Examining Predictive Accuracy Among Discounting Models

Both descriptive and normative arguments claim that the discount rate to be applied to public projects should be elicited from individual intertemporal preferences. We present a methodology to analyze data from experimental surveys on intertemporal preferences. Focusing on the exponential and the hyperbolic discounting models, we model the experimental data published by Thaler (1981) by means of different specifications. Standard measures of goodness of prediction are then applied to fitted data to select among alternative specifications. We first present our approach by applying it to simulated data. We then present a procedure for statistical estimation of the sample discount rate, testing four specifications.

[1]  Michael J. Moore,et al.  Rates of time preference and valuations of the duration of life , 1989 .

[2]  Howard Kunreuther,et al.  Time Insensitivity for Protective Investments , 1998 .

[3]  Bounded Rationality in Individual Decision Making , 1998 .

[4]  K. Arrow,et al.  Is there a role for benefit-cost analysis in environmental, health, and safety regulation? , 1996, Science.

[5]  P. Fishburn,et al.  Discount-neutral utility models for denumerable time streams , 1997 .

[6]  G. Loewenstein,et al.  Do Workers Prefer Increasing Wage Profiles? , 1991, Journal of Labor Economics.

[7]  B. McNeil,et al.  Fallacy of the five-year survival in lung cancer. , 1978, The New England journal of medicine.

[8]  Colin Camerer.  Bounded Rationality in Individual Decision Making , 1998 .

[9]  Howard Rachlin,et al.  Temporal Patterning in Probabilistic Choice , 1994 .

[10]  D. A. Kenny,et al.  The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. , 1986, Journal of personality and social psychology.

[11]  L. Robin Keller,et al.  Valuing environmental outcomes: Preferences for constant or improving sequences , 2002 .

[12]  Valuing Lives Lost or Saved over Time , .

[13]  D. Kahneman,et al.  Duration neglect in retrospective evaluations of affective episodes. , 1993, Journal of personality and social psychology.

[14]  G. Loewenstein.  Anticipation and the Valuation of Delayed Consumption , 1987 .

[15]  D. Kahneman,et al.  When More Pain Is Preferred to Less: Adding a Better End , 1993 .

[16]  J. Olsen,et al.  On what basis should health be discounted? , 1993, Journal of health economics.

[17]  Drazen Prelec,et al.  Preferences for sequences of outcomes. , 1993 .

[18]  R. Naylor.  Firm profits and the number of firms under unionised oligopoly , 2001 .

[19]  L. Robin Keller,et al.  Fair Processes for Societal Decisions Involving Distributional Inequalities , 1995 .

[20]  R. Herrnstein,et al.  Preference Reversals Due to Myopic Discounting of Delayed Reward , 1995 .

[21]  G. Chapman.  Expectations and Preferences for Sequences of Health and Money , 1996 .

[22]  E. Keeler,et al.  Discounting of Life-Saving and Other Nonmonetary Effects , 1983 .

[23]  Marjorie K. Shelley.  Outcome signs, question frames and discount rates , 1993 .

[24]  R L Keeney,et al.  A Framework to Guide Thinking and Analysis Regarding Climate Change Policies , 2001, Risk analysis : an official publication of the Society for Risk Analysis.

[25]  H. Klarman,et al.  Cost Effectiveness Analysis Applied to the Treatment of Chronic Renal Disease , 1968 .

[26]  R. Herrnstein,et al.  Choice and delay of reinforcement. , 1967, Journal of the experimental analysis of behavior.

[27]  C. B. Tilanus,et al.  Applied Economic Forecasting , 1966 .

[28]  Charles M. Harvey,et al.  Value functions for infinite-period planning , 1986 .

[29]  R. Lind,et al.  Reassessing the government's discount rate policy in light of new theory and data in a world economy with a high degree of capital mobility , 1990 .

[30]  Richard J. Herrnstein,et al.  The matching law , 1997 .

[31]  Industry profits and market size under bilateral oligopoly , 2001 .

[32]  K. Kirby,et al.  Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts , 1995 .

[33]  M. K. Stevenson.  The impact of temporal context and risk on the judged value of future outcomes , 1992 .

[34]  G. Ainslie.  Derivation of "Rational" Economic Behavior from Hyperbolic Discount Curves , 1991 .

[35]  D. Kahneman,et al.  Patients' memories of painful medical treatments: real-time and retrospective evaluations of two minimally invasive procedures , 1996, Pain.

[36]  P. Samuelson.  A Note on Measurement of Utility , 1937 .

[37]  David M. Eddy,et al.  Screening for cancer : theory, analysis, and design , 1984 .

[38]  R. Thaler.  Some empirical evidence on dynamic inconsistency , 1981 .

[39]  A. Tversky,et al.  On the elicitation of preferences for alternative therapies. , 1982, The New England journal of medicine.

[40]  A. Rapoport,et al.  Discount rates inferred from decisions: an experimental study , 1987 .

[41]  U. Ben-Zion,et al.  Discount rates inferred from decisions: an experimental study , 1989 .

[42]  Daniel Kahneman,et al.  Experiences extended across time: Evaluation of moments and episodes , 1992 .

[43]  G. Loewenstein,et al.  Anomalies in Intertemporal Choice: Evidence and an Interpretation , 1992 .

[44]  Michael J. Moore,et al.  The Quantity-Adjusted Value of Life , 1988 .

[45]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[46]  G. Loewenstein,et al.  Decision making over time and under uncertainty: a common approach , 1991 .

[47]  K. Kirby,et al.  Delay-discounting probabilistic rewards: Rates decrease as amounts increase , 1996, Psychonomic bulletin & review.

[48]  David R. Anderson,et al.  Model Selection and Multimodel Inference , 2003 .

[49]  G. Loewenstein.  Frames of mind in intertemporal choice , 1988 .

[50]  Itamar Simonson,et al.  Evaluations of pairs of experiences: A preference for happy endings , 1991 .

[51]  D. Ariely.  Combining experiences over time: the effects of duration, intensity changes and on‐line measurements on retrospective pain evaluations , 1998 .

[52]  Gretchen B. Chapman,et al.  The magnitude effect: Temporal discount rates and restaurant tips , 1998 .

[53]  G. Chapman.  Temporal discounting and utility for health and money. , 1996, Journal of experimental psychology. Learning, memory, and cognition.

[54]  W. Viscusi,et al.  Measures of Mortality Risks , 1997 .

[55]  A. Tversky,et al.  Contingent weighting in judgment and choice , 1988 .

[56]  Martin Ahlbrecht,et al.  An empirical study on intertemporal decision making under risk , 1997 .

[57]  Productivity and External Knowledge. The Italian Case , 2000 .

[58]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[59]  T. D. Kemper,et al.  Preference for Different Sequences of Increasing or Decreasing Rewards , 1996 .

[60]  T. Koopmans.  Stationary Ordinal Utility and Impatience , 1960 .