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This paper studies the welfare implications of a PAYG pension system in an overlapping generations (OLG) model with demographic uncertainty and incomplete markets. In the absence of public pensions, small cohorts tend to be favoured by the changes in relative prices implied by demographic shocks. PAYG defined-benefit systems can help to share the financial risks created by this type of demographic uncertainty across generations. Our careful quantitative analysis test this possibility with unfavourable results: the overall welfare impact of the public pensions is negative, due to the prominence of the crowding-out effect over the insurance effect.

In the last two decades, developed countries have witnessed growing concerns regarding the financial sustainability of their Pay As You Go (PAYG) pension systems. It is widely agreed that the ability to extend current pension benefits to future generations of retirees is severely compromised.1 This gloomy prospect has triggered a very lively public debate, and moved the study of the properties of alternative intergenerational arrangements to the top of the academic research agenda. This paper is a contribution to that fast-growing literature. Two different demographic processes are commonly held responsible for the problems ahead: a universal trend towards higher longevity and the short-term problems posed by the retirement of the baby-boomers (the large cohorts born during the fifties and the sixties). In this paper we concentrate on the latter process: the consequences of large swings in the size of cohorts. We take a long view on changes in the age-composition of the population, and envisage the large cohorts of baby-boomers as one particular instance of a cyclical pattern governing the size of the workforce. We provide empirical evidence supporting the existence of such a ‘demographic cycle’ in the case of the US economy and explore whether it may lead to a justification for PAYG pensions entirely based on efficiency grounds. Even after several decades of strong research efforts, the existence of such a justification is still an open question. Classical overlapping generations (OLG) models formulated in deterministic, dynamically efficient settings leave no room for a welfare improving PAYG pension system (Diamond, 1965 and Auerbach and Kotlikoff, 1987).2 This is mainly due to the crowding-out of private savings. In stochastic economies, in contrast, social security can enhance welfare by substituting some missing or imperfect private insurance markets (Diamond, 1977). Once equipped with truly quantitative general equilibrium models, economist have explored this possibility intensively. Early efforts focused on idiosyncratic risks and found that the overall impact of social security was negative.3 Attention then shifted to the intergenerational risk sharing of aggregate risks in the context of incomplete financial markets. Krueger and Kubler (2004b) find that in economies with stochastic production where returns to labour and capital are imperfectly correlated the positive diversification effect of PAYG pensions does not overcome the welfare costs of the crowding-out effect. The consideration of the uncertainties involved in the demographic process itself has progressed more slowly, hindered by the computational difficulties involved. Initial research efforts have taken place in the only tractable setting: the two-period OLG model pioneered in Bohn (2001). He explores the optimal dynamic response to a demographic shock by analytically solving a log-linear approximation of the economy's equilibrium conditions. He finds that defined-benefit (DB) social security systems are ex ante more efficient than defined-contribution or privatized systems. This is a consequence of the favourable movements in wages and interest rates enjoyed by small cohorts of workers. As individuals do not know ex ante if they are going to belong to a large or small cohort, and they cannot insure against this risk in private markets, there is room for public transfer schemes to improve upon a purely private solution. In particular, DB pension schemes may achieve a more balanced distribution of the burden implied by demographic shocks by mitigating the effect of changes in the relative prices (small cohorts pay larger contributions, while retirees also participate in wage increases via higher pensions). Our target in this paper is to quantify the welfare impact of the insurance role of PAYG-DB pension systems, and compare it to that of the crowding-out of private savings. We add to the literature by exploring whether previous theoretical results extend to models with larger time-disaggregation. In these models big and small cohorts overlap in the labour force, with the result of smaller fluctuations in the labour input. Besides, individuals are simultaneously wage earners and capital earners during large parts of their life-cycle, smoothing the effects of changes in relative prices. Finally, shorter periods allow individuals to adapt their behaviour to the state of the economy more frequently. All these elements are important for a truly quantitative evaluation of the welfare impact of public pensions with demographic shocks. We address them in this paper by proceeding in the following way. We start by presenting evidence on demographic shocks and their empirical link with factor prices in Section 2. In Section 3 we illustrate the insurance role of DB pensions in a two-period exchange economy with a financial asset. We then move on to our basic model: an OLG economy with a standard neoclassical production function. The model is described in Section 4, calibrated to the US economy in Section 5, and solved in Section 6, where we present our basic simulation findings. The robustness of the results to the particular parameters employed is the topic of Section 7. The paper concludes with some final comments and directions for future research in Section 8. Our main results can be summarized as follows. We show first that, in the absence of crowding-out, PAYG-DB pension systems can be welfare improving in an ex ante way (our two-period exchange economy is an example). Secondly, we show how the insurance role of public pensions extends to a four-period, carefully calibrated production model. In this case, however, the positive effect is not strong enough to compensate for the welfare consequences of the crowding-out of private capital (with the exception of the cohorts of advanced age at the time the system is introduced). In the long run, small cohorts lose the equivalent of 1.32% of their life cycle income with a pension paying 2% of average wages. Large cohorts fare better, but still suffer a 1.06% loss in life-cycle income. These general conclusions are robust to changes in the calibrated values of preferences, technology and demographic shocks. Of course, one should be cautious in interpreting the numbers in our experiment as an overall rejection of real-world public pension systems.4 Finally, these findings only apply to the US economy, but the qualitative message may be of broader interest as demographic cycles seem to be fairly common in countries with mature populations, and international trade and capital flows may extend their effects to younger and faster growing economies (see Kenc and Sayan, 2001). Evidence supporting the stochastic treatment of demographic patterns and the linkage of the age structure of the population and factor prices is presented in the next section.

In a world where the size of the incoming cohorts fluctuates along a long run trend, factor prices can experience significant cyclical variation. In a purely private economy these price movements systematically favour smaller-size cohorts at the expense of larger-size cohorts. Defined-benefit, Pay As You Go pension systems counteract these swings in factor prices by charging higher effective contributions on smaller cohorts. PAYG-DB pensions have, then, an insurance effect against aggregate demographic risk that may lead to welfare gains. In this paper, we quantitatively explore the trade off between this insurance effect and the classical crowding-out of private savings. Our results are not positive for public pensions: we find significant welfare benefits deriving from risk sharing, but they are not enough to compensate for the reductions in per capita income generated by the crowding-out. This should not be interpreted as an overall rejection of real-world pension systems, as we are focusing on a very specific insurance effect and abstracting from a range of other aspects already discussed in the literature. Our contribution is a precise quantitative evaluation of this highly specific trade-off. The present analysis may be improved in several ways. First, it may be important to include the costs associated with raising children, as in, e.g., Brooks (2002). This could either dampen or reinforce the welfare impact of changes in factor prices depending on the sign of its auto-correlation, a quite difficult empirical matter. Second, it may be interesting to consider the uncertainty surrounding human longevity. This is important because public pensions help to cope with lifespan risk at the individual level and because there is substantial uncertainty about the speed and scope of longevity increases at the aggregate level, a type of risk that private markets find very difficult to insurance against. One last modelling aspect that may be reconsidered is the use of a one-sector model where installed capital can be consumed without costs. When capital is only partially reversible retirees may incur large capital losses when trying to sell their assets to the younger cohorts. This reinforces the damaging effect of demographic contractions, increasing the possibility of a positive role for PAYG pensions.