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Econ107 Applied Econometrics
5S
p
e
c
i
ﬁ
cation: Choosing Independent and Depen-
dent Variables (Studenmund, Chapters 6, 7)
Before we estimate an equation, we have to specify it. Specifying an econometric
equation consists of three parts:
•
choosing the correct independent variables,
•
choosing the correct functional form,
•
choosing the correct form of the stochastic error term.
A speci
ﬁ
cation error results when one of these choices is made incorrectly. We study
ﬁ
rst choosing the independent variables and then choosing the correct functional
form. The last choice will be studied in later topics.
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Speci
ﬁ
cation: Choosing the Independent Variables
We
ﬁ
rst deal with the choice of independent variables. Misspeci
ﬁ
cation of independent
variables may be due to
•
omitted (relevant) variables,
•
redundant variables (including irrelevant variables).
An example of wage equation
Huge attention in labor economics has focused on the estimation of wage equation
to characterize the payo
f
of schooling/education. For simplicity, we consider the
following linear regression model:
ln
W
i
=
β
0
+
β
1
S
i
+
β
2
T
i
+
ε
i
,
(1)
where
•
W
i
is the wage rate of worker
i,
2

•
S
i
is the years of schooling (formal education) of worker
i,
•
T
i
is the e
f
ective years of on-the-job training of work
i.
The idea is that we have two forms of human capital:
general human capital
obtained
through formal education and
speci
ﬁ
chumancap
i
ta
l
obtained through vocational
education, apprenticeship programmes, etc. Both may increase wages (i.e.,
β
1
>
0
and
β
2
>
0), but usually not at the same rate (i.e.,
β
1
6
=
β
2
).
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