×

Beyond optimality: Managing children, assets, and consumption over the life cycle. (English) Zbl 1133.91344

Summary: To raise children, to guarantee a certain way of life, and to retire with a certain amount of capital can be accomplished in many different ways, particularly when couples are faced with the possibility of unemployment or poor returns to savings while trying to balance current and future consumption both personally and for their children. Not any trajectory is successful, but those which are successful are myriad. Agents’ heterogeneity is modelled both by the whole state space where each state corresponds to a different situation, and by the set of attainable states, which reflects uncertainty inherent both in decision-making and in external shocks. The delineation of all manageable states of consumption, reproduction, and saving identifies the timing of when to have children, and when and how much to consume and save. Discontinuities of consumption when a child is born are fully taken into account through continuous-discrete differential inclusions. The theory is illustrated with an empirical example; international comparison shows that lower fertility is associated with smaller sets of timely decisions.

MSC:

91B06 Decision theory
91D10 Models of societies, social and urban evolution
91B14 Social choice
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aubin, J.-P., Dynamic Economic Theory: A Viability Approach (1997), Springer-Verlag Birkhäuser: Springer-Verlag Birkhäuser Boston, Basel · Zbl 0876.90032
[2] Aubin, J.-P., Impulse Differential Inclusions and Hybrid Systems: A Viability Approach. Lecture Notes (1999), University of California at Berkeley: University of California at Berkeley Berkeley
[3] Aubin, J.-P.; Bonneuil, N.; Maurin, F.; Saint-Pierre, P., Viability of pay-as-you-go systems, Journal of Evolutionary Economics, 11, 555-571 (2001)
[4] Barro, R. J.; Becker, G. S., Fertility choice in a model of economic growth, Econometrica, 57-2, 481-501 (1989) · Zbl 0665.90013
[5] Becker, G. S.; Barro, R. J., A reformulation of the economic theory of fertility, The Quaterly Journal of Economics, 1-25 (1988)
[6] Bensoussan, A.; Menaldi, J. L., Hybrid control and dynamic programming, Dynamics of Continuous, Discrete and Impulse Systems, 3, 395-442 (1997) · Zbl 0897.49022
[7] Bonneuil, N., Capital accumulation, inertia of consumption and norms of reproduction, Journal of Population Economics, 7, 49-62 (1994)
[8] Bonneuil, N., Computing the viability kernel in large state dimension, Journal of Mathematical Analysis and Applications, 323, 2, 1444-1454 (2006) · Zbl 1111.65059
[9] Bonneuil, N.; Boarini, R., Preserving transfer benefit for present and future generations, Mathematical Population Studies, 11, 3-4, 181-204 (2004) · Zbl 1093.91522
[10] Banks, J.; Blundell, R.; Tanner, S., Is there a retirement-savings puzzle, American Economic Review, 88-4, 769-788 (1998)
[11] Cardialaguet, P., Quincampoix, M., Saint-Pierre, P., 1999. Set-valued numerical methods for optimal control and differential games. In: Theory and Numerical Methods, Annals of the International Society of Dynamical Games. Birkhäuser, Boston, Basel, pp. 177-247.; Cardialaguet, P., Quincampoix, M., Saint-Pierre, P., 1999. Set-valued numerical methods for optimal control and differential games. In: Theory and Numerical Methods, Annals of the International Society of Dynamical Games. Birkhäuser, Boston, Basel, pp. 177-247. · Zbl 0982.91014
[12] Caroll, C. D., The Buffer-stock theory of saving: some macro-economic evidence, Brookings Papers of Economic Activity, 2, 61-135 (1992)
[13] Caroll, C. D., How does future income affect current consumption, Quarterly Journal of Economics, 109, 1, 111-147 (1994)
[14] Caroll, C. D., Buffer-stock saving and the life cycle/permanent income hypothesis, Quaterly Journal of Economics, 112, 1, 1-57 (1997) · Zbl 0882.90023
[15] Caroll, C. D., A theory of the consumption function, with and without liquidity constraints, Journal of Economic Perspectives, 15, 3, 23-45 (2001)
[16] Day, R. H., Multiple-phase economic dynamics, (Maruyama, T.; Takahashi, W., Multiple-phase economic dynamics (1995), Springer-Verlag: Springer-Verlag Berlin), 25-45 · Zbl 0826.90021
[17] Deaton, A., Saving and liquidity constraints, Econometrica, 59, 5, 1221-1248 (1991)
[18] Deaton, A., Understanding Consumption (1992), Clarendon Press: Clarendon Press Oxford
[19] Duval, R., 2003. The Retirement Effects of Old-Age Pension and Early Retirement Schemes in OECD Countries. OECD Economic Department Working Papers, p. 370.; Duval, R., 2003. The Retirement Effects of Old-Age Pension and Early Retirement Schemes in OECD Countries. OECD Economic Department Working Papers, p. 370.
[20] Ekert, O.; Trognon, A., Évolution du coût de l’enfant avec le revenu : une méthode. In: Standards of Living and Families: Observation and Analysis, ((1994), INED and John Libbey: INED and John Libbey Paris), 135-164
[21] Elmendorf, D., Kimball, M.S., 1991. Taxation of labor income and the demand for risky assets. NBER Working paper series, p. 3904.; Elmendorf, D., Kimball, M.S., 1991. Taxation of labor income and the demand for risky assets. NBER Working paper series, p. 3904.
[22] Epstein, L. G.; Zin, S. E., Substitution, risk aversion, and the temporal behavior of consumption and asset returns: an empirical analysis, Journal of Political Economy, 99-2, 263-286 (1991)
[23] Esping-Andersen, G., The Three Worlds of Welfare Capitalism (1990), Princeton University Press: Princeton University Press Princeton, NJ
[24] Esping-Andersen, G., Social Foundations of Postindustrial Economies (1999), Clarendon Press: Clarendon Press Oxford, England
[25] Grimm, M.; Bonneuil, N., Labor market participation of French women over the life-cycle, European Journal of Population, 17-3, 235-260 (2001)
[26] Grossman, S. J.; Melino, A.; Shiller, R. J., Estimating the continuous-time consumption-based asset-pricing model, Journal of Business and Economic Statistics, 5, 315-327 (1987)
[27] Hall, R. E., Stochastic implications of the life-cycle permanent income hypothesis: theory and evidence, Journal of Political Economy, 86, 971-987 (1978)
[28] Hansen, L. P.; Singleton, K. J., Generalized instrumental variables estimation of nonlinear rational expectations models, Econometrica, 50, 1269-1286 (1983) · Zbl 0497.62098
[29] Hayek, F. A., Individualism and Economic Order (1948), Chicago University Press: Chicago University Press Chicago
[30] Heckhausen, J., Developmental regulation across the life span: an action-phase model of engagement and disengagement with developmental goals, (Heckhausen, J., Motivational Psychology of Human Development: Developing Motivation and Motivating Development (2000), Elsevier Science: Elsevier Science New York), 213-231
[31] Heckman, J.; Willis, R., Estimation of a stochastic model of reproduction: an econometric approach, (Terleckj, N., Household Production and Consumption (1975), Columbia University Press: Columbia University Press New York)
[32] Hicks, J., Causality in Economics (1979), Basic Book: Basic Book New York
[33] Kahneman, D., New challenges to the rationality assumption, (Arrow, K. J.; Colombatto, E.; Perlman, M.; Schmidt, C., The Rational Foundations of Economic Behaviour (1996), Macmillan and St. Martin’s Press: Macmillan and St. Martin’s Press Basingstoke-New York), 203-219
[34] Keynes, J. N., A tract on monetary reform, (Keynes, J. M., Essays on Persuasion (1931), Rupert Hart-Davis: Rupert Hart-Davis London)
[35] Kimball, M. S., Precautionary motives for holding assets, (Eastwell, J.; Milgate, M.; Newman, P., The New Palgrave Dictionary of Money and Finance (1992), Norton: Norton New York), 158-161
[36] Krusell, P.; Smith, A. A., Income and wealth heterogeneity, portfolio choice, and equilibrium asset returns, Macroeconomic Dynamics, 1, 387-422 (1997) · Zbl 0915.90060
[37] Krusell, P.; Smith, A. A., Income and wealth heterogeneity in the macroeconomy, Journal of Political Economy, 106-5, 867-896 (1998)
[38] Leisering, L., Government and the life course, (Martimer, J. T.; Shanahan, M. J.., Handbook of the Life Course (2003), Kluwer Academic/Plenum: Kluwer Academic/Plenum New York), 205-225
[39] Mayer, K. U., Whose lives? How history, societies, and institutions define and shape life courses, Research in Human Development, 1-3, 161-187 (2004)
[40] Mehra, R.; Prescott, E. C., The equity premium: a puzzle, Monetary Economics, 15, 145-161 (1985)
[41] Moffit, R., Profiles of fertility labor supply and wages of married women: a complete life-cycle model, Review of Economic Studies, 51, 263-278 (1984)
[42] Newman, J. L., A stochastic dynamic model of fertility, Research in Population Economics, 6, 41-68 (1988)
[43] Newman, J. L.; McCulloch, C. E., A hazard rate approach to the timing of births, Econometrica, 52, 4, 939-962 (1984)
[44] Ríos-Rull, J.-V., Life-cycle economies and aggregate fluctuations, Review of Economic Studies, 63, 465-489 (1996) · Zbl 0855.90021
[45] Quincampoix, M.; Veliov, V., Viability with a target: theory and applications. In: Applications of Mathematics in Engineering, ((1998), Heron Press: Heron Press Sofia, Bulgaria), 47-54
[46] Saint-Pierre, P., Approximation of the viability kernel, Applied Mathematics and Optimisation, 29, 187-209 (1994) · Zbl 0790.65081
[47] Saint-Pierre, P., Hybrid kernels and capture basins for impulse constrained systems, (Tomlin, C.; Greenstreet, M., Proceedings of Hybrid Systems: Computation and Control, HSCC, Lecture Notes in Computer Science 2289 (2002), Springer: Springer Berlin), 378-392 · Zbl 1050.93041
[48] Sapir, J., Les trous noirs de l’économie (2000), Albin Michel: Albin Michel Paris
[49] Shackle, G. L.S., Decision Order and Time in Human Affairs (1969), Cambridge University Press: Cambridge University Press Cambridge
[50] Settersten, R. A., Age structuring and the rhythm of the life course, (Mortimer, J. T.; Shanahan, M. J., Handbook of the Life Course (2003), Kluwer Academic/Plenum: Kluwer Academic/Plenum New York)
[51] Simon, H. A., Administrative Behavior A Study of Decision-Making Processes in Administrative Organizations (1945), The Free Press: The Free Press Glencoe
[52] Tasiran, A., Fertility Dynamics: Spacing and Timing of Births in Sweden and the United States Contributions to Economic Analysis Series 229 (1995), North Holland: North Holland Amsterdam
[53] Thurow, L., The optimum lifetime distribution of consumption expenditures, The American Economic Review, 324-330 (1969)
[54] Wolpin, K., An estimable dynamic stochastic model of fertility and child mortality, The Journal of Political Economy, 92-5, 852-874 (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.