Small noise asymptotics for a stochastic growth model

• 成果类型: Article
• 署名作者: Williams, N
• 署名单位: Princeton University; National Bureau of Economic Research
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2003.12.007
• 发表日期: 2004
• 页码: 271-298
• 关键词: economic fluctuations; asymptotic methods; large deviations

摘要

We develop analytic asymptotic methods to characterize time-series properties of nonlinear dynamic stochastic models. We focus on a stochastic growth model which is representative of the models underlying much of modern macroeconomics. Taking limits as the stochastic shocks become small, we derive a functional central limit theorem, a large deviation principle, and a moderate deviation principle. These allow us to calculate analytically the asymptotic distribution of the capital stock, and to obtain bounds on the probability that the log of the capital stock will differ from its deterministic steady-state level by a given amount. This latter result can be applied to characterize the probability and frequency of large business cycles. We then illustrate our theoretical results through some simulations. We find that our results do a good job of characterizing the model economy, both in terms of its average behavior and its occasional large cyclical fluctuations. (C) 2004 Elsevier Inc. All rights reserved.