Using Simulation as a Tool in Selecting a Retirement Age under Defined Benefit Pension Plans

Article excerpt

Abstract

This paper examines how simulation modeling can be used to select a retirement age under defined benefit pension plans. This approach construes the variables affecting pension benefits as probabilistic variables. Simulations are then run to generate probabilistic values for the real value of pension benefits for alternative retirement ages. By construing variables affecting pension benefits as probability distributions, this approach reflects the uncertainty facing individuals contemplating retirement. By generating estimates of retirement benefits as probability distributions rather than as single deterministic values, the model provides individuals with a more realistic and complete frame of reference for making the retirement decision. (JEL D12, J26)

Introduction

As the baby boom generation (i.e., the approximately 75 million Americans born between 1946 and 1964) continues to age and approaches the retirement years, there is an increasing interest in the various aspects of retirement planning. Important aspects of retirement planning include (a) determining retirement income needs, (b) assessing work-leisure preferences, and (c) developing saving and investment strategies for meeting retirement income needs.

At what age should the individual retire? In an abstract sense, this depends primarily on (a) the work-leisure preferences of the individual and (b) the individual's accumulated wealth relative to the resource needs during the retirement period.

For individuals covered by defined benefit pension plans, the benefits provided by such plans are usually an important source of income during the retirement years (McDonnell 2000). But how do individuals covered by such plans choose their retirement age? If they retire today, will the benefits provided by the plan be sufficient to meet their wants during the retirement years? What will be the effect on pension benefits of working an additional 1, 2, 5, or 10 years?

This paper examines how simulation modeling can be used as a tool to assist individuals who are attempting to select a retirement age under a defined benefit pension plan. The approach construes the critical variables affecting the real value (at the time of retirement) of average annual pension benefits received over the retirement period as probabilistic variables. Monte Carlo simulations are then run to generate probabilistic values for the real value of average annual pension benefits during the retirement years under alternative retirement ages. By construing input variables such as the wage growth rate, the inflation rate, and life expectancy as probability distributions, this approach properly reflects the uncertainty facing individuals contemplating retirement. By generating estimates of retirement benefits as probability distributions rather than as single deterministic values, the model provides the individual with a more realistic and complete frame of reference for making the retirement decision. For illustration purposes the simulations are constructed using the provisions of the State of Delaware Pension Plan. However, the approach could easily be adapted to any situation for any defined benefit plan.

Review of Literature

There has been little research that specifically examines the effect that choosing alternative retirement dates by individuals covered by defined benefit pension plans has on the real value of their pension benefits. A number of predictive models that attempted to explain the age at which individuals have chosen to retire have been developed and tested (Samwick 1998). Montalto, Yuh, and Hanna (2000) attempted to explain the planned retirement age rather than the actual retirement age. All of these models were developed within the framework of the traditional work-leisure and/or life cycle models. These studies found the following factors to affect the actual or planned retirement age: (a) pension and social security benefits received at the time of retirement, Co) earnings from employment immediately prior to retirement, (c) type of employment, (d) health, (e) accumulated wealth, and (f) a host of demographic variables. …