Détermination du taux d'épargne des ménages dans un modèle à générations imbriquées

In this paper, the overlapping generations model is used to study the macroeconomic implications of the Life Cycle theory. We adopt a continuous time version of the model with possibly several categories of agents per generation. We consider an economy with two interest rates (lending and borrowing), with an unfunded pension system, with intergenerational transfers. We establish algebraically the personal saving rate of such an economy for balanced growth paths and we identify its determinants. We demonstrate that the assumption of imperfect capital market is essential, one hand to obtain realistic levels of the personal saving rate, and on the other hand to ensure that the major implication of the Life Cycle theory stated by Modigliani (namely, the saving rate is an increasing function of the economic growth rate) is verified. With the imperfect capital market assumption, the personal saving rate is shown to be an increasing function of the difference between the borrowing and the lending rates, a decreasing function of the replacement rate of the unfunded pension system, an increasing function of intergenerational transfers, an increasing function of the economic growth rate irrespective of the factors of growth. A numerical simulation permits to appreciate the respective role of these determinants.