The Economics of Bequests in Pensions and Social Security

Experience in private pension plans and recent policy discussions about investment-based reforms of Social Security suggest that some form of bequest is likely to be part of any such reform that is enacted. This paper provides a first examination of the potential magnitudes of such bequests and of their effect on retirement annuities and asset accumulation. The most likely form of bequest, the preretirement bequest' made when employees die before normal retirement age, reduces the funds available for post-retirement annuities by about 16 percent or, equivalently, requires a one-sixth increase in the Personal Retirement Account saving rate to maintain the same level of post-retirement annuities. We also analyze a variety of post-retirement bequest options. The least costly option that we consider is adding a ten-year-certain' feature to the life annuity, thereby providing a bequest whenever the retiree dies before age 77. This would reduce annuities, relative to providing only preretirement bequests, by about 6 percent. The most costly option that we consider would provide a bequest equal to the remaining actuarial value of the PRA annuity at the time of death and would require reducing all annuities by about 23 percent unless the PRA saving rate is raised. We analyze the size distribution of bequests that would result under different bequest rules and consider the implications for aggregate capital accumulation.

Individual Risk in an Investment-Based Social Security System

This paper examines the risk aspects of an investment-based defined contribution Social Security plan. We focus on the risk after the plan is fully phased in. Individuals deposit a fraction of wages to a Personal Retirement Account (PRA), invest these funds in a 60:40 equity-debt mix, and in a similarly invested annuity at age 67. The value of the assets follows a random walk with mean and variance of a 60:40 equity-debt portfolio over the period 1946-95, a mean log return of 5.5 percent (net of administrative costs of 0.4 percent) and a standard deviation of 12.5 percent. We study he stochastic distributions of this process by doing 10,000 simulations of the 80-year experience of the cohort that reached age 21 in 1998. The resulting annuities are compared to the future defined benefits specified in current law (the benchmark' benefits). With no uncertainty, a 5.5 percent log return would permit the benchmark benefits to be purchased with PRA deposits of 3.1 percent of payroll, only one-sixth of the pay-as-you-go tax needed for the benchmark benefits. Saving a higher share of wages provides a cushion' that protects the individual from the risk of an unacceptably low level of benefits. For example, PRA deposits of 6 percent of wages reduces the probability that the benefits are less than the benchmark to 0.17 and the probability that they are less than 61 percent of the benchmark to 0.05. PRA deposits of 9 percent of wages (half of the tax rate required in a pay-as-you-go system) would substantially reduce these risks. This pure investment-based plan is an extreme case. The investment risk can be reduced further by using a mixed system that combines pay-as-you-go and investment-based components or that makes intergenerational transfers conditional on the performance of stock and bond prices.

Individual Risk and Intergenerational Risk Sharing in an Investment-Based Social Security Program

This paper examines the risk aspects of a fully phased-in investment-based defined contribution Social Security plan. Individuals save a fraction of wages in a Personal Retirement Account (PRA) invested in a 60:40 equity-debt mix and receive a similarly invested variable annuity from age 67. The value of the portfolio follows a random walk with historic (1946-1995) mean log real return of 5.5 percent and standard deviation of 12.5 percent. We study 10,000 stochastic distributions of this process for the 80 year experience from 1998 to 2077. With a nonstochastic 5.5 percent rate of return, individuals could purchase the future benefits promised in the current Social Security law (the benchmark' level of benefits) by saving 3.1 percent of earnings, just one-sixth of the payroll tax that Social Security actuaries project will be needed in the paygo system. A higher saving rate provides a cushion' that reduces the risk of unacceptably low benefits. For example, saving 6 percent implies a median annuity at age 67 or 2.1 times the benchmark benefits and only a 17 percent chance that the annuity is less than the benchmark. In 95 percent of the potential investment experience the annuity exceeds 61 percent of the benchmark benefit. With a 9 percent saving rate (half of the tax rate required in a pay- as-you-go system), there is only a 6 percent chance that the annuity is less than the benchmark and in 95 percent of the potential investment experience the annuity exceeds 92 percent of the benchmark benefit. We also study a modified plan in which retirees face no risk of receiveing less than the benchmark benefit because the government provides a conditional pension transfer to any retiree whose annuity is less in any year than the benchmark level of benefits. With a six percent saving rate, a conditional transfer is required in only about 40 percent of the simulations. The expected value of the transfers is substantially less than the expected incremental corporate tax revenue that results from the Personal Retirement Account saving. Additional tax revenue is needed in fewer than one percent of the simulations. In short, a pure defined contribution plan, with a saving rate equal to one third of the long-run projected payroll tax, invested in a 60:40 equity-debt Personal Retirement Account could provide a retirement annuity that is likely to be substantially more than the benchmark benefit while exposing the retiree to relatively little risk that the annuity will be less than the benchmark. Even this risk can be completely eliminated by a conditional guarantee plan that imposed only a very small risk on future taxpayers.

Individual Risk in an Investment-Based Social Security System

This paper examines the risk aspects of an investment-based defined contribution Social Security plan. We focus on the risk after the plan is fully phased in. Individuals deposit a fraction of wages to a Personal Retirement Account (PRA), invest these funds in a 60:40 equity-debt mix, and in a similarly invested annuity at age 67. The value of the assets follows a random walk with mean and variance of a 60:40 equity-debt portfolio over the period 1946-95, a mean log return of 5.5 percent (net of administrative costs of 0.4 percent) and a standard deviation of 12.5 percent. We study he stochastic distributions of this process by doing 10,000 simulations of the 80-year experience of the cohort that reached age 21 in 1998. The resulting annuities are compared to the future defined benefits specified in current law (the benchmark' benefits). With no uncertainty, a 5.5 percent log return would permit the benchmark benefits to be purchased with PRA deposits of 3.1 percent of payroll, only one-sixth of the pay-as-you-go tax needed for the benchmark benefits. Saving a higher share of wages provides a cushion' that protects the individual from the risk of an unacceptably low level of benefits. For example, PRA deposits of 6 percent of wages reduces the probability that the benefits are less than the benchmark to 0.17 and the probability that they are less than 61 percent of the benchmark to 0.05. PRA deposits of 9 percent of wages (half of the tax rate required in a pay-as-you-go system) would substantially reduce these risks. This pure investment-based plan is an extreme case. The investment risk can be reduced further by using a mixed system that combines pay-as-you-go and investment-based components or that makes intergenerational transfers conditional on the performance of stock and bond prices.Economic

The Transition to Investment-Based Social Security when Portfolio Returns and Capital Profitability are Uncertain

In this paper we study the transition from a pay-as-you-go system of Social Security pensions to an investment-based system in an economy in which portfolio returns and capital profitability are both uncertain. The paper extends earlier studies by Feldstein and Samwick that modeled the transition process in a nonstochastic environment and by Feldstein and Ranguelova that examined the implication of portfolio risk after the transition to an investment-based system has been completed. We analyze transitions to a mixed system that maintains the current 12.4 percent pay-as-you-go tax rate as well as to a system that is completely investment-based. We model intergenerational guarantees and assess the risk of such guarantees to taxpayers. We find that transitions to either a completely investment-based system or a mixed system that maintains current law benefits can be done with little additional saving in the early years (a maximum of three percent) and substantially lower combinations of taxes and saving deposits in the later years. The extra risk to retirees and/or taxpayers is relatively small, making the investment-based plans preferable to a pure pay-as-you-go system for reasonable degrees of risk aversion.

Computer-assisted tree taxonomy by automated image recognition

We present an algorithm that performs image-based queries within the domain of tree taxonomy. As such, it serves as an example relevant to many other potential applications within the field of biodiversity and photo-identification. Unsupervised matching results are produced through a chain of computer vision and image processing techniques, including segmentation and automatic shape matching. The matching itself is based on a nearest neighbours search in an appropriate feature space. Finally, we briefly report on our efforts to set up a webservice to allow the general public to perform such queries online