The twentieth century has seen a phenomenal decline in mortality and an increase in productivity level. These two important events likely affect people's choices of schooling years and retirement age. We first show that in a standard life-cycle model, positive feedback exists between optimal schooling years and retirement age choices. We then evaluate the impact of a mortality or productivity shock on an endogenous variable (schooling years or retirement age) by decomposing it into the direct and indirect effects, where the indirect effect arises from feedback from the other endogenous variable. Finally, we extend the model by including the utility benefit of schooling and show that a negative correlation of schooling years and retirement age is possible. Apart from clarifying the apparently similar concepts of positive co-movement and positive feedback, our results have implications relevant to the economic demography literature.

中文翻译：

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死亡率下降、生产力提高以及上学和退休选择之间的积极反馈

二十世纪，死亡率显着下降，生产力水平提高。这两个重要事件可能会影响人们对受教育年限和退休年龄的选择。我们首先表明，在标准生命周期模型中，最佳受教育年限和退休年龄选择之间存在正反馈。然后，我们通过将其分解为直接和间接影响来评估死亡率或生产力冲击对内生变量（受教育年限或退休年龄）的影响，其中间接影响来自其他内生变量的反馈。最后，我们通过包含上学的效用收益来扩展模型，并表明受教育年限和退休年龄之间存在负相关是可能的。