Numerical Methods
Syllabus and a running outline:
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?)
Derivative-free methods
Representing AR process as Markov chains
A survey of inequality data in the US
Burdett-Mortensen (1998) to understand residual inequality
Abowd-Karmarz-Margolis & Postel-Vinay Robin (2002) to understand residual inequality
Local, perturbation methods and how to solve mostly-smooth neoclassical growth models
Order-n local approximation
Perturbation around a non-stochastic steady state
Computing the approximation by undetermined coefficients
Approximating derivatives by finite differences
Tests for accuracy
Ad hoc tests for accuracy
Euler Equation errors
Den Haan Marcet test statistic based on simulations
Improving the accuracy by non-linear change of variables
Estimating models by using models
What is the "goal" of calibration
How to treat the data
Why simulate
Which moments to match
Making outcomes continuous in parameters
Global methods for solving models with heterogenity
Value function iteration and solving on the full state space
Functional approximation
Integration
Endogenous grid points and generalized endogenous grid points
Parameterized expectations and simulations to solve the model
Some thoughts on microdata sources and how to use them
Lecture Slides and Resources:
Some introduction to the lingo
programming essentials slides
fortran and matlab templates (code)
c template (code)
aruoba, fernandez-villaverde, rubio-ramierez
ars techinca: why are some languages faster?
Root finding and markov chain approximation
solving equilibrium models of unemployment with search and matching
root-finding and optimization (+ MP) slides
multi-dimension and constrained optimization slides
rouwenhorst method, f90 (code)
rouwenhorst method, c (code)
root finding (code)
Perturbation methods and numerical derivatives
solving mostly smooth growth models
perturbation methods, undetermined coefficients slides
accuracy tests with assid on changes of variables slides
CKM slides
fernandez-villaverde, rubio-ramirez
Estimating models using models
taking bizarre models to bizarre data
simulation-based estimation slides
cooley and prescott
gourieroux, monfort and renault
Global methods
solving models everywhere
value function iteration slides
endogenous grids method + parameterized expectations slides
fernandez-villaverde and barillas
hatchondo, martinez and sapriza
Homework:
mortensen-pissarides model with aggregate fluctuations ( hw 1 ) due 2/11
business-cycle model with many shocks ( hw 2 ) due 3/1
estimating less-than-obvious parameters ( hw 3 ) due 3/24
value function iteration ( hw 4 ) ??/??
Final project due May 11
Papers and Assignments:
hornstein, krusell, violante (Masahiro) 2/9
mortensen, nagypal (Alejandro) 2/9
cooley, prescott (Lingxio) 2/25
kumhof, benes (David) 2/25
guvenen, smith (Ying-Ting) 3/3
chatterjee, eyigungor (Juan) 3/21
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 ++
Awesome people who teach even better courses