Dynamic Stochastic Modeling of Economic Growth with Uncertainty

Abstract

This study develops a dynamic stochastic framework utilizing stochastic differential equations to characterize long-term economic growth amid uncertainty. The model considers many sources of randomness, including mean-reverting productivity shocks, technological advancements, and stochastic capital accumulation. Employing Lyapunov methods, we ascertain stability criteria and demonstrate the existence and uniqueness of solutions. Numerical simulations and Bayesian estimation techniques are employed to enhance model evaluation, facilitating parameter inference and uncertainty quantification. The paradigm encapsulates essential stylized features of economic growth, including volatility persistence and nonlinear adjustment dynamics, as evidenced by empirical calibration. The proposed approach provides a more flexible and continuous-time representation of economic uncertainty compared to traditional DSGE models. The results offer new insights for macroeconomic modeling and policy evaluation, emphasizing the significant impact of stochastic shocks on long-term development paths.