Numerical Methods (2012)
Course plan:
Root finding and how to solve the Mortensen-Pissarides model and various disputes within the discipline
Bisection, Brent's method
Quasi-Newton (and what's quasi- about it?)
Nelder & Mead's simplex and efficient derivative-free least-squares
Representing AR process as Markov chains
Local methods for dynamic models. Solving the RBC model with bells and whistles
The Method of undetermined coefficients
What is Dynare and what can I do with it?
Using Dynare to estimate models
Approximation error! How to tell when close enough is close enough?
Optimal change of variables
Value function iteration. Solve the RBC again with fewer bells and whistles
What is the curse of dimensionality, why do I run into it and why did it crush a generation?
Solving the curse of dimensionality: Linear Programming and Approximate Linear Programming
Endogenous grid method: sometimes it's better to take a step backwards, then turn around and take two more steps backwards
Some econometrics stuff
What are the aggregate data sources and what are the micro data sources
Stata! With application to Juhn, Murphy, Pierce (1993)
Estimation by simulation
What's hot in the IO world?
Parallel Computing
MPI and OpenMP. When does the right hand know what the left hand is doing?
Graphics cards: how robbing a Best Buy can expedite your PhD (CUDA).
Global optimization: efficient ways to find a needle in a haystack... but with a computer
Lecture Slides:
Some introduction to the lingo
programming essentials
Fortran and Matlab templates
Root finding
Solving equilibrium models of unemployment with search and matching
slides
More optimization, constrained optimization, and derivative-free methods
Discretizing AR(1) processes
Local, perturbation methods
Undetermined Coefficients
Neoclassical growth models with lots of states
slides
Accuracy of your solutions
Some informal, ad hoc thoughts
Den Haan Marcet statistic and Euler Equation Errors
Improving accuracy by an optimal change of variables
slides
Installing Dynare and using it for basic models
Dynare for easy calibration
a simple calibarion loop and David's modification of JFV's RBC code
Indirect Inference, Simulation Methods for Estimation
Matching models to data
slides
Value function iteration by discretization
Functional approximation and Chebyshev polynomials
slides
Endogenous grid points as a modification of policy function iteration
Generalized endogenous grid method to include additional choices or states
slides
Learning Stata by doing
Juhn Murphy Pierce (1993) code and data or trainer set
Parallel computation
Why is there overhead cost and how does it differ by the technology?
How do I convert my code?
Genetic Algorithm for Optimization!
slides and MPI code and GA on GPU CUDA code
Homework:
Mortensen-Pissarides model with aggregate fluctuations Homework
RBC on Dynare Homework
Value function iteration Homework
Other Resources:
Outside Links for Fortran
Free compiler and IDE Silver Frost
Java-based IDE Photran plugin for Eclipse
Programs including splines, optimization and integration routines: John Burkardt's Fortran programs
Help and example programs Fortran Wiki
Lots of f90 routines, including translated TOMS algorithms Alan Miller's Fortran Software
Fortran implementation of GSL FGSL
Lots of links to libraries Numerical Methods for Fortran Programmers
Outside Links for C
Microsoft's C++ Visual C++ Express
Java-based IDE Eclipse CDT
The mother of scientific libraries GSL
A bunch of software ALGLIB
Free constrained optimization IPOPT
Bayesian Filtering Bayes ++
Text Books
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