Glossary

Monte Carlo Simulation

A computational technique that uses repeated random sampling to approximate the distribution of a quantity that is analytically intractable. In econometrics, Monte Carlo experiments are used to study the finite-sample properties of estimators and test statistics.

Definition

Why It Matters

Many statistical problems lack closed-form solutions, and asymptotic approximations may be poor in small samples. Monte Carlo simulation allows researchers to study the behaviour of estimators and tests under controlled conditions, assess their size and power, and evaluate the consequences of assumption violations. In applied work, Monte Carlo methods underpin risk management (Value-at-Risk), portfolio simulation, and policy impact projections under uncertainty.

Example

A researcher investigating the size distortion of the ADF test in small samples runs 10,000 Monte Carlo replications. In each replication, a random walk of length T = 50 is generated, the ADF test is applied, and the proportion of rejections at the nominal 5% level is recorded. The simulation reveals an actual rejection rate of 8.3%, indicating size distortion that would not be apparent from asymptotic theory alone.

Related Terms

Software Notes

SPSS: Use Transform > Compute Variable with RV functions for basic simulations, or Python/R integration for complex designs.
R: Use replicate() or for loops with rnorm(), runif(), etc. The MonteCarlo package provides a structured framework for simulation studies.
Stata: Use simulate to run replications: simulate stat = r(stat), reps(10000): program_name. For bootstrap-based Monte Carlo, combine with bootstrap.