The following model investigates the relationship between annual wage in logarithm form (LWAGE) and years of work experience (EXPER), years of schooling (EDUC), whether an individual is a union member (UNION) using data for 1,260 individuals. UNION is a dummy variable, with 0 meaning that the individual is not a union member and 1 denoting otherwise. Table Six provides the results from a simple linear regression model, while Tables Seven and Eight present results from diagnostic testing of this model. Table Nine presents further analysis.
Table Six
Dependent Variable: LWAGE
Method: Least Squares
Sample: 1,260
Included observations: 1,260
Variable Std. Error t-Statistic Prob.
0.277500 0.081437 3.407558 0.0007
EXPER 0.017670 0.001253 14.10546 0.0000
EDUC 0.079169 0.005714 13.85586 0.0000
UNION 0.238594 0.033222 7.181775 0.0000
Table Seven
Heteroskedasticity Test: Breusch-Pagan-Godfrey
Null hypothesis: Homoskedasticity
F-statistic: 4.279287
Prob. F(3,1256): 0.0051
Obs*R-squared: 0.0052
Prob. Chi-Square(3): 0.0001
Scaled explained SS: 20.38491
Prob. Chi-Square(3): 0.0002
Table Eight
Heteroskedasticity Test: White
Null hypothesis: Homoskedasticity
F-statistic: 2.404967
Prob. F(8,1251): 0.0141
Obs*R-squared: 19.08464
Prob. Chi-Square(8): 0.0144
Scaled explained SS: 30.51657
Prob. Chi-Square(8): 0.0002
Further analysis generated the findings reported in Table Nine.
Table Nine
Dependent Variable: LWAGE
Method: Least Squares
Sample: 1,260
Included observations: 1,260
Huber-White-Hinkley (HC1) het errors and covariance
Variable C EXPER EDUC UNION
Coefficient Std. Error t-Statistic Prob.
0.277500 0.083471 3.324504 0.0009
0.017670 0.001251 14.12661 0.0000
0.079169 0.005872 13.48330 0.0000
0.238594 0.030783 7.750763 0.0000
(e) Explain what is meant by heteroskedasticity and discuss why this problem needs to be addressed if detected in a model.
(b) Explain in detail the approach of Weighted Least Squares used by applied economists to address heteroskedasticity in empirical work.
(c) Provide a detailed and comparative account of the two tests of heteroskedasticity (the Breusch-Pagan test and the White test). According to the outputs presented above in Tables Seven and Eight, what are your conclusions on the two heteroskedasticity detecting tests? By comparing Tables Six and Nine, discuss the impacts on the estimation results if heteroskedasticity is present.