Sensitivity Analysis of Stationary States in Optimal Growth : a Differentiable Approach

Abstract

This paper provides a sensitivity analysis of stationary states in a discrete time model of capital accumulation. We classify the stationary states in terms of the concept of regularity, and investigate the properties of the regular stationary states that are robust to any small perturbation in economies. We prove that the set of regular stationary economies is an open dense subset of the space of economies. More specifically, if the space of economies is identified with the set of discount rates, then the regular stationary economies form a subset of full measure. Moreover, if the space of economies is identified with the set of pairs of a discount rate and a return function, then the economies that generate a regular stationary state exist generically.