Musau, Andrew (2009): Modeling Alternatives to Exponential Discounting.
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One area that is often overlooked by economists and social scientists is discounting. Most economic models of intertemporal choice make use of Samuelson's (1937) DU model which leads to an exponential discount function. Divergences from what economic modelling predicts and empirical findings are on the most part attributed to factors other than the discount function employed. We review the literature on the DU model and identify its behavioral anomalies. We look into suggested quasi-hyperbolic and hyperbolic models that in part account for these anomalies. We analyze an infinite IPD game and demonstrate that under quasi-hyperbolic discounting, cooperation emerges as an SPE at a higher level of the discount factor. We further demonstrate that the unemployment equilibrium in the Shapiro & Stiglitz (1984) Shirking model is not static under both hyperbolic and quasi-hyperbolic discounting.
|Item Type:||MPRA Paper|
|Original Title:||Modeling Alternatives to Exponential Discounting|
|Keywords:||intertemporal, exponential, quasi-hyperbolic, hyperbolic.|
|Subjects:||A - General Economics and Teaching > A1 - General Economics > A10 - General|
|Depositing User:||Andrew Musau|
|Date Deposited:||23. Jul 2009 06:10|
|Last Modified:||17. Feb 2013 19:40|
Ainslie, G. (1975): Specious Reward: A Behavioral Theory of Impulsiveness and Impulse Control", Psychological Bulletin, 82(4), 463-96.
Ainslie, G. & R. J. Herrnstein (1981): Preference Reversal and Delayed Reinforcement", Animal Learning Behavior, 9(4), 476-82.
Arrow, K. J. (1976): The rate of discount for long-term public investment. In H. Ashley, R. L. Rudman and C. Whipple (eds.), Energy and the Environment,. Pergamon, New York.
Axtell, R. L. & G. J. McRae (2006): A General Theory of Behavioral and Social Discounting", Working paper, Center on Social and Economic Dynamics, The Brookings Institution (Washington D.C.).
Baumol, W. J. (1970): On the discount rate for public projects. In R. H. Haveman and J. Margolis (eds.), Public Expenditures and Policy Analysis. Markham,Chicago.
Benzion, U., A. Rapoport & J. Yagil (1989): Discount Rates Inferred from Decisions: An Experimental Study", Management Sciene, 35(3), 270-84.
Blanchard, O. & S. Fischer (1989): Lectures on Macroeconomics. MIT Press, Cambridge, Massachusetts.
Chapman, G. B. (2000): Preferences for Improving and Declining Sequences of Health Outcomes", Journal of Behavioral Decision Making, 13, 203-18.
Chapman, G. B. & A. S. Elstein (1995): Valuing the Future: Temporal Discounting of Health and Money", Medical Decision Making, 15(4), 373-86.
Chung, S. & R. Herrnstein (1961): Relative and absolute strengths of response as a function of frequency of reinforcement", Journal of the Experimental Analysis of Animal Behavior, 4, 262-72.
Folta, T. B. & K. D. Miller (2002): Real Options in Equity Partnerships", Strategic Management Journal, 23(1), 655-65.
Fredrick, S., G. Loewenstein & T. O'Donoghue (2002): Time Discounting and Time Preference: A Critical Review", Journal of Economic Literature, 40(2),351-401.
Goodin, R. E. (1982): Discounting Discounting", Journal of Public Policy, 2(1),53-71.
Green, L., E. B. Fischer, S. Perlow & L. Sherman (1981): Preference Reversal and Self Control: Choice as a Function of Reward Amount and Delay", Behavioral Analysis Letters, 1(1), 43-51.
Green, L., N. Fristoe & J. Myerson (1994): Temporal Discounting and Preference Reversals in Choice Between Delayed Outcomes", Psychonomic Bulletin Review, 1(3), 383-89.
Green, L., J. Myerson & E. McFadden (1997): Rate of Temporal Discounting Decreases with Amount of Reward", Memory and Cognition, 25(5), 715-23.
Herrnstein, R. (1981): Self-Control as Response Strength, in Quantification of Steady-State Operant Behavior. Christopher M. Bradshaw, Elmer Szabadi and C.F. Lowe, eds. Elsevier, New Holland.
Holcomb, J. H. & P. S. Nelson (1992): Another Experimental Look at Individual Time Preference", Rationality Society, 4(2), 199-220.
Hsee, C. K., R. P. Abelson & P. Salovey (1991): The Relative Weighting of Position and Velocity in Satisfaction", Psychological Science, 2(4), 263-66.
Kirby, K. N. & N. N. Marakovic (1995): Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting with Subjects and Amounts", Org. Behav. Human Decision Proc., 64, 22-30.
Laibson, D. (1997): Golden eggs and hyperbolic discounting", The Quarterly Journal of Economics, 112(2), 443=77.
Loewenstein, G. (2007): Exotic Preferences: Behavioral Economics and Human Motivation. Oxford University Press USA, New York, NY.
Loewenstein, G. & D. Prelec (1992): Anomalies in Intertemporal Choice: Evidence and an Interpretation", The Quarterly Journal of Economics, 107(2), 573-97.
Loewenstein, G. & D. Prelec (1993): Preferences for Sequences of Outcomes", Psychology Review, 100(1), 91=108.
Loewenstein, G. & N. Sicherman (1991): Do Workers Prefer Increasing Wage Profiles?", Journal of Labor Economics, 9(1), 67-84.
Loewenstein, G. & R. H. Thaler (1989): Anomalies: Intertemporal Choice", The Journal of Economic Perspectives, 3(4), 181-93.
Mazur, J. E. (1987): An Adjustment Procedure for Studying Delayed Reinforcement, in The Effect of Delay and Intervening Events on Reinforcement Value. Michael L. Commons, James E. Mazur, John A. Nevin and Howard Rachlin,eds. Erlbaum, Hillsdale, New Jersey.
McKerchar, L., L. Green, J. Myerson, T. S. Pickford, J. C. Hill & S. C. Stout (2009): A comparison of four models of delay discounting in humans", Behavioural Processes, 81(2), 256-59.
Milgrom, P. & J. Roberts (1981): Economics, Organization and Management. Prentice Hall, Englewood Cliffs, New Jersey.
Mill, J. S. (1848): Principles of Political Economy (reprint 1848 ed.). Colonial Press, New York.
Mischel, W., J. Grusec & J. C. Masters (1969): Effects of Expected Delay Time on Subjective Value of Rewards and Punishments", Journal of Personality Soc. Psych., 11(4), 363-73.
O'Donoghue, T. & M. Rabin (1999): Doing It Now or Later", American Economic Review, 89(1), 103=24.
Pender, J. L. (1996): Discount Rates and Credit Markets: Theory and Evidence from Rural India", Journal of Development Economics, 50(2), 257-96.
Phelps, E. S. & R. Pollak (1968): On Second-Best National Saving and Game Equilibrium Growth", The Review of Economic Studies, 35(2), 185-99.
Pigou, A. C. (1932): The Economics of Welfare, 4th ed. Macmillan, London.
Rae, J. (1834): The Sociological Theory of Capital (reprint 1834 ed.). Macmillan, London.
Ramsey, F. P. (1928): A mathematical theory of savings", Economic Journal, 38, 543-59.
Rawls, J. (1972): A Theory of Justice. Clarendon Press, Oxford.
Redelmeier, D. A. & D. N. Heller (1993): Time Preference in Medical Decision Making and Cost-Effectiveness Analysis", Medical Decision Making, 13(3), 212-17.
Samuelson, P. A. (1937): A Note on Measurement of Utility", The Review of Economic Studies, 4(2), 155-61.
Shapiro, C. & J. E. Stiglitz (1984): Equilibrium Unemployment as a Worker Discipline Device", The Review of Economic Studies, 74(3), 433-44.
Shelley, M. K. (1993): Outcome Signs, Question Frames and Discount Rates", Management Science, 39(2), 806-15.
Shy, O. (1995): Industrial Organization: Theory and Applications. MIT Press, Cambridge, Massachusetts.
Sidgwick, H. (1907): Methods of Ethics, 7th ed. Macmillan, London.
Slonim, R., J. Carlson & E. Bettinger (2007): Possession and discounting behavior", Economic Letters, 97, 215-21.
Solow, R. M. (1956): A Contribution to the Theory of Economic Growth", The Quarterly Journal of Economics, 70(1), 65-94.
Sozou, P. D. & R. M. Seymour (2003): Augmented Discounting: Interaction between Ageing and Time-Preference Behaviour", Biological Sciences, 270(1519), 1047-53.
Streich, P. & J. S. Levy (2007): Time Horizons, Discounting, and Intertemporal Choice", Journal of Conflict Resolution, 51(2), 199-226.
Strotz, R. H. (1956): Myopia and Inconsistency in Dynamic Utility Maximization", The Review of Economic Studies, 23(3), 165-80.
Thaler, R. H. (1981): Some Empirical Evidence on Dynamic Inconsistency", Economic Letters, 8, 201-07.
Varey, C. & D. Kahneman (1992): Experiences Extended Across Time: Evaluation of Moments and Episodes", Journal of Behavioral Decision Making, 5(3), 169-85.