حقوق بازنشستگی تامین مالی شده و به اشتراک گذاری ریسک بین نسلی و بین المللی در تعادل عمومی

We explore intergenerational and international risk sharing in a general equilibrium multiple-country model with two-tier pensions systems. The exact design of the pension system is key for the way in which risks are shared over generations. The laissez-faire market solution fails to provide an optimal allocation because the young cannot share in the financial risks. However, the existence of wage-indexed bonds combined with a pension system with a fully funded second tier that pays defined wage-indexed benefits can reproduce the first best. If wage-indexed bonds are not available, mimicking the first best is not possible, except under special circumstances. We also explore whether national pension funds want to deviate from the first best by increasing domestic equity holdings. With wage-indexed bonds this incentive is absent, while there is indeed such an incentive when wage-indexed bonds do not exist. Highlights ► We study risk sharing in a multi-country two-tier pension system. ► Under a laissez-fair market solution young cannot share in the financial risks. ► Two-tier system can mimic optimal international and intergenerational allocation. ► Wage-indexed bonds are necessary to replicate first-best allocation. ► Each country wants to deviate from the first best by holding more domestic equity.

This paper explores intergenerational and international risk sharing in a general equilibrium multiple-country model with two-tier pensions systems. The first tier is a pay-as-you-go (PAYG) pillar that consists of a lump-sum component and a part that is linked to the wage of the young generation. The second tier involves a fully funded pillar that also pays a benefit indexed to the wage of the young generation. Our analysis is of interest from the perspectives of institutional design and of policy making. Given the ageing of their populations, many countries are reforming their pension systems by introducing a funded pension pillar.2 Also the World Bank see e.g. Holzmann and Hinz (2005) has recommended pension funding to complement traditional public PAYG pension arrangements. The design of the funded component is of crucial importance for the way in which risks are shared over various generations. Our model features a productivity shock and a depreciation shock (a financial shock) in each country. The laissez-faire market solution fails to provide an optimal allocation, because the young are born after the shocks have materialized and so cannot trade these risks. Introduction of a pension fund with benefits defined in wage-indexed terms allows for optimal intergenerational risk sharing within each country.3 Essential in this regard is that the pension fund features a (ex post) mismatch between its assets and liabilities. For example, if pension benefits are defined in wage-indexed terms, any equity investment by the pension fund is effectively owned by the young generation and, in this way, the young share in the equity risks. Specific investment portfolios of the pension fund allow for the optimal allocation of the fundamental economic shocks between the young and old generations so that intergenerational risk sharing becomes optimal. While intergenerational risk sharing within each country may be optimal for given national resources, allocations can still be suboptimal when viewed from the perspective of an international planner. In the presence of multiple countries that are each characterised by their own shocks, replication of the international planner’s optimum (the ‘first best’) is possible only if pension funds have access to wage-indexed bonds of all countries.4 In particular, we show that in the presence of these wage-indexed bonds, a properly designed pension system with a fully funded second tier that pays a defined wage-indexed benefit reproduces the first best. If these wage-indexed bonds are not available, mimicking the first best is impossible, except under special circumstances. The analysis in this paper thus assigns an important role to the combination of a proper design of a two-tier pension system and the degree to which asset markets are complete. Having identified the circumstances under which the first best can be replicated, we explore whether the national pension funds (or their designers) have an incentive to invest in accordance with the first-best allocation. The answer to this question depends on the incentive of pension funds to increase domestic equity investments and thereby again on the presence of wage-indexed bonds. With such bonds, the consequences for the factor returns of equity shifts in pension portfolios are spread evenly throughout the world, because countries’ investment portfolios are sufficiently diversified in terms of both wages and equity. This is not the case, however, if wage-indexed bonds are absent. An increase in domestic equity holdings lowers the return on domestic equity but raises the domestic wage rate. This benefits the old generation to the extent that they have internationally diversified their equity investments but have a large stake in domestic wages through the pension system (via the wage-linked component of the first tier or the wage-indexed benefit they may receive via the second tier) that they cannot diversify by selling wage-indexed bonds to foreigners. The lower return on the domestic equity position of the pension fund causes only limited harm to the young as residual claimants of the defined-benefit pension fund, because they hold only a limited amount of domestic equity while the rest is held abroad. At the same time, they benefit substantially from the higher domestic wage (and more so if the wage-linked first- or second-tier pension payments to the old are smaller) if the lack of wage-indexed bonds prevents them from sharing domestic wage risks internationally. In order to not unduly complicate the analysis, we make a number of simplifying assumptions. In particular, we assume that participation by the young in the pension system is mandatory. Hence, the young cannot escape their obligation to pay when the system requires them to do so. We also assume that payments on assets can be enforced across jurisdictions. Moreover, labour supply is exogenous and, hence, unaffected by the contribution level. A growing literature explores intergenerational risk sharing through the pension system. A large part of this literature deals with risk sharing through PAYG systems – see, for example, Hassler and Lindbeck, 1997, Thøgersen, 1998, Krueger and Kubler, 2002, Bohn, 2009 and Wagener, 2004 and Campbell and Nosbusch (2007). Exceptions are De Menil and Sheshinski (2003) and Miles and Černý (2006). Matsen and Thøgersen (2004) investigate intergenerational risk sharing in two-tier pension systems but they do not include funded defined-benefit systems, while Oksanen (2006) and Teulings and De Vries (2006) explore funding in a partial equilibrium context. The current paper extends the literature into various directions. In particular, we combine intergenerational and international risk sharing within two-tier pension systems with a defined wage-indexed benefit pension fund and we explore the consequences of the presence of wage-indexed bonds in this context. The remainder of the paper is structured as follows. Section 2 lays out the economy. In Section 3 we present the international planner. The market economy and the pension sector are discussed in Section 4. Section 5 investigates whether and how the market economy can mimic the international planner. In Section 6 we explore the consequences of an increase in domestic equity investment and whether the pension fund has an incentive to deviate from the first best. Section 7 concludes the main text. The Appendix generalises some of our results.

This paper has explored the circumstances that lead to first-best risk sharing. First-best risk sharing requires the simultaneous optimal sharing of risks between generations and across countries. We investigated the role of two-tier pension systems with a fully funded second tier and of the presence of wage-indexed debt in achieving first-best risk sharing. First, absence of wage-indexed debt substantially limits the scope for first-best risk sharing. In particular, it reduces the scope for international risk sharing. Second, given that the young are born after the shocks have materialized, they cannot directly trade assets with the old generation and in this way share risks with this generation. Hence, the pension system potentially plays an important role facilitating intergenerational risk sharing. A fully funded DWB second tier (in combination with a properly designed first tier) can produce optimal intergenerational risk sharing. As a consequence, the combination of wage-indexed debt and a pension system with a DWB fully funded second tier allows for first-best risk sharing. One may wonder whether a suitably chosen set of wage and capital taxes would achieve the international planner’s allocation.10 We conjecture that also here the existence of wage-indexed debt is important. Suppose that wage-indexed debt is absent. By taxing capital returns, one achieves optimal risk sharing of these returns between generations in all countries because the old generations invest in capital from all countries. Wage risks, in contrast, cannot be optimally shared internationally by taxing wages, because each country can tax only its own workers and, hence, only share national wage risk between the two domestic generations. If wage-indexed debt is available, the old generations trade not only in equity but also in wage claims from all the countries and we thus conjecture that an appropriate combination of wage and capital tax rates in the various countries achieves not only optimal intergenerational but also optimal international risk sharing. We also explored the incentive of national pension funds to deviate from the first-best allocation by increasing domestic equity investments. This incentive also crucially depends on the absence or presence of wage-indexed bonds. Pension funds are of non-negligible size and through their investment policies they can affect factor prices. With wage-indexed bonds benefits or costs of factor price movements are spread equally through the world, because all countries hold investment portfolios that are sufficiently diversified in the fundamental shocks hitting the various countries. Without wage-indexed bonds such diversification is not possible, however, and a unilateral shift in a DWB pension fund’s domestic equity investment may move factor prices to the benefit of the country’s inhabitants. In particular, starting from optimal intergenerational risk sharing, both generations will benefit from an increase in domestic equity investment. While the fall in the domestic equity return affects them only to a minor extent due to the diversification of the equity positions in their investment portfolios, the induced increase in the wage rate benefits them through the stake they have in domestic wages either directly as wage earners or via the pension system. Hence, a key overall policy implication of our findings is that the introduction of wage-indexed bonds may be beneficial in a world with funded pension systems. Another general conclusion is that unlike PAYG systems, which only condition on domestic shocks, pension funds are particularly desirable when asset markets are complete, because this allows those funds to provide for international risk sharing. We have neglected a number of complications associated with the trade of wage risk. We view wage-indexed bonds as instruments of particular interest, because wages can be easily observed for the purpose of linking pay-outs to them. Nevertheless, in reality wages are not uniquely defined due to the various ambiguous components (for example, bonuses). Hence, the introduction of wage-linked securities would require a very precise description of what constitutes the relevant wage. Furthermore, once payments are linked to wages, the issuers of wage-indexed securities may try to find ways to influence wage setting. We abstracted from this possibility. We have assumed also that participation by the young generation in the pension system is mandatory. Relaxing this assumption would lead to a breakdown of the DWB second pillar, because the young generation would refuse to pay into the funded pillar if they suffer from negative mismatch risk.11 Moreover, if the capital buffers in the funded system become large due to unexpectedly good returns, the old generation may lobby for higher pensions. In anticipation of this, the young might refuse to voluntarily enter into a risk-sharing arrangement with the old.12 We have also assumed that payments on assets can be enforced across international borders, which may be problematic in practice. Finally, we assumed that the labour supply is exogenous. With endogenous labour supply, the wage-linked contributions by the young generation to the two pension pillars may well become distortionary so that the pension system would involve a trade-off between efficiency and risk sharing. The analysis can be extended into a number of other directions as well. One extension would be to allow for small pension funds (relative to the national economy). If these funds would behave in a competitive way, they ignore the effects of their decisions on factor prices so that they would perfectly diversify their portfolios. In the absence of wage-linked bonds, coordination of those pension funds at the national level would worsen the allocation, while full (national and international) coordination would bring us back to the same equilibrium as with full decentralisation. Hence, an intermediate degree of coordination would be the least desirable situation. Another extension would allow for a richer menu of shocks. In particular, one might introduce demographic shocks (such as fertility and longevity shocks – see, for example, Auerbach and Hassett, 2007 and Andersen, 2005). With these additional shocks, the economy would ideally avail of instruments whose pay-offs are contingent on these shocks. Such instruments are however not yet traded on a large scale in public markets. The interesting question arises then how to best design the pension system to address this market incompleteness. Acknowledgements We thank an anonymous referee, Leon Bettendorf, Casper van Ewijk and participants at Netspar meetings and at seminars at the Institute for Advanced Studies, Vienna, the University of Amsterdam and the University of Groningen for helpful comments on earlier versions of this paper. All remaining errors are our own responsibility