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Reexamination of the Serendipity Theorem from the stability viewpoint

Published online by Cambridge University Press:  11 March 2019

Akira Momota Open the ORCID record for Akira Momota [Opens in a new window] ,
Tomoya Sakagami  and
Akihisa Shibata
Akira Momota*
Affiliation:
Ritsumeikan University, Kusatsu, Shiga, Japan
Tomoya Sakagami
Affiliation:
Kumamoto Gakuen University, Kumamoto, Japan
Akihisa Shibata
Affiliation:
Kyoto University, Kyoto, Japan
*
*Corresponding author. E-mail: [email protected]
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Abstract

This paper reexamines the Serendipity Theorem of Samuelson (1975) from the stability viewpoint, and shows that, for the Cobb–Douglas preference and CES technology, the most-golden golden-rule lifetime state being stable depends on parameter values. In some situations, the Serendipity Theorem fails to hold despite the fact that steady-state welfare is maximized at the population growth rate, since the steady state is unstable. Through numerical simulations, a more general case of CES preference and CES technology is also examined, and we discuss the realistic relevance of our results. We present the policy implication of our result, that is, in some cases, the steady state with the highest utility is unstable, and thus a policy that aims to achieve the social optima by manipulating the population growth rate may lead to worse outcomes.

Keywords

Overlapping generations modelpopulation growthSamuelson's Serendipity Theoremstability

JEL classification

I18: Government Policy • Regulation • Public Health E13: Neoclassical C62: Existence and Stability Conditions of Equilibrium
Type
Research Papers
Information
Journal of Demographic Economics , Volume 85 , Issue 1 , March 2019 , pp. 43 - 70
Copyright
Copyright © Université catholique de Louvain 2019 

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References

Abio, Gemma (2003) Interiority of the optimal population growth rate with endogenous fertility. Economics Bulletin 10(4), 1–7.Google Scholar
Bental, Benjamin (1989) The old age security hypothesis and optimal population growth. Journal of Population Economics 1(4), 285–301.Google Scholar
Chirinko, Robert S. (2008) σ: the long and short of it. Journal of Macroeconomics 30(2), 671–686.Google Scholar
de la Croix, David and Doepke, Matthias (2003) Inequality and growth: why differential fertility matters. American Economic Review 93(4), 1091–1113.Google Scholar
de la Croix, David and Michel, Philippe (2002) A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations. Cambridge, UK: Cambridge University Press.Google Scholar
de la Croix, David, Pestieau, Pierre and Ponthière, Grégory (2012) How powerful is demography? The Serendipity Theorem revisited. Journal of Population Economics 25(3), 899–922.Google Scholar
Deardorff, Alan V. (1976) The optimum growth rate for population: comment. International Economic Review 17(2), 510–515.Google Scholar
Diamond, Peter A. (1965) National debt in a neoclassical growth model. American Economic Review 55(5), 1126–1150.Google Scholar
Eckstein, Zvi and Wolpin, Kenneth I. (1985) Endogenous fertility and optimal population size. Journal of Public Economics 27(1), 93–106.Google Scholar
Felder, Stefan (2016) “How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012). Journal of Population Economics 29(3), 957–967.Google Scholar
Galor, Oded and Ryder, Harl E. (1989) Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital. Journal of Economic Theory 49(2), 360–375.Google Scholar
Hansen, Lars Peter and Singleton, Kenneth J. (1983) Stochastic consumption, risk aversion, and the temporal behavior of asset returns. Journal of Political Economy 91(2), 249–265.Google Scholar
Havránek, Tomáš, Horvath, Roman, Iršová, Zuzana and Rusnak, Marek (2015) Cross-country heterogeneity in intertemporal substitution. Journal of International Economics 96(1), 100–118.Google Scholar
Hotz, V. Joseph, Kydland, Finn E. and Sedlacek, Guilherme L. (1988) Intertemporal preferences and labor supply. Econometrica 56(2), 335–360.Google Scholar
Hurd, Michael D. (1989) Mortality risk and bequests. Econometrica 57(4), 779–813.Google Scholar
İmrohoroğlu, Ayşe, İmrohoroğlu, Selahattin and Joines, Douglas H. (1995) A life cycle analysis of social security. Economic Theory 6(1), 83–114.Google Scholar
İmrohoroğlu, Ayşe, İmrohoroğlu, Selahattin and Joines, Douglas H. (1998) The effect of tax-favored retirement accounts on capital accumulation. American Economic Review 88(4), 749–768.Google Scholar
Jaeger, Klaus (1989) The serendipity theorem reconsidered: the three-generations case without inheritance. In: Klaus F. Zimmermann (ed.) Economic Theory of Optimal Population, pp. 75–87. Berlin Heidelberg: Springer.Google Scholar
Jaeger, Klaus and Kuhle, Wolfgang (2009) The optimum growth rate for population reconsidered. Journal of Population Economics 22(1), 23–41.Google Scholar
Juselius, Mikael (2008) Long-run relationships between labor and capital: indirect evidence on the elasticity of substitution. Journal of Macroeconomics 30(2), 739–756.Google Scholar
Konishi, Hideo and Perera-Tallo, Fernando (1997) Existence of steady-state equilibrium in an overlapping-generations model with production. Economic Theory 9(3), 529–537.Google Scholar
Klump, Rainer, McAdam, Peter and Willman, Alpo (2008) Unwrapping some euro area growth puzzles: factor substitution, productivity and unemployment. Journal of Macroeconomics 30(2), 645–666.Google Scholar
Kuhle, Wolfgang (2007) The Optimum Growth Rate for Population in the Neoclassical Overlapping Generations Model. Frankfurt, Germany: Peter Lang.Google Scholar
Kumru, Cagri S. and Thanopoulos, Athanasios C. (2015) Temptation-driven behavior and taxation: a quantitative analysis in a life-cycle model. Economic Inquiry 53(3), 1470–1490.Google Scholar
Michel, Philippe and Pestieau, Pierre (1993) Population growth and optimality. Journal of Population Economics 6(4), 353–362.Google Scholar
Momota, Akira and Horii, Ryo (2013) Timing of childbirth, capital accumulation, and economic welfare. Oxford Economic Papers 65(2), 494–522.Google Scholar
Pestieau, Pierre and Ponthiere, Gregory (2014) Optimal fertility along the life cycle. Economic Theory 55(1), 185–224.Google Scholar
Pestieau, Pierre and Ponthiere, Gregory (2017) Optimal fertility under age-dependent labour productivity. Journal of Population Economics 30(2), 621–646.Google Scholar
Ponthière, Grégory (2013) Fair accumulation under risky lifetime. Scottish Journal of Political Economy 60(2), 210–230.Google Scholar
Samuelson, Paul A. (1975) The optimum growth rate for population. International Economic Review 16(3), 531–538.Google Scholar
Samuelson, Paul A. (1976) The optimum growth rate for population: agreement and evaluations. International Economic Review 17(2), 516–525.Google Scholar
Stelter, Robert (2016) Over-aging – Are present-day human populations too old? Mathematical Social Sciences 82, 116–143.Google Scholar
Thimme, Julian (2017) Intertemporal substitution in consumption: a literature review. Journal of Economic Surveys 31(1), 226–257.Google Scholar
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