Elasticity of substitution and the lifecycle model: A simple example

In the standard lifecycle model, consumption grows at a constant rate during the lifetime of an individual or household. The empirical study, however, shows that income and consumption moves together and have hump-shaped paths during the life of an individual or household. In explaining this comovement and humpshapedness, two approaches are prominent. One is to introduce the uncertain income. The other is to introduce the hump-shaped labor productivity. This paper follows the latter approach. We show that, in this approach, the sizes of two elasticities of substitution (the intertemporal elasticity of substititution and the elasticity of substitution between consumption and leisure) are important. We show that the smaller is the intertemporal elasticity of substitution and the larger the elasticity of substitution between consumption and leisure, the more hump-shaped and co-moving are the income and the consumption.