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On optimality, endogeneous discounting and wealth accumulation

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  • Ingmar, SCHUMACHER

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Department of Economics)

Abstract

We endogenize the discount rate via a broad measure of wealth and provide empirical evidence that wealth the discount rate negatively. We demonstrate that the Pontryagin conditions require positive felicity for intuitive results, whereas the concavity of the Hamiltonian requires negative felicity for optimality. This dilemna also holds for the endogenizations of Obstfeld (1990) and followers. We solve the model with positive felicity and resolve when optimality is possible. We discuss the impact on technological change, savings and convergence which are more in line with empirics. Finally, we discuss time consistency of a planner who cannot predict his preferences.

Suggested Citation

  • Ingmar, SCHUMACHER, 2006. "On optimality, endogeneous discounting and wealth accumulation," Discussion Papers (ECON - Département des Sciences Economiques) 2006058, Université catholique de Louvain, Département des Sciences Economiques.
  • Handle: RePEc:ctl:louvec:2006058
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    as
    1. de Walque, Damien, 2004. "Education, information, and smoking decisions : evidence from smoking histories, 1940-2000," Policy Research Working Paper Series 3362, The World Bank.
    2. Abhijit V. Banerjee & Andrew F. Newman, 1991. "Risk-Bearing and the Theory of Income Distribution," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 211-235.
    3. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
    4. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    5. Gary S. Becker & Casey B. Mulligan, 1997. "The Endogenous Determination of Time Preference," The Quarterly Journal of Economics, Oxford University Press, vol. 112(3), pages 729-758.
    6. Becker, Robert A & Boyd, John H, III, 1992. "Recursive Utility and Optimal Capital Accumulation II: Sensitivity and Duality Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(4), pages 547-563, October.
    7. Barro, Robert J. & Lee, Jong-Wha, 1993. "International comparisons of educational attainment," Journal of Monetary Economics, Elsevier, vol. 32(3), pages 363-394, December.
    8. Rodolfo Nayga, 2001. "Effect of Schooling on Obesity: Is Health Knowledge a Moderating Factor?," Education Economics, Taylor & Francis Journals, vol. 9(2), pages 129-137.
    9. Kenkel, Donald S, 1991. "Health Behavior, Health Knowledge, and Schooling," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 287-305, April.
    10. Rabah Amir, 1985. "A Characterization of Globally Optimal Paths in the Non-Classical Growth Model," Cowles Foundation Discussion Papers 754, Cowles Foundation for Research in Economics, Yale University.
    11. Grossman, Michael, 2006. "Education and Nonmarket Outcomes," Handbook of the Economics of Education, in: Erik Hanushek & F. Welch (ed.), Handbook of the Economics of Education, edition 1, volume 1, chapter 10, pages 577-633, Elsevier.
    12. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 407-437.
    13. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, vol. 11(2), pages 272-289, April.
    14. Christopher D. Carroll, 1997. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," The Quarterly Journal of Economics, Oxford University Press, vol. 112(1), pages 1-55.
    15. Sander, William, 1995. "Schooling and Quitting Smoking," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 191-199, February.
    16. Deaton, Angus & Paxson, Christina, 1994. "Intertemporal Choice and Inequality," Journal of Political Economy, University of Chicago Press, vol. 102(3), pages 437-467, June.
    17. Samwick, Andrew A., 1998. "Discount rate heterogeneity and social security reform," Journal of Development Economics, Elsevier, vol. 57(1), pages 117-146, October.
    18. David Fielding & Sebastian Torres, 2009. "Health, Wealth, Fertility, Education, and Inequality," Review of Development Economics, Wiley Blackwell, vol. 13(1), pages 39-55, February.
    19. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541, Elsevier.
    20. Lant Pritchett & Lawrence H. Summers, 1996. "Wealthier is Healthier," Journal of Human Resources, University of Wisconsin Press, vol. 31(4), pages 841-868.
    21. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
    22. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 45-75, August.
    23. Gregory Mankiw, 1995. "The Growth of Nations," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 26(1, 25th A), pages 275-326.
    24. Anne Case & Darren Lubotsky & Christina Paxson, 2002. "Economic Status and Health in Childhood: The Origins of the Gradient," American Economic Review, American Economic Association, vol. 92(5), pages 1308-1334, December.
    25. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    26. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
    27. repec:fth:harver:1504 is not listed on IDEAS
    28. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    29. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 611-635, August.
    30. Lawrance, Emily C, 1991. "Poverty and the Rate of Time Preference: Evidence from Panel Data," Journal of Political Economy, University of Chicago Press, vol. 99(1), pages 54-77, February.
    31. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    32. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 281-313.
    33. Shi, Shouyong & Epstein, Larry G, 1993. "Habits and Time Preference," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 61-84, February.
    34. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
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    Cited by:

    1. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    2. Borissov, Kirill, 2013. "Growth and distribution in a model with endogenous time preferences and borrowing constraints," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 117-128.

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    More about this item

    Keywords

    Endogenous time preference; Stability; Optimal growth; Recursive utility;
    All these keywords.

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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