. A model for the hours worked by a sample of worker is as follows:
hoursi = β0 + β1educi + β2experi + β3wagei + ui
,
where hoursi
is the number of hours worked annually by person i, educi
is their years of
education completed, experi
is their years of experience in the labour force and wagei
is
hourly wage.
You have been provided with the following additional output from an auxiliary regression
constructed from the residuals and fitted values from the model above.
Call:
lm(formula = I(residuals^2) ~ fitted + I(fitted^2), data = gujhours)
Residuals:
Min 1Q Median 3Q Max
-2347004 -339793 -237643 56389 17170462
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.095e+05 1.198e+05 3.419 0.000663 ***
fitted -3.751e+02 2.716e+02 -1.381 0.167587
I(fitted^2) 5.523e-01 1.312e-01 4.209 2.88e-05 ***
—
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 1133000 on 750 degrees of freedom
Multiple R-squared: 0.0942,Adjusted R-squared: 0.09178
F-statistic: 39 on 2 and 750 DF, p-value: < 2.2e-16
(a) Explain what is meant by the term Heteroskedasticity in the context of the model
above.
[4 MARKS]
(b) Explain how you can test for the presence of Heteroskedasticity in the model for
hours worked using the auxiliary regression provided.
[9 MARKS]
(c) Describe how you can correct the standard errors of the model to alleviate any
(d) The following regression results for the model have been made available to you
hours \i = 277.75
(155.96)
[160.63]
+ −10.37
(12.5)
[13.32]
educi + 34.4
(3.471)
[19.47]
experi + 94.54
(9.09)
[25.6]
wagei
.
Here the usual OLS standard errors are reported in parenthesis (.) and the NeweyWest standard errors are reported in square brackets [.]. What can you say about
the impact of Heteroskedasticity regarding inferences from your model?
[5 MARKS]