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Optimal onset and exhaustion of retirement savings in a life-cycle model

Published online by Cambridge University Press:  02 November 2010

MARIE-EVE LACHANCE
MARIE-EVE LACHANCE
Affiliation:
Department of Finance, College of Business Administration, San Diego State University, San Diego, CA, USA (e-mail: Marie.Lachance@sdsu.edu)
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Abstract

This paper facilitates the exploration of optimal individual retirement savings strategies within a life-cycle framework by providing a convenient tool to implement a model suggested by Yaari (1965) with an uncertain lifetime and borrowing constraints. The solution is given both for the general case and for cases leading to closed-form equations such as power utility and Gompertz mortality. Illustrations for a wide range of parameters indicate that starting to save for retirement in the first phase of one's career is rarely optimal. Of course, this is not to say that young workers should not save for other motives – a limitation of this model is that risks besides mortality are not considered. The conclusion should also be interpreted cautiously as it is difficult to represent every possible individual circumstance and saving incentive in a single model. The intuition behind the result is that an efficient strategy allocates the burden of financing retirement first to periods with higher income (i.e. lower opportunity costs), creating the potential for an initial period without savings when income grows.

Type
Articles
Information
Journal of Pension Economics & Finance , Volume 11 , Issue 1 , January 2012 , pp. 21 - 52
Copyright
Copyright © Cambridge University Press 2011

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References

Cagetti, M. (2003) Wealth accumulation over the life cycle and precautionary savings. Journal of Business and Economic Statistics, 21(3): 339–353.Google Scholar
Campbell, J. Y. and Viceira, L. M. (2002) Strategic Asset Allocation. New York: Oxford University Press.CrossRefGoogle Scholar
Carroll, C. (1997) Buffer-stock saving and the life cycle/permanent income hypothesis. The Quarterly Journal of Economics, 112(1): 1–55.CrossRefGoogle Scholar
Cocco, J. F., Gomes, F. J., and Maenhout, P. J. (2005) Consumption and portfolio choice over the life cycle. The Review of Financial Studies, 18(2): 491–533.CrossRefGoogle Scholar
Davies, J. B. (1981) Uncertain lifetime, consumption, and dissaving in retirement. The Journal of Political Economy, 89(3): 561–577.CrossRefGoogle Scholar
Deaton, A. (1991) Saving and liquidity constraints. Econometrica, 59(5): 1221–1248.Google Scholar
Duflo, E., Orszag, P., Gale, W., Saez, E., and Liebman, J. (2007) Savings incentives for low- and moderate-income families in the United States: why is the saver's credit not more effective? Journal of the European Economic Association, 5(2–3): 647–661.Google Scholar
Gourinchas, P.-O. and Parker, J. A. (2002) Consumption over the life-cycle. Econometrica, 70(1): 47–89.Google Scholar
He, H. and Pages, H. F. (1993) Labor income, borrowing constraints, and equilibrium asset prices. Economic Theory, 3: 663–696.CrossRefGoogle Scholar
Hubbard, R. G., Skinner, J., and Zeldes, S. P. (1995) Precautionary saving and social insurance. Journal of Political Economy, 103(2): 360–399.Google Scholar
Karatzas, I. and Shreve, S. E. (1998) Methods of Mathematical Finance, Applications of Mathematics, Volume 39, New York: Springer-Verlag.Google Scholar
Leung, S. F. (1994) Uncertain lifetime, the theory of the consumer, and the life-cycle hypothesis. Econometrica, 62(5): 1233–1239.Google Scholar
Leung, S. F. (2000) Why do some households save so little? A rational explanation. Review of Economic Dynamics, 3: 771–800.CrossRefGoogle Scholar
Leung, S. F. (2001) The life-cycle model of saving with uncertain lifetime and borrowing constraint: characterization and sensitivity analysis. Mathematical Social Sciences, 42: 179–201.CrossRefGoogle Scholar
Leung, S. F. (2007) The existence, uniqueness, and optimality of the terminal wealth depletion time in life-cycle models of saving under uncertain lifetime and borrowing constraint. Journal of Economic Theory, 134: 470–493.Google Scholar
Mariger, R. P. (1987) A life-cycle model with liquidity constraints: theory and empirical results. Econometrica, 55(3): 533–557.Google Scholar
Merton, R. C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3: 373–413.Google Scholar
Milevsky, M. A. (2006) The Calculus of Retirement Income: Financial Models for Pension Annuities and Life Insurance. New York: Cambridge University Press.CrossRefGoogle Scholar
Mitchell, O. S., Utkus, S. P. and Yang, T. (2007) Turning workers into savers? Incentives, liquidity, and choice in 401(k) plan design. National Tax Journal, 60(3): 469–489.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007) Numerical Recipes 3rd Edition: The Art of Scientific Computing. New York: Cambridge University Press.Google Scholar
Samwick, A. A. (2006) Saving for retirement: understanding the importance of heterogeneity. Business Economics (January): 21–27.CrossRefGoogle Scholar
Thaler, R. H. and Benartzi, S. (2004) Save more tomorrow: using behavioral economics to increase employee saving. Journal of Political Economy, 112(1): 164–187.Google Scholar
Yaari, M. E. (1965) Uncertain lifetime, life insurance, and the theory of the consumer. The Review of Economic Studies, 32(2): 137–150.Google Scholar