زمان بندی کارآمد از بازنشستگی

This study introduces a retirement decision into the classic Merton model. A familiar result is that you should retire if and when the marginal utility of another year's wages is equal to the disutility of work. A new result is that at the point of retirement your exposure to risky assets should not jump. Under power utility and constant time preference, the retirement timing problem has a closed form solution; the nine inputs to the formula in question give rise to nine comparative-static results on retirement timing. Further specialization of preferences, to log consumption utility and zero time preference, reduces the required number of inputs to four. Journal of Economic Literature Classification Numbers: E21, G11, J26.

Fundamental questions in personal finance are deciding when to retire, and whether to rebalance your portfolio at the point of retirement. These questions are considered here within a theoretical life cycle setting. Highlighted are two closed-form solutions to the retirement timing problem. One solution, based on power utility and constant time preference, identifies nine variables that could affect the retirement decision. The other solution, based on log utility and zero time preference, sees the number of variables reduced to four; this simplified formula is especially easy to 1 I thank Hazel Bateman, John Burbidge, Lisa Magnani, Olivia Mitchell, John Piggott, Sachi Purcal, Mike Sherris, David Throsby, Rob Trevor, and Graham Voss for helpful feedback. Two anonymous referees made insightful comments. Thanks are due to Carol White for research and editorial assistance. Financial support from the Australian Research Council is gratefully acknowledged. In 1999 the author visited the Department of Economics at the University of Sydney, which proved to be a hospitable environment for revising this paper.

This study began with a fairly general formulation of the retirement timing problem. It derived a familiar efficiency condition: Retire if and when the marginal utility of another year’s wages is equal to your disutility of work. A new result was that your portfolio should not be rebalanced at the point of retirement. Next, upon having specialized the utility function, this study derived and interpreted two closed form solutions to the retirement timing problem. The more complex formula required nine inputs. It was the basis for nine comparative-static exercises that shed light on the time-local effects of changes, in the state variable and the parameter inputs, on the timing of retirement. The simpler formula required four inputs. It implies that your planned span of retirement should be proportional to your assets
wage ratio at the time of retirement, with the factor of proportionality being given by your disutility of work. 10 A rearrangement of Ž30., suggested by Professor David Throsby of Macquarie University, gives lŽŽTR*.
F.Y, a formulation which could be used to estimate the arduousness of work in different industries. Given the difficulties of obtaining data on F which should include equity in the family home, the present value of pension entitlements, along with nonpension fungible wealth a more practical way of estimating l comes from the observation lY
CŽR*.. In other words, the agent is revealed as having had an arduous job to the extent that her wage at retirement is high relative to her consumption standard at retirement. For example, we would expect to observe high values of Y
CŽR*. in the case of coal miners, and low values in the case of college professors