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 liquidity constraints and pre retirement consumption one of the primary goals of the social security retirement program is the maintenance of consumption in old age in the past decade since the pioneering paper by feldstein 13 studies have examined the impact of the system on consumption over the entire life cycle and not just in old age empirical work has tested the impact on consumption of the individual wealth transfers accompanying the introduction of a pay as you go social security system extending this discussion of the impact of social security on pre retirement consumption hubbard 21 has shown in the context of lifetime uncertainty that even an actuarially fair fully funded social security system can raise lifetime consumption hence previous partial equilibrium estimates of the impact of social security on consumption drawn solely from consideration of the intergenerational wealth transfer at the introduction of the system are underestimates of the potential effect 2 an important assumption in the approaches cited above is that of perfect capital markets i e that individuals can borrow against prospective gains from participating in the social security system such an assumption is at variance with actual limitations on borrowing e g upward sloping interest rate schedules collateral requirements and quantity restrictions hayashi 18 found that approximately twenty percent of all consumption in the u s is accounted for by liquidity constrained consumers 3 flavin 16 found that the estimate of the marginal propensity to consume is affected dramatically by the inclusion of proxies for liquidity constraints suggesting that liquidity constraints are an important part of the observed excess sensitivity of consumption to current income since its inception in 1935 old age and survivors insurance oasi provided

estimating griliches k shifts griliches k shift a crucial parameter in the welfare evaluation of technological change is shown to be equal to the radial rate of technological change plus a vector of commodity bias parameters obtained from the distance function the analysis permits decomposition of sectoral productivity growth into productivity growth by commodity the k shifts estimated for wheat corn soybeans and beef in u s agriculture indicate a decrease in the marginal cost of production of corn soybeans and wheat during the 1950 1993 years

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

social security and the failure of annuity markets abstract this paper investigates the effect of asymmetric information on the market for annuities when individuals are assumed to differ in the probability distribution of dying individual behaviour under life insured and term insured annuities is investigated the market for such annuities is studied when the insurer cannot distinguish long lived from short lived retirees unlike the well known results of rothschild and stiglitz it is shown that if an equilibrium exists it can be either a pooling or a separating equilibrium given the same information as the private sector a planner will be able to achieve an optimum under certain circumstances

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

aggregate and distributional effects of fair social security abstract in an overlapping generations economy with production endogenous labor supply a bequest motive and uncertain lifetime we show that a fair fully funded social security program reduces the aggregate levels of output employment capital and savings we determine the necessary and sufficient conditions for this social security program to increase the inequality of the income distribution the conclusions apply to the entire non stationary competitive equilibrium path taken by the economy following the introduction of social security

taxation insurance and precautionary labor we examine optimal taxation and social insurance with adverse selection in competitive insurance markets in a previous literature it has been shown that with perfect insurance markets social insurance improves welfare since it is able to redistribute without creating distortions this result has been taken as robust to the introduction of adverse selection as this would only provide additional justifications for social insurance we show however that adverse selection can weaken the case for social insurance compared to a situation with perfect markets whenever social insurance mitigates private underinsurance it also causes welfare reducing effects by decreasing precautionary labor supply and hence tax revenue in addition adverse selection may reduce the redistributive potential of social insurance we illustrate our general results using different equilibrium concepts for the insurance market notably we derive conditions under which a complete renunciation of social insurance is optimal and the government only relies on income taxation to achieve its redistributive objectives

on analyzing the world distribution of income consideration of world inequality should cause reexamination of the key concepts underlying the welfare approach to measuring income inequality and its relation to measuring poverty this reexamination leads to exploration of a new measure that allows poverty and inequality to be considered in the same framework incorporates different approaches to measuring inequality and allows varied expressions of the cost of inequality applied to the world distribution of income for 1820 1992 the new measure provides different perspectives on the evolution of global inequality

the politics of redistributive social insurance this paper analyses the political support for a social insurance that includes elements of redistribution when there exists an imperfect private insurance alternative individuals differ both in their income and risk the social insurance is compulsory and charges an income related contribution with pooling of risks the private insurance is voluntary and charges a contribution based on individual risks however due to the adverse selection problem private insurance companies provide only partial insurance adopting a non expected utility model we show that there is a general majority support for social insurance and that this support is increasing with risk aversion we also show that a mixed insurance is politically impossible regardless of the degree of redistribution of social insurance and the joint distribution of risk and income in the population lastly we analyse how the political support for social insurance is affected by any change in its redistributive component and the possibility of using genetic tests

the family as an incomplete annuities market families can self insure against uncertain dates of death through implicit or explicit agreements with respect to consumption and interfamily transfers interfamily transfers need have nothing to do with altruistic feelings they may simply reflect risk sharing behavior of completely selfish family members although family annuity markets are incomplete even small families can substitute by more than 70 percent for perfect market annuities given adverse selection and transaction costs family risk pooling may be preferred to public market annuities in the absence of public annuities these risk sharing arrangements provide powerful incentives for marriage and family formation

social insurance and redistribution with moral hazard and adverse selection rochet 1991 showed that with distortionary income taxes social insurance is a desirable redistributive device when risk and ability are negatively correlated this finding is re examined when ex post moral hazard and adverse selection are included and under different informational assumptions individuals can take actions influencing the size of the loss in the event of accident or ill health social insurance can be supplemented by private insurance but private insurance markets are affected by both adverse selection and moral hazard we study how equity and efficiency considerations should be traded off in choosing the optimal coverage of social insurance when those features are introduced the case for social insurance is strongest when the government is well informed about household productivity

pay as you go social security and the distribution of altruistic transfers this paper studies the impact of an unfunded social security system on the distribution of altruistic transfers in a framework where savings are due to both life cycle and random altruistic motivations we show that the effect of social security on the distribution of these transfers depends crucially on the strength of the bequest motive in explaining savings behaviour we measure this strength by the expected weight that individuals attach to the utility of future generations on the one hand if the bequest motive is strong then an increase in the social security tax raises the bequests left by altruistic parents on the other hand when the importance of altruism in motivating savings is sufficiently low the increase in the social security tax could result in a reduction of the bequests left by altruistic parents under some conditions on the attitude of individuals toward risk and on the relative returns associated with private saving and social security some implications concerning the transitional effects of introducing an unfunded social security scheme are also discussed

ranking income distributions a large variety of policy questions involve choices between social states and a consequent ordering of the feasible alternatives when these social states are related to the levels of welfare experienced by individuals or households two central issues stand out in determining the relative desirability of different social outcomes one of these is the essentially positive exercise of achieving comparability between households with different characteristics such as composition or preferences operating in different environments for example facing different price structures the other concerns the normative judgments implicit in the evaluation of alternative allocations of resourcesthe emphasis placed on inequality between households and the extent to which greater inequality can be compensated by higher average living standards this paper focuses on the second of these issues and in doing so we abstract from the problem of household comparability by considering a population of n households identical in all respects except for their incomes the question of ordering social states then becomes one of ranking income distributions over a group of anonymous households or individuals borrowing the usual assumptions imposed on consumer preferences we may suppose that a social ordering of income distributions can be represented by a welfare function 2

longevity and public old age pensions i introduction conventional economic analysis of intertemporal or intergenerational resource allocation takes longevity as exogenously determined by biological or technological factors within this framework the institution of a mandatory public old age pensions of a pay as you go type unambiguously reduces capital accumulation the intuition behind this result is that when the young expect an old age pension after retirement and at the same time pay an earmarked payroll tax that lowers disposable income the ability and the incentive to save are reduced such a result however ignores the possibility that an individual who has a survivorship contingent title to an old age pension might use resources to increase the likelihood of survival to acquire the promised pension the fact that over the past century both longevity and the size of old age pensions have risen suggests that a more complete model that incorporates longevity as a choice variable may be useful in understanding the simultaneous increase in longevity and old age pensions ehrlich and chuma 1990 consider the demand for longevity in a world where the certain length of life is a fixed function of health care expenditures thus making longevity endogenous in their model consumers choose the optimal depreciation rate for human capital by choosing the path of health care expenditures their work paves the way for consideration of the effect of longevity contingent property rights on behavior in a more recent paper philipson and becker 1998 build on the work of ehrlich and chuma by modeling longevity contingent claims in the form of old age pensions among other things they find that an increase in a longevity contingent old age pension will induce individuals to live longer as a result of this longer life philipson and becker question the traditional result that pay as you go old age pensions always reduce the capital stock because workers who choose greater longevity may also choose to save more during their working years to finance their longer retirement period in this paper we introduce endogenous and uncertain lifetime into a two period overlapping generations olg model we depart from the traditional diamond type olg model by measuring longevity as the probability of survival into the second period and by allowing individuals to affect their survival probability through spending on longevity extending activities within this framework we examine the effects of a pay as you go old age pension on longevity and capital accumulation under two polar assumptions concerning the existence and absence of a fair intragenerational annuity market in either case the longevity effect of an increase in the old age pension is neutral while the capital stock effect is strictly negative if the interest rate and population growth rate are equal e g if the economy is on a golden rule path surprisingly increasing the old age pension produces both a negative longevity and savings effect for the more relevant case where the interest rate is larger than the population growth rate that an increase in the old age pension produces a negative capital stock effect is anticipated but the neutral or negative effect on longevity is counterintuitive it is counterintuitive because the empirical evidence seems to show lockstep increases in both longevity and government provided retirement benefits in the form of pensions and heath care benefits furthermore longevity insurance conjures up the moral hazard problem where increased utilization is expected with government provision the funding pool expands with use the cost being borne by workers the fact that the workers bear the burden of increasing the old age pension helps explain the longevity results we obtain when the population grows at the same rate as the return on capital an increase in the pension is offset by a dollar for dollar reduction in private savings leaving second period consumption unchanged

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

the individual life cycle annuity market imperfections and economic growth we study the effects of an annuity market imperfection on individual agents life cycle decisions and on the macroeconomic growth rate in an overlapping generations model with single sector endogenous growth our model features both age dependent mortality and labour productivity we model imperfect annuities by introducing a load factor on the annuity rate faced by finitely lived agents our main finding is that annuity market imperfections decrease economic growth because less assets are necessary for consumption late in life in addition we find that both the quantitative and qualitative effects of annuity market imperfections are grossly overestimated in a partial equilibrium analysis because it disregards general equilibrium repercussions

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

unveiling the ethics behind inequality measurement dalton s contribution to economics this article assesses the importance of dalton s 1920 paper in the economic journal for subsequent developments in income distribution analysis

on the contribution of economics to the evaluation and formation of social insurance policy if one had to choose a single policy that best characterizes the postwar behavior of governments it might well be their expansion of social insurance today s citizen of a typical developed country is insured through government programs against unemployment disability medical expenses impoverishment in youth and middle age through welfare systems impoverishment in old age through old age pensions loss of spousal support due to divorce through social security dependent benefits fluctuating earnings through progressive tax systems early death of a spouse via survivor s insurance and late death via annuity insurance the remarkable growth of social insurance has occurred against a backdrop of increased geographic mobility dramatic changes in demographics and at least in the united states a dissolution of the family the extent to which social insurance has been the cause of family decline and demographic change or its result is one of many complex questions that economics or any other social science is unlikely to ever fully answer economic analysis while not being able to discover the precise recipe leading to our social insurance institutions has at least been able to taste many of the key ingredients economics has and can provide real insight into a the need for social insurance programs b the appropriate size of such programs and c how social insurance programs affect the economy this paper seeks to illustrate each of these three kinds of economic contributions to the evaluation and formation of social insurance policy section i drawing on my 1987 article presents an efficiency argument for compulsory saving through a progressive social security system section ii drawing on my paper with avia spivak and laurence summers 1982 and on alan auerbach s and my 1987b paper illustrates an analysis of the appropriate size of social insurance programs examining in turn the questions of whether households save enough and buy enough life insurance or whether more government intervention in these matters is appropriate section iii drawing on my 1989 book illustrates how social insurance programs can affect the economy by discussing potential savings effects of health insurance particularly an asset tested medicaid scheme section iv concludes the paper with suggestions for future research and policy options as indicated the paper draws on my own and coauthored research and it provides only limited references for no better reason than easing my task and saving space in so doing i do not pretend to suggest that this is more than a very small subset of a huge volume of research sparked in the 1970s in large part by martin feldstein

uncertainty and optimal social security systems this paper examines the annuity aspect of social security within the framework of an overlapping generations model the duration of life is assumed to be uncertain under a fully funded system demand for social security is determined by each generation so as to maximize expected lifetime utility taking into account the welfare of future generations under a pay as you go system with intergenerational transfers demand for retirement benefits by the working population takes into account taxes paid by descendants it is shown that the two modes of finance are equivalent in terms of all real aggregates effects of changes in expected lifetime and in the birth rate are analyzed starting at the optimal level a compulsory balanced increase in social security taxes and benefits is shown to increase short run savings

welfare and comparative statics implications of fair social security a steady state analysis abstract this paper examines the steady state welfare and comparative statics implications of fair social security in an overlapping generations model with uncertain lifetime the model is designed to capture the effects of lifetime uncertainty extending over the individual s entire lifespan the effects of intentional and unintentional bequests and the effects of the earning profile he shows that the welfare effects depend on the size of the benefits and the structure of the social security tax in particular even fair social security may have negative welfare implications if the underlying tax structure is ill designed some comparative statics implications are analyzed

the economic effects of social security toward a reconciliation of theory and measurement abstract in this paper we argue that actuarial valuation of social security benefit streams is theoretically inconsistent with the assumption of pure life cycle motives instead we show that the simple discounted value of future benefits ignoring the possibility of death is often a good approximation to the relevant concept of value this observation motivates a re examination of existing empirical evidence concerning the economic effects of social security we focus our attention on studies of distributional equity and personal saving behavior in both cases we argue that the use of simple rather than actuarial discounting of survival contingent income streams produces results that differ dramatically from previous findings specifically estimates based on actuarial valuation may overstate the importance of redistribution between and within generations and may understate the depressive effect of social security on personal wealth accumulation by a factor of three or more

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

education social security and growth abstract we study the role of government s allocation of tax revenues between two outlays public investment in education a transfer to the young generation and social security benefits to the older generation in an overlapping generations economy with pay as you go social security and altruistically motivated transfers from parents to children we analyze how the allocation of the tax revenues between the two outlays affects growth and welfare in competitive equilibria a we obtain comparative dynamics results for nonstationary equilibria subject to a change in the allocation profile b for stationary equilibria we show that for a given allocation profile of the tax revenues educational subsidies can either increase the growth rate or decrease it depending on the parameters of the model preferences production function and the tax rate c if government seeks to allocate funds in a way that maximizes the growth rate we demonstrate that under some plausible conditions it is not optimal to maintain pay as you go social security however if parents preferences combine strong concern for their retirement with significant degree of altruism towards their children then pay as you go social security system does enhance growth and welfare

uncertain lifetimes and the welfare enhancing properties of annuity markets and social security this paper explores the implications of social security programs and annuity markets through which agents who are characterized by different distributions of length of lifetime share deathrelated risks when annuity markets operate a non discriminatory social security program affects only the intragenerational allocation of resources in the absence of private information regarding individual survival probabilities such a program will lead to a non optimal intragenerational allocation of resources however the presence of adverse selection considerations gives rise to a pareto improving role for a mandatory non discriminatory social security program

pareto optima and competitive equilibria with adverse selection and moral hazard this paper explores the extent to which standard general equilibrium analysis of pareto optima and of competitive equilibria can be applied to environments with moral hazard and adverse selection problems allowing for lotteries contracts with random components we first establish that an adverse selection insurance economy a moral hazard insurance economy a signaling economy and a private information labor market economy are all special cases of a simple general structure we then show that techniques for characterizing pareto optimal contracts as solutions to concave programming problems are useful and nice and appear to be broadly applicable allowing for lotteries we show how to characterize the optimal allocations for the adverse selection insurance and labor market economies we then show that standard existence and optimality theorems for competitive equilibria apply in the linear space containing lotteries if agents with characteristics which are distinct and privately observed at the time of initial trading enter the economy wide resource constraints in a homogeneous way other kinds of diversity are not critical for economies with moral hazard which satisfy the homogeneity condition competitive contract markets single out a subset of the optima and thus can be consistent with apparent unemployment and with a random allocation of labor supplied though all households are averse to risk the adverse selection insurance and signaling economies however do not satisfy the homogeneity condition and are difficult to decentralize efficiently with a price system

noncooperative equilibrium and market signalling among many recent developments in the economics of information none has generated more controversy than the concept of market signalling introduced by a michael spence if buyers are less well informed about product quality than sellers and no additional information is available market clearing prices must reflect some weighted average of product quality then if potential sellers of the highest quality products have the greatest opportunity costs and these costs exceed price they will not enter the market this adverse selection phenomenon is however offset if sellers of higher quality products can adopt activities that operate as a signal to potential buyers intuitively an activity is a potential signal if entering into it has a lower marginal cost for sellers of higher quality products for example the fly bynight operator faces a higher advertising cost per unit of sales than the new entrant who plans to build and then maintain his reputation or in the labor market productivity on the job is positively correlated with performance in school therefore the higher productivity worker has on average a lower personal cost of obtaining a given set of educational credentials similarly in purchasing insurance the marginal cost of accepting a higher coinsurance rate for a specific loss is lower for those with a lower probability of loss but on closer inspection it turns out that informational equilibria that is equilibria in which signalling is needed to distinguish product quality do not have the stability properties of classical walrasian equilibria in papers by michael rothschild and joseph stiglitz and the author 1975 1977 it has been shown that unless the difference between quality levels is sufficiently large there is for every set of signal price pairs s some alternative s 4 s which if offered by a single seller would improve his lot that is there is no cournot nash signalling equilibrium one possible inference that might be drawn from this result is that signalling could not be an important phenomenon in a competitive economy after all if any attempt at signalling were to result in interference in the form of competitive responses there would be no opportunity for individuals to identify the correlation between the level of the signal and the underlying quality of the product however this is too simplistic since the interference cannot take place until after signalling has been established it is therefore more appropriate to suppose that an economy is initially in a state of informational equilibrium with signals reflecting product quality and to ask whether the potential instability is likely to lead to a general collapse of the equilibrium following the approach adopted by charles wilson there have been several related attempts to introduce quasi dynamic considerations in which every agent takes into account the reaction by other agents when contemplating a defection from the initial set of signal price pairs s it is then argued that the set s forms a stable equilibrium if for every alternative s that would make a single defector better off this same signalprice pair would make the defector worse off after the reaction by other agents where these attempts differ is in the university of california los angeles this research was supported by national science foundation grant soc 76 13443 to the rand corporation

the comparison of multi dimensioned distributions of economic status the literature on inequality measurement has been largely concerned with single dimensioned indicators this paper explores some of the issues which arise when there are several dimensions to inequality and these are not readily reduced to a single index concentrating particularly on the two dimensioned case we make use of results on multi variate stochastic dominance in portfolio theory extending these and applying them to the measurement of inequality the use of the dominance conditions is illustrated by an application to the international distribution of income and life expectancy

public pensions as optimal social contracts abstract a simple overlapping generations model is modified to allow for an externality experienced by the young from consumption by the elderly this sets up a game between generations in which one generation s strategy may be to save too little and rely on gifts from the young e g public assistance for retirement income social security can therefore be viewed as a pareto optimal contract to restore efficient intertemporal allocation a funded public pension plan corresponds to forced saving but is vulnerable in that the next young generation may stop contributing rely on its children for retirement assistance and meanwhile reap the consumption externality from the current elderly s social security benefits this suggests a forced giving or pay as you go type of compulsory pension plan such as exists in most nations which also has the advantage of aiding the initial old generation and therefore generating an immediate consumption externality for the initial young the approach can also be used to explain other aspects of existing social security

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

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

ex ante inequality of opportunity in health decomposition and distributional analysis of biomarkers abstract we use a set of biomarkers to measure inequality of opportunity iop in the risk of major chronic conditions in the uk applying a direct ex ante iop approach we find that inequalities in biomarkers attributed to circumstances account for a non trivial part of the total variation for example observed circumstances account for 20 of the total inequalities in our composite measure of multi system health risk allostatic load we propose an extension to the decomposition of ex ante iop to complement the mean based approach analysing the contribution of circumstances across the quantiles of the biomarker distributions shapley decompositions show that for most of the biomarkers the percentage contribution of socioeconomic circumstances education and childhood socioeconomic status relative to differences attributable to age and gender increase towards the right tail of the biomarker distribution where health risks are more pronounced

voluntary public health insurance we look at the consequences of allowing public health insurance puhi to be voluntary when its coverage can be supplemented in the market puhi redistributes with respect to risk and income and the market is affected by adverse selection we argue that making puhi voluntary does not lead to its collapse since individuals always participate in it additionally in some cases a voluntary puhi scheme increases market efficiency because participation in it sends a signal to private insurers of an individual s health risk type the welfare consequences depend on the status quo if in the status quo no political support exists for a compulsory puhi making it voluntary constitutes a pareto improvement and in some cases all individuals are strictly better off if instead the status quo implements compulsory puhi making it voluntary then results in less redistribution

a game theoretic foundation of competitive equilibria with adverse selection we construct an extensive form game that captures competitive markets with adverse selection it allows firms to offer any finite set of contracts so that cross subsidization is not ruled out moreover firms can withdraw from the market after initial contract offers have been observed we show that a subgame perfect equilibrium always exists in fact when withdrawal is costless the set of equilibrium outcomes may correspond to the entire set of feasible contracts we then focus on robust equilibria that continue to exist for small withdrawal costs we show that the miyazaki wilson contracts are the unique robust equilibrium outcome

informational diversity over time and the optimality of monetary equilibria abstract the temporal realizations of a random state variable in an overlapping generations model create an informational diversity between members of different generations and require a reexamination of the optimality that competitive equilibria might display in such an environment using an optimality criterion that reflects this informational diversity we prove the optimality of competitive equilibrium in a model with a fixed stock of fiat money a single spot market and good endowments that follow a markov process the need for an optimality criterion that incorporates informational diversity is further motivated by studying the same model with the operation of complete contingent commodities markets

on the measurement of poverty official statistics in the united states and the united kingdom show a rise in poverty between the 1970 s and the 1980 s but scepticism has been expressed with regard to these findings in particular the methods employed in the measurement of poverty have been the subject of criticism this paper re examines three basic issues in measuring poverty the choice of the poverty line the index of poverty and the relation between poverty and inequality one general theme running through the paper is that there is a diversity of judgments which enter the measurement of poverty and that it is necessary to recognize these explicitly in the procedures adopted there is likely to be disagreement about the choice of poverty line affecting both its level and its structure in this situation we may only be able to make comparisons and not to measure differences and the comparisons may lead only to a partial rather than a complete ordering the first section of the paper discusses the stochastic dominance conditions which allow such comparisons illustrating their application by reference to data for the united states the choice of poverty measure has been the subject of an extensive literature and a variety of measures have been proposed in the second section of the paper a different approach is suggested considering a class of measures satisfying certain general properties and seeking conditions under which all members of the class which includes many of those proposed give the same ranking those sceptical about measures of poverty often assert that poverty and inequality are being confounded the third section of the paper distinguishes four different viewpoints and relates them to theories of justice and views of social welfare