Modeling Pension Systems

This study is devoted to a formal analysis of pension systems. For simplicity, it concentrates on old-age pensions, which ensure financial support during a period when most people lose much of their earning capacity. It excludes consideration of the important issue of disability and survivors’ pensions, which require separate treatment.

We saw in Chapter 1 that a basic feature of human life is that the consumption path is much smoother than the earning path; people consume even when they do not, earn. Another, equally important, characteristic is the so-called longevity risk that is, the date of the death of any person is known in advance neither to him nor to others. Indeed, there are people who die just before retiring, and there are others who live for a hundred years. In the former case, lifetime consumption may be much lower than lifetime earnings; in the latter case, lifetime consumption may be much higher than lifetime earnings. Furthermore, this uncertainty makes self- or family financing much more difficult than it would be in a deterministic world (Fischer, 1973 and Walliser, 2000, 2001). Here we shall examine the ideal system of life insurance with life annuity and then turn to real-life complications.

We have already made several remarks on the distribution of pensions in discussing the flat (rate) benefit and the effect of the date of retirement (Chapter 4). But the discussion of the distribution of pensions has been left to this chapter.

Flexible retirement means that the age at which an employee retires is a choice variable for him. (For the much neglected case in which the employer chooses, see the survey by Spiezia (2002).) Anyone who wants to retire before normal retirement age may do so, but he will receive lower annual benefit since he contributes for a shorter period and draws the benefit for a longer expected period. Similarly, if somebody can (and is allowed to) work longer, he will receive higher annual benefit since he contributes for a longer period and obtains the benefit for a shorter expected period. It is obvious that an actuarially fair solution would be to reward work beyond normal retirement by the amount the Social Security saves by receiving the contributions for a longer period and paying benefits for a shorter period, and similarly to charge early retirees by as much as the Social Security loses by receiving contributions for a shorter period and paying benefits for a longer period (Sheshinski, 1978; Crawford-Lilien, 1981; Stock-Wise, 1990, Samwick, 1998; Gruber-Wise, eds. 1999 and Guegano, 2000).

First of all, recall our outline of the method of Generational Accounting at the end of Chapter 8. In the present chapter we depict the corresponding calculations of R. I. Gál, A. Simonovits and G. Tarcali concerning the Hungarian pension system (Gal et al., 2001). We emphasize the following specifics of our work.