences. To do this, we will first analyze the concept of delay effect and later the different definitions of the interval effect. The main conclusion of this paper is twofold. On the one hand, if the benchmark for valuation is fixed, the delay effect coincides with the so-called decreasing interval effect. On the other hand, if the assessment reference point is the beginning of each interval, both anomalies are different. These findings make necessary to redefine the concept of interval effect. Finally, we will analyze the relationship between the interval effect, the delay effect and the subadditivity

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.

Intertemporal Discrete Choice

The discounted logit is widely used to estimate time preferences using data from field and laboratory experiments. Despite its popularity, it exhibits the of the scale: choice probabilities depend on the scale of the value function. When applied to intertemporal choice, the problem the scale implies that logit probabilities are sensitive to the temporal distance between the choice and the outcomes. This is a failure of an intuitive requirement of stationarity although future values are discounted geometrically. As a consequence, patterns of choice following from the structure of the logit may be attributed to non-stationary discounting. We solve this problem introducing the discounted Luce rule. It retains the flexibility and simplicity of the logit while it satisfies stationarity. We characterize the model in two settings: dated outcomes and consumption streams. Relaxations of stationarity give observable restrictions characterizing hyperbolic and quasi-hyperbolic discounting. Lastly, we discuss an extension of the model to recursive stochastic choices with the present bias.

Markov decision processes with quasi-hyperbolic discounting

We study Markov decision processes with Borel state spaces under quasi-hyperbolic discounting. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, we prove the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function. We also show that randomisation can be restricted to two actions in every state of the process. Moreover, we prove that under some conditions, this equilibrium can be replaced by a deterministic one. For models with countable state spaces, we establish the existence of deterministic Markov perfect equilibria. Many examples are given to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting.

Cost overruns and delays in infrastructure projects: the case of Stuttgart 21

PurposeWe investigate causes for the cost overrun and delay of the railway project Stuttgart 21. Besides, we try to forecast the actual costs and completion date at an early stage.Design/methodology/approachThe results of exploratory research show the causes for the cost overrun and delay of Stuttgart 21; we compare our findings with other railway projects. To estimate the costs at an early stage, the reference class forecasting (RCF) model is applied; to estimate the time, we apply an OLS regression.FindingsWe find that the following causes are relevant for the cost overrun and delay of Stuttgart 21: scope changes, geological conditions, high risk-taking propensity, extended implementation, price overshoot, conflict of interests and lack of citizens' participation. The current estimated costs are within our 95% confidence interval based on RCF; our time forecast underestimates or substantially overestimates the duration actually required.Research limitations/implicationsA limitation of our approach is the low number of comparable projects which are available.Practical implicationsThe use of hyperbolic function or stepwise exponential discount function can help to give a clearer picture of the costs and benefits. The straightforward use of the RFC for costs and OLS for time should motivate more decision-makers to estimate the actual costs and time which are necessary in the light of the rising demand for democratic participation amongst citizens.Social implicationsMore realistic estimates can help to reduce the significant distortion at the beginning of infrastructure projects.Originality/valueWe are among the first who use the RCF to estimate the costs in Germany. Furthermore, the hyperbolic discounting function is added as a further theoretical explanation for cost underestimation.

Lanchester duopoly model revisited: Advertising competition under time inconsistent preferences

In this paper, we study a finite time horizon advertising dynamic game under the assumption of time-inconsistent preferences. Specifically, we consider two types of discounting, heterogeneous discounting and hyperbolic discounting. In the case of heterogeneous discounting, the relative importance of the final function will increase/decrease as the end of the planning horizon approaches compared with current payoffs. Whereas when agents discount future payoffs hyperbolically, their discount rates diminish rapidly in earlier stages and then slowly in the long term. We compute time-inconsistent and time-consistent feedback Nash equilibrium strategies, and compare them with those of the standard discounting case. Our results reveal that heterogeneous discounting would lead to some last-minute changes, i.e., some adapting behaviours in the last years in accordance with their increasing/decreasing valuations of the final state. Under some circumstances, the change can be so radical that the pre-commitment solution takes the contrary path of time-consistent strategies. Concerning the competition under hyperbolic discounting, the temporal evolution of advertising efforts show a quite different nature. Different strategies exhibit disparity in the beginning, and encounter in the neighbourhood in the end, which is contrary to the heterogeneous discounting. Besides, a strong commitment power might induce over investment.

Consumption and life insurance decisions under hyperbolic discounting and taxation

In this study, we investigates the time-inconsistent agent's optimal consumption, life insurance purchase, and investment decisions under a tax system. We find analytically that the marginal propensity to consume (MPC) for the time-inconsistent (naïve or sophisticated) agent is larger than that of the time-consistent agents. Based on the numerical results, we show that the time-inconsistent preferences result in a lower demand for life insurance, which may explain why people purchase insufficient life insurance. Further, the sophisticated agent reacts more sensitively to an insurance tax rate increase than the time-consistent agent.

Cognitive bias: how understanding its impact on antibiotic prescribing decisions can help advance antimicrobial stewardship

The way clinicians think about decision-making is evolving. Human decision-making shifts between two modes of thinking, either fast/intuitive (Type 1) or slow/deliberate (Type 2). In the healthcare setting where thousands of decisions are made daily, Type 1 thinking can reduce cognitive load and help ensure decision making is efficient and timely, but it can come at the expense of accuracy, leading to systematic errors, also called cognitive biases. This review provides an introduction to cognitive bias and provides explanation through patient vignettes of how cognitive biases contribute to suboptimal antibiotic prescribing. We describe common cognitive biases in antibiotic prescribing both from the clinician and the patient perspective, including hyperbolic discounting (the tendency to favour small immediate benefits over larger more distant benefits) and commission bias (the tendency towards action over inaction). Management of cognitive bias includes encouraging more mindful decision making (e.g., time-outs, checklists), improving awareness of one's own biases (i.e., meta-cognition), and designing an environment that facilitates safe and accurate decision making (e.g., decision support tools, nudges). A basic understanding of cognitive biases can help explain why certain stewardship interventions are more effective than others and may inspire more creative strategies to ensure antibiotics are used more safely and more effectively in our patients.