A Life-Cycle Model with Ambiguous Survival Beliefs

On average, “young”people underestimate whereas “old”people overestimate their chances to survive into the future. We adopt a Bayesian learning model of ambiguous survival beliefs which replicates these patterns. The model is embedded within a non-expected utility model of life-cycle consumption and saving. Our analysis shows that agents with ambiguous survival beliefs (i) save less than originally planned, (ii) exhibit undersaving at younger ages, and (iii) hold larger amounts of assets in old age than their rational expectations counterparts who correctly assess their survival probabilities. Our ambiguity-driven model therefore simultaneously accounts for three important empirical findings on household saving behavior. JEL Classification: D91, D83, E21.

[1]  Athanasios C. Thanopoulos,et al.  Social Security and Self Control Preferences , 2008 .

[2]  Norbert Schwarz,et al.  Statistical Analysis of Choice Experiments and Surveys , 2005 .

[3]  Kota Saito.  Strotz Meets Allais: Diminishing Impatience and the Certainty Effect: Comment , 2011 .

[4]  J. Andreoni,et al.  Risk Preferences Are Not Time Preferences , 2012 .

[5]  Larry G. Epstein,et al.  Dynamically Consistent Beliefs Must Be Bayesian , 1993 .

[6]  J. Schreiber.  Foundations Of Statistics , 2016 .

[7]  Michael G. Palumbo,et al.  Uncertain Medical Expenses and Precautionary Saving Near the End of the Life Cycle , 1999 .

[8]  Annamaria Lusardi,et al.  Financial Literacy and Planning: Implications for Retirement Wellbeing , 2005 .

[9]  F. Peracchi,et al.  Subjective survival probabilities and life tables: Evidence from Europe , 2011 .

[10]  A. Yaron,et al.  Sources of Lifetime Inequality , 2007 .

[11]  David A. Love,et al.  The Trajectory of Wealth in Retirement , 2008 .

[12]  J. Siegel.  Stocks for the long run : the definitive guide to financial market returns and long-term investment strategies , 2008 .

[13]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[14]  David Kelsey,et al.  When is ambiguity–attitude constant? , 2012 .

[15]  Paolo Ghirardato,et al.  Revisiting Savage in a conditional world , 2002 .

[16]  A. Tversky,et al.  Options traders exhibit subadditive decision weights , 1996 .

[17]  I. Gilboa.  Expected utility with purely subjective non-additive probabilities , 1987 .

[18]  Larry G. Epstein,et al.  Learning Under Ambiguity , 2002 .

[19]  Faruk Gul,et al.  Temptation and Self‐Control , 1999 .

[20]  Joel L. Horowitz,et al.  Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators , 1996 .

[21]  David I. Laibson,et al.  Dynamic Choices of Hyperbolic Consumers , 2001 .

[22]  Alexander Zimper,et al.  Investment behavior under ambiguity: The case of pessimistic decision makers , 2006, Math. Soc. Sci..

[23]  Chin-Diew Lai,et al.  Modelling Deceleration in Senescent Mortality , 2011 .

[24]  C. Pires.  A Rule For Updating Ambiguous Beliefs , 2002 .

[25]  O. Attanasio,et al.  Differential Mortality and Wealth Accumulation , 1995 .

[26]  C. Carroll.  The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence , 1992 .

[27]  Susann Rohwedder,et al.  Wealth Dynamics and Active Saving at Older Ages , 2013 .

[28]  Itzhak Gilboa,et al.  Updating Ambiguous Beliefs , 1992, TARK.

[29]  A. Zimper,et al.  A parsimonious model of subjective life expectancy , 2007 .

[30]  Eric French,et al.  Why Do the Elderly Save? The Role of Medical Expenses , 2009, Journal of Political Economy.

[31]  Lee M. Lockwood.  Incidental Bequests: Bequest Motives and the Choice to Self-Insure Late-Life Risks , 2014 .

[32]  David Laibson,et al.  Self-Control and Saving for Retirement , 1998 .

[33]  J. Worden,et al.  The Psychology of Death , 1973 .

[34]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[35]  David Laibson,et al.  Saving or Retirement on the Path of Least Resistance , 2004 .

[36]  David I. Laibson,et al.  Life-cycle consumption and hyperbolic discount functions , 1998 .

[37]  Massimo Marinacci,et al.  Learning from ambiguous urns , 2002 .

[38]  Alexander Ludwig,et al.  Demographic Change, Human Capital and Welfare , 2010 .

[39]  Ronald Lee,et al.  Modeling and forecasting U. S. mortality , 1992 .

[40]  Sukyung Chung,et al.  The relationship between individual expectations and behaviors: Mortality expectations and smoking decisions , 2007 .

[41]  Chris I. Telmer,et al.  Cyclical Dynamics in Idiosyncratic Labor Market Risk , 2004, Journal of Political Economy.

[42]  S. Thorp,et al.  Cohort and target age effects on subjective survival probabilities: Implications for models of the retirement phase , 2015 .

[43]  Todd E. Elder.  The Predictive Validity of Subjective Mortality Expectations: Evidence From the Health and Retirement Study , 2013, Demography.

[44]  Albert Ando,et al.  The "Life Cycle" Hypothesis of Saving: Aggregate Implications and Tests , 2007 .

[45]  Richard Gonzalez,et al.  Curvature of the Probability Weighting Function , 1996 .

[46]  James G. MacKinnon,et al.  Bootstrap J tests of nonnested linear regression models , 2002 .

[47]  K. Kurihara.  Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data , 2013 .

[48]  A. Tversky,et al.  An axiomatization of cumulative prospect theory , 1993 .

[49]  Joseph G. Altonji,et al.  Small Sample Bias in GMM Estimation of Covariance Structures , 1994 .

[50]  J. Quiggin.  A theory of anticipated utility , 1982 .

[51]  Marciano M. Siniscalchi,et al.  Dynamic Choice Under Ambiguity , 2006 .

[52]  D. McFadden,et al.  Subjective Survival Curves and Life Cycle Behavior , 1998 .

[53]  L. Eeckhoudt,et al.  Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities , 2006 .

[54]  D. Canning,et al.  The Effect of Subjective Survival Probabilities on Retirement and Wealth in the United States , 2006 .

[55]  Peter Roelofsma,et al.  Strotz Meets Allais : Diminishing Impatience and the Certainty Effect , 2008 .

[56]  Douglas H. Joines,et al.  Time-Inconsistent Preferences and Social Security , 2003 .

[57]  M. Cagetti,et al.  Wealth Accumulation Over the Life Cycle and Precautionary Savings , 2003 .

[58]  Alexander Zimper,et al.  On attitude polarization under Bayesian learning with non-additive beliefs , 2009 .

[59]  Jorn-Steffen Pischke,et al.  Measurement Error and Earnings Dynamics: Some Estimates from the PSID Validation Study , 1995 .

[60]  S. Preston,et al.  Demography: Measuring and Modeling Population Processes , 2000 .

[61]  Adrian Bruhin,et al.  Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting , 2010 .

[62]  J. Je,et al.  Theoretical estimation of maximum human lifespan , 2009, Biogerontology.

[63]  Alain Chateauneuf,et al.  Choice under uncertainty with the best and worst in mind: Neo-additive capacities , 2007, J. Econ. Theory.

[64]  D. Hamermesh,et al.  Expectations, Life Expectancy, and Economic Behavior , 1985 .

[65]  L. Gavrilov,et al.  Biodemography of old-age mortality in humans and rodents. , 2015, The journals of gerontology. Series A, Biological sciences and medical sciences.

[66]  Mohammed Abdellaoui,et al.  The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation , 2011 .

[67]  David I. Laibson,et al.  Golden Eggs and Hyperbolic Discounting , 1997 .

[68]  J. Gampe.  Human mortality beyond age 110 , 2010 .

[69]  A. Rubinstein.  International Economic Review " Economics and Psychology " ? the Case of Hyperbolic Discounting * , 2003 .

[70]  On the composition of risk preference and belief. , 2004, Psychological review.

[71]  Miles S. Kimball,et al.  Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Survey , 1995 .

[72]  D. Schmeidler.  Integral representation without additivity , 1986 .

[73]  Michael D. Hurd,et al.  Mortality Risk and Bequests , 1989 .

[74]  A. Zimper.  Asset pricing in a Lucas fruit-tree economy with the best and worst in mind☆ , 2012 .

[75]  R. Berk,et al.  Limiting Behavior of Posterior Distributions when the Model is Incorrect , 1966 .

[76]  N. Nicholls,et al.  The impact of statistical learning on violations of the sure-thing principle , 2015 .

[77]  B. Bosworth,et al.  The Decline in Saving: Evidence from Household Surveys , 1991 .

[78]  Ted O’Donoghue,et al.  Doing It Now or Later , 1999 .

[79]  C. I. Jones,et al.  The Value of Life and the Rise in Health Spending , 2004 .

[80]  J. Eichberger,et al.  Updating Choquet Beliefs , 2007 .

[81]  N. Nicholls,et al.  Subjective Life Expectancy , 2015 .

[82]  R. H. Strotz.  Myopia and Inconsistency in Dynamic Utility Maximization , 1955 .

[83]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[84]  Alexander Zimper,et al.  Do Bayesians Learn Their Way Out of Ambiguity? , 2011, Decis. Anal..

[85]  G. Angeletos,et al.  The Hyperbolic Consumption Model: Calibration, Simulation, and Empirical Evaluation , 2022 .

[86]  Massimo Marinacci,et al.  Differentiating ambiguity and ambiguity attitude , 2004, J. Econ. Theory.

[87]  N. Pavoni,et al.  Optimal Life�?Cycle Capital Taxation Under Self�?Control Problems , 2017 .

[88]  P. Wakker.  Prospect Theory: For Risk and Ambiguity , 2010 .

[89]  S. Thorp,et al.  Die Young or Live Long: Modeling Subjective Survival Probabilities , 2013 .

[90]  M. Salm.  Subjective Mortality Expectations and Consumption and Saving Behaviours Among the Elderly , 2010 .

[91]  O. Mitchell,et al.  Financial Illiteracy, Education, and Retirement Saving , 1996 .

[92]  David Kjellberg.  Measuring Expectations , 1999, Identification Problems in the Social Sciences.

[93]  J. Muth.  Rational Expectations and the Theory of Price Movements , 1961 .

[94]  Max Groneck,et al.  Ambiguous Survival Beliefs and Hyperbolic Discounting in a Life-Cycle Model , 2013 .