Heteroskedasticity worksheet
For these exercises use mid14gss.dta, which contains the variables below:
age: respondent’s age
male: 1 if male, 0 if female
black: 1 if black, 0 if not
househ: number of people in the household
childs: number of children (both residential and non-residential)
educ: educational attainment in years of schooling
inc06: family income, in thousands of dollars
tvhours: hours per day watching tv
rel: a standardized scale of religiosity from five items (mean=0, s.d. = 1), higher values=more
religious*
conserv: a standardized scale of political conservatism (mean=0, s.d.=1), higher values=more conservative*
Predict conservatism using age, education, income, gender, race, and religiosity
1) Check for heteroskedasticity by plotting residuals against fitted values. Does it look like you have heteroskedasticity?
2) Add a smoothed regression line to the scatter plot using the lowess command. Does this change your assessment?
3) Based on a plot of residuals against each of your included covariates, do you think one variable in particular is causing heteroskedasticy?
Education looks problematic:
And maybe religiosity:
4) Can we fix the heteroskedasticity by adding a squared term for the education covariate(s)?
No
5) Test the original regression for heteroskedasticity using the Breusch-Pagan test. Do you reject or fail to reject the null hypothesis of homoscedasticity?
Reject:
. ivhettest, nr2
OLS heteroskedasticity test(s) using levels of IVs only
Ho: Disturbance is homoskedastic
White/Koenker nR2 test statistic : 52.454 Chi-sq(6) P-value = 0.0000
6) Based on the auxiliary regression used in the Breusch-Pagan tests, which variables are the most likely culprits for causing heteroskedasticity?
. reg r2 age c.educ inc06 male black rel
Source | SS df MS Number of obs = 1074
------+------F( 6, 1067) = 9.13
Model | 47.9831203 6 7.99718671 Prob > F = 0.0000
Residual | 934.472991 1067 .875794744 R-squared = 0.0488
------+------Adj R-squared = 0.0435
Total | 982.456112 1073 .915616134 Root MSE = .93584
------
r2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
age | .0016935 .0017864 0.95 0.343 -.0018119 .0051988
educ | .0484885 .0106529 4.55 0.000 .0275855 .0693916
inc06 | .0071345 .006197 1.15 0.250 -.0050252 .0192941
male | -.0012675 .0597298 -0.02 0.983 -.1184687 .1159337
black | -.313183 .085517 -3.66 0.000 -.4809836 -.1453824
rel | .0551263 .0295905 1.86 0.063 -.0029359 .1131886
_cons | .1040123 .1717598 0.61 0.545 -.233013 .4410377
------
7) Does the White test for heteroskedasticity (simple version) give the same result?
Yes
. reg r2 conhat conhat2
Source | SS df MS Number of obs = 1074
------+------F( 2, 1071) = 12.12
Model | 21.74384 2 10.87192 Prob > F = 0.0000
Residual | 960.712272 1071 .897023596 R-squared = 0.0221
------+------Adj R-squared = 0.0203
Total | 982.456112 1073 .915616134 Root MSE = .94711
------
r2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
conhat | .2647934 .0752187 3.52 0.000 .1172007 .4123861
conhat2 | -.2943126 .1325408 -2.22 0.027 -.5543816 -.0342435
_cons | .8844795 .0360335 24.55 0.000 .8137752 .9551837
------
. di e(r2)*e(N)
23.769901
. di chi2tail(2,23.77)
6.893e-06
8) Re-estimate the original regression model with standard errors robust to heteroskedasticity. What changed?
Not much
9) Assuming heteroskedasticity is related to education, estimate a weighted least squares regression. Does this change your conclusions at all?
No
10) Making no assumptions about the form of heteroskedasticity, estimate a feasible general least squares model. Again, do any of your conclusions change?
No
. estimates table ols robust wls fgls, stat(r2 rmse) b(%7.3g) se(%6.3g) t(%7.3g)
------
Variable | ols robust wls fgls
------+------
age | -.00024 -.00024 .00012 -.00059
| .0018 .0017 .0017 .0017
| -.138 -.139 .0731 -.352
educ | -.0181 -.0181 -.00143 -.0132
| .0104 .011 .0121 .01
| -1.73 -1.65 -.118 -1.32
inc06 | .0254 .0254 .024 .0223
| .0061 .0062 .0064 .0069
| 4.19 4.1 3.75 3.26
male | .145 .145 .118 .11
| .0586 .0585 .0578 .0553
| 2.48 2.48 2.05 1.99
black | -.771 -.771 -.722 -.665
| .0839 .0695 .0736 .0644
| -9.2 -11.1 -9.8 -10.3
rel | .282 .282 .28 .231
| .029 .0296 .0292 .0283
| 9.7 9.5 9.58 8.16
_cons | .124 .124 -.0999 .0878
| .168 .168 .175 .157
| .733 .733 -.569 .558
------+------
r2 | .163 .163 .158 .154
rmse | .918 .918 .898 .867
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legend: b/se/t