Intergenerational Risk Sharing Research Articles

Linear risk sharing in intergenerational pension

ABSTRACT We introduce and analyze a novel collective defined contribution plan (CDC) that guarantees at least a target benefit as a lump sum upon retirement. The guarantee is provided by the remaining working generations under a pre-determined linear intergenerational risk sharing (IRS) rule. Through a simulation-based study, we show that the CDC scheme consistently outperforms the comparable individual DC scheme (IDC) in terms of risk-adjusted performance. An extensive sensitivity analysis indicates that this outperformance is robust, especially in a ‘double-hit’ scenario where the underlying market dynamics and the demographics are severely worse than expected. Our work indicates that guaranteed retirement benefits can be organized via a CDC scheme with IRS in a way that it is, first, beneficial for all generations to join and, second, resilient against demographic change.

Optimal investment problem for a hybrid pension with intergenerational risk-sharing and longevity trend under model uncertainty

This paper studies the optimal investment problem for a hybrid pension plan under model uncertainty, where both the contribution and the benefit are adjusted depending on the performance of the plan. Furthermore, an age and time-dependent force of mortality and a linear maximum age are considered to capture the longevity trend. Suppose that the plan manager is ambiguity averse to the financial market and is allowed to invest in a risk-free asset and a risky asset. The plan manager aims to find optimal investment strategies and optimal intergenerational risk-sharing arrangements by minimizing the unstable contribution risk, the unstable benefit risk and the discontinuity risk under the worst-case scenario. By applying the stochastic optimal control approach, robust optimal strategies are derived under the worst-case scenario for a penalized quadratic cost function. Through numerical analysis and three special cases, we find that the intergeneration risk-sharing is achieved in our collective hybrid pension plan effectively. And it also shows that when people live longer, postponing the retirement seems a reasonable way to alleviate the stress of the aging problem.

Intergenerational risk sharing in a defined contribution pension system: analysis with Bayesian optimization

AbstractWe study a fully funded, collective defined contribution (DC) pension system with multiple overlapping generations. We investigate whether the welfare of participants can be improved by intergenerational risk sharing (IRS) implemented with a realistic investment strategy (e.g., no borrowing) and without an outside entity (e.g., shareholders) that helps finance the pension fund. To implement IRS, the pension system uses an automatic adjustment rule for the indexation of individual accounts, which adapts to the notional funding ratio of the pension system. The pension system has two parameters that determine the investment strategy and the strength of the adjustment rule, which are optimized by expected utility maximization using Bayesian optimization. The volatility of the retirement benefits and that of the funding ratio are analyzed, and it is shown that the trade-off between them can be controlled by the optimal adjustment parameter to attain IRS. Compared with the optimal individual DC benchmark using the life cycle strategy, the studied pension system with IRS is shown to improve the welfare of risk-averse participants, when the financial market is volatile.

Are deficits free?

Deficit finance, a.k.a. pay-go policy, is free when growth rates routinely exceed safe government borrowing rates. Or so many say. This note presents four counterexamples based on four versions of a simple OLG economy. In each version the growth rate exceeds the safe rate for one of four reasons – uninsured idiosyncratic risk, uninsured aggregate risk, policy uncertainty, and imperfect financial intermediation. Deficit finance does not directly address any of these problems. What works, respectively speaking, is progressive taxation, bilateral intergenerational risk-sharing, early policy resolution, and improved intermediation. The four examples thus show that seemingly free deficits may be more costly than they appear. Indeed, inefficient pay-go policy can even lower the government’s borrowing rate, encouraging yet more deficit finance.

Intergenerational Risk Sharing with Market Liquidity Risk

Intergenerational Risk Sharing with Market Liquidity Risk

Intergenerational Risk Sharing in a Collective Defined-Contribution Pension System: A Simulation Study with Bayesian Optimization

Pension reform is a crucial societal problem in many countries, and traditional pension schemes, such as Pay-As-You-Go and Defined-Benefit schemes, are being replaced by more sustainable ones. One challenge for a public pension system is the management of a systematic risk that affects all individuals in one generation (e.g., that caused by a worse economic situation). Such a risk cannot be diversified within one generation, but may be reduced by sharing with other (younger and/or older) generations, i.e., by intergenerational risk sharing (IRS). In this work, we investigate IRS in a Collective Defined-Contribution (CDC) pension system. We consider a CDC pension model with overlapping multiple generations, in which a funding-ratio-linked declaration rate is used as a means of IRS. We perform an extensive simulation study to investigate the mechanism of IRS. One of our main findings is that the IRS works particularly effectively for protecting pension participants in the worst scenarios of a tough financial market. Apart from these economic contributions, we make a simulation-methodological contribution for pension studies by employing Bayesian optimization, a modern machine learning approach to black-box optimization, in systematically searching for optimal parameters in our pension model.

Structure of intergenerational risk-sharing plans: optimality and fairness

In this paper, we derive optimal designs for a stylized Intergenerational Risk Sharing (IRS) pension plan. We study a Defined Ambition plan under which both contributions and pension benefits are adjusted based on the funding level. Our objective function focuses on the stability of members' lifetime consumption, both in the contribution and benefit phases, formulating the optimization as an ergodic control problem. We illustrate the drawbacks of unconstrained optimization and demonstrate the importance of including regulatory requirements for the sake of fairness across generations. Our results show that a linear risk sharing protocol is transparent, and with reasonable constraints on the funding level, can deliver a risk sharing plan that is fair with respect to intergenerational risk transfers, and is sustainable.

Structure of Intergenerational Risk-Sharing Plans: Optimality and Fairness

In this paper, we discuss optimal design for stylized Intergenerational Risk Sharing (IRS) pension plans. We study an IRS plan under which both contributions and pension benefits are adjusted based on the level of pension assets. Our optimization focuses on the stability of members’ lifetime consumption, both in the contribution and benefit phases, through formulating the optimization as an ergodic control problem. We illustrate the drawbacks of unconstrained optimization and demonstrate the importance of including regulatory requirements for the sake of fairness across generations. In this formulation, the employers are not included; implicitly, it is assumed that employer contributions would be paid as salary to the workers if not required for the plan, so the employer risk is eliminated.

Optimal Intergenerational Risk-Sharing When Stock and Labor Markets Are Co-Integrated

Optimal Intergenerational Risk-Sharing When Stock and Labor Markets Are Co-Integrated

PENSION FUND RESTORATION POLICY IN GENERAL EQUILIBRIUM

When the financial positions of pension funds worsen, regulations prescribe that pension funds reduce the gap between their assets (invested contributions) and their liabilities (accumulated pension promises). This paper quantifies the business cycle effects and distributional implications of various types of restoration policies. We extend a canonical New-Keynesian model with a tractable demographic structure and, as a novelty, a flexible pension fund framework. Fund participants accumulate inflation-indexed or non-indexed benefits and funding adequacy is restored by revaluing previously accumulated pension wealth (Defined Contribution (DC)) or changing the pension fund contribution rate on labor income (Defined Benefit (DB)). Economies with DC pension funds respond similarly to adverse capital quality shocks as economies without pension funds. DB pension funds, however, distort labor supply decisions and exacerbate economic fluctuations. While DB pension funds achieve intergenerational risk-sharing, welfare analyses indicate that the negative effects of the induced distortions are sizeable.

Optimal Risk-Sharing in Pension Funds When Stock and Labor Markets are Co-Integrated

A well established believe in the pension industry is that collective pension funds should take more stock market risk (compared to individual retirement accounts) since risk may be shared with future generations. We extend the OLG model of Gollier (2008) by adding labor income risk in the spirit of Benzoni, Collin-Dufresne, and Goldstein (2007) and show that this idea may be misguided. For the empirical range of parameter values reported by Benzoni et. al., we find that optimal risk-sharing actually implies that collective pension funds should take less stock market risk, not more. If labor income and dividend income are co-integrated, efficient risk-sharing policies should transfer risk from future generations to current generations instead of the other way around. Furthermore, we find that the potential welfare gains from intergenerational risk-sharing are significantly lowered.

Intergenerational Risk Sharing in Life Insurance: Evidence from France

We study intergenerational risk sharing in Euro-denominated life insurance contracts. These savings products represent 80% of the life insurance market in Europe. Using regulatory and survey data for the French market, which is €1.3 trillion large, we analyze the patterns of intergenerational redistribution implemented by these products. We show that contract returns are an order of magnitude less volatile than the return of assets underlying these contracts. Contract return smoothing is achieved using reserves that absorb fluctuations in asset returns and that generate intertemporal transfers across generations of investors. We estimate the average annual amount of intergenerational transfer at 1.4% of contract value, i.e., €17 billion or 0.8% of GDP. Finally, we provide evidence that smoothing makes contract returns predictable, but inflows react only weakly to these predictable returns.

Intergenerational Risk Sharing in Individual Retirement Schemes

Individual retirement savings schemes could benefit from risk-sharing mechanisms between generations that take behavioral aspects into account. We introduce a novel risk-sharing mechanism that incorporates nominal loss-aversion in two ways. First, the system avoids out-of-pocket wealth transfers by sharing only a fraction of positive returns over a high-water mark of pension assets. Secondly, payments from a generation insurance fund are targeted at nominal pension shortfalls below a reference point, which mitigates the loss experience at retirement. From a simulation of overlapping generations with stochastic asset returns and interest rates we find that the generation insurance scheme outperforms a pure individual retirement scheme by a significant margin: a similar risk of pension shortfall can be achieved with a contribution rate that is up to 20% lower. The efficiency gains vary with the extent of risk sharing over generations but remain large for sensible parameter values.

How Would Investing in Equities Have Affected the Social Security Trust Fund?

Some observers believe that investing a portion of the Social Security Trust Fund in equities would strengthen its finances and improve the program’s intergenerational risk-sharing. However, equity investments would also expose the program to greater financial risk and potentially greater political risk. Monte-Carlo simulation methods are used to investigate whether equity investments would likely strengthen the long-term outlook of the Trust Fund relative to the current policy of investing 100 percent of reserves in U.S. government bonds. The issues surrounding equity investments also go beyond expected returns on the Trust Fund portfolio. Concerns of government interference with the allocation of capital in the economy and with corporate decision-making as well as the accounting treatment of equity investments are also discussed.This paper found that:- Both prospective and retrospective analyses suggest that investing a portion of the Social Security Trust Fund in equities would have improved its finances.- Little evidence exists that Trust Fund equity investments would disrupt the stock market.- Accounting for returns on a risk-adjusted basis would not show any up-front gains from equity investment, but gains would become evident over time if higher returns were realized.- Equity investments could be structured to avoid government interference with capital markets or corporate decision-making. The policy implications of this paper are:- Investing a portion of trust fund assets in equities would likely reduce the need for higher payroll taxes.- At the 50th percentile of outcomes, equity investing has the potential to maintain a healthy Trust Fund ratio through the 75-year period.- The experience with the Thrift Savings Plan provides a road map for separating the government from actual investment decisions.

Intergenerational Risk Sharing and Endogenous Labour Supply within Funded Pension Schemes

Funded defined‐benefit pensions add to welfare on account of providing intergenerational risk sharing, but lower it on account of inducing labour supply distortions. We show that a properly designed funded defined‐benefit pension scheme involves a welfare improvement even if contributions are distortionary and even if individuals face potentially correlated wage and equity risks. Numerical calculations indicate that diversification gains from risk sharing are large compared to the losses related to labour supply distortions. This result withstands a number of extensions, like the introduction of a short‐sale constraint for individuals or the inclusion of a labour income tax.

Intergenerational Risk-Sharing Through Funded Pensions and Public Debt

We explore the benefits of intergenerational risk-sharing through both private funded pensions and via the public debt. We use a multi-period overlapping generations model with a PAYG pension pillar, a funded pension pillar and a government. Shocks are smoothed via the public debt and variations in the indexation of pension entitlements and the pension contribution rate, which both respond to funding ratio of the pension fund. The intensity of these adjustments increases when the funding ratio or the public debt ratio get closer to their boundaries. The best-performing pension arrangement is a hybrid funded scheme in which both contributions and entitlement indexation are deployed as stabilization instruments. We find trade-offs between the optimal use of these instruments. We also find that entitlement indexation and the response of the tax rate to public debt movements are complements. We compare different taxation regimes and conclude that a regime in which pension benefits are taxed, while contributions are paid before taxes, is preferred to a regime in which contributions are paid after taxes, while benefits are untaxed.

Bond Market Clienteles, the Yield Curve, and the Optimal Maturity Structure of Government Debt

We propose a clientele-based model of the yield curve and optimal maturity structure of government debt. Clienteles are generations of agents at different life cycle stages in an overlappinggenerations economy. An optimal maturity structure exists in the absence of distortionary taxes and induces efficient intergenerational risksharing. If agents are more risk-averse than log, then an increase in the long-horizon clientele raises the price and optimal supply of long-term bonds. But while a welfare-maximizing government caters to clienteles, it does not accommodate fully their demand, and limits issuance of long-term bonds to a level where these earn negative expected excess returns.

Intergenerational Risk Sharing, Pensions, and Endogenous Labour Supply in General Equilibrium*

AbstractWe show that a two‐tier pension system, with a pay‐as‐you‐go first tier and a fully funded, defined wage‐indexed second tier, can provide for optimal intergenerational risk‐sharing without distorting the labour supply, thereby achieving the first best. Other arrangements with a fully‐funded second tier fail to achieve the first best.

Intergenerational Risk Sharing in Time-Consistent Funded Pension Schemes

Intergenerational risk sharing by funded pension schemes may increase welfare in an ex ante sense. However, it also suffers from a time inconsistency problem. In particular, young generations may be unwilling to start participating in a pension scheme if this requires them to make huge transfers to older generations. This paper explores if limiting the transfers between generations can make a funded pension scheme time-consistent. The paper finds that this is possible indeed in a more or less realistic economic environment; it is not the case in general however. The form of the time-consistent scheme (how strong are the limits to transfers) is found to be very responsive to the economic environment. The time-consistent scheme offers lower welfare than the original time-inconsistent scheme, but higher welfare than a defined-contribution scheme without any intergenerational risk sharing.

Voluntary Participation and Intergenerational Risk Sharing in a Funded Pension System

We explore the feasibility of a funded pension system with intergenerational risk sharing when participation in the system is voluntary. Typically, the willingness of the young to participate depends on their belief about the future young's willingness to do so. We characterise equilibria with voluntary participation and show that the likelihood of their existence increases with risk aversion and financial market uncertainty. We find that it is likely that mandatory participation is necessary to sustain a funded pension pillar and to let participants benefit from intergenerational risk sharing. Published in the 'European Economic Review' .