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The author is indebted to the participants in a departmental seminar for their many helpful comments on an earlier version of this paper. He is particularly grateful to Peter Heller for his ideas and comments. The author, of course, is solely responsible for the paper’s content.
This paper was prepared when Peter Heller was in charge of the Government Expenditure Analysis Division.
Intertemporal considerations in public finance gained importance with the work of Auerbach and Kotlikoff (1987). However, their general equilibrium approach is based on the absence of market constraints, on perfect foresight, and on homogeneous cohorts. Thus, they are able to deal with some aspects of intergenerational equity, but not with intra-generational equity on a lifetime income basis.
An equality measure G is a simple transformation of an inequality measure I, G = 1 - I, yielding the value 1 if incomes are equally distributed. Because these equality measures facilitate analytical presentation and interpretation, they will be used throughout this paper. A relative equality measure is invariant with respect to proportionate changes of all incomes: G(x) = G(λ • x), λ > 0.
Similar considerations recently led Bernheim (1987a) to propose the simple discounted value of future benefits (ignoring the possibility of death) as a good approximation for the relevant concept of value. He also rejected the use of the actuarial value of social security benefits in the face of market constraints. His approach differs from the proposed approach with respect to the choice of the counterfactual.
Life-insured annuities are annuities that yield benefits until the death of the insured. Term-insured annuities provide benefits for a specified number of years or until death, whichever occurs first. In our two-period model, both types of annuities collapse.
An alternative measure for the economic lifetime income would be the minimum expenditure to realize
This assumes that the individual does not consume his entire lifetime income in the first period.
We assume the SWF to be strict S-concave (which is implied in assuming symmetry and quasi-concavity, but is a weaker condition), to be increasing along its rays (i.e., a proportionate income increase for all increases the welfare level, F(λ x) > F(x) for all λ > 1), and identical individual preferences.
For recent research with respect to imperfect annuity markets see, for example, Bernheim (1987b), Townley (1988), and Kahn (1988). With respect to imperfect credit markets, see, for example, Stiglitz and Weiss (1981), Bester (1985), Williamson (1987), and Kanemoto (1987).
This result is easily verified if the well-known concept of tax progressivity is applied, x -