Quasi-Hyperbolic Discounting and Retirement
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Behavioural Economics University of Oxford Vincent P
Behavioural Economics University of Oxford Vincent P. Crawford Michaelmas Term 2012 Behavioural Decision Theory: Present-Bias and Time-Inconsistency in Intertemporal Choice (with very large debts to David Laibson and Ted O’Donoghue; material from their slides is used with permission) Revised 18 October 2013 1 The standard model of intertemporal choice in economics is time-separable utility with exponential discounting (Ramsey 1928 EJ, Samuelson, 1937 REStud): ⋯ With exponential discounting, your trade-offs between receiving utils today and receiving them with delay are independent of when that delay occurs: • If you prefer 10 utils now to 15 next week, then you must also prefer 10 utils in 25 weeks to 15 in 26 weeks. This agreement implies “time-consistent” (or “dynamically consistent”) choice, in that early and later selves agree on the ranking of plans, so that the mere passage of time (with no new information) doesn’t change the ranking. (In more general models, receiving new information over time could affect your preferences over plans conditional on the information received. But if your preferences are time-consistent, receiving new information over time cannot alter your preferences over plans contingent on resolution of uncertainty.) Thus, an exponential planner can simply maximize lifetime utility at the start of his life without worrying about later selves overturning his decisions. 2 For an exponential discounter, if it’s beneficial to do something next week/month/year/etc., other things equal it’s (even more) beneficial to do it Now. But people often seem to deviate systematically from these implications of the exponential discounting model. -
Uncertainty and Hyperbolic Discounting
Uncertainty and Hyperbolic Discounting By PARTHA DASGUPTA AND ERIC MASKIN* Empirical studies in economics and behav- they have become more impatient than they ioral ecology suggest that, ceteris paribus, ani- were in January. mals and humans appear to place less weight on Both the O’Donoghue-Rabin and Strotz ex- the future than on the present, i.e., they act as amples accord with “hyperbolic discounting,”2 though they discount future payoffs. Further- which has attracted considerable interest among more (and more interestingly), they do so with economists because it appears to shed light on discount rates that increase as the time before important economic phenomena such as house- those payoffs are realized grows shorter.1 In hold saving behavior (see David Laibson, 1997; other words, subjects act as though they become B. Douglas Bernheim et al., 2001; Christopher less patient when payoffs are more imminent. Harris and Laibson, 2003). An anecdotal (human) example is offered by One might ask whether there is some reason Ted O’Donoghue and Matthew Rabin (1999): for such behavior. The point of view that we when offered the choice in February between a take is that, to a considerable extent, animal and painful seven-hour task (e.g., preparing a tax human behavior is shaped by preferences that return) on April 1 and a painful eight-hour task are the outcome of evolutionary forces. That is, on April 15, most of us, they suggest, will opt cravings, urges, or instincts—the operational for the earlier date. But as April 1 approaches, manifestations of preferences—induce the ani- we are apt to change our minds, if we can, and mal or human to make the right choice in the postpone the pain to April 15, even though it “average” situation that it, he, or she is likely to will then be greater. -
Arxiv:1705.10602V2 [Math.OC] 22 Apr 2020 Time-Consistent Investment and Consumption Strategies Under a General Discount Functi
Time-consistent investment and consumption strategies under a general discount function I. Alia ∗ F. Chighoub † N. Khelfallah ‡ J. Vives § April 23, 2020 Abstract In the present paper we investigate the Merton portfolio management problem in the context of non-exponential discounting, a context that give rise to time-inconsistency of the decision maker. We consider equilibrium policies within the class of open-loop controls, that are characterized, in our context, by means of a variational method which leads to a stochastic system that consists of a flow of forward-backward stochas- tic differential equations and an equilibrium condition. An explicit representation of the equilibrium policies is provided for the special cases of power, logarithmic and exponential utility functions. Keys words: Stochastic Optimization, Investment-Consumption Problem, Merton Port- folio Problem, Non-Exponential Discounting, Time Inconsistency, Equilibrium Strategies, Stochastic Maximum Principle. MSC 2010 subject classifications, 93E20, 60H30, 93E99, 60H10. 1 Introduction Background The common assumption in classical investment-consumption problems under discounted utility is that the discount rate is assumed to be constant over time which leads to the dis- arXiv:1705.10602v2 [math.OC] 22 Apr 2020 count function be exponential. This assumption provides the possibility to compare outcomes occurring at different times by discounting future utility by some constant factor. But on the other hand, results from experimental studies contradict this assumption indicating that dis- count rates for the near future are much lower than discount rates for the time further away in future. Ainslie, in [1], established experimental studies on human and animal behaviour ∗Laboratory of Applied Mathematics, University Mohamed Khider, Po. -
A Monthly Struggle for Self-Control? Hyperbolic Discounting, Mental Accounting, and the Fall in Consumption Between Paydays
A Monthly Struggle for Self-Control? Hyperbolic Discounting, Mental Accounting, and the Fall in Consumption Between Paydays David Huffman IZA Bonn Matias Barenstein US Federal Trade Commission First draft: November, 2002 This version: December, 2005 Abstract An alternative conception of consumer choice has recently gained the attention of economists, which allows for two closely related departures from the standard model. First, consumers may have dynamically inconsistent preferences. Second, as a rational response to this dynamic inconsistency, the consumer may use external commitment devices or personal rules in an attempt to limit overspending. We use data from a large, representative sample of households in the UK to test the relevance of these twin predictions in the field. We find evidence that consumption spending declines between paydays, and jumps back to its initial level on the next payday. The decline is too steep to be explained by dynamically consistent (exponential) impatience, and does not appear to be driven by stockpiling or other rational motives. On the other hand a model with dynamically inconsistent (quasi-hyperbolic) time preference can explain the decline, for reasonable short-term and long-term discount rates. We also investigate whether households in our sample appear to make an effort at self-control, using a strategy emphasized in the literature: a mental accounting rule that limits borrowing during the pay period and thus puts a cap on overspending. We find that households who are able to borrow, in the sense that they own a credit card, nevertheless exhibit the spending profile characteristic of credit constraints. Investigating their behavior in more detail, we find that these households treat funds from the current and future income accounts very differently during the pay period. -
Risk Preferences Impose a Hidden Distortion on Measures of Choice Impulsivity
RESEARCH ARTICLE Risk preferences impose a hidden distortion on measures of choice impulsivity Silvia Lopez-Guzman1*, Anna B. Konova1, Kenway Louie1, Paul W. Glimcher1,2 1 Center for Neural Science, New York University, New York, United States of America, 2 Institute for the Study of Decision Making, New York University, New York, United States of America * [email protected] a1111111111 a1111111111 Abstract a1111111111 a1111111111 Measuring temporal discounting through the use of intertemporal choice tasks is now the a1111111111 gold standard method for quantifying human choice impulsivity (impatience) in neurosci- ence, psychology, behavioral economics, public health and computational psychiatry. A recent area of growing interest is individual differences in discounting levels, as these may predispose to (or protect from) mental health disorders, addictive behaviors, and other dis- OPEN ACCESS eases. At the same time, more and more studies have been dedicated to the quantification of individual attitudes towards risk, which have been measured in many clinical and non-clin- Citation: Lopez-Guzman S, Konova AB, Louie K, Glimcher PW (2018) Risk preferences impose a ical populations using closely related techniques. Economists have pointed to interactions hidden distortion on measures of choice between measurements of time preferences and risk preferences that may distort estima- impulsivity. PLoS ONE 13(1): e0191357. https:// tions of the discount rate. However, although becoming standard practice in economics, dis- doi.org/10.1371/journal.pone.0191357 count rates and risk preferences are rarely measured simultaneously in the same subjects Editor: Pablo Brañas-Garza, Middlesex University, in other fields, and the magnitude of the imposed distortion is unknown in the assessment of UNITED KINGDOM individual differences. -
The Role of Time Preference on Wealth
THE ROLE OF TIME PREFERENCE ON WEALTH _______________________________________ A Thesis presented to the Faculty of the Graduate School at the University of Missouri-Columbia _______________________________________________________ In Partial Fulfillment of the Requirements for the Degree Master of Science _____________________________________________________ by ANDREW MARK ZUMWALT Dr. Deanna L. Sharpe, Thesis Co-Supervisor Dr. Sandra J. Huston, Thesis Co-Supervisor December 2008 The undersigned, appointed by the dean of the Graduate School, have examined the thesis entitled THE ROLE OF TIME PREFERENCE ON WEALTH presented by Andrew Mark Zumwalt, a candidate for the degree of master of science, and hereby certify that, in their opinion, it is worthy of acceptance. Professor Deanna L. Sharpe Professor Sandra J. Huston Professor Thomas Johnson ad maiorem dei gloriam ACKNOWLEDGEMENTS All throughout my life, I have been supported by strong individuals. These people have been the pillars of my success, and without their influence and guidance, I would be nowhere near where I am now. I can only hope that I have, in turn, enriched their lives. I aspire to fulfill a similar role for the young men and women I meet. While I believe that my success has been caused by the cumulative efforts of many individuals, I would like to take this limited space to thank those that have helped with this part of my life. First, I would like to thank the members of my committee. Dr Thomas Johnson’s experience from agricultural economics provided insight into overlooked ideas in my research when viewed in a broader context. He has also been extremely understanding with regard to interesting timetables, and I’ve thoroughly enjoyed learning from him in both inside and outside the classroom. -
Hyperbolic Discounting and Learning Over Multiple Horizons
HYPERBOLIC DISCOUNTING AND LEARNING OVER MULTIPLE HORIZONS William Fedus Carles Gelada Yoshua Bengio Google Brain Google Brain University of Montreal (Mila) University of Montreal (Mila) [email protected] CIFAR Senior Fellow [email protected] [email protected] Marc G. Bellemare Hugo Larochelle Google Brain Google Brain [email protected] [email protected] ABSTRACT Reinforcement learning (RL) typically defines a discount factor (γ) as part of the Markov Decision Process. The discount factor values future rewards by an exponential scheme that leads to theoretical convergence guarantees of the Bellman equation. However, evidence from psychology, economics and neuroscience sug- 1 gests that humans and animals instead have hyperbolic time-preferences ( 1+kt for k > 0). In this work we revisit the fundamentals of discounting in RL and bridge this disconnect by implementing an RL agent that acts via hyperbolic discount- ing. We demonstrate that a simple approach approximates hyperbolic discount functions while still using familiar temporal-difference learning techniques in RL. Additionally, and independent of hyperbolic discounting, we make a surprising discovery that simultaneously learning value functions over multiple time-horizons is an effective auxiliary task which often improves over a strong value-based RL agent, Rainbow. 1 INTRODUCTION The standard treatment of the reinforcement learning (RL) problem is the Markov Decision Process (MDP) which includes a discount factor 0 ≤ γ < 1 that exponentially reduces the present value of future rewards (Bellman, 1957; Sutton & Barto, 1998). A reward rt received in t-time steps is t devalued to γ rt, a discounted utility model introduced by Samuelson (1937). This establishes a time- preference for rewards realized sooner rather than later. -
Behavioural Economics Mark.Hurlstone @Uwa.Edu.Au Behavioural Economics Outline
Behavioural Economics mark.hurlstone @uwa.edu.au Behavioural Economics Outline Intertemporal Choice Exponential PSYC3310: Specialist Topics In Psychology Discounting Discount Factor Utility Streams Mark Hurlstone Delta Model Univeristy of Western Australia Implications Indifference Discount Rates Limitations Seminar 7: Intertemporal Choice Hyperbolic Discounting Beta-delta model CSIRO-UWA Behavioural Present-Bias Strengths & Economics Limitations BEL Laboratory [email protected] Behavioural Economics Today Behavioural Economics • mark.hurlstone Examine preferences (4), time (2), and utility @uwa.edu.au maximisation (1) in standard model) Outline (1) (2) (3) (4) Intertemporal Choice Exponential Discounting Discount Factor Utility Streams Delta Model Implications Indifference Discount Rates • Intertemporal choice—the exponential discounting Limitations model Hyperbolic Discounting • anomalies in the standard Model Beta-delta model Present-Bias • behavioural economic alternative—quasi-hyperbolic Strengths & Limitations discounting [email protected] Behavioural Economics Today Behavioural Economics • mark.hurlstone Examine preferences (4), time (2), and utility @uwa.edu.au maximisation (1) in standard model) Outline (1) (2) (3) (4) Intertemporal Choice Exponential Discounting Discount Factor Utility Streams Delta Model Implications Indifference Discount Rates • Intertemporal choice—the exponential discounting Limitations model Hyperbolic Discounting • anomalies in the standard Model Beta-delta model Present-Bias • behavioural -
Present-Bias, Quasi-Hyperbolic Discounting, and Fixed Costs
ARTICLE IN PRESS YGAME:1750 JID:YGAME AID:1750 /FLA [m3G; v 1.30; Prn:28/12/2009; 11:48] P.1 (1-19) Games and Economic Behavior ••• (••••) •••–••• Contents lists available at ScienceDirect Games and Economic Behavior www.elsevier.com/locate/geb Present-bias, quasi-hyperbolic discounting, and fixed costs ✩ ∗ Jess Benhabib a,AlbertoBisin a ,b,AndrewSchottera ,b, a NYU, United States b CESS, United States article info abstract Article history: In this paper we elicit preferences for money–time pairs via experimental techniques. Received 28 January 2008 We estimate a general specification of discounting that nests exponential and hyperbolic Available online xxxx discounting, as well as various forms of present bias, including quasi-hyperbolic discounting. We find that discount rates are high and decline with both delay and amount, as most JEL classification: of the previous literature. We also find clear evidence for present bias. When identifying C91 D03 the form of the present bias, little evidence for quasi-hyperbolic discounting is found. The D90 data strongly favor instead a specification with a small present bias in the form of a fixed cost, of the order of $4 on average across subjects. With such a fixed cost the curvature of discounting is imprecisely estimated and both exponential and hyperbolic discounting cannot be rejected for several subjects. © 2009 Elsevier Inc. All rights reserved. 1. Introduction A vast literature in experimental psychology has studied time preferences by eliciting preferences over various alternative rewards obtained at different times, that is, over reward–time pairs.1 Representations of such time preferences include a specification of discounting. -
The Geographies of Soft Paternalism in the UK: the Rise of the Avuncular State and Changing Behaviour After Neoliberalism
The Geographies of Soft Paternalism in the UK: the rise of the avuncular state and changing behaviour after neoliberalism Rhys Jones, Jessica Pykett and Mark Whitehead, Aberystwyth University Forthcoming, Geography Compass Abstract Soft paternalism or libertarian paternalism has emerged as a new rationality of governing in the UK under New Labour, denoting a style of governing which is aimed at both increasing choice and ensuring welfare. Popularised in Thaler and Sunstein’s best-selling title, Nudge, the approach of libertarian paternalism poses new questions for critical human geographers interested in how the philosophies and practices of the Third Way are being adapted and developed in a range of public policy spheres, including the environment, personal finance and health policy. Focusing specifically on the case of the UK, this article charts how soft paternalism appeals to the intellectual influences of behavioural economics, psychology and the neurosciences, amongst others, to justify government interventions based on the ‘non-ideal’ or irrational citizen. By identifying the distinctive mechanisms associated with this ‘behaviour change’ agenda, such as ‘choice architecture’, we explore the contribution of behavioural geographies and political geographies of the state to further understanding of the techniques and rationalities of governing. 1 The Geographies of Soft Paternalism: the rise of the avuncular state and changing behaviour after neoliberalism 1. Introduction: The Chicago School comes to Britain Mark II. On March 24 2009, David Cameron stood next to the eminent behavioural economist Richard Thaler at the London Stock Exchange. David Cameron was in the City of London to deliver his keynote speech on banking reform and the Tory’s response to the credit crunch. -
Variable-Time-Preference-He-Et-Al.Pdf
Cognitive Psychology 111 (2019) 53–79 Contents lists available at ScienceDirect Cognitive Psychology journal homepage: www.elsevier.com/locate/cogpsych Variable time preference ⁎ T Lisheng Hea, , Russell Golmanb, Sudeep Bhatiaa,1 a University of Pennsylvania, United States b Carnegie Mellon University, United States ARTICLE INFO ABSTRACT Keywords: We re-examine behavioral patterns of intertemporal choice with recognition that time pre- Decision making ferences may be inherently variable, focusing in particular on the explanatory power of an ex- Intertemporal choice ponential discounting model with variable discount factors – the variable exponential model. We Stochastic choice provide analytical results showing that this model can generate systematically different choice Preference variability patterns from an exponential discounting model with a fixed discount factor. The variable ex- Computational modeling ponential 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. -
Time Preference and Economic Progress
Alexandru Pătruți, 45 ISSN 2071-789X Mihai Vladimir Topan RECENT ISSUES IN ECONOMIC DEVELOPMENT Alexandru Pătruți, Mihai Vladimir Topan, Time Preference, Growth and Civilization: Economic Insights into the Workings of Society, Economics & Sociology, Vol. 5, No 2a, 2012, pp. 45-56. Alexandru Pătruti, PhD TIME PREFERENCE, GROWTH AND Candidate Bucharest University of Economic CIVILIZATION: ECONOMIC Science Department of International INSIGHTS INTO THE WORKINGS Business and Economics Faculty of International Business OF SOCIETY and Economics 6, Piata Romana, 1st district, ABSTRACT. Economic concepts are not mere ivory 010374, Romania tower abstractions disconnected from reality. To a +4.021.319.19.00 certain extent they can help interdisciplinary endeavours E-mail: [email protected] at explaining various non-economic realities (the family, education, charity, civilization, etc.). Following the Mihai Vladimir Topan, insights of Hoppe (2001), we argue that the economic PhD Lecturer concept of social time preference can provide insights – Bucharest University of Economic when interpreted in the proper context – into the degree Science Department of International of civilization of a nation/region/city/group of people. Business and Economics More specifically, growth and prosperity backed by the Faculty of International Business proper institutional context lead, ceteris paribus, to a and Economics diminishing of the social rate of time preference, and 6, Piata Romana, 1st district, therefore to more future-oriented behaviours compatible 010374, Romania with a more ambitious, capital intensive structure of +4.021.319.19.00 production, and with the accumulation of sustainable E-mail: [email protected] cultural patterns; on the other hand, improper institutional arrangements which hamper growth and Received: July, 2012 prosperity lead to an increase in the social rate of time 1st Revision: September, 2012 preference, to more present-oriented behaviours and, Accepted: Desember, 2012 ultimately, to the erosion of culture.