Abstract This paper develops a model with overlapping generations to show that human capital formation can potentially attenuate factor price movements in response to fertility shocks if education spending per child is inversely related to the size of the generation subject to the fertility shock. The degree of attenuation depends on the effectiveness of education spending in producing human capital. We also find this attenuation effect concentrates generational consumption risk around the generation subject to the fertility shock. The combination of these two results suggest that there is an inverse relationship between the degree of factor price movements and lifetime consumption profiles in response to fertility shocks. Relatively larger generations will experience larger drops in lifetime consumption and relatively smaller generations will experience larger increases in lifetime consumption the less factor prices move in response to generational size. Thus, factor price smoothing does not necessarily translate into welfare smoothing across all generations.

中文翻译：

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教育支出，生育冲击和世代消费风险

摘要本文建立了一个具有重叠世代的模型，该模型表明，如果每个孩子的教育支出与受世代冲击的世代规模成反比，则人力资本形成可以潜在地减弱因生育冲击而引起的要素价格变动。衰减程度取决于教育支出在产生人力资本方面的有效性。我们还发现，这种衰减效应将世代消费风险集中在受生育力冲击影响的世代周围。这两个结果的结合表明，响应生育力冲击，要素价格变动的程度与终生消费状况之间存在反比关系。相对较大的世代将经历较大的终身消费下降，而相对较小的世代将经历较大的终身消费增长，要素价格随世代规模变化而变化的幅度较小。因此，要素价格的平滑并不一定转化为所有世代​​的福利平滑。