In: Math
In the case that you would have to use heteroscedastic standard errors but instead falsely use homoscedastic standard errors. What implications would this have regarding unbiasedness, efficiency...
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Conclusion: Property of unbiasedness remains.
However, Variance of OLSE ( b= (X'X)-1X'Y) computed
in case of heteroscedastic variance V(y)=
will be greater than the variance of OLSE computed in case of
homoscedastic variance. If we use homoscedastic variance to obtain
estimates of parameter
instead od
heteroscedastic variance.