Monte Carlo Studies

Monte Carlo methods have been used for centuries, but only in the past several decades has the technique gained the status of a full-fledged numerical method capable of addressing the most complex applications. The Monte Carlo method may be thought of as similar to a political poll, where a carefully selected statistical sample is used to predict the behavior or characteristics of a large group.

Enrico Fermi in the 1930's used Monte Carlo in the calculation of neutron diffusion, and later designed the Fermiac, a Monte Carlo mechanical device used in the calculation of criticality (The point at which a nuclear reaction is self-sustaining) in nuclear reactors.

In the 1940's, a formal foundation for the Monte Carlo method was developed by von Neumann, who established the mathematical basis for probability density functions (PDFs), inverse cumulative distribution functions (CDFs), and pseudorandom number generators. The work was done in collaboration with Stanislaw Ulam, who realized the importance of the digital computer in the implementation of the approach.

Before digital computers were available to the labs, "computer" was a job title. Parallel computing was done by rows and columns of mathematicians. The applications, which arose mostly from the Manhattan Project, included design of shielding for reactors.

Uses of Monte Carlo methods have been many and varied since that time. In the late 1950's and 1960's, the method was tested in a variety of engineering fields. At that time, even simple problems were compute-bound. Many complex problems remained intractable through the seventies. With the advent of high-speed supercomputers, the field has received increased attention, particularly with parallel algorithms which have much higher execution rates.

In econometrics, the general idea behind a Monte Carlo study is to (1) model the data-generating process, (2) generate several sets of artificial data, (3) employ these data and an estimator to create several estimates, and (4) use these estimates to gauge the sampling distribution properties of that estimator.

A useful reference is the paper:

Design and analysis of Monte Carlo experiments
Written by Kleijnen, J.P.C. (Tilburg University, Center for Economic Research)