源码、讲义1.1.1一阶求解逻辑

1、1.1.1 DSGE模型一阶求解方法简介Solution logic IPreparationFOC, First order conditions ；#endogenous variables = #equations；Calibration and Estimation of ParametersEstimation: MLE,GMM,SMM,Bayesian Method;Calibration: long run moments from data;Soultion：Find the Policy function1st: log-linearization and 1st order

2、 Taylor approximation; Details later;2nd: 2nd order Taylor approximation around steady states; Results analysis: various moments and IRFSolution logic IIClassical 1st order solution methods： B&K(1980) ： Blanchard, O. J. and C. M. Kahn (1980). The Solution of Linear Difference Models under Rational E

3、xpectations. Econometrica 48(5): pp. 1305-1311.Schur Method(Klein,2000) “Using the generalized Schur form to solve a multivariate linear rational expectations model.” JEDC,24(10): 1405-1423.Uhlig(1999)：A toolkit for analyzing nonlinear dynamic stochastic models easily.Reference： McCandless, G.，2008，

4、The ABCs of RBCs: An Introduction to Dynamic Macroeconomic Models，Harvard University PressIf B is invertibleIf B is not invertibleUsing Blanchard-Kahns MethodUsing Generalized Schur Method,i.e. QZ positionMethod 1: BK & Schur MethodMethod 1: BK & Schur Methodx_t: predetermined variables which were d

5、etermined in last period;y_t: non-predetermined variables which are determined at current period;The difference between predetermined and non-predetermined is that the values of the former at time t do not depend on the values of time t shocks, while the latter does.Method 2: Uhlig MethodProblem:Sol

6、ution:x_t is the endogenous state variables;y_t is the endogenous control variables,sometime called jump variables;Note:SummaryBK(1980) and Schur Method from Klein(2000)：smaller application scope; simple and easy to understand, need to be very familiar with program tools, like Matlab;Uhlig(1999)：larger application scope; Coefficients of Undetermined Methods; A standby package could be used which was provided by the author.By Dynare, find a solution is much easier