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

slides

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:

  1. Mortensen-Pissarides model with aggregate fluctuations Homework

  2. RBC on Dynare Homework

  3. Value function iteration Homework


Other Resources: