Agriculture Reference
In-Depth Information
and vice versa. For example, the price of potato
can depend not only on its past values but also on
the lag values of production area under potato and
lag values of area under competing crops grown
during the potato season. For the time being, let us
restrict to two variables only, that is, price of
potato (
12.6
Partial Correlation
As has already been mentioned, the effect of
variables on other variables may not be the same
under multiple variable condition than what is
found in bivariate condition. The interac-
tion effects among the variables play great role
in depicting one-to-one association, measured in
terms of simple correlation coefficient also. Thus,
the simple correlation coefficient under multiple
variable condition may not portray the exact pic-
ture. Before calculation of correlation coefficient
between any two variables under multiple variable
condition, one must eliminate the effects of other
variables on both variables under consideration.
Precisely, we would like to know what the corre-
lation would be between
P
r
) and production of potato (
P
).
P
rt
¼ α
1
P
1
þ α
2
P
2
þ α
3
P
3
þ
þ β
1
P
r
1
þ β
2
P
r
2
þ β
3
P
r
3
þu
1
t
X
n
i¼
1
α
i
P
ðtiÞ
þ
X
n
i¼
1
β
j
P
rðtjÞ
þ u
1
t
¼
(12.1)
and
P
t
¼ λ
1
P
r
1
þ λ
2
P
r
2
þ λ
3
P
r
3
þ
þ γ
1
P
1
þ γ
2
P
2
þþu
2
t
m
i¼
1
λ
i
P
rðtiÞ
þ
m
j¼
1
γ
j
P
jðtjÞ
:
X
1
,say,after
eliminating the effects of all other variables such
as
Y
and
¼
(12.2)
X
k
on both of these variables. This is
called the partial correlation of
X
2
,
X
3
,
...
,
We are to find out whether the (1) price of
potato is caused by production of jute, that is,
P
α
i
6¼
X
1
, and the
coefficient is written as
r
y1.23
...k
¼ r
01.23
...k
.Itis
in general differs from the ordinary correlation
coefficient
Y
and
0and
P
γ
j
¼
0; (2) production is caused
by the price of potato, that is,
P
α
i
¼
0and
r
01
for
Y
and
X
1
. Using the correla-
P
λ
j
6¼
0; (3) two-way causality, that is, both
price causes production and production causes
price, that is, coefficients are statistically signifi-
cantly different from zero in both regressions; and
(4) existence of no causality, that is, coefficients
are not statistically significant from zero.
tion matrix
, one can work out the partial corre-
lation as follows:
<
R
01
ðR
00
R
11
Þ
r
01
:
2
¼
2
;
where
1
0
1
r
00
r
00
r
02
@
A
<¼
r
10
r
11
r
12
Solution. The step-by-step procedure is as
follows:
1. Regress current price on all lagged price only
and get residual sum of square (RSS
1
).
2. Regress current price on all lagged price and
include lagged productions also. Get RSS
2
.
3. Calculate
r
20
r
21
r
22
0
@
1
A
for three variable case
1
r
01
r
02
¼
r
10
1
r
12
r
20
r
21
1
and this can be generalized for
k
variables
X
1
,
ð
RSS
1
RSS
2
Þ =
X
2
,
X
k
as well.
Thus, partial correlation coefficient between
...
,
F ¼
with
m
,
RSS
2
=
ðn kÞ
n k
d.f., where
m
is the number of lagged
r
ij:
123
...k
¼
R
ij
ðR
ii
R
jj
Þ
i
th and
j
th variables
2
;
i 6¼ j
,
is the number of parameters
estimated in Step 2.
4. If Cal
productions and
k
k
where the correlation matrix now has (
+1)
H
0
:
P
α
i
¼
rows and columns and
R
jj
, has usual
meanings as described earlier. It is to be noted
that
R
ij
,
R
ii
, and
F >
Tab F,
then
0is
rejected, that is, production causes price.
5. Repeat the Steps 1-4 with the mode 2, that is,
to check whether
1.
Though, using MS Excel package, we may not
directly get the partial correlation coefficients,
1
r
ij:
123
...k
P
r
! P
and conclude
accordingly.
