Uses of Simulation and High Performance Computing in Econometrics

Michael Creel

UAB

Outline

Disclaimer

    This presentation is heavily biased toward my own work. I'm only attempting to give examples of things that work pretty well. I'm not attempting to give a broad picture of all the possibilities.

What is econometrics?

  • An economic model is a mathematical representation of how economic agents behave.
  • Econometrics is the application of statistical methods to estimate the parameters of economic models.
  • Economic data provides information, which is used to choose parameters to make the model resemble economic reality.
  • Wikipedia entry
  • my notes

Example of econometric model

Uses of simulation in econometrics

  • Monte Carlo
  • Bootstrapping
  • Solving a model: PEA
  • Simulation-based estimation

Monte Carlo

  • Econometric theory usually gives analytic results for behavior of estimators as the sample size goes to infinity (asymptotic theory). This may be a poor approximation to behavior in finite samples.
  • Wikipedia entry: notice the bit about simulating pi
  • In econometrics, typically, an estimation method is proposed, and Monte Carlo is used to evaluate how well it works.
  • go to PK cluster, and look over mc_example1

Bootstrapping

  • Wikipedia entry
  • Most analytical results for the behavior of econometric estimators are based on asymptotics. These results may not be reliable in finite samples.
  • Bootstrapping is a means of learning about finite-sample performance by resampling.

Bootstrapping

  • The basic idea is to compute a statistic using artificial samples, and to then use the empirical distribution of replications of the statistic
  • Resampling may be done using a number of techniques:
    • resample from data (single obsns or blocks).
    • resample from residuals after fitting model
    • etc...

Bootstrapping

    go to PK cluster, and look over bootstrap_example1

Solving a model: PEA

  • Sometimes, simulation must be used simply to solve a model. Solving the model is required before data can be simulated from the model.
  • This is not always easy to do.

Solving a model: PEA

  • For example, an agent's beliefs about future events can influence current decisions.
  • If beliefs are rational, they should be correct, on average. Such beliefs are known as "rational expectations".
  • The functional form of rational expectations is in general not known when the model is nonlinear. Without knowing the form of expectations, the model can't be solved.

Solving a model: PEA

  • Simulation methods can be used to fit a model of expectations to data generated by the model. When the data generated by the model, conditional on expectations, is consistent with the model of expectations, a solution has been found.
  • go to PK cluster, and look over pea_example

Simulation-based estimation

Simulation-based estimation

Simulation-based estimation

Simulation-based estimation

    go to PK cluster, and look over SNM

How well does this work?

The "ParallelKnoppix" cluster

  • Running ParallelKnoppix
  • 2 servers, each has 2 Xeon 3.6 GHz CPUs and 8GB RAM
  • Donated by Intel Software for development of ParallelKnoppix - thanks!

PelicanHPC

  • PelicanHPC is the successor to PK - its foundation is Debian Live, so much easier to maintain and customize
  • Pelican homepage
  • switch to VMware to show PelicanHPC
[any material that should appear in print but not on the slide]