The dynamic analysis of continuous-time life-cycle savings growth models

Abstract

Working with the framework of a continuous-time overlapping-generations model, this paper examines equilibrium growth paths (consistent with perfect foresight). In particular, we develop a methodology for characterizing the adjustment paths converging to new stationary states following exogenous shocks. The solution technique yields sequences of derivatives approximating the true dynamic paths and bounds for the errors of approximation. In practice, aggregating behavior over discrete-time intervals can save a great deal of effort -- considerably enhancing the set of models feasible for analysis; our error bounds enable us to aggregate without compromising our results to an unknown degree.