A model for joint pension risks

CPB background document

The ageing process, the low growth rates in productivity, and the low interest rate economy require a consideration of risks related to pension funds and public expenditures on social security. We therefore model demographic risk, productivity risk and financial risk with VAR(1) submodels, and find a low dependence between the annual shocks in the three different models. The joint distribution of the risk factors enables us to evaluate the long run effect of several policy measures on Dutch social security. Examples include the implementation of a new pension scheme and its transition process, or the optimal mix of pay-as-you-go (PAYG) and funded pension schemes.

Broer (2010) provides an extensive literature on the dependencies between the three key risk factors. More recently, Aro and Pennanen (2014) price mortality linked derivatives by relating mortality to several financial variables. Niu and Melenberg (2014) augment a mortality model with GDP per capita.

The impact of each risk factor on the sustainability of a pension scheme depends on the type of the scheme. Starting with demographic risk, most developed countries are confronted with declining population growth rates, and shrinking population sizes in the coming decades. As a consequence, the number of retirees for each worker is expected to increase substantially during the next decades. For this fraction, Van Duin and Stoeldraijer (2014) project an increase from 29 percent in 2014 to 39 percent in 2040 if the retirement age is adjusted to life expectancy, and even 51 percent without this adjustment. Such demographic risk is of particular interest for a PAYG pension scheme because it relies on intergenerational risk sharing.

Productivity risk makes future wages uncertain. This is particularly important in a defined benefit (DB) PAYG scheme if the payments to retirees are corrected for wage inflation. Through nominal wage rigidity, an adverse productivity shock has most impact on the replacement rates of the current working population in this DB PAYG scheme. Suppose productivity growth is lower than wage growth. Thus, the current working generation faces a relatively high contribution rate to pay the wage indexed defined benefit of the old. In the long run, wages will adjust such that the current working generation is faced with lower wages, and ultimately lower pension benefits in this PAYG scheme. In a funded scheme, the current workers experience the direct effect of the productivity shock. Due to this shock, the indexation of the pension benefits will be lower at some point in time in a funded DB scheme. Therefore, the current retirees may also suffer from the productivity shock. In a funded defined contribution (DC) scheme, retirees may also suffer through their capital holdings provided capital returns are affected by the productivity shock.

Following the reasoning above, financial risk, e.g., risks in capital returns, has most impact on the replacement rates in a funded DC scheme as it affects the pension benefits of all generations. In a funded DB scheme, the response to financial shocks is smoothed by adjustments in pension contribution rates or pension benefits. Private capital holdings amplify the effects to shareholders.

Though the risks are in isolation relevant for pensions, the dependencies between the risks may amplify or mitigate certain effects. For instance, the joint effect of a low mortality, a wage growth that exceeds productivity growth, and a low capital return is very problematic in a DB scheme, particularly with wage indexing. Such risks are highly relevant for the Netherlands as the first pillar is a DB PAYG scheme, and most schemes in the second pillar are most similar to a funded DB scheme. Our results indicate a moderate instantaneous dependence between the risks.

To model the risks for the next decades, we outline an a-theoretical parsimonious VAR(1) model for the Netherlands. Demographic risk is described in Section 2, wage-productivity risk in Section 3, and financial risk in Section 4. The joint model is estimated in Section 5. Section 6 discusses potential improvements of the current model. Conclusions are in Section 7. 

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