Summary Comparison of OLS, HC1, HC2, and HC3 Confidence Intervals for the Depression Model - Afifi & Clark Data

 
Width of HC1, HC2 and HC3 95% CI as Percentage of OLS CI
Variable OLS bk OLS LB OLS UB OLS WID HC1 % HC2 % HC3 %
Age -0.0809 -0.1467 -0.0150 0.1317 99.8 99.9 101.6
Female 2.4754 0.3253 4.6254 4.3001 89.9 90.0 91.6
L10inc -5.8429 -9.4403 -2.2454 7.1949 108.8 109.6 112.2
Educatn -0.7668 -1.6262 0.0926 1.7188 103.8 104.1 106.1
Cath 0.9409 -1.8930 3.7748 5.6678 89.6 89.7 91.3
Jewi 4.9555 1.1819 8.7290 7.5471 87.3 88.6 91.5
None 3.5449 0.7797 6.3102 5.5305 110.5 110.7 112.6
Cons 19.7763 13.7022 25.8503 12.1482 106.5 107.3 109.9

Column Headings

OLS bk - OLS coefficient estimate
OLS LB - Lower bound of OLS 95% confidence interval
OLS UB - Upper bound of OLS 95% confidence interval
OLS WID - Width of OLS 95% confidence interval
HC1 % - Width of HC1 95% confidence interval as percentage of OLS width
HC2 % - Width of HC2 95% confidence interval as percentage of OLS width
HC3 % - Width of HC3 95% confidence interval as percentage of OLS width
Despite the significance of the Cook-Weisberg aka Breusch-Pagan test, indicating significant heteroscedasticity, the increase in the width of the confidence interval implied by the Huber-White robust standard errors (HC1) is modest, with a maximum increase of 10.5% for the coefficient of None relative to the confidence interval based on OLS standard errors; for some variables, the robust interval is actually smaller than the OLS interval, with the maximum reduction occuring in the interval for the coefficient of Jewi (12.7%).
Use of the alternative robust estimates HC2 and HC3 entails a systematic, but very slight, increase in the width of the corresponding confidence intervals; this trend affects the coefficients of all the independent variables.

Last modified 15 Apr 2002