3. Linearization and the Jordan Decomposition

Readings:

For the Blanchard-Kahn (Jordan) decomposition:

(1) Blanchard, O., and C. M. Kahn. (1980). The solution of linear difference models under rational expectations. Econometrica 48(5), 1305-1311.

• This is the first paper that explicitly shows how a DSGE model, without a closed form solution, can be solved and simulated.

(2) Ellison, Martin (2009). "Real Business Cycle Theory", mimeo, University of Oxford.

• Several lecture notes by Martin Ellison can be found here. Ellison has a simple but ingenious way of overcoming the problem of singularity in the state space representation.

For general coverage:

(6) DeJong, D. N., & Dave, C. (2011). Structural Macroeconometrics, 2nd Edition, Princeton University Press.

• See chapter 4 (Linear Solution Techniques) where Klein's and Sims approaches are discussed, besides also the Uhlig method (1999) of undetermined coefficients.

(7) Caraiani, P. (2018). Introduction to Quantitative Macroeconomics Using Julia: From Basic to State-of-the-Art Computational Techniques. Academic Press.

• See chapter 3 (Solving and Simulating DSGE Models): besides having a brief discussion of the various linearized methods to solve DSGEM, it provides also Julia code for various cases. Note that the Julia code in the book is for Julia 0.6, and has to be adapted to Julia 1.5 in order to run.

(8) McCandless, G. (2008). The ABCs of RBCs. Harvard University Press.

• This book offers an excellent source of material related to the Real Business Cycle literature, and there is access to many Matlab scripts for replication.