How long does a generation last? Assessing the relationship between infinite and finite horizon dynamic models

Guerrazzi, Marco (2021): How long does a generation last? Assessing the relationship between infinite and finite horizon dynamic models.

Abstract

This paper aims at assessing the temporal relationship that exists between the time reference of dynamic models with infinite and finite horizon. Specifically, comparing the optimal inter-temporal plans arising from an infinite-horizon model and a 2-period overlapping generations model in their stationary equilibria, I offer a straightforward way to determine the number of time periods of the former that may form a unit of time of the latter. In this way, I show that the theoretical length of a generation is an increasing function of the discount factor of the optimizing agent and I provide an economic rationale for such a relationship grounded on consumption smoothing.

• Item Type: MPRA Paper
• Language: English
• Keywords: Infinite horizon; Overlapping generations; Consumption smoothing; Discount rate
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C68 - Computable General Equilibrium Models; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E30 - General

References

Cass, D. (1965), Optimum Growth in an Aggregative Model of Capital Accumulation, Review of Economic Studies, Vol. 32, No. 3, pp. 233-240.

Diamond, P.A. (1965), National Debt in a Neoclassical Growth Model, American Economic Review, Vol. 55, No. 5, pp. 1126-1150.

Farmer, R.E.A., Plotnikov D. (2012), Does Fiscal Policy Matter? Blinder and Solow Revisited, Macroeconomic Dynamics, Vol. 16, No. S1, pp. 149-166.

Farmer, R.E.A. (2010), Expectations, Employment and Prices, Oxford University Press: New York.

Galor, O., Weil, D.N. (1996), The Gender Gap, Fertility, and Growth, American Economic Review, Vol. 86, No. 3, pp. 374- 387.

Guerrazzi, M. (2010), Nominal Wage Indexation, Quasi-Equilibria and Real Wage Dynamics, Bulletin of Economic Research, Vol. 62, No. 3, pp. 279-294.

Guerrazzi, M. (2007), Local Dynamics under Perfectly Flexible Wages, Economia Politica, Vol. 24, No. 2, pp. 65-288.

Koopmans, T.C. (1965), On the Concept of Optimal Economic Growth in Johansen, J. (ed.), The Economic Approach to Development Planning, Elsevier: Amsterdam.

Kydland, F.E., Prescott, E.C. (1982), Time to Build and Aggregate Fluctuations, Econometrica, Vol. 50, No. pp. 1345-1370.

Long, J.B., Plosser, C.I. (1983), Real Business Cycles, Journal of Political Economy, Vol. 91, No. 6, pp. 39-69.

Ramsey, F.P. (1928), A Mathematical Theory of Saving, Economic Journal, Vol. 38, No. 152, pp. 543-559.

Samuelson, P.A. (1958), An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money, Journal of Political Economy, Vol. 66, No. 6, pp. 467-482.

Thomson, R., Pritchard, J.K., Shen, P., Oefner, P.J., Feldman, M.W. (2000), Recent Common Ancestry of Human Y Chromosomes: Evidence from DNA Sequence Data, Proceedings of the National Academy of Sciences of the United States of America, Vol. 97, No. 13, pp. 7360-7365.

Weiss, K.M. (1973), Demographic Models for Anthropology, in Wobst, H.M. (ed.) Memoirs of the Society for American Archaeology, Cambridge University Press: Cambridge (Massachusetts), No. 27, pp. 1-186.