Purpose: This paper aims to analytically show that in an over-lapping-generation (OLG) model, low earning cohorts bear unwanted risk and absorb higher economic cost than high earning cohorts do. Design/methodology/approach: This paper aims to consider the individual's risk appetite, using a simple utility function, based on consumptions and discount rates in each period. This paper calibrates the model according to teh Israeli pension system as a representative of a small open developed organization for economic cooperation and development country. Israel is considered as unique case study in the pension landscape, as it implements almost pure defined contribution pension scheme with continuous trend of pension market capitalization (Giorno and Jacques, 2016). Hence, this study finds Israel suitable for examining the theoretical mix of pension scheme. That model enables exploring combined solutions for adequate old age benefits, involving the first and the second pension pillars, under fiscal constraints. Findings: It comes out that for risk-averse individuals, the optimal degree of funding is negatively correlated to asset returns' volatility and positively correlated to earning decile level. The neglect of risk and individual's current earning level will thus overstate the contribution level and funded percentage from total contributions. Moreover, even in an economy with minimum government intervention, and highly developed private pension fund with high average of rate of return, the authors find it is optimal that the pension system contains a sizeable unfunded pillar. This paper innovates by revealing a socio-economic anomaly in design of mix pension systems in favor of high earning cohorts on the expense of economic loss of low earning cohorts. Practical implications: The model presented in this paper could be implemented in countries with mix pension systems, as an alternative to public social transfers or means tested, alleviating poverty and inequality in old age. Additionally, this model could raise the public awareness of the financial sustainability of the unfunded pay-as-you-go pillar to diversify financial risk in pension systems, especially for low earning cohort in society. Social implications: One area of research that is particularly relevant in this context concerns the issue of alleviating poverty and income inequality. It is often stressed that the prevention of old age poverty is among the central targets of well-designed pension system (Holzmann and Hinz, 2005). The conceptualization of minimum pension guarantee used in this composition allows to clearly capturing the notion of such a poverty and social targets as an integral part of the pension system rolls. Originality/value: This paper innovates by revealing a socio-economic anomaly in design of mix pension systems in favor of high earning cohorts on the expense of economic loss of low earning cohorts. That comes to realize through the level of total contribution rates and funded share that are generally optimal for high earning cohorts but not for low earning cohorts. This paper identifies that the effect of anomaly is most significant in a market characterized with high income-inequality level. This paper finds that imposing intra-generational risk sharing instrument in the form of minimum pension guarantee can re-balance pension design among different earning cohorts. This solution demonstrates balancing effect on the entire economy.

Using funded and unfunded pillars, the optimal pension structure is estimated using an over-lapping generation model, calibrated to the average OECD countries. While simulating different pillar sizes, a socio-economic characteristic was revealed in which low-earning groups are prone to unexpected market risks than high-earning cohorts and support a larger contribution than better-off individuals. This led to high contribution rates for funded pillars and low contributions rates for social security pillars. This suboptimal allocation leads to inefficient hedging capability for the pension portfolio. An alternative is a minimum pension guarantee as an efficient system stabilizer as it rebalances the economic cost among different earning cohorts. However, the guarantee might be expensive to implement if not capitalized early in the working phases in an era of aging populations, low birth rates, and deep financial crisis.

This study introduces multiplayer game in the modern pension market. Particularly, this study claims that low earners and high earners have different interests when playing in funded pension market scheme. This differentiating is enabled by avoiding the entire society as a single earning cohort. This study using financial position, demonstrates a socio-economic anomaly in the funded pension system, which is in favor of high-earning cohorts at the expense of low-earning cohorts. This anomaly is realized by a lack of insurance and exposure to financial and systemic risks. Furthermore, the anomaly could lead to a pension re-reform back to an unfunded scheme system, due mostly to political pressure. This study found that a minimum pension guarantee is a rebalance mechanism for this anomaly, which increases the probability of a sustainable pension scheme. Nowadays when countries try to balance between social expenses and awaking financial markets, one may find this theory highly relevant. It is obviously one of the cases where social targets meat financial equilibrium and here they are in the same side. Specifically, it is argued that implementing the guarantee with an intra-generational, risk-sharing mechanism is the most efficient way to reduce the effect of this abnormality.

In this study, we derive the financial position of pension actors in the market during pension system transition toward more funded capitalized scheme, mainly via an option benefit model. This is enabled by not considering the economy as a single earning cohort. We analytically demonstrate a socio-economic anomaly in funded pension system, which is in favor of high earning cohorts on the expense of low earning cohorts. This anomaly is realized by lack of insurance and exposure to financial and systemic risks. Furthermore, the anomaly might lead to pension re-reform back to unfunded scheme, mostly due to political pressure. We find that minimum pension guarantee is a rebalance mechanism to this anomaly, which increases the probability to sustainable pension scheme. Specifically, we argue that implementing the guarantee with an intra-generational, risk-sharing mechanism is the most efficient way to reduce the effect of this abnormality. Moreover, we exhibit the convergence process toward implementing minimum pension guarantee in many countries, which have capitalized their pension systems during the last three decades, particularly among Latin America and Central East Europe (CEE) countries. Received: 11 December 2020 / Accepted: 5 August 2021 / Published: 5 September 2021