Papers

There are two versions of the paper on the small sample properties on heteroscedasticity consistent covariance matrix tests.

Longer Version: This draft contains details on the simulations and tables with many results:

• Long, J.S and L.H. Ervin, 1998, "Correcting for Heteroscedasticity with Heteroscedasticity Consistent Standard Errors in the Linear Regression Model: Small Sample Considerations." Working Paper.
• Click to view; right-click and "Save Link As" to save to disk.

Shorter Version: This draft removes many of the technical details:

• Long, J.S and L.H. Ervin, 2000, "Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model." Forthcoming, The American Statistician 54:217-224.
• Click to view; right-click and "Save Link As" to save to disk.

This paper is a follow-up to an earlier paper:

• Long, J.S. and Pravin Trivedi, 1992, "Some Specification Tests for the Linear Regression Model." Sociological Methods and Research 21:161-204. Reprinted in Bollen, Kenneth A. and J.S. Long (editors), 1993, Testing Structural Equation Models. Beverly Hills:Sage University Press.

Software Used in Monte Carlo Simulations

The simulations were run using Stata 6.0. There are three zip files which contain the key files used for the simulations:

• hcado.zip: contains the ado files used by Stata to run the simulations. These files must be put on the adopath so that Stata can load them as needed.
• hcpop.zip: contains programs used to generate the population data sets
• hcdo.zip: contains the Stata programs (.do files) and output logs (.log files) used to run the simulations and summarize the results.

The contents of these files are now described.

hcado.zip: ado files for generating x's and error structures, running simulations, and evaluating results. These ado files generate the x variables:

• hcbase.ado-population used for all populations except several experiments with different data structures.
• hcbased2.ado-population where x2 is a dummy variable.
• hcbaseq.ado-population where all variables have the same variance
• hcbasebi.ado-population where one of the x’s is bimodal.

These files generate the error structures. R2=.4 unless noted otherwise:

• hc123c.ado-het on x1,x2 & x3, chi-square errors.
• hc123n.ado-het on x1,x2 & x3, normal errors.
• hc1c4.ado-het on x1, chi-square errors.
• hc1n4.ado-het on x1, normal errors.
• hc2dbg.ado-het on binary x2 with large amount of het.
• hc2dsm.ado-het on binary x2 with small amount of het.
• hc34c.ado-het on x3 & x4, chi-square errors.
• hc34cb.ado-het on x3 & x4, chi-square errors with bimodal x.
• hc34n.ado-het on x3 & x4, normal errors.
• hc3c3.ado-het on x3, chi-square errors, R2=.26.
• hc3c4.ado-het on x3, chi-square errors.
• hc3cb.ado-het on x3, chi-square errors with bimodal x.
• hc3eqc.ado-het on x3, chi-square errors, equal variances for x’s.
• hc3n2.ado-het on x3, normal errors, R2=.2.
• hc3n4.ado-het on x3, normal errors.
• hc3n7.ado-het on x3, normal errors, R2=.7.
• hc3na.ado-het on x3, normal errors, R2 =.2, revised method to generate errors.
• hc3nn.ado-het on x3, normal errors, R2 =.4, revised method to generate errors.
• hc3nz.ado-het on x3, normal errors, R2 =.8, revised method to generate errors.
• hcc4.ado-chi-squared errors.
• hccb.ado-chi-squared errors with bimodal x.
• hcn2.ado-normal errors, R2=.2.
• hcn4.ado-normal errors, R2=.4.
• hcn7.ado-normal errors, R2=.7.
• hcneq4.ado-normal errors, with standardized variance for x1,x2,x3,x4.
• hct4.ado-t 5df errors, R2=.4.
• hchet.ado-computes ratio of standard deviations of residuals in 5-15 percentile and 85-95 percentile.

These ado files control the simulations and summarize results:

• hcmonte.ado-control program for simulations.
• hcscrn.ado-simulations with screening tests.
• hctest.ado-compute heteroscedasticity tests.
• hcresult.ado-create file merging results
• hcsum.ado,hcsum2.ado,hcsum3.ado,hcsum4.ado-summarize results in various ways.
• hcplt.ado-plot results.
• hcpltall.ado-plot all results.
• hcpltht.ado-plot results of het tests.
• hcpltim.ado-plot IM test.
• hcpltpw.ado-plot power.
• hcpltpw2.ado-plot power with screening.
• hcpltsc.ado-plot results with screening.
• hcpltsz.ado-plot size.
• hcpltsz2.ado-plot size with screening.
• hcpower.ado-compute power curves.

hcpop.zip: do files for creating the population files.

• jslhc1.do-generate population data used for standard simulations.
• jslhc2.do-generate population data with bimodal x.
• jslhc3.do-generate population data with equal variances for x’s.
• jslhc4.do-generate population data with binary x2.

hcdo.zip: do files for running the simulations and summarizing the results. These do files have the commands for each set of simulations. In general there will be 4 do files for each data structure:

• : ...sim: run simulations
• : ...sum: create a summary file of all results
• : ...res: list key results
• : ...plot: plot key results

The do files for different data structures are:

• 123c_.do-het on x1,x2 & x3, chi-square errors.
• 123n_.do-het on x1,x2 & x3, normal errors.
• 1c4_.do-het on x1, chi-square errors.
• 1n4_.do-het on x1, normal errors.
• 2dbg_.do-het on binary x2 with large amount of het.
• 2dsm_.do-het on binary x2 with small amount of het.
• 34c_.do-het on x3 & x4, chi-square errors.
• 34n_.do-het on x3 & x4, normal errors.
• 3c4_.do het on x3, chi-square errors.
• 3eqc_.do-het on x3, chi-square errors, equal variances for x’s.
• 3n4_.do-het on x3, normal errors.
• 3na_.do-het on x3, normal errors, R2 =.2, revised method to generate errors.
• 3nn_.do-het on x3, normal errors, R2 =.4, revised method to generate errors.
• 3nz_.do-het on x3, normal errors, R2 =.8, revised method to generate errors.
• c4_.do-chi-squared errors.
• n4_.do-normal errors.
• t4_.do-t 5df errors.