# Basic Monte Carlo Simulation for Beginning Econometrics

This material is replicated on a number of sites
as part of the
SERC Pedagogic Service Project

#### Summary

Summary: Beginning econometrics students often have an uneven preparation in statistics. Simulation can help with both an understanding of the analytically derived means and variances of regression estimators and the intuition of a sampling distribution. The instructional problem, however, is that many simulations are either black boxes to students or written in a programming language that is not easily understood by beginning students. The Stata simulate command opens up the use of very basic programs using Stata commands students use at the Stata command line.

## Learning Goals

The learning goal of the simulation is to give students a clearer understanding of the behavior of OLS estimators.

## Context for Use

The simulation can be used in a classroom by an instructor. A microcomputer and projector are necessary. Students should have previously used Stata for estimating simple regressions and calculated some scalar r() values before seeing the simulation.

## Description and Teaching Materials

The simulation uses the following files:

reg_simple.do ( 257bytes Mar19 10)

sample_size_9.dta ( 351bytes Mar19 10)

sample_size_16.dta ( 379bytes Mar19 10)

sample_size_25.dta ( 415bytes Mar19 10)

sample_size_100.dta ( 715bytes Mar19 10)

The instructor loads the data file. The program is loaded using the do command. The program lists in the Stata results window, and the instructor can discuss what each line is doing and why. It is helpful to run the program and discuss the results for one sample. The simulate command is then used to generate 10000 samples and create a data file of the slopes and variances of the estimators. Students use the summarize command and histograms to evaluate the results. The simulate command is

simulate r(seb1) r(b1) r(seb2) r(b2), seed(10101) reps(10000) nodots: reg_simple.

reg_simple.do ( 257bytes Mar19 10)

sample_size_9.dta ( 351bytes Mar19 10)

sample_size_16.dta ( 379bytes Mar19 10)

sample_size_25.dta ( 415bytes Mar19 10)

sample_size_100.dta ( 715bytes Mar19 10)

The instructor loads the data file. The program is loaded using the do command. The program lists in the Stata results window, and the instructor can discuss what each line is doing and why. It is helpful to run the program and discuss the results for one sample. The simulate command is then used to generate 10000 samples and create a data file of the slopes and variances of the estimators. Students use the summarize command and histograms to evaluate the results. The simulate command is

simulate r(seb1) r(b1) r(seb2) r(b2), seed(10101) reps(10000) nodots: reg_simple.

**TIME REQUIREMENT:**

Instructor preparation: 30 minutes if the instructor is using Stata

Both class preparation and class simulation will take one 50 minute class period.Instructor preparation: 30 minutes if the instructor is using Stata

Both class preparation and class simulation will take one 50 minute class period.

## Teaching Notes and Tips

The simple regression program can be expanded over the semester to simulate many econometric issues.

## Assessment

If students have access to a microcomputer lab with Stata, the various data sets of different sizes provide a good source for a homework problem to test if the behavior of the estimators in different sizes has been understood.

In addition, all traditional assessment tools can be used. For more information about assessment, see the SERC assessment module.

In addition, all traditional assessment tools can be used. For more information about assessment, see the SERC assessment module.

## References and Resources

The simulation should be clearly tied to the econometrics text students are using in the course.