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

(11.7.7)
t
=
(0.27) (1.06)
r
2
=
0
.
172
Comparing Eq. (11.7.7) with Eq. (11.7.3) (the latter not having been corrected for
heteroscedasticity), we see that the parameter estimates have not changed (as we
would expect), the standard error of the intercept coefficient has decreased slightly,
and the standard error of the slope coefficient has increased slightly. But remember
that the White procedure is strictly a large-sample procedure, whereas we have only
14 observations.
EXAMPLE 11.11
Table 11.6 on the textbook website provides salary and related data on 94 school districts
in Northwest Ohio. Initially, the following regression was estimated from these data:
ln(Salary)
i
=
β
1
+
β
2
ln(Famincome) 
+
β
3
ln(Propvalue) 
+
u
i
Where Salary 
=
mean salary of classroom teachers ($), famincome 
=
mean family income
in the district ($), and propvalue 
=
mean property value in the district ($).
Since this is a double-log model, all the slope coefficients are elasticities. Based on the
various heteroscedasticity tests discussed in the text, it was found that the preceding
model suffered from heteroscedasticity. We, therefore, obtained (White’s) robust standard
errors. The following table gives the results of the preceding regression with and without
robust standard errors.
Variable
Coefficient
OLS se
Robust se
Intercept
7.0198
0.8053
0.7721
(8.7171)
(9.0908)
ln(famincome)
0.2575
0.0799
0.1009
(3.2230)
(2.5516)
ln(propvalue)
0.0704
0.0207
0.0460
(3.3976)
(1.5311)
R
2
0.2198
Note:
Figures in parentheses are the estimated 
t
ratios.
Although the coefficient values and 
R
2
remain the same whether we use OLS or
White’s method, the standard errors have changed; the most dramatic change is in the
standard error of the ln(propvalue) coefficient. The usual OLS would suggest that the es-
timated coefficient of this variable is highly statistically significant, whereas White’s robust
standard error suggests that this coefficient is not significant even at the 10 percent level.
The point of this example is that if there is heteroscedasticity, we should take it into
account in estimating a model. 
EXAMPLE 11.10
(
Continued
)
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