COMPOUND INTEREST-PROMISSORY NOTES

Compound interest-Promissory notes

Compound interest-Promissory notes

Introduction

With the decline of traditional defined benefit (DB) pension plans in the past two decades, there has been a corresponding shift to defined contribution (DC) plans by many U.S. corporations. The Social Security (SS) system may also have reductions in its scheduled benefit payouts in order to move it to permanent solvency. Because DC plans are typically self-managed by their participants and lack the withdrawal discipline featured in the life annuity distributions of most DB plans and of SS, a legitimate concern arises that many retirees may run out of their DC funds or under consume given that the length of life is uncertain.

To protect people against this longevity risk, some experts have suggested embedding annuitization as a default or mandatory option into DC plans. Despite the superior nature of annuities as insurance against longevity, however, most retired households have historically shown relatively little interest in voluntarily annuitizing their wealth. Various factors have been cited as the potential explanations to this “annuity puzzle”. Among them, uncertain health expenses have recently gained particular attention. The literature has thus far yielded inconclusive findings. Uncertain uninsured health expenses and their negative correlation with life expectancy at the age of annuity selection upon retirement reduce the attractiveness of annuities (Palumbo, 1999).

Uncertain health expenses, if occurring in late life, may actually increase the demand for annuities. Our study, to our knowledge, is the first analysis in a rich and sensible stochastic lifecycle framework to address all the major risks and choices for households in the retirement phase. Our model assumes that annuitization can be made at any age and in any amount, in contrast to a one-time choice of annuitization upon retirement, as analyzed in many previous studies. In addition, we consider jointly the household investment choices of bonds, equities, and annuities.

Literature Review

Our work builds on and extends the relevant literature. One strand examines the relationship between health expenses and general household saving behavior. That study, using a lifecycle model, shows that uncertain health expenses play a potentially important role in generating precautionary saving, which helps explain the slow rates of dissaving among elderly Americans in retirement. They argue that the precautionary saving with uncertain health expenses and bequest motives are likely the main driving forces for the non-dissaving in old ages and saving variations across income groups. These two saving motives need not be mutually exclusive in that the precautionary savings may end up being part of the bequest eventually left to heirs.

A Lifecycle Model Starting at Retirement

Preferences

We set up a discrete-time lifecycle model in retirement with age t? {0...T}, where t = 0 indicates the retirement age and T the maximum lifespan. Households in the model are assumed to have Epstein-Zin-Weil-type preferences defined over consumption, and a bequest where applicable. Let it C~ denote the utility generating composite consumption adjusted by household size t n (see below) and it M is the non-annuitized wealth for household i at time ...