Rational stochastic bubble
In Trimborn, Koch, and Steger, "Multidimensional transitional dynamics: A simple numerical procedure", Macroeconomic Dynamics, vol. 12, 2008, 301-319, the relaxation algorithm is proposed as a simple and powerful method for determining the solution of many dynamic macroeconomic models with forward-looking expectations numerically. An associated MATLAB program has been developed and described by Trimborn, Koch, and Steger. The program is designed for conducting simulation studies of the transition path in continous-time macroeconomic models. Among other things the program can handle models which exhibit saddle-point stability. This is useful in particular when an analytical solution to the model is not available. The reduced form system of differential equations is sufficient. The algorithm can even cope with situations where no explicit solution for the steady state values exist.
How to use Relaxation in MATLAB
In MATLAB open Desktop - mark Command Window, Current Directory, Workspace, Toolbar, Current Directory Toolbar, and Titles.
Notice that the number of mesh points may be important for the properties of the numerical procedure. In Relaxsetting.m increase the number of mesh points if the convergence towards steady state seems awkward. This might help.
Last updated March 9, 2012