Approximating and Simulating the Real Business Cycle: Linear Quadratic Methods, Parameterized Expectations, and Genetic Algorithms

This paper compares three approximation methods for solving and simulating real business cycle models: linear quadratic (including log- linear quadratic) methods, the method of parameterized expectations, and the genetic algorithm. Linear quadratic (LQ), log-linear quadratic (log- LQ) and parameterized expectations (PE) methods are commonly used in numerical approximation and simulation of wide classes of real business cycle models. This papers examines what differences the genetic algorithm (GA) may turn up, as the volatility of the stochastic shocks and the relative risk parameter increase in value. Our results show that the GA either closely matches or outperforms the LQ, loq-LQ and PE for approximating an exact solution. For higher degrees of nonlinearity and stochastic volatility, the GA gives slightly different results than the LQ and PE methods. Our results suggest that the GA should at least compliment these approaches for approximating such models.