UvA-DARE (Digital Academic Repository) Essays in pension economics and intergenerational risk sharing Vos, S.J. Link to publication

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1 UvA-DARE (Digital Academic Repository) Essays in pension economics and intergenerational risk sharing Vos, S.J. Link to publication Citation for published version (APA): Vos, S. J. (2012). Essays in pension economics and intergenerational risk sharing Amsterdam: Universiteit van Amsterdam General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam ( Download date: 31 Oct 2018

2 Contents 1 Introduction and Overview 1 2 Intergenerational risk sharing, pensions and endogenous labour supply in general equilibrium The command economy Individuals and preferences Investment and production The resource constraints The social planner s solution The decentralized economy The pension systems Individual budget constraints Individual and firm optimization Market equilibrium conditions Optimality of pension systems Pension fund optimality conditions Optimality of different pension systems Discussion Appendix to Chapter A Derivation of the planner s solution B Individual first-order conditions B.1 Period 1 individual first-order conditions B.2 Period 0 individual first-order conditions C Infinite horizon model C.1 Notation C.2 Social Planner C.3 Decentralised economy

3 3 Sharing of Demographic Risks in a General Equilibrium Model with funded Pensions The command economy Individuals and preferences Demographics Production Resource constraints The social planner s solution The decentralized economy The pension arrangements Individual budget constraints and generational accounts Individual and firm optimization Market equilibrium conditions Optimal pension policy The optimum under perfect demographic foresight Demographic uncertainty Calibration Numerical results Measures for welfare comparison No demographic uncertainty Deterministic variation in demographic variables Introducing demographic uncertainty Fertility risk Mortality risk Simultaneous presence of both types of demographic risk Robustness: varying the degree of risk aversion Conclusion Appendix to Chapter A Description of solution of model B Proof of Proposition B.1 Part (i) B.2 Part (ii) C Derivatives of expressions in Proposition C.1 DRB C.2 DWB

4 4 Voluntary Participation and Intergenerational Risk Sharing in a Funded Pension System Introduction Model and autarky solution Introduction of a pension fund Individuals The pension fund The participation constraint Recursive formulation of the participation constraint Equilibrium definition Solutions for r Properties of the solutions for r Assumption about initial beliefs Feasible pension fund rules The optimal pension fund rule A numerical example Conclusion Appendix to Chapter A Details on first-order condition pension fund without participation constraint B Details on U p (r, r = r) B.1 U p (r, r = r ) approaches U a from below as r r B.2 Second-order derivative of U p (r, r = r) C Calibration of the returns process Redesigning the Dutch occupational pension contract: Simulation of alternative contracts involving soft and hard entitlements Introduction The Model Demographics Wage income and pension fund contributions Second-pillar entitlements and liabilities under the old contract Assets Economic shocks The timing Pension fund policy The current contract

5 5.3.2 Proposals for the new contract The Rolling Window contract The Fraction contract The Split contract Contribution policy Calibration and simulation Calibration The simulation setup Results Indexation to wages Indexation to prices Robustness checks Conclusion Appendix to Chapter A Derivation of (5.14) B Indexation Policy Rolling Window proposal B.1 Reduction of hard entitlements B.2 Indexation of hard entitlements B.3 Indexation of soft entitlements B.4 Figures for base scenario B.5 Figures for replacement rates base scenario Bibliography 161