On approximating DSGE models by series expansions

Arbeitspapier

We show how to use a simple perturbation method to solve non-linear rational expectation models. Drawing from the applied mathematics literature we propose a method consisting of series expansions of the non-linear system around a known solution. The variables are represented in terms of their orders of approximation with respect to a perturbation parameter. The final solution, therefore, is the sum of the different orders. This approach links to formal arguments the idea that each order of approximation is solved recursively taking as given the lower order of approximation. Therefore, this method is not subject to the ambiguity concerning the order of the variables in the resulting state-space representation as, for example, has been discussed by Kim et al. (2008). Provided that the model is locally stable, the approximation technique discussed in this paper delivers stable solutions at any order of approximation.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: ECB Working Paper ; No. 1264

Classification and Topics

• Classification: Wirtschaft ; Computational Techniques; Simulation Modeling
• Subject: Non-linear difference equations ; Perturbation methods ; Series expansions ; Solving dynamic stochastic general equilibrium models ; Nichtlineare Dynamik ; Rationale Erwartung ; Dynamisches Gleichgewicht ; Iteratives Verfahren ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Lombardo, Giovanni
• Event: Veröffentlichung
• (who): European Central Bank (ECB)
• (where): Frankfurt a. M.
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/153698
• Last update: 10.03.2025, 11:43 AM CET