THE WELFARE EFFECTS OF PAY‐AS‐YOU‐GO RETIREMENT PROGRAMS: THE ROLE OF TAX AND BENEFIT TIMING

I. INTRODUCTION The study of two-period overlapping generation (OLG) models has yielded important insights into the welfare effects of pay-as-you-go retirement programs in dynamically efficient economies. A pay-as-you-go program offers windfall gains during its start-up phase but lowers steady-state utility because its steady-state rate of return equals the economy's growth rate, which, under dynamic efficiency, is lower than the marginal product of capital. Shutting down or scaling back the program allows future generations to earn higher returns but imposes a transition cost on current generations who have paid into the program but have not yet received full benefits. The future generations' gains and the transition cost are equal in present value. It is well known that these results extend to continuous-time and multiperiod OLG models. I show, however, that the two-period model fails to capture the role of one important factor. The magnitude of a pay-as-you-go program's welfare effects depends on its life cycle timing--the ages at which each cohort pays taxes and receives benefits. In the two-period model, taxes must be paid in "Period 1" and benefits must be received in "Period 2." In contrast, actual programs have flexibility in the allocation of taxes within the working lifetime and benefits within the retirement years. I show that the program's steady-state welfare loss is smaller when taxes are paid at later ages or benefits received at earlier ages. These effects arise because the pay-as-you-go program's rate-of-return shortfall is less harmful to each cohort when compounded over a shorter or later time period. Shifting taxes to older ages or benefits to younger ages therefore aids future generations in a manner similar to reducing the size of the pay-as-you-go program. Like a reduction in program size, though, such a timing shift imposes a transition cost on current generations, equal in present value to future generations' gains. Specifically, shifting taxes to older workers boosts lifetime taxes for some of the cohorts working at the time of implementation, while shifting benefits to younger retirees reduces lifetime benefits for some of the cohorts retired at that time. In a simple calibration of the U.S. Social Security program, instituting a payroll tax exemption during the first 10 yr of working life (with a revenue-neutral tax increase on older workers) would reduce the program's steady-state welfare loss by about one-sixth but would raise lifetime taxes for most of the cohorts working at the time of implementation. Policy changes that raised benefits for younger retirees (with a budget-neutral benefit reduction for older retirees) would also generate steady-state welfare gains and transition costs, but of smaller magnitudes. In Section II, I review the familiar analysis of pay-as-you-go retirement programs in two-period OLG models. In Section III, I explain the role of tax and benefit timing in a continuous-time OLG model under the assumption that all taxes are paid at one age and all benefits are received at another age. In Section IV, I show that these results generalize to the more realistic case in which taxes and benefits are paid at multiple ages. I examine the implications for tax timing in Section V and those for benefit timing in Section VI. Section VII concludes. II. REVIEW OF TWO-PERIOD MODELS I begin by reviewing the basic properties of pay-as-you-go retirement programs in the familiar two-period OLG model. Technology is linear, implying fixed factor prices, and labor supply is inelastic. In each period t, the number of workers is [N.sup.t] and the perworker wage [G.sup.t]. The gross-of-principal one-period marginal product of capital is R. I assume R > NG, so that the economy is dynamically efficient. Consider a simple pay-as-you-go retirement program. In period t, each of the [N.sup.t] workers pays [tau][G.sup. …