optimal actuarial fairness in pension systems a note abstract given a compulsory pension system we calculate the optimal ratio of marginal contributions to benefits this ratio is independent of the labor supply elasticity it increases in the rate of return in the pension system and decreases in the government s discount rate

social security life insurance and annuities for families abstract 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

the effect of social security on the steady state distribution of consumption abstract abel has shown that the introduction of a fully funded social security ss would decrease the variances of the steady state distribution of young period and old period consumptions eckstein et al have shown that a perfect ss would increase the steady state expected utility of consumptions we intend to give a caveat on their positive results by showing that the assumptions from which the above propositions are derived have some unrealistic implications and that by replacing these assumptions with more reasonable ones we may obtain very different results the only positive conclusion we are certain of is that a marginal ss insurance in the no insurance situation can always reduce the steady state coefficient of variation of both young and old period consumption distributions

cohort mortality risk or adverse selection in annuity markets abstract we show that tests for adverse selection in annuity markets using prices are not identified within the uk annuity market different annuity products create the potential for a rothschild stiglitz separating equilibrium as different risk types could choose different annuities empirical analyses using the money s worth suggest that prices are indeed consistent with this explanation however we show that this pattern of annuity prices would also result from the actions of regulated annuity providers who must reserve against cohort mortality risk annuity products that might attract different consumer risk types also have different risks for the provider

health investment saving and public policy this paper develops an overlapping generations model in which agents invest in health to prolong life in both working and retirement periods it explores how unfunded social security with or without health subsidies affects life expectancy economic growth and welfare in particular by extending life at a possible cost of capital accumulation health subsidies and a pay as you go pension can improve welfare especially in the short run

is everything neutral in his well known analysis of the national debt robert barro introduced the notion of a dynastic family this notion has since become a standard research tool particularly in the areas of public finance and macroeconomics in this paper we critique the assumptions on which the dynastic model is predicated and argue that this framework is not a suitable abstraction in contexts in which the objective is to analyze the effects of public policies we reach this conclusion by formally considering a world in which each generation consists of a large number of distinct individuals as opposed to one representative individual we point out that family linkages form complex networks in which each individual may belong to many dynastic groupings the resulting proliferation of linkages between families gives rise to a host of neutrality results including the irrelevance of all public redistributions distortionary taxes and prices since these results are not at all descriptive of the real world we conclude

income uncertainty and the demand for annuities abstract two well known results concerning the demand for annuities in an overlapping generations model are i egoistic agents should annuitize all their wealth and ii altruistic agents should segment their savings between riskless bonds for bequests and annuities for own consumption this paper extends the analysis by considering income uncertainty it is shown that while the segmentation result holds under future generation s income uncertainty fgiu altruistic agents do not segment their savings in the presence of second period income uncertainty spiu the intuition for this result is that income uncertainty in the second period of life is contingent on being alive and therefore at the optimum the covariance between one s offspring s consumption and life uncertainty is not zero as in the case of certainty and fgiu the effects of precautionary savings on the demand for annuities are also analyzed

rising longevity education savings and growth this paper examines the impact of declines in adult mortality on growth in an overlapping generations model with public education and imperfect annuity markets a decline in mortality affects growth through three channels first it raises the saving rate and thereby increases the rate of physical capital accumulation second it reduces accidental bequests lowers investment and thereby lowers the rate of physical capital accumulation third it may lead the median voter to increase the tax rate for public education initially but lower the tax rate in a later stage starting from a high mortality rate as found in many third world populations the net effect of a decline in mortality is to raise the growth rate however starting from a low mortality rate such as is found in most industrial populations the net effect of a further decline in mortality is to reduce the growth rate the findings appear consistent with recent empirical evidence

future costs in cost effectiveness analysis this paper resolves several controversies in cea generalizing garber a m phelps c e 1997 economic foundations of cost effectiveness analysis journal of health economics 16 1 1 31 the paper shows accounting for unrelated future costs distorts decision making after replicating meltzer d 1997 accounting for future costs in medical cost effectiveness analysis journal of health economics 16 1 33 64 quite different conclusion that unrelated future costs should be included in cea the paper shows that meltzer s findings result from modeling the budget constraint as an annuity which is problematic the paper also shows that related costs should be included in cea this holds for a variety of models including a health maximization model cea should treat costs in the manner recommended by garber and phelps

comment on kotlikoff shoven and spivak in the absence of perfect annuity markets individual consumers generally undertake precautionary saving to provide resources for their future consumption in the event that they live longer than expected kotlikoff shoven and spivak in this issue hereafter kss have provided us with a well conceived and well executed study of the effects of various annuity arrangements on individual and aggregate saving in the presence of lifetime uncertainty each of these authors has had a long standing interest in this area and their current paper reflects their accumulated expertise their results indicate that a potentially sizable fraction of u s household wealth represents precautionary saving resulting from the absence of perfect annuity markets the strategy of the kss paper is to develop simple models of individual saving behavior on the basis of utility maximization and then to aggregate the behavior of individuals both intraand intertemporally by comparing the results of models that differ in the specification of bequest motives and opportunities for creating annuities kss provide insights about the effects of various annuity arrangements on saving and capital accumulation although the models are all conceptually simple analytic solutions cannot be obtained in many cases therefore kss provide numerical solutions to their models in addition because the models are conceptually

external financing and balance of payments adjustment in developing countries getting a better policy mix there are a number of alternative strategies for dealing with current account balance of payments deficits one is to ignore them altogether on the grounds that they do not matter here the argument is that in the long term the imbalance between domestic investment and savings which the deficit reflects will be automatically corrected and that mindful of this private external finance will be available to cover excess expenditure in the short term net capital inflows will finance short term net inward transfers of real resources if in long run equilibrium there is a close positive correlation between investment and saving across countries net external financing will be merely a cyclical deviation from this

effects of aspirations and habits on the distribution of wealth we analyze how the introduction of habits and aspirations affects the distribution of wealth when the labor productivity of individuals is subject to idiosyncratic shocks and when bequests arise from a joy of giving motive in the presence of either bequests or aspirations labor income shocks are transmitted intergenerationally and this transmission together with contemporaneous shocks determines the distribution of wealth we show that the introduction of aspirations habits decreases increases the average wealth and increases decreases both its intragenerational variability and the degree of intergenerational mobility therefore a distinction between aspirations and habits is relevant because they involve different implications for the distribution of wealth

estate taxes consumption externalities and altruism we study how the introduction of consumption externalities affects the efficiency of the dynamic equilibrium in an economy displaying dynastic altruism when the bequest motive is inoperative consumption externalities affect the intertemporal margin between young and old consumption and thus modify the intertemporal path of consumption and capital the optimal tax policy that solves this intertemporal inefficiency consists of a tax on capital income and a pay as yougo social security system the later solves the overaccumulation of capital due to the inoperativeness of the bequest motive and the former solves the inefficient allocation of consumption due to consumption externalities when the bequest motive is operative consumption externalities only cause an intratemporal inefficiency that affects the allocation of consumption between the generations living in the same period but do not affect the optimality of the capital stock level this suboptimal allocation of consumption implies in turn that the path of bequest is also suboptimal the optimal tax policy in this case consists of an estate tax and a capital income tax the estate tax corrects the intratemporal inefficiency but generates an intertemporal inefficiency which is corrected by means of an appropriate capital income tax

the demand for enhanced annuities abstract this paper examines market reaction to the introduction of enhanced annuities in a market for deferred standard annuities the previous literature shows that individuals can try to avoid risk classification by contracting a standard annuity earlier in their life this paper offers a new perspective to the timing of the annuity purchase under the assumption that individuals already have an idea about their future risk type when young which becomes clearer over time it shows that enhanced annuities can crowd out earlier standard annuities completely if the individuals have incomplete knowledge of their future risk type however if individuals are sufficiently risk averse and there is a sufficiently high proportion of low risks in the population both products can remain in the market where lower risk types buy enhanced annuities while the higher risks stick to the early standard annuities the paper identifies the equilibrium candidate with both annuity types to be pareto superior and the unique equilibrium

social insurance and the optimum piecewise linear income tax abstract this paper calculates optimal linear income taxes when differences in income are caused by random factors luck rather than by unobserved individual skills as assumed in the classical theory of income taxation as first shown by varian 1980 varian h r 1980 redistributive taxation as social insurance journal of public economics 14 49 68 in the former case income taxation acts as social insurance by introducing life uncertainty and precautionary behavior we find higher optimal marginal tax rates than those found by varian we also find that in the context of a piecewise two bracket linear tax schedule the second marginal tax is higher than the first a finding that contrasts with results recently obtained in the framework of classical income taxation theory which show a lower second marginal tax

social security and unsecured debt abstract in this paper we use a calibrated life cycle model to explore quantitatively ways of reducing the burden of social security in a world populated by both optimizing and rule of thumb consumers social security contributions force young households with upward sloping income profiles to save a sizeable portion of their income for retirement when their optimal consumption plan would likely have them either saving little or borrowing we first use household data to document that young households have accumulated social security contributions that are large relative to debt holdings then using a calibrated life cycle model we show that both allowing households to use social security wealth to pay off their debt and exempting young households from social security contributions but in both cases requiring higher contributions later mitigate many of the inefficiencies of social security from the perspective of life cycle financial planning specifically in our preferred experiment which exempts households whose heads are under 30 from making social security contributions we find that certainty equivalent consumption increases by 3 4 for optimizing households and by 3 3 for rule of thumb households

adverse selection in the annuity market and the role for social security i study the role of social security in providing insurance when there is adverse selection in the annuity market i calculate welfare gain from mandatory annuitization in the social security system relative to a laissez faire benchmark using a model in which individuals have private information about their mortality i estimate large heterogeneity in mortality using the health and retirement study despite that i find small welfare gain from mandatory annuitization social security has a large effect on annuity prices because it crowds out demand by high mortality individuals welfare gain would have been significantly larger in the absence of this effect

adverse selection private information and lowballing in insurance markets recent contributions to the adverse selection literature have focused on a multiperiod competitive environment in this setting a clean distinction arises between the predictions of competing models cooper and hayes extend the model of rothschild and stiglitz to multiple periods the result is a self selecting equilibrium characterized by price highballing or systematically overcharging new business kunreuther and pauly suggest that information asymmetries between competing insurance firms render such price quantity policies infeasible their model results in a pooling equilibrium that is characterized by price lowballing or systematically undercharging new business our evidence is consistent with the kunreuther and pauly model and reveals the persistence of adverse selection in the automobile insurance market copyright 1990 by the university of chicago

uncertainty resolution and the timing of annuity purchases abstract this paper considers the question of why the annuity market is thin a model is presented in which consumers have the option of purchasing annuities before discovering their survival probability they can then recontract the initial choice after the resolution of this form of uncertainty it is shown that consumers purchase insurance against their own survival probability type at a very young age and do not undertake further transactions this characterization is then used to analze the effects of introducing future income uncertainty and to investigate the trade off between old age insurance motive and portfilio flexibility

the distribution of wealth and welfare in the presence of incomplete annuity markets this paper examines the implications of the absence of complete annuity markets on the distribution of wealth and welfare of agents whose saving decisions are obtained under uncertainty regarding the length of their life the absence of annuities is shown to yield a unique nondegenerate intragenerational distribution of wealth which is fully characterized this characterization is then used to evaluate the pareto desirability of an annuity system alternative welfare criteria that can be used when the proposed change has differential impacts on the initial state of subsequent generations are considered

advantageous effects of regulatory adverse selection in the life insurance market we analyse the effects of regulations prohibiting the use of information to risk rate premiums in a life insurance market new information derived from genetic tests is likely to become increasingly relevant in the future many governments prohibit the use of this information thereby generatingregulatory adverse selection in our model individuals early in their lives know neither their desired level of life insurance later in life nor their mortality risk but learn both over time we obtain both positive and normative results that differ qualitatively from those in standard static models legislation prohibiting the use of genetic tests for ratemaking may increase welfare the effort to sequence the human genome completely is now effectively com pleted although a comprehensive understanding of the effects of most genes on health and mortality risks will still take substantial further effort it is likely that in the medium term future more and more information relevant to ratemaking in the life health and long term care insurance markets will become available in particular we will learn the effects of many genes on the likelihood of various illnesses and consequently individualslife expectancy 1 moreover new genetic tests for these genes will likely become much cheaper 2 allowing this information to be used by insurers raises the prospect of substantial changes in future pricing

what makes annuitization more appealing we conduct and analyze two large surveys of hypothetical annuitization choices we find that allowing individuals to annuitize a fraction of their wealth increases annuitization relative to a situation where annuitization is an all or nothing decision very few respondents choose declining real payout streams over flat or increasing real payout streams of equivalent expected present value highlighting the effects of inflation increases demand for cost of living adjustments frames that highlight flexibility control and investment significantly reduce annuitization a majority of respondents prefer to receive an extra bonus payment during one month of the year that is funded by slightly lower payments in the remaining months concerns about later life income spending flexibility and counterparty risk are the most important self reported motives that influence the annuitization decision

adverse selection in insurance markets policyholder evidence from the u k annuity market in this paper we investigate the importance of adverse selection in insurance markets we use a unique data set consisting of all annuity policies sold by a large u k insurance company since the early 1980s to analyze mortality differences among individuals who purchased different types of policies we find systematic relationships between ex post mortality and annuity policy characteristics such as whether the annuity will make payments to the estate in the event of an untimely death and whether the payments from the annuity rise over time these mortality patterns are consistent with the presence of asymmetric information in the annuity market we find no evidence of substantive mortality differences however across annuities of different size even though models of insurance market equilibrium with asymmetric information would predict such differences we also find that the pricing of various features of annuity contracts is consistent with the self selection patterns we find in mortality rates our results therefore suggest that selection may occur across many specific features of insurance contracts and that the absence of selection on one contract dimension does not preclude its presence on others this highlights the importance of considering the detailed features of insurance contracts when testing theoretical models of asymmetric information

capital accumulation and uncertain lifetimes with adverse selection this paper examines the implications of adverse selection in the private annuity market for the pricing of private annuities and the consequent effects on constrption and bequest behavior with privately known heterogeneous mortality probabilities adverse selection causes the rate of return on private annuities to be less than the actuarially fair rate based on population average mortality however a fully funded social security system with compulsory participation can offer an implied rate of return equal to the actuarially fair rate based on population average mortality thus since social security offers a higher rate of return than private annuities consumers cannot completely offset the effects of social security by transacting in the private annuity market using an overlapping generations model with uncertain lifetimes we demonstrate that the introduction of actuarially fair social security reduces the steady state rate of return on annuities and raises the steady state levels of average bequests and average consumption of the young the steady state national capital stock rises or falls according to the strength of the bequest motive this abstract was borrowed from another version of this item

false diagnoses pitfalls of testing for asymmetric information in insurance markets established tests for asymmetric information in insurance markets are examined the most commonly used that information is symmetric if high and low cover contracts have the same loss rate is inconsistent with standard assumptions that imply that under symmetric information all contracts o er full cover incomplete cover and symmetric information can be reconciled if there are claim processing costs but now existing tests fare badly partly due to the divergence between marginal and average selection effects ignoring the nature of loading factors may cause recent studies to mismeasure the welfare costs of asymmetric information but these problems are remedial

adverse selection in the annuities market and the impact of privatizing social security the observation that few americans purchase life annuities has often been attributed to adverse selection a still unanswered question is whether observable price increases caused by adverse selection can be generated endogenously in a life cycle model this paper calibrates a pure life cycle model for a characteristic us cohort and reproduces three stylized facts adverse selection increases annuity prices by 7 10 percent the cost of adverse selection rises with the age of the annuitant and the cost is smaller for females than for males social security privatization could reduce annuity prices by between 2 and 3 percent

the effects of annuities bequests and aging in an overlapping generations model of endogenous growth we examine the effects of introducing actuarially fair annuity markets into an overlapping generations model of endogenous growth the complete annuitisation of agents wealth is not in general dynamically optimal the degree of annuitisation that is dynamically optimal depends nonmonotonically on the expected length of retirement and on the pay as you go social security tax rate the government has an incentive to restrict the availability of actuarially fair annuities contracts and can often move the economy from a pay as you go to a fully funded social security system via voluntary contributions to a government sponsored actuarially fair pension today accompanied by reductions in social security taxes tomorrow

ricardian equivalence in the presence of capital market imperfections abstract it is a common claim that ricardian equivalence fails if capital markets are imperfect the validity of this claim is examined for the case of informationally imperfect capital markets we present three alternative models of adverse selection and analyze the effects of debt finance in these models it is shown that a debt financed tax cut can lead to pareto improvement in some cases in the theoretically most preferable model however ricardian equivalence survives in spite of genuine imperfections in the capital market the results point to the importance of specifying the exact nature of imperfection

birth death and taxes abstract this paper analyzes the effects of lump sum tax policy in an overlapping generations model in which consumers have uncertain longevity it extends previous analyses by considering the case in which private insurance arrangements are actuarially unfair in addition it considers the polar case of actuarially fair insurance and the polar case of no insurance a general condition for debt neutrality is derived this condition depends explicitly on the degree of actuarial unfairness in insurance and on the extent to which parents care about the utility of their children

a note on the aggregate effects of social security abstract in an overlapping generations economy of karni and zilcha 1989 a fully funded social security program is shown to reduce the aggregate levels of output consumption employment and capital when the social security and the existing private annuities are equally unfair actuarially

precautionary saving and accidental bequests this paper presents a simple general equilibrium model of precautionary saving and accidental bequests this model is used to analyze the implications of individual lifetime uncertainty for aggregate consumption and capital accumulation a precautionary demand for saving arises because an individual consumer does not know in advance the date at which he will die and he wants to avoid low levels of consumption in the event that he lives longer than expected an implication of this precautionary saving is that when death does occur the consumer is generally holding some wealth which is then passed on to his heirs in the form of an accidental bequest even if all consumers have the same ex ante mortality probabilities there will be some intracohort variation in the date of death consequently there will be a nondegenerate distribution of bequests left by consumers in a cohort this nondegenerate distribution of bequests left by one generation induces variation in the distributions of wealth consumption and bequests of subsequent generations the importance of bequests in aggregate saving has been established by laurence kotlikoff and lawrence summers 1981 who reported that 80 percent of u s household wealth is inherited wealth one interpretation of this finding is that the simple life cycle model without bequest motives is an inadequate description of saving behavior in the united states but the model i present demonstrates that accidental bequests by selfish consumers can account for a potentially sizeable fraction of aggregate wealth although some part of bequests especially by the wealthy undoubtedly results from an explicit bequest motive accidental bequests also play a role in the intergenerational transfer of wealth as well as in the intragenerational variation in wealth in order to focus on the role of accidental bequests i purposely exclude a bequest motive from the specification of the utility function the effects of lifetime uncertainty on individual consumption behavior were first examined formally in a seminal paper by menachem yaari 1965 yaari s model provided the basic framework for virtually all subsequent work on uncertain lifetimes including well known papers by nils hakansson 1969 stanley fischer 1973 robert barro and james friedman 1977 david levhari and leonard mirman 1977 and kotlikoff and avia spivak 1981 however all of these papers focused on the consumption decision of an individual and ignored the effect of accidental bequests on the behavior of the recipients of these accidental bequests 2 as will be shown at various points in this paper changes in the economic environment can have effects on aggregate behavior which differ sharply from the effects on individual behavior because of the endogenous adjustment of bequests the effects of department of economics harvard university cambridge ma 02138 this paper is a revised version of bequests and social security with uncertain lifetimes nber working paper no 1372 june 1984 i thank olivier blanchard john burbidge christopher cavanagh robert clower stanley fischer benjamin friedman elhanan helpman mervyn king nobuhiro kiyotaki laurence kotlikoff robert mcdonald james pesando julio rotemberg lawrence summers lars svensson mark watson and jeffrey wolcowitz for valuable conversations and correspondence i also thank the participants in seminars at boston university columbia university cornell university federal reserve board harvard university university of iowa mit university of minnesota university of montreal national bureau of economic research north carolina state university the wharton school and yale university and two anonymous referees for their helpful comments i also thank the national science foundation for financial support 1 in the presence of perfect annuity and life insurance markets there may or may not be bequests depending on the presence or absence of a bequest motive but there would be no accidental bequests 2 kotlikoff and spivak focus on the role of the family in providing an incomplete annuities market but stop short of a full scale overlapping generations model in which the distribution of bequests is determined endogenously

aspirations habit formation and bequest motive we analyze how the presence of endogenous preferences affects the altruistic bequest motive from parents to children we will show that the existence of habits raises the threshold value of the intergenerational discount factor above which altruistic bequests are positive while aspiration formation could push this value down therefore the dynamic inefficiency of the economy with no altruism is not sufficient to prevent the bequest motive from being operative under aspiration formation we also discuss the implications of public debt when the bequest motive is inoperative and preferences exhibit habit and aspiration formation

the taxation of life annuities under adverse selection abstract this paper studies how annuities should be taxed in a mirrlees type model in the presence of adverse selection and a positive link between income and longevity the government is able to address the adverse selection problem by implementing a progressive marginal tax rate on annuities this amounts to subsidizing small annuities purchased by low incomes and taxing large annuities purchased by high incomes numerical simulations suggest that the taxation is significant and becomes more pronounced as annuitants get older