Heterogeneous Ability, Life Expectancy, and Social Security : Four Essays

Abstract

Though the present thesis is not intended as a monograph, its respective chapters are interrelated: The major research question is whether the German public pension system (or potentially any annuity-based pension system) causes redistribution between income groups. Especially the relationship between life expectancy and income, usually perceived to be increasing, gives rise to the conjecture that poor individuals subsidize the pensions of the rich. I analyze the income-life expectancy relationship theoretically and empirically in Chapters 2 and 4, respectively. The redistributive mechanism is empirically analyzed in Chapter 3. Chapter 5 proposes a policy instrument which is capable of neutralizing the redistributive effects.The thesis consists of a literature overview in Chapter 1, and of four self-contained essays in Chapters 2 through 5. In Chapter 2 (To Work or to Work Out: A Moral-Hazard Interpretation of Labor Supply, Retirement, and Investments in Longevity), I analyze a moral-hazard model with multiple tasks, in which a single agent engages in three different activities, labeled work, delayed retirement, and work out (interpreted as investments in longevity). The latter imposes higher effort costs on weekly labor supply, but increases possibilities for life time labor supply. Work-out does not affect aggregate output and does therefore not accrue to the benefit of the principal. Second best incentives for work out are U-shaped in the agent's ability, and so is the effort level supplied by the agent.In Chapter 3 (Rich and Healthy - Better than Poor and Sick? An Empirical Analysis of Income, Health, and the Duration of the Pension Benefit Spell), I analyze the relationship between duration of the pension benefit spell and pension benefit claims from the German public pension system, with a special emphasis on differential results with respect to health. This relationship is crucial and causal for a potential structural pattern of redistribution between different income and health groups, induced by the public pension system. Evidence for such redistribution from poor to rich is present for most of the specifications in my analysis. The most adequate specification is partially--linear, does therefore not impose any parametrical restrictions between duration and benefit claims, and allows for potential endogeneity. The relationship I extract is clearly positive. Additionally I find that the income gradient is steeper for pensioners in bad health, meaning that redistribution from less able to more able individuals is more pronounced the worse the health status is.Subsequently, in Chapter 4 (Non-Monotonicity in the Longevity-Income Relationship), I show that for major sub-groups of pensioners in the public pension system in Germany who died between 1994 and 2005, the relationship between income and life expectancy is non-monotonous. This cannot be explained by anomalies in the data or as an artifact of the estimation technique, and so I provide a fundamental conjecture based on different elasticities of labor supply over the income distribution. Finally, in Chapter 5 On the Fairness of Early Retirement Provisions, joint with Prof. Dr. Friedrich Breyer), we discuss several notions of 'fairness' of early retirement provisions in pay-as-you-go financed public pension systems and we claim that the 'right' notion of fairness depends upon the objectives pursued in the design of pension systems. We point out the problems attached to the extreme positions 'efficiency' and 'welfare maximization' and propose a more modest concept of equity called 'distributive neutrality', which is based on the notion that the ratio between total benefits and total contributions to the pension system should not depend systematically on the individual's ability. By applying this concept to the German retirement benefit formula and taking empirically estimated relationships between duration of the benefit spell and income into account, we show that at the present discount rate of 3.6 per cent per year there is systematic redistribution from low to high earners, which would be attenuated if the discount rate were raised. This seemingly paradoxical finding is due to the fact that in our data set, there is a negative relationship between earnings and retirement age.