امنیت اجتماعی، بیمه عمر و سالیانه برای خانواده ها

In this paper we ask whether an aspect of social security, namely its role as a provider of insurance against uncertain life spans, is welfare enhancing. To this end we use an OLG model where agents have a bequest motive and differ in sex and marital status and where families are formed and destroyed and their characteristics evolve (exogenously) according to U.S. demographic patterns of marriage, divorce, fertility and mortality. We compare the implications of social security under a variety of market structures that differ in the extent to which life insurance and annuities are available. We find that social security is a bad idea. In economies where the private sector provides annuities and life insurance, it is a bad idea for the standard reason that it distorts the intertemporal margin by lowering the capital stock. In the absence of such securities social security is still a very bad idea, only marginally less so compared with economies with annuities and life insurance. We also explore these issues in a world where people live longer and we find no differences in our answers. As a by-product of our analysis we find that the existence of life insurance opportunities for people is important in welfare terms while that of annuities is not.

One of the possible rationales for social security is market failure. A particular type of market failure is the absence of annuities, or insurance against surviving beyond a certain age. In the U.S. annuities are either very expensive or inexistent which may indicate that there is a market failure and social security provides benefits that are effectively annuities. The usefulness of social security as a provider of annuities has been explored in a variety of papers such as Abel (1986), Hubbard and Judd (1987), Imrohoroğlu et al. (1995), and Conesa and Krueger (1999), but always in a context that identifies agents with households or with individuals that have no concerns over others. In the environments postulated by these papers there is no rationale for insuring against dying too early (or life insurance as is known) just against living too long (annuities). Yet, the average adult holds up of $50,000 (in face value) of life insurance. We think that because life insurance and annuities are securities that insure the same event (even if with opposite signs) they should be studied in an environment that provides a role for both type of securities. In this paper we revisit the issue of the usefulness of social security under a variety of market structures with respect to the existence of life insurance and annuities. What we bring to the table is that we do model households as families and not as individual agents which provides a rationale for the existence of life insurance and hence it provides for a much better modeling of the margins that may be of concern when facing death. Models where all households are single individuals are badly suited to answer questions about the possible role of social security as a substitute for market imperfections because they assume that all people would purchase annuities if available and this is just wrong. Most people purchase life insurance which makes it unlikely that they would also purchase annuities. Moreover, our model environment also allows us to incorporate altruism towards dependents, providing a unified picture of the various risks and considerations associated to the timing of death. We use a two-sex OLG model where agents are indexed by their marital status, which includes never married, widowed, divorced, and married (specifying the age of the spouse) as well as whether the household has dependents. Agents change their marital status as often as people do in the U.S. Our environment, that is placed in a model that replicates an aggregate (small open) economy, poses that individuals in a married household solve a joint maximization problem that takes into account that, in the future, the marriage may break up because of death or divorce. This paper uses the theory of multiperson households and the estimates in Hong and Ríos-Rull (2006) where agents in multiperson households have access to life insurance markets and where we estimated preference parameters that generate equilibrium patterns of life insurance holdings like those in the data. In that paper we looked at the effects of publicly provided life insurance, specifically the Survivors’ Benefits portion of the U.S. social security system.1 In this paper, we extend Hong and Ríos-Rull (2006) to incorporate alternative market structures with respect to the existence of securities contingent on the survival of individuals. We take the benchmark economy to be one with existence of life insurance and inexistence of annuities markets but where the assets of those that die and do not have survivors are rebated lump sum among survivors2—which we believe most closely resembles the U.S. economy; a Pharaoh economy with life insurance where the assets of the deceased without dependants disappears; an economy with access to both annuities and life insurance; and finally an economy where there are not markets for either life insurance or annuities. We ask whether social security, because it has a role as provider of insurance against uncertain life span is welfare enhancing. To answer this question, we compare the allocations of the various economies that differ in the private provision of securities based on individual survival with and without a social security program and compare its allocations and compute a measure of welfare associated to the policy change. A second output of our work is to learn the value of completing markets by adding private annuities (and life insurance). This paper is the first to our knowledge that has addressed simultaneously the existence of annuities and of life insurance. Our main finding is that social security's negative effect in terms of distortion of the intertemporal margin is much more quantitatively important than any positive role that it may have by providing a substitute for annuities and/or life insurance in economies where these markets do not exist. We also explore these issues in a world with people live longer and we find no differences in our answers. We also find that life insurance is important in the sense that its absence reduces people's welfare. The existence or inexistence of annuities, however, does not generate wildly different allocations and their absence may even have good welfare implications. This seemingly surprising fact (after all annuities provide a larger set of options)3 is due to the fact that there is an externality in giving in this model since it provides utility not only to the giver but also to the receiver, so some distortions that increase bequests may be welfare increasing, and to this extent social security by being an annuity contributes to reduce bequests.4 This paper proceeds under the assumption of a small open economy. The reasons are three: First, we are pushing the limits of computability (with the current specification we use a massive parallel machine with 26 processors running for days). Second, the negative effects of social security via lower capital and lower wages are well understood already. Third, the use of the small open economy assumption allows us to incorporate transition analysis that allow us to consider our numbers as appropriate measures of welfare. We take into account the initial distribution of bequests when doing the welfare analysis. This margin turned out to be quantitatively small. Section 2 briefly describes the logic of how the presence or absence of life insurance and annuities shape the decision making of agents. Section 3 poses the model we use and describes it in detail. Section 4 describes and calibrates the model, that includes the current social security system and fairly priced life insurance but assumes the absence of annuities. Section 5 compares the performance of the benchmark model economy with the other market structures. In Section 6 we take away social security and compare allocations and assess the welfare implications of the policy. Section 7 revisits the welfare implications of social security policies under a higher longevity. Section 8 concludes.

One of possible rationales for the existence of social security is market failure, in particular the absence of annuities. In this paper we have argued that the usefulness of social security should be looked at in the context of models that treat explicitly families as different to individual agents because annuities, life insurance, and social security are related to the risks associated to the timing of people's death. We have used an OLG model of multiperson households where agents may change their marital status through marriage, divorce, and death of spouses. We have calibrated the model to match the pattern of life insurance holdings in the U.S. as well as key statistics of the aggregate U.S. economy and we have used our model to understand the role of annuities markets and the welfare implication of current social security system. We have find that the existence of life insurance is important in enhancing welfare of agents while the existence of annuities does not improve welfare when there is strong bequest motive due to the externality implied by bequests. We have also confirm that social security acts as a deterrent to savings and that it lowers welfare. Last but not least, we have found that while social security plays some role as a provider of annuities (and also life insurance) such a beneficial role is much smaller than the pernicious effect that imposes on the savings decision for the standard reasons of affecting the incentives and not being actuarially fair and, consequently, the provision of annuities cannot be used as a justification of the program.