Approximate solutions to dynamic models: Linear methods - Harald Uhlig (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2006)
Linear Methods are often used to compute approximate solutions to dynamic models, as these models often cannot be solved analytically. Linear methods are very popular, as they can easily be implemented. Also, they provide a useful starting point for understanding more elaborate numerical methods. It shall be described here first for the example of a simple real business cycle model, including how to easily generate the log-linearized equations needed before solving the linear system. For a general framework, formulas are provided for calculating the recursive law of motion. The algorithm described here is implemented with the toolkit programs available per http://www.wiwi.hu-berlin.de/wpol/html/toolkit.htm .
Keywords: C60; C61; C63; E32; 330; numerical methods; linear solution method; loglinearization; dynamic stochastic general equilibrium methods; recursive law of motion