Optimal Retirement for Heterogeneous Individuals Determinants of the Retirement Age and Consumption Pattern
In the past most people’s timing of pension and retirement was ﬁxed. Currently people live longer and are allowed ﬂexibility in retirement and savings allocation during the working period. While the cost of retirement is increasing with extended life-expectancies and worsened economic climate, there still is an observed desire for early retirement. As a result the topic has become increasingly discussed in politics. There are however few related works which provide a model for the retire-ment age. In this work we consider what factors determine the ideal retirement age, by presenting a quantitative life-cycle model for the voluntary optimal retirement problem. To obtain a solution the life-cycle optimization problem is reformulated as a continuous Markov decision problem. This is then solved by an intuitive and ﬂexible dynamic programming strategy, which determines the ideal retirement age, ideal consumption path, and corresponding ideal (dis)saving path. The ﬂexibility of this approach allows it to be applied within various pension regulations, individ-ual speciﬁc preferences and parameters. In this work it has been applied within a Dutch context to simulate how a Dutch citizen would ideally like to resolve their optimal retirement moment and consumption pattern if they were given consider-able ﬂexibility. Factors as the investment return, longer (healthy) lifespan, income and state pension levels, the marginal utility of consumption, and the desire for leisure, all aﬀect this decision.
We ﬁnd that the slope of consumption with age is determined by the relative height of the return on investment, compared to the rate of time preference. As a consequence this also determines when and how much should be saved. When the return on investment is high the optimizing agent starts saving earlier, does not have to save much for their pension beneﬁts, and chooses to retire later. When the return on investment is very low, the agent chooses to postpone retirement a little, however retirement savings start much later. For the retirement moment, we ﬁnd that a 20% ceteris-paribus increase in factors as the income level, public pension level, and desire for leisure, alter the ideal retirement age on the order of 0.5 to 2 years each. The size of these eﬀects however depend on how the disutility of labour increases with age.