INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 77 There are two ways in which this can be demonstrated. First is the case where there are only two explanatory variables to demonstrate that the estimators are unbiased if the model is correctly specified and the Gauss–Markov conditions are fulfilled. The second method is to run a simple regression of
Y on one of the
X variables, having first purged both
Y and the
X variable of the components that could be accounted for by the other explanatory variables. The estimate of the slope coefficient and its standard error thus obtained are the same as in the multiple regression. It follows that a scatter
diagram plotting the purged Y against the purged
X variable will provide a valid graphical representation of their relationship that can be obtained in no other way.
…[2.62] If thegraphical illustration is particularly interested in, in the relationship between earnings and
schooling a direct plot of EARNINGS on
S would give a distorted view of the relationship. This is because
ASVABC is positively correlated with
S and
having some consequences as S increases. These are [1]
EARNINGS will likely increase, because is positive [2]
ASVABC will tend to increase, because
S and
ASVABC are positively correlated and [3]
EARNINGS will receive
a lift due to the increase in ASVABC and the fact that is positive. That is, the variations in
EARNINGS will overstate the apparent influence of
S because in part they will be due
to associated variations in ASVABC. And the outcome of this is that in a simple regression the estimator of will be biased. The graphical illustration is shown in Figure 3.1.
