The Blanchard-Kahn Method of Solving Dsge Models - A Case of the Basic New Keynesian Model - Sobczak, Karolina (Studia Oeconomica Posnaniensia, 2015)
In the opinion of many economists, DSGE (dynamic stochastic general equilibrium) models can be viewed as a leading stream of modern macroeconomic theory [Galí 2008; Baranowski et al., 2013]. However, it is difficult to find any works which introduce DSGE methodology, especially for readers who are not familiar with the issue. In the Polish literature there are no introductory contributions. Therefore, we would like to present an overview of the fundamentals of DSGE models to fill this gap. To this end we use the basic New Keynesian model, which assumes product differentiation, monopolistic competition and staggered price setting [Calvo 1983]. Solving the equations of the DSGE model system is achieved by means of numerical methods. One of the first techniques proposed for solving linear rational expectations models originates from Blanchard and Kahn [Blanchard, Kahn, 1980]. The method uses the log-linear approximation of optimal conditions for the initial optimization problem underlying the model [Sims 2002]. It is based on matrix calculus and determines the properties of the eigenvalues of the system matrices. The problem of the eigenvalues translates into the problem of selecting appropriate values for the structural parameters of the model or their combinations. This method makes it possible to determine if there exists a locally unique stable solution to the system.