Working Paper: NBER ID: w10194
Authors: Noah Williams
Abstract: 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.
Keywords: stochastic growth model; asymptotic methods; business cycles; capital accumulation
JEL Codes: E32; C32
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| stochastic shocks (D89) | capital accumulation trajectories (E22) |
| noise level (Q53) | convergence of capital trajectories (F21) |
| stochastic nature of technology shocks (O33) | frequency and magnitude of business cycles (E32) |
| stochastic growth model (O41) | likelihood of recessions (E32) |