Three essays on actuarial social security theory

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This thesis focuses on two of the basic instruments for improving PAYG pension systems, the actuarial balance (ABS) and the notional account (NDC). Research in these instruments involve, generally, only the retirement contingency. The thesis explores the possibilities to generalize, adding two new contingencies, permanent disability and dependence (LTC). The main objectives of the thesis, which also determine its three-chapter form, are as follows: 1.- To develop a theoretical basis for drawing up a Swedish-type actuarial balance sheet (ABS) for a defined benefit pay-as-you-go (DB PAYG) pension scheme with retirement and disability benefits. The idea of compiling this type of AB from an integrated perspective, combining both retirement and disability contingencies, which are closely linked and account for a very high proportion of pension spending in DB systems, has not previously been explored. 2.- To analyze the possibility of integrating the retirement (old-age) and permanent disability contingencies in a generic NDC framework. To do this we develop a multistate overlapping generations model (MOLG). Given that NDC schemes have positive features that could help to improve the efficiency of disability insurance (DI), it is not unreasonable to develop a theoretical model that would fully integrate the disability contingency into an NDC framework. In the model, the account balances of participants who do not survive are distributed as inheritance capital to the accounts of the (non-disabled) active survivors on a birth cohort basis. 3.-To examine the possibility of embedding public long-term care (LTC) insurance within the retirement pension system, i.e. introducing life care annuities (LCAs) annuities in a generic NDC framework. To do this we develop a multistate overlapping generations model (MOLG) that includes the so-called survivor dividend and give special attention to the assumptions made about mortality rates for dependent persons and LTC incidence rates, which largely determine the contribution rate assigned to LTC. Prestigious researchers, who use very different methodologies in their work and have very different ideas as to what pension systems should be, agree that there are some very good reasons for creating collective LTC coverage mechanisms to complement family and volunteer care arrangements. These objectives are in line with the trend seen in some countries of applying actuarial analysis methodology to the field of public PAYG pension system management. In congruence with the objectives mentioned at the beginning, the thesis is divided into three main chapters, to which are added this introductory chapter, the general conclusions, an overview of critical aspects, and suggested future lines of research. The work methodology followed is based on the multi-state transition model (Haberman & Pitacco (1999)), which describes a subject’s random movements between various states. The subject in this case will always be a person (active, retired, dependent, deceased...). The approach also includes the use of overlapping generations models, a types of model that play an important role in analysing a number of questions: models of pensions and pension savings, housing models, education models, public debt models, etc. In short, this thesis combines both types of model in what is termed an actuarial or multi-state overlapping generations model (MOLG). This methodology brings an actuarial approach to the accounting framework for organizing, summarizing and interpreting data on transfer systems and the lifecycle developed in Lee (1994a), Willis (1988) and Arthur & McNicoll (1978), which to some degree inspired the models subsequently developed by Settergren & Mikula (2005), Boado-Penas et al. (2008) and Vidal-Meliá & Boado-Penas (2013).
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