The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

In short, if we persist in using the usual testing
procedures despite heteroscedasticity, whatever conclusions we draw or inferences we
make may be very misleading.
To throw more light on this topic, we refer to a
Monte Carlo
study conducted by Davidson
and MacKinnon.
7
They consider the following simple model, which in our notation is
Y
i
=
β
1
+
β
2
X
i
+
u
i
(11.4.1)
They assume that 
β
1
=
1,
β
2
=
1, and 
u
i
∼
N
(0,
X
α
i
). As the last expression shows, they
assume that the error variance is heteroscedastic and is related to the value of the regressor
X
with power 
α
. If, for example, 
α
=
1, the error variance is proportional to the value of 
X
; if
α
=
2, the error variance is proportional to the square of the value of 
X
, and so on. In Sec-
tion 11.6 we will consider the logic behind such a procedure. Based on 20,000 replications
and allowing for various values for 
α
, they obtain the standard errors of the two regression
coefficients using OLS (see Eq. [11.2.3]), OLS allowing for heteroscedasticity (see
Eq. [11.2.2]), and GLS (see Eq. [11.3.9]). We quote their results for selected values of 
α
:
Standard error of 
ı
ˆ
1
Standard error of 
ı
ˆ
2
Value of 
Å
OLS
OLS
het
GLS
OLS