Evaluation of the Australian Wage Subsidy Special Youth ...

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Heteroskedasticity is a violation of this assumption. Heteroskedasticity can introduce a
form of mis-specification if the modelling assumes homoskedasticity. The worth of
allowing the heteroskedasticity to be of undefined form is that the form it takes is usually
unknown. Furthermore, as Gujurati (1988) p326 points out, due to data problems the
investigation of heteroskedasticity is often sheer speculation. The possibility of
heteroskedasticity in cross-sectional or longitudinal data, involving heterogeneous units is
very high however.
The Huber-White variance estimates can be interpreted as trading off efficient estimation
of the variance-covariance matrix for estimates that accommodate a degree of slack and
so potentially allow for the issue of minor mis-specification. The point estimates of
coefficients are unaffected. The replication results applying the Huber-White variance
estimation are shown in Column 3 of Table 7.1. The first two columns show the
Richardson (1998) results and the earlier replication estimation to better enable
comparison. The t-statistics for some variables are quite different, smaller in size,
reflecting more cautious estimates of error. The impact is not even across variables,
which suggests some variables might be more affected by heteroskedasticity than others.
The SYETP treatment variable loses statistical significance under the Huber-White
variance estimates, with the significance level falling to 14 per cent from 1 per cent. The
conventional levels of statistical significance are not now met, and the 95 per cent
confidence interval for the SYETP coefficient now ranges from –0.50 to 3.69 whereas
before it was 0.50 to 2.69. Other variables generally were not affected strongly in this
way.
The results above indicate that the assumption of homoskedasticity may be violated in the
data. Given that the survey design used a clustered sample, one potential source of
heteroskedasticity may be due to spatial correlation. 158 Maddala (1983) points out that
little work studies the effects of violations of the different assumptions for this type of
model. For the general class of limited dependent variable models, he reports that
findings show the estimates are neither consistent nor efficient when there is
158 As the clusters are not known in the data, this cannot be examined.