Tjalling C. Koopmans Research Institute Discussion Paper Series nr: 04-28 Growing Old and Staying Young: Population Policy in an Ageing Closed Economy Bas van Groezen Lex Meijdam Tjalling C. Koopmans Research Institute Utrecht School of Economics Utrecht University Vredenburg 138 3511 BG Utrecht The Netherlands telephone +31 30 253 9800 fax +31 30 253 7373 website www.koopmansinstitute.uu.nl The Tjalling C. Koopmans Institute is the research institute and research school of Utrecht School of Economics. It was founded in 2003, and named after Professor Tjalling C. Koopmans, Dutch-born Nobel Prize laureate in economics of 1975. In the discussion papers series the Koopmans Institute publishes results of ongoing research for early dissemination of research results, and to enhance discussion with colleagues. Please send any comments and suggestions on the Koopmans institute, or this series to [email protected] ontwerp voorblad: WRIK Utrecht How to reach the authors Please direct all correspondence to the first author. Bas van Groezen Utrecht University Utrecht School of Economics Vredenburg 138 3511 BG Utrecht The Netherlands. E-mail: [email protected] Lex Meijdam Department of Economics and CentER for Economic Research Tilburg University P.O. Box 90153 5000 LE Tilburg The Netherlands Email: [email protected] This paper can be downloaded at: http://www.koopmansinstitute.uu.nl Utrecht School of Economics Tjalling C. Koopmans Research Institute Discussion Paper Series 04-28 Growing Old and Staying Young: Population Policy in an Ageing Closed Economy Bas van Groezena Lex Meijdamb a b Utrecht School of Economics Utrecht University Department of Economics and CentER for Economic Research Tilburg University November 2004 Abstract This paper analyses the relation between public pensions, fertility and child care in a closed economy OLG-model with endogenous fertility. It it shown that it is optimal to introduce child allowances if the government redistributes income from the young to the old, and rises when longevity increases. Keywords: ageing, child allowances, closed economy, endogenous fertility, overlapping generations, pensions, social security JEL classification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