Essays on public annuities

Abstract

In the first chapter I review the public annuity (PA) programs launched in recent decades, including Sweden’s premium pension program since 1999, Singapore’s Lifelong Income for the Elderly program since 2009, the Hong Kong Mortgage Cooperation Annuity program since 2018, and Lithuania’s centralized pension annuity program in 2020. I observe some common features in these programs, as well as the diversity in terms of policies. These diversities raise questions regarding the type, the number, the form of PA plans offered, etc. In the second chapter I develop a consistent analytical framework to examine the number, the form and the timing of offering the PA plan, taking into account of two sources of heterogeneities: health states and bequest preferences. With a useful measure of the severity of adverse selection, I find that offering a small number of contracts is enough when the heterogeneities are limited. When the heterogeneities are substantial, however, offering the PA with guarantee payment enhances efficiency. Regarding the offering time, a deferred PA offered at a young age eliminates adverse selection but crowds out the transaction of the immediate PA offered at an older age. In the third chapter I further develop a simple analytical model to study the pros and cons of a voluntary PA plan with ceiling versus a mandatory plan with flexibility. I find that the idea of restrictive flexibility unifies these plans. Introducing either of the two plans reduces the severity of adverse selection in the PA market, but distorts the private annuity market. I also conduct welfare analysis, and find that the healthy group loses but the intermediate health group benefits. The least healthy group loses if the mandatory plan with flexibility is adopted but benefits if the voluntary plan with ceiling is implemented. In the last chapter I extend Chapter 3 by adding wealth heterogeneity. This extension allows me to examine two different types of ceiling restriction: the wealth-dependent ceiling and the uniform ceiling. In particular, I assume that the wealth and the health are correlated. I find that the efficiency of the ceiling depends on the degree of the correlation. When the correlation is weak, the wealth-dependent ceiling performs better than the uniform ceiling. The opposite is true when the correlation is strong enough. However, when the ceiling is set to be sufficiently high, the uniform ceiling always performs better. These results are robust when considering different distribution functions and different degrees of risk aversion. These results are useful to countries planning to introduce public annuities by providing some guidance regarding which plan the government would choose.