Abstract
Since the mid 1990s some European countries (including Italy) implemented a Notional Defined Contribution (NDC) pension system. Such a system is based on pay-as-you-go funding, while the pension amount is a function of the individual lifelong contribution. Despite many appealing features, the NDC system presents some drawbacks: first, it is vulnerable to demographic and economic shocks compromising the financial sustainability; second, it could fail to guarantee adequate pension benefits to pensioners. In order to reduce the first limit, automatic balance mechanisms (ABMs) have been proposed in literature and also implemented in Sweden, while solutions that combine financial sustainability and social adequacy have been applied only in a pay-as-you-go point system. The aim of this paper is to insert into the Italian NDC architecture ABMs that preserve social adequacy under financial sustainability constraints. Godinez-Olivares et al. (Insur Math Econ 69:117–126, 2016) built ABMs for a Defined Benefit pension system using nonlinear optimization techniques to calculate the optimal paths of the control variables representing the main drivers of the system: contribution rate, retirement age and indexation of pensions. Following this line of research, we have developed a nonlinear optimization model for the Italian NDC system based on three control variables: pensions indexation, notional rate and contribution rate. The objective function considers both social adequacy and contribution rate sustainability, under liquidity and sustainability constraints. In the numerical application we apply the model to the Italian pension system and test the sensitivity of the results to different economic scenarios and objective function parameters.
Highlights
Traditional pension schemes in social security usually combine a Defined Benefit structure (DB) with a pay-as-you-go mechanism (PAYG)
With reference to the financial sustainability of the system, we measure it by the total unfunded liabilities (T U L) over a fixed time horizon (0, T ) that we define as the difference between the present value of future benefits and the present value of future contributions discounted at the notional rate g(t), consistently with the rate of return that remunerate the notional account: T
Notional Defined Contribution (NDC) systems have been introduced in order to confront the sustainability issues in traditional DB pension systems
Summary
Traditional pension schemes in social security usually combine a Defined Benefit structure (DB) with a pay-as-you-go mechanism (PAYG). The main parameters of a NDC scheme are: the contribution rate (fixed due to the DC structure), the normal retirement age, the notional rate (virtual rate of return given to the account), the indexation parameter (adaptation of the benefits after retirement), the conversion factor (transformation of the notional account into a lifetime annuity) and the eventual automatic adjustment mechanism (eventual ex post corrections on the notional rate and/or the indexation parameter) This philosophy has been successfully implemented in different European countries The closest contribution in the literature to our paper is from Gannon et al (2016), that developed ABMs in a DB system, introducing a nonlinear optimization problem based on three decision variables: contribution rate, indexation of pensions and retirement age. A numerical illustration is presented in Sects. 5 and 6 lays out this paper’s conclusion
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