Pension Funds Saving Individuation.

ASSA BIRATI [*]

This paper considers a pension insurance problem using an intertemporal framework. We assume a deterministic framework in order to obtain tractable and yet revealing results regarding the propensity to save for retirement. The essential conclusions of this paper include

a condition for a single switch, that is, when the saver will decide the switching time, prior to retirement, to start saving. Because of the linear objective used in this paper, saving rates were found to be of the bang-bang type. In addition, we show that the tax effects are important. The richer the saver, the greater the tax advantages for pension savings. (JEL E20)

Introduction

Pension savers tend to underestimate the financial requirements to support future needs. This may lead to future economic distress as well as to a growing social condition where governments signal their inability to meet future needs. There are further darker clouds pending over the future of pension funds and the need to overhaul past practices. This has a particularly important effect on persons who do not have sufficient wealth to support their future needs and who rely mostly on withdrawals made by employers and payments made to social security [Blake, 1995, 1998]. This state of affairs has led the search for new approaches in saving rates and saving modes [Atkinson, 1987; Bodie et al., 1987]. Explicitly, the traditional pension saving approach consisting of investment in fixed income obligations, generally issued and backed by the government, is now amended to provide greater investment flexibility. This flexibility, it is believed, may be much more responsive to market forces on one hand and better tail ored to individual savers needs on the other. By the same token, pension funds based on pay-as-you-go (PAYGO) systems have been severely criticized. PAYGO consists of paying pensions to retired persons out of taxes collected on the working population. For example, China [Feldstein, 1998] has revised the PAYGO scheme to a flexible and mixed system involving an investment that is partly based on a defined contribution.

Samuelson [1958] showed that in an economy without capital stock and in equilibrium, a completely unfunded PAYGO pension system has a positive real rate of growth of aggregate real wages (that is, the sum of the growth rate of population and the growth rate of productivity). This has justified the practice to let one generation pay the retirement payments of another. However, when capital stock is considered, the cost of pensions may be reduced by the fact that the marginal productivity of capital is greater than the marginal productivity of work. This has justified the mixed pension system where a portion of the retirement is funded, leading to lower, long-run costs. This is particularly true today when we note that increased longevity of the population is imposing an added tax burden on the working population. This burden has other negative effects such as tax avoidance and lower productivity. These schemes, and the added tax benefits they may have, are sensitive to pensioners' wealth and their tax brackets, thereby affecting pensioners' welfare [Brugiavini, 1993; Feldstein, 1990; Samwick, 1998; Freidman and Warshavsky, 1990]. The purpose of this paper is to consider a simple dynamic savings problem to study pension retirement schemes. In particular, we will address two essential problems: taxation relief and mixture of the pension package on pensioners' welfare. The point of view taken in this paper emphasizes the individual saver. Finally, proofs to the basic propositions of the paper are relegated to a more extensive paper by the same authors.