One of them is the homoskedasticity
(constant variance) of the errors in relation to any independent variable.
Both the tests indicate the presence of heteroskedasticity in the model as the probability is less than 0.05 so we cannot accept the null hypothesis of constant variance or homoskedasticity
. This calls for the estimation of robust standard errors which yield consistent estimates of the true standard errors.
In Panel D, we plot rejection rates at the 5% level based on three different approaches to obtaining standard error estimates--assuming homoskedasticity
(i.i.d.), allowing for heteroskedasticity, and clustering on the running variable, as recommended by Lee and Card (2008) to address potential model misspecification.
(2013), we implement the modified Wald test for group wise for testing the hypotheses of homoskedasticity
. The results obtained (chi-squared (101):45,498.77, p-value: 0.000) fail to accept the null hypothesis of homoskedasticity
The main consequence of this structure in the error term is the breakdown of the homoskedasticity
assumption of the estimation.
Table 4 reports the results of the White test, where the null is homoskedasticity
. In all three equations, we fail to reject homoscedasticity.
Pagan-Hall General test and Pagan-Hall Test w/assumed Normality statistics show reveal homoskedasticity
. Since half of tests reveal the presence of heteroskedasticity, it is safer to assume heteroskedasticity and GMM should be preferred.
In order to establish distribution of the idiosyncratic components, the authors made the assumption of homoskedasticity
across time periods--pointed out in Bai and Ng  to be undesirable--and that [e.sub.i] = ([e.sub.11], [e.sub.12], ..., [e.sub.iT]), i = 1, ...
If we cannot reject the null hypothesis of homoskedasticity
, then we have an additional argument that point shaving does not exist.
[U.sub.it] are independent and equally distributed errors with zero mean and dispersion [[sigma].sub.2] (homoskedasticity
Thus we accept the null hypothesis of homoskedasticity
. So, to verify the validity of the instruments we should applied the Sargan statistics.
Thus, the [H.sub.0] of homoskedasticity