The dynamic analysis of continuous-time life-cycle savings growth models
This paper develops a methodology for investigating the dynamic behavior of continuous-time decentralized over-lapping generations models. The paper begins with an illustration of the method for deriving dynamic multipliers for the simple Solov model in which the savings ratio is constant and for the overlapping generations model. In the second model, the author assumes a competitive economy producing a single output which serves as both consumption and investment. Each household lives for T periods with a constant mortality rate. There are neither bequests nor inheritances, and the instantaneous utility function is of the Bergson type. The paper then provides an approximation solution which extends the method developed by Kantorovich and Krylov to the case of an infinite interval. The procedure involves generating a sequence of derivative approximations of the true dynamic path. As such the author is able to solve a discrete-time linear system and compute the dynamic multiplier along the transition path between steady-state equilibria. A property of the method is that it yields unique upper bounds for the approximation errors induced in discretization. These upper bounds allow the researcher to work with coarser grids than he otherwise could. These possibilities are numerically illustrated in section 6.
continuous-time decentralized over-lapping generations models
scientific article; zbMATH DE number 4055327
scientific article