A turnpike theorem involving a modified Golden Rule

In the current study, we investigate efficient capital accumulation in a stochastic neoclassical aggregate growth model. The underlying uncertainty is driven by Brownian-motion shocks and the major results do not rely on the specification of production functions. The stochastic balanced path of the capitallabor ratio is naturally derived by a martingale, and the corresponding modified Golden Rule path of capital accumulation is well-defined. The powerful martingale theory is thus employed, and a stochastic turnpike theorem involving the modified Golden Rule is proved. That is, the underlying path of capital accumulation is asymptotically efficient in the sense of consumption maximization. We focus on asymptotic turnpike theorems and our turnpike theorem only relies on the requirement that the modified Golden-Rule path of capital accumulation is reachable in any almost surely finite Markov time. Finally, it is asserted that the modified Golden-Rule path of capital accumulation indeed provides us with a robust turnpike under very weak assumptions.