Observational equivalence of the overlapping generations and the discounted dynamic programming frameworks for one-sector growth

Two alternative frameworks for one-sector growth are considered: an overlapping generations model with two-period lived, strictly selfish agents and a discounted dynamic programming model with infinitely lived agents. It is shown that under certain assumptions the two models are observationally equivalent, i.e., generate identical timepaths for all aggregate variables. One of the key assumptions is that the steady-state real interest rate in the overlapping generations model be strictly greater than the growth rate. The result is proved for the deterministic case and extension to a stochastic case is indicated.