This preview shows page 1. Sign up to view the full content.
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
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 STAFF

Click to edit the document details