PAYG pensions, tax-cum-subsidy and A-Pareto efficiency

An overlapping generation’s small open economy with endogenous fertility and time cost of children is analysed to show that the command optimum can be decentralised in a market setting using a PAYG transfer from the young to the old and a tax-cum-subsidy policy (i.e., a linear wage tax on labour income collected and rebated in a lump-sum way within the younger working-age generation). Indeed, the latter instrument stimulates fertility and then reduces the opportunity cost of children. Moreover, by applying the generalised notion of Pareto efficiency introduced by Golosov et al. (2007) in a context of endogenous population, some normative conclusions can be drawn: since only the utilities of those who are actually born are evaluated, we apply the concept of A-efficiency and conclude that when PAYG pensions are in existence, the tax-cum-subsidy policy can effectively be used as an alternative to the child allowance to internalise the externality of children, while also representing an A-Pareto improvement.     

Social Security Systems,Human Capital,and Growth in a Small Open Economy

We consider a small open economy in which the level of public education funding is determined by popular vote. We show that growth can be enhanced by the introduction of pay‐as‐you‐go pensions even if the growth rate of aggregate wages falls short of the interest rate. The reason is that the pay‐as‐you‐go (PAYG) system allows future retirees to partially internalize positive externalities of public education due to the positive effect of higher future labor productivity on their pension benefits. The majority support for education funding will be especially strong when the PAYG benefit formula is flat, i.e., progressively redistributive. If a flat benefit PAYG pension system is in place then the economy will achieve the highest growth rate relative to the alternative pension system designs. While such PAYG pension system may be opposed by the majority of working individuals due to inferior returns to their pension contributions relative to a funded scheme, it is likely to be politically sustained by a coalition of older individuals and lower income workers.     

On myopia as rationale for social security

It has been argued that “paternalistically motivated forced savings constitutes an important, and to some the most important, rationale for social security retirement systems.” This paper revisits the role played by myopia in generating a theoretical rationale for pay-as-you-go (PAYG) social security in dynamically efficient economies. If the competing asset is linear storage and myopic agents are allowed to borrow against future pension benefits, there is no welfare-rationale for PAYG pensions. Sufficiently strong myopia may justify such pensions only if agents cannot borrow against their future pension, but then they are at a zero-saving corner. With enough myopia, co-existence of positive optimal pensions and positive private saving is possible if the return to saving declines with saving, as in a model with a neoclassical technology.     

The Intergenerational State Education and Pensions

When credit markets to finance investment in human capital are missing, the competitive equilibrium allocation is inefficient. When generations overlap, this failure can be mitigated by properly designed social arrangements. We show that public financing of education and public pensions can be designed to implement an intergenerational transfer scheme supporting the complete market allocation. Neither the public financing of education nor the pension scheme we consider resemble standard ones. In our mechanism, via the public education system, the young borrow from the middle aged to invest in human capital. They pay back the debt via a social security tax, the proceedings of which finance pension payments. When the complete market allocation is achieved, the rate of return implicit in this borrowing–lending scheme should equal the market rate of return.     

Endogenous retirement and public pension system reform in Spain

Population aging has spurred developed countries around the world to reform their PAYG pension systems. In particular, delaying legal retirement ages and reducing the generosity of pension benefits have been widely implemented changes. This paper assesses the potential success of these policies in the case of the Spanish economy, and compares them with the results obtained by the (rather modest) reforms already implemented in 1997 and 2001. This evaluation is accomplished in a heterogeneous-agent dynamic general equilibrium model where individuals can adjust their retirement ages in response to changes to the pension rules. We check the ability of the model to reproduce the basic stylized facts of retirement behavior (particularly the pattern of early retirement induced by minimum pensions). The model is then used to explore the impact of pension reforms. We find that already implemented changes actually increase the implicit liabilities of the system. In contrast, delaying the legal retirement age and extending the averaging period in the pension formula to cover most of the individual's life-cycle can reduce the implicit liabilities substantially. These findings reveal the failure of the Spanish political system to distribute the costs of population aging more evenly across the generations.     

Idiosyncratic risk and financial policy

In economies subject to uninsurable idiosyncratic risks, competitive equilibrium allocations are constrained inefficient: reallocations of assets support Pareto superior allocations. This is the case even if the asset market for the allocation of aggregate risks is complete.     

Effect of social security on fertility and savings: an overlapping generations model

Old-age pension schemes do not exist in most developing countries, so adults bear children as security investments for the future. This phenomenon leads to unduly high rates of population growth. It has been hypothesized that introducing social security programs in such countries would increase savings rates and reduce the number of children born over the long term. The author studies the general equilibrium effects of some social security programs on rates of population growth and capital accumulation within an overlapping generations framework with endogenous fertility and savings. Specifically, Raul's overlapping generations growth model is extended to study the general equilibrium effects of payroll-tax-financed and child-tax-financed social security programs. It is shown that if the rate of intergenerational income transfers from young to old or child care cost is low, competitive equilibrium leads toward overpopulation and capital accumulation in a modified Pareto optimal sense; a social security program in such a case is therefore Pareto improving. A fully-funded system is not neutral when financed by child taxes. Finally, it is also shown that unlike in the case of exogenous fertility where competitive equilibrium attains steady state only asymptotically, fertility, when endogenous, may attain a unique globally steady state in finite time.     

On the interaction between risk sharing and capital accumulation in a stochastic OLG model with production

We analyze the interaction between risk sharing and capital accumulation in a stochastic OLG model with production. We give a complete characterization of interim Pareto optimal competitive equilibrium allocations. Furthermore, we provide tests of Pareto optimality/suboptimality based on (risky) rates of return only.     

Fair allocations in large economies

The purpose of this paper is the study of problems of equity in an economy with many agents. Conditions are given under which every equitable and Pareto optimal allocation is a competitive equilibrium with equal incomes for all agents. The results are also of potential relevance for the literature on incentive compatibility since the allocations that are obained through incentive mechanisms in large economies turn out to be equitable.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.     

A three way equivalence

In view of the well known core equivalence results in atomless economies, coincidence of market game equilibrium allocations with competitive allocations is tantamount to a three way equivalence between market game mechanisms, competitive equilibria and the core. Based on this idea we study equilibrium refinements of market games, which allow us to use the core equivalence machinery in order to provide an exact market game characterization of competitive equilibria.     

Information-constrained optima with retrading: An externality and its market-based solution

This paper studies the efficiency of competitive equilibria in environments with a moral hazard problem and unobserved states, both with retrading in ex post spot markets. The interaction between private information problems and the possibility of retrade creates an externality, unless preferences have special, restrictive properties. The externality is internalized by allowing agents to contract ex ante on market fundamentals determining the spot price or interest rate, over and above contracting on actions and outputs. Then competitive equilibria are equivalent with the appropriate notion of constrained Pareto optimality. Examples show that it is possible to have multiple market fundamentals or price-islands, created endogenously in equilibrium.     

Pensions and fertility incentives

Abstract.  This paper discusses the welfare implications of a pay‐as‐you‐go pension reform by introducing a child benefit in an endogenous fertility setting. In the model of a small open economy, higher fertility is associated with a reduction of lifetime labour supply. The optimum share of fertility‐related pensions is always below unity, but generally positive. The former is true, since individuals do not take into account the impact of their labour supply choice on the parent generation. It is demonstrated that child allowances are equivalent to fertility‐related pensions as instruments to achieve the optimum allocation. JEL classification: H23, H55, J13     

Retrading in market games

When agents are not price takers, they typically cannot obtain an efficient real location of resources in one round of trade. This paper presents a non-cooperative model of imperfect competition where agents can retrade allocations, consistent with Edgeworth's idea of recontracting. We show (a) there are Pareto optimal allocations, including competitive equilibrium allocations, that can be approximated arbitrarily closely when trade is myopic, i.e., when agents play a static Nash equilibrium at every round of retrading; (b) any converging sequence of allocations generated by myopic retrading can be supported along some retrade-proof subgame perfect equilibrium path when traders anticipate future rounds of trading.     

Efficiency and options on the market index

Summary. In a static exchange economy, when all the endowments are issued as securities on a stock exchange, Pareto optimal allocations may be reached by trading options on the market index (see Breeden and Litzenberger (1978)). We extend this result when some of the risks cannot be exchanged on the market. Options on an appropriate index, which typically differs from the market index, depending on the correlation of the non-tradable risks with the exchanged securities, are still an appropriate tool to support a (constrained) efficient equilibrium. This suggests that the recent development of derivatives based on interest rates may be an efficient way to reach a Pareto optimal allocation of risks. Received: June 16, 1997; revised version: July 25, 1997     

Millian Efficiency with Endogenous Fertility

Should governments implement policies that affect fertility decisions on efficiency grounds? What is the correct notion of efficiency to use? To address these issues, this paper develops an extension of the notion of Pareto efficiency, referred to as Millian efficiency , to evaluate symmetric allocations in an overlapping generations setting with endogenous fertility. This extension is based on preferences of those agents who are actually alive, and exclusively allows for welfare comparisons of symmetric allocations. First, we provide necessary and sufficient conditions to determine whether an allocation is Millian efficient or not, and we show that the sufficient conditions for dynamic efficiency offered by Cass (1972) and Balasko and Shell (1980) cannot be directly applied when fertility decisions are endogenous. Second, we characterize Millian efficient allocations as the equilibria of a decentralized price mechanism, and we present a sufficient condition for dynamic efficiency that uses the sequence of prices associated to such decentralized equilibria. Finally, we analyse how intergenerational policies should be designed to restore efficiency and achieve net welfare gains in two different settings in which markets yield inefficient allocations: dynamic inefficiencies and financial market incompleteness regarding human capital. In the former, a pay-as-you-go social security system eliminates dynamic inefficiencies, provided pensions are explicitly linked with fertility decisions. In the latter, a specific link between social security and public education becomes a necessary condition for Millian efficiency.     

Public pensions and growth

This paper investigates the relationship between the size of an unfunded public pension system and economic growth in an overlapping generation economy, in which altruistic parents finance the education of their children and leave bequests. Unlike the existing literature, we model intergenerational altruism by assuming that children's income during adulthood is an argument of parental utility. Unfunded public pensions can promote growth when families face liquidity constraints preventing them from investing optimally in the education of their children. We consider two alternative ways of financing a public pension system, either by levying social contributions in a lump-sum manner or in proportion to labour income. We find that there is no case for unfunded public pensions in economies where bequests are operative. By contrast, there exists a growth-maximising size of the public pension system in economies where bequests are not operative and individuals are sufficiently patient.     

Pension Plan Funding,Technology Choice,and the Equity Risk Premium

In this paper, the impact of Lazear contracts with defined‐benefit pensions on aggregate technology composition and the aggregate risk premium is examined. In the presence of capital market constraints affecting workers, defined‐benefit pensions bias the economy towards risk‐free production. Leveraging the risky technology relaxes the constraints and results in more risky production and a fall in the aggregate risk premium. This effect holds with risky debt and low pension shortfall risk but breaks down with high pension shortfall risk. A key prediction is that as Lazear contracts become less common, risky production will increase and the aggregate risk premium will fall.     

To Trade Or Not To Trade: Economies With A Variable Number Of Tradeables*

We present a general equilibrium model that encompasses the endogenous selection and shadow‐pricing of a set of tradeable commodities, with home‐based and social production activities. In the model, a market system is a set of costly social institutions which embody the trade and production technologies available in the economy. Our equilibrium concept describes the pricing of market institutions, thus pricing the tradeability of a commodity. We obtain the existence and the decentralization of Pareto‐efficient allocations. We discuss an example regarding the transition of a guild‐based economy into a market‐based economy.