EC742/792
Readings for linear
rational expectations models lectures
There is an immense literature on solving linear rational expectations models. In this pair of lectures, I will give an overview of the theory and the computational approaches in the literature. Although I am not a computational expert, I have worked in this area and will use some of my own papers as these allow for consistency of style etc.
There is also a large variety of computer programs that are available for this purpose. Every author cited below has made computational programs available, as have many others. The best general purpose website is DYNARE (see link below), but I will provide an introduction to programs that I have written with Mark Watson. Part of the reason for this is that these programs have proved to be reliable in extremely large systems, while others have not always proved so. And I understand the computational issues involved in the KWRE (King-Watson Rational Expectations) approach.
On Tuesday, I will discuss the theory of LRE using the * references from the Theory section below and the following slides PPT
On Thursday, I will discuss solving some RE models using the KWRE package based on the algorithm described in KW2002 (under System reduction algorithms below) and, tangentially, some other approaches. I will post some presentation materials later, that will parallel the solution code ZIP and part of a user's manual PDF.
Since this class involves
international finance/open economy macro students, there are two observations.
First, the development of singular model methodology was stimulated in part by
difficulties in applying straight forward reduction methods from early RBC
theory (see the discussion in KW2002). Second, international models will be one
application that we will consider, using some documents and programs written by
Anthony Landry for past generations of EC792 students. An overview of the
two models that Anthony constructs are is contained in "Solving international
real business cycle models" PDF.
His programs for the two models ZIP worked when I ran them:
I did have to edit the "setpath.m" file to
reflect the location of my programs, but it was smooth sailing after that.
Background
Any discussion of RE models has to start with two articles. If you have not read them, you should do so.
John F. Muth, “Rational Expectations and the
Theory of Price Movements,”
I usually start by discussing these papers first. Accordingly, the first 20 slides of this PDF presentation are good background to both theory and computational parts of the lectures, but will not be explicitly covered.
Theory
* Blanchard, O.J. and C.M. Kahn, "The Solution of Linear
Difference Models Under Rational Expectations," Econometrica 1980. PDF
Watson, M.W., "Recursive solution
methods for dynamic linear rational expectations models", Journal of Econometrics, Volume 41, Issue 1, May
1989, Pages 65-89 PDF
* King, R.
G. and M.W. Watson, "The Solution of Singular Linear Difference Systems Under Rational Expectations," International Economic Review, 39
(4), November 1998. PDF
Binder,
Michael & Pesaran, M Hashem,
1997. "Multivariate Linear
Rational Expectations Models: Characterization of the Nature of the Solutions
and Their Fully Recursive Computation," Econometric Theory, Cambridge University Press, vol. 13(6), pages
877-88, December.
System
reduction algorithms
* King, R.G.
and M.W. Watson, System Reduction and Model Solution Algorithms for Singular
Linear Rational Expectations Models, in Computational
Economics, 20 (1-2), October 2002, 57-86. PDF
* Klein, P.,
"Using the generalized Schur form to solve a multivariate linear rational
expectations model," Journal
of Economic Dynamics and Control, Elsevier, vol. 24(10), September 2002,
1405-1423. [programs available in GAUSS and MATLAB, via the internet] PDF
Sims, C.A., “Solving
Linear Rational Expectations Models", Journal of Computational
Economics,20(1-2),
2001, p.1-20. [programs on his Princeton website].
An alternative
algebraic approach
*Gary Anderson and
George Moore. "A Linear Algebraic Procedure for Solving Linear Perfect
Foresight Models." Economics Letters, 17, 1985. PDF
Websites:
AIM (the Anderson-Moore approach developed at the FRB)
http://www.federalreserve.gov/Pubs/oss/oss4/aimindex.html
DYNARE (more than just linear models, also
perturbation methods and estimation algorithms)
http://www.cepremap.cnrs.fr/dynare/
UHLIG TOOLKIT
Harald Uhlig has produced a " "A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily"
http://www2.wiwi.hu-berlin.de/institute/wpol/html/toolkit.htm