Regression Analysis on Retirement Decisions and Incentives

Introduction to Regression in Retirement Research

Regression analysis can be defined as a multipurpose and powerful statistical technique used to simultaneously estimate the effects of numerous independent variables on a single dependent variable (Cohen & Cohen, 1983; Fox, 1997; Pedhazur, 1997). The simultaneous assessment of independent variables makes it feasible to better understand, calculate, and explain a dependent variable; to estimate their independent and collective effects; to discard spurious effects; to determine more precisely the direction and magnitude of their outcomes; and to manage the likelihood of Type I errors.

Over the years, many analyses and research studies have examined the relationship between retirement and the incentives provided through pensions and Social Security. Most of this research has been conducted within the framework of a single-equation, reduced-form model, which is most commonly utilized in behavioral and policy studies. A clear example is that the Social Security Administration has adopted this type of model to forecast the results of a change in existing policy — specifically, raising the age of entitlement for initial Social Security retirement benefits.

There were, however, several circumstances in which the coefficients estimated in retirement equations for variables reflecting the prospective incentive from Social Security and pensions to continue working would permit calculation of an individual's response to a change in compensation. For instance, if people acted in accordance with a simple life-cycle model and if capital markets were perfect, the likely relationship between retirement effects and measures of changes in assets from Social Security or pensions with continued work would illustrate how monetary incentives shape retirement outcomes, and how changes in these arrangements would govern retirement behavior.

Pensions, Social Security, and Retirement Incentives

However, there are other circumstances in which not all conditions hold. For instance, if capital markets are imperfect — such that a certain group of individuals faces limited liquidity — the coefficient on a variable measuring the change in the future value of pensions and Social Security cannot be used to predict the consequence of a variation in Social Security policy. The value of future work depends on unobserved preferences; therefore, the coefficient estimated in the retirement equation must vary to account for changes in policy.

Studies on retirement have consistently shown that the rewards of pensions and Social Security exert a strong influence on the decision to continue working, and these two factors are therefore integrated in the analysis. Research on saving is only now beginning to incorporate the incentives of pensions and Social Security, even though pension and Social Security reimbursements represent a large share of retirement financing. Many studies still omit these two incentive sources when examining saving behavior (Gustman and others, 1999). Moreover, even when pensions and Social Security are included as components of wealth, significant uncertainties remain.

Gale (1998) argues that in order to accurately measure the pension offset in an individual's wealth, factors such as pension value, assets, lifetime earnings, and each stage of the life cycle must be properly calculated and incorporated into the equation. Using a simple life-cycle model and data from the Survey of Consumer Finances, he finds substantial pension offsets. However, Gustman and Steinmeier (1999) followed a similar approach using the Health and Retirement Study (HRS) data and, contrary to Gale's findings, found only minor pension offsets.

Using the HRS data carries several advantages: the individuals whose earnings are sampled are nearing retirement age, making it easier and more precise to measure their lifetime earnings and total lifetime assets. Lifetime earnings are calculated using both self-reported salary records and records obtained from the Social Security Administration, while pension values are calculated using detailed descriptions of pension plans acquired directly from employers. Gustman and Steinmeier (1999) established that if lifetime earnings and retirement income are held constant, individuals who receive pensions hold more financial assets than those who do not. They ultimately conclude that pensions cannot substitute for other forms of savings or tax-favored saving methods when the concept is addressed within a wealth equation.