The BoxCox test for functional form:
(See GHJ: pp. 345346.)
♦
There are two candidate models: a linear form and a loglog form. The latter would come
from a CobbDouglas specification, but you could also use a semilog model – the key is that
the dependent variable is in natural log form:
(1)
01
1
2
2
ii
i
i
YX
X
u
β
ββ
=+
+
+
(2)
1
2
2
ln
ln
ln
i
i
X
u
α
αα
+
+
♦
Estimate each model, save the residual sums of squares:
RSS
L
is the residual sum of squares
from the linear model, and
RSS
LL
is the residual sum of squares for the log model.
♦
Transform the residual sum of squares for the linear model:
2
L
G
RSS
Y
,
where
12
n
Gn
YY
Y
Y
=⋅
"
♦
Calculate the test statistic:
2
2
(1)
ln
2
L
G
LL
RSS
Y
n
l
RSS
χ
⎛⎞
⎜⎟
=
⎝⎠
∼
Or:
()
2
2
(1)
ln
ln
2
L
LL
G
n
RSS
lR
S
S
Y
=−
∼
♦
Compare – the key is to check the terms within the absolute value bars, because the test
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This note was uploaded on 12/08/2011 for the course ECON 702 taught by Professor Staff during the Spring '08 term at UMass (Amherst).
 Spring '08
 STAFF

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