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

John Duffy - University of Pittsburgh and Paul D. McNelis - University of Georgetown

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 paper suggests that a genetic algorithm/neural network approximation technique may provide a more suitable alternative especially in models with a high degree of nonlinearity and/or stochastic volatility. We show that our genetic algorithm (GA) solution technique either closely matches or outperforms the LQ and PE methods for approximating exact solutions. For models with higher degrees of nonlinearity and/or stochastic volatility, the GA gives solutions that are different from, though broadly consistent with, solutions obtained using PE. Our results suggest that the GA should at least complement these other methods for solving such models.

Scheduled for Session 3.6 Numerical Methods