A note on Gollier's model for a collective pension scheme

Gollier proposed in 2008 a model for the analysis of pension schemes that is helpful to focus attention on the impact of intergenerational risk sharing and on the role of the participation constraint. He uses the model to analyze the relative attractiveness of a collective scheme with respect to schemes that may be implemented by individuals for themselves. The analysis makes use of an assumption concerning the ownership rights of investment returns realized by generations that are between career start and retirement at the time of the transition from an individual to a collective system. The present paper investigates the consequences of adopting an alternative assumption. In a calibration exercise, the increase of the effective rate of return obtained by switching from an existing ‘autarky’ scheme to an infinite-horizon ‘collective’ scheme is found to be 8 basis points, as opposed to 72 basis points as reported by Gollier. Additionally, the effects are considered of changes in the specification of agents' preferences, aiming to express the specific nature of retirement income provision in the second pillar. The Black–Scholes assumptions are used to model the economic environment, so that many results can be obtained in closed form.