DSGE Models: Solution & Estimation Techniques

Instructor:

Possible topics

• Function approximation and numerical integration
• Simple popular solution techniques
• General discussion of solution techniques
  • Perturbation methods
  • Projection methods
• Solving and simulating models with heterogeneous agents
• Accuracy tests
• Kalman filter
• Bayesian estimation of DSGE models
• Models with heterogeneous agents

Dates for 2011 LSE course

Outline for 2011 LSE course

• Slides:
  • Introduction to numerical methods
  • Dynare & Business Cycle Properties
• programs:
  • In part #2 of Dynare Programs you can find a program "dynareloop.m" that shows you how to loop over parameter values. (It is in the zip file at the end of part 2).
  • In homotophy you can find a Matlab file that shows you how to use the homotophy idea to find the steady state with Dynare
• Assignment:
  • In Monday assignment you are asked to loop over different parameter values to see whether a simple matching model can overcome the Shimer puzzle (i.e. that employment is not volatile enough).
  • In Monday assignment answer You can find example programs for Monday's assignment.

• Slides:
  • Function approximation .
  • Numerical integration .
  • The basics of projection methods
  • Accuracy tests
• Notes:
  • Function approximation .
  • Numerical integration .
  • Parameterized Expectations "Stochastic" and "non-stochastic (or projections) PEA.
• programs:
  • In projectionsimple you can find programs to solve the standard growth model with projection methods.
  • In part #2 of Dynare Programs you can find a program "accuracy.m" that shows you how to calculate Euler equation errors and how to calculate the DHM statistic. The file dyneuler.m shows how to calculate dynamic Euler equation errors.
• Assignment:
  • In Tuesday assignment you are asked to solve a simple asset pricing model with projection methods and show that the risk premium is time varying
  • In Tuesday assignment answer You can find example programs for Tuesday's assignment.

• Slides:
  • Kalman Filter & Bayesian Estimation .
• Assignment:
  • In Thursday assignment you are asked to extract the long-term productivity component.
  • In Thursday assignment answer You can find example programs for Thursday's assignment.

• Slides:
  • parts of "theory of models with heterogeneous agents" and "different proceudres to simulate models with heterogeneous agents".
• Assignment:
  • In Monday assignment you are asked to solve the Aiyagari model and show that you have to use an equilibrium model to understand the effect of uncertainty on aggregate savings
  • In Monday assignment answer You can find example programs for Monday's assignment.

• Slides:
  • Krusell-Smith algorithm
  • Explicit Aggregation algorithm (XPA)
• Notes:
  • In Handbook chapter you can find a survey paper on algorithms to solve and simulate models with aggregate risk and heterogeneous agents.
• Assignment:
  • In Tuesday assignment you are asked to solve a model with idiosyncratic and aggregate risk and understand the differences between a model with a representative agent and a model with many different types of agents.
  • In Tuesday assignment answer You can find example programs for Tuesday's assignment.

• Slides:
  • Solving models when agents have heterogeneous beliefs
• Assignment:
  • In Assignment you are asked to solve a model in which agents have different beliefs. In particular, there are rational agents and irrlational agents, but in contrast to common practice in the literature the rational agents here are truly rational. You'll see that it is actually not that difficult to be rational here.
  • In assignment answer You can find example programs for this assignment.

More Notes & Slides

More Assignments

• In Dynare and matching you find a simple exercise to investigate the importance of the wage rule in a labor martket matching model
• The old homework #1 .
• The old homework #2 .
• The old homework #3 .
• Stuff you can use for the assignments:
  • 5 Legendre nodes
  • 11 Legendre nodes
  • 15 Legendre nodes
  • 101 Legendre nodes
  • Matlab function to calculate Chebyshev nodes
  • Matlab function to calculate Hermite nodes and weights
  • Matlab function to calculate Legendre nodes and weights
  • Matlab function to HP filter the data

Links to matlab tutorials

• simple Matlab program to get started
• simple Matlab program that calls Dynare
• On line Matlab tutorial
• Very short Matlab primer (pdf file)
• Matlab primer
• Matlab primer

Links to useful code

• Code to accompany the classic textbook on numerical methods by Ken Judd can be found here
• A useful Matlab toolbox with for many basic problems (integration, approximation) and examples for bigger problems that accompanies the book by Miranda & Fackler can be found here
• Harald Uhlig's toolbox to solve DSGE models using linearization techniques can be found here
• The program to solve and estimate DSGE models using perturbation methods can be found here
• My own website with algorithms to solve a variety of models can be found through the software link on my home page

Links to useful reading material

• Teaching notes by Jesus Fernandez-Villaverde and Juan Rubio-Ramirez on many numerical topics such as solution methods, Bayesian estimation and filtering can be found here

Textbooks on numerical methods

• Ken Judd: Numerical methods in Economics
• Mario Miranda and Paul Fackler: Applied Computational Economics and Finance
• Alfonso Novales, Esther Fernandez, and Jesus Ruiz: Economic Growth - Theory and numerical solution methods
• Burkhard Heer and Alfred Maussner: Dynamic General Equilibrium Modeling

• London School of Economics
• Universitat Pompeu Fabra
• CREST-ENSAE
• Mannheim University
• European Central bank
• Bank of Portugal
• Stockholm School of Economics
• University of Rochester
• London Business School
• Tinbergen Institute
• University of California at San Diego