سه مدل تصمیم بازنشستگی برای سهم بازنشستگی تعریف شده اعضای طرح : یک مطالعه شبیه سازی

This paper examines the hypothetical retirement behavior of defined contribution (DC) pension plan participants. Using a Monte Carlo simulation approach, we compare and discuss three retirement decision models: the two-thirds replacement ratio benchmark model, the option-value of continued work model and a newly-developed “one-year” retirement decision model. Unlike defined benefit (DB) pension plans where economic incentives create spikes in retirement at particular ages, all three retirement decision models suggest that the retirement ages of DC participants are much more smoothly distributed over a wide range of ages. We find that the one-year model possesses several advantages over the other two models when representing the theoretical retirement choice of a DC pension plan participant. First, its underlying theory for retirement decision-making is more feasible given the distinct features and pension drivers of a DC plan. Second, its specifications produce a more logical relationship between an individual’s decision to retire and his/her age and accumulated retirement wealth. Lastly, although the one-year model is less complex than the option-value model as the DC participants’ scope is only one year, the retirement decision is optimal over all future projected years if projections are made using reasonable financial assumptions.

It is widely known that defined contribution (DC) pension plans are on the rise around the world in the private pension plan domain as well as in state pension systems, in both developed and non-developed countries.1 As DC pension plans emerge, more consideration should be given to the consequential effect on retirement behavior patterns. Defined benefit (DB) pension plans have historically dominated the pension plan world and past published research has focused almost exclusively on the retirement behavior of DB plan participants while saying very little on the retirement conduct of DC plan participants. For instance, numerous studies have investigated the influence of DB pension plan benefits on retirement behavior using the popular “option-value of continued work” retirement decision model (Stock and Wise, 1990a), including Stock and Wise, 1990a and Stock and Wise, 1990b, Lumsdaine et al., 1990, Lumsdaine et al., 1992 and Lumsdaine et al., 1994, Samwick (1998a), Hakola (1999), Coile and Gruber (2000), Harris (2001), Samwick and Wise (2001), Hurd et al. (2003), Piekkola and Deschryvere (2004), Gruber and Wise (2004), and Asch et al. (2005). A central feature in the development of the option-value model was to capture the influence of pension benefit incentives on the retirement decision. It has been predominantly used to model the retirement behavior of DB participants since important incentives are present in the DB pension accrual pattern. For instance, this decision model takes account of DB plan rules concerning early and sometimes late retirement. Our goal is to investigate the less familiar retirement decision-making process of a worker with a DC pension plan. Retirement decision models found to be helpful in capturing the retirement behavior of DB plan members may or may not be be suitable in describing a DC member’s approach to retirement. Recent empirical studies have suggested that the rules governing retirement behavior under a DB pension plan do not match those under a DC pension plan. Friedberg and Webb (2000) reported that they have found substantial changes in the retirement patterns among US workers, to which they attributed to the spread of DC type plans in the US. This paper explores three hypothetical approaches taken among DC plan participants in their decision to retire. We first examine the two-thirds retirement decision model, where workers retire once their accumulated pension fund can replace two-thirds of their earnings. This model can be criticized as not being “forward looking” since potential increments in future pension and employment income do not affect the retirement decision. We next consider the option-value of continued work model (Stock and Wise, 1990a), which takes into consideration all future retirement opportunities in the retirement decision. The option-value model is a well developed and researched model that has been discussed and applied by numerous authors as noted above. Finally, we present the one-year (OY) retirement decision model. The two features that distinguish the OY model from the option-value model are (1) the OY model approaches the retirement decision by regarding only the added value of delaying retirement by one year rather than all future retirement possibilities, and (2) there is a second leisure component in the OY model. This study builds on the stochastic simulation model developed in MacDonald and Cairns (2007), which is summarized in Section 2. Section 3 follows, describing each retirement decision model.2 Section 4 explores the theoretical retirement behavior of DC pension plan members. Section 5 presents the simulated results. Section 6 investigates the optimality of the retirement choice generated by the OY model. Section 7 examines the implied relationship between an individual’s choice to retire and his/her current pension and age under each retirement decision model. This section also tests the sensitivity of the utility function parameter estimates. Section 8 gives a few suggestions for future work and, finally, Section 9 summarizes the primary findings. The conclusions reached in this paper are theoretical—they are based on a qualitative examination of the three models (Section 4) and the simulated retirement behavior generated by each (Sections 5, 6 and 7). In future work, we hope to ascertain which of the models best describes the retirement behavior of DC participants by testing each model against empirical data.

In this paper, we examine the implied underlying behavior of a DC participant who makes his/her retirement decision according to one of three retirement decision models. We first consider the two-thirds model, which assumes that a DC participant sets a two-thirds replacement ratio target and exits the workforce once that target is achieved. We next look at the popular option-value model that optimizes the decision over all projected future retirement opportunities. Finally, we develop the one-year (OY) model. This model, although similar in its use of utility functions to the option-value model, postulates that the DC participant’s ability and desire to gauge future retirement opportunities is limited to the coming year. By stochastically simulating the economic variables–inflation, financial market returns and annuitization rates–we found that across all three retirement decision models the index-linked bond was the best performing asset for low-risk portfolios in terms of offering the youngest retirement age with the least amount of risk. If the member can tolerate some risk, it is in his/her best interest to invest the majority of his/her funds in equities owing to the much lower average retirement age that results from an equity portfolio. We caution, however, that our model is estimated from historical data, and the high equity premiums could potentially not continue in the future (Siegel, 2005). In a study that tested wealth shocks on retirement timing, Sevak (2002) wrote “Unlike DB pensions, DC pensions do not provide workers with sharp incentives to retire at particular ages. Whereas DB pensions have non-linear accrual rates, DC accrual should be relatively smooth. Thus, the growth of DC pension plans could account for the ‘flattening out’ of male retirement ages…While the rules of the pension plan may not suggest spikes in retirement at particular ages, variation in the value of accounts due to market performance may cause fluctuation in retirement timing due to wealth effects. This has not yet been examined in the literature” (pg. 2). The findings of our study support these assertions—that is, owing to the age-neutral pension accruals of DC plans and the implied influence of wealth on a DC participant’s choice to retire within all three models, retirement is smoothly distributed over a substantial range of ages, and the magnitude of the range is a direct result of the uncertainty in the financial market (more risky investment strategies generate larger ranges). As Lumsdaine et al. (1990) explained, empirical analysis reveals the superior model as being that which better approximates the variables that govern actual retirement behavior. In other words, the better it mimics actual retirement decisions, the better the model. Our paper is not intended to prove that the OY model is the closest approximation to actual DC retirement behavior. We would require data and a statistical analysis to make such a claim. Rather, it is to explore the implied underlying retirement behavior of each model in a DC environment. From a theoretical perspective, we found three advantages of the OY model over the option-value model: • Its underlying theory for retirement decision-making is more feasible given the distinct features and pension drivers of a DC pension plan, where: – Far-off financial forecasting is not worthwhile since: ∗ future DC pension income is extremely unpredictable and ∗ there are no age-related incentives in the pension accruals. – Retirement prospects can generally be known with some certainty one year in advance (although a risky investment strategy could still result in a sudden and unexpected change in wealth). • In addition to being computationally less burdensome, the OY model’s retirement decisions are optimal over the worker’s projected lifetime under the vast majority of scenarios (the very few exceptions being unusual financial market projections). In other words, the OY model produces the same retirement decision regardless of whether the value of immediate retirement is weighed against all future years or simply the subsequent year. The underlying reason is that DC pension plans lack financial incentives to retire or not retire at particular ages; consequently, the age-neutral pension accruals enable the worker to make an optimal decision by looking only one year ahead. • Finally, there is a more logical relationship between the worker’s decision to retire and his/her current retirement savings and age. Unlike the option-value model, the minimum replacement ratio that triggers retirement under the OY model declines with age once a worker is in their mid-sixties and begins a steep descent after age 70. We believe that this is likely the general behavior of older individuals, who would tolerate a lower replacement ratio with each passing year since: – continuing to work could be less viable or welcomed; – they could compensate for a deficient replacement ratio through additional personal savings or by tapping into other financial resources (such as housing equity); – they could be more apt to reduce spending so that retirement becomes financially viable; and/or – their financial needs could decrease with age. We also prefer the OY model to the two-thirds model because: • The OY model assumes a realistic variety of replacement ratios at retirement. • The OY model is forward-looking, but limits itself to the relatively certain immediate future. As DC pension plans continue to spread and empirical data emerges, we expect future work investigating DC retirement behavior to grow. A useful area for future work would be to test the retirement decision models against empirical data.