Geoscience Reference
In-Depth Information
A test for
structural
change
Structural change refers to a long-term shift in the agricultural
production. Over the last few decades, the structure of agri-
cultural production around the world has been changing. The
factors influencing this change have to be addressed.
Consider a dataset for two periods of time with Period I,
say drought, having n
1
observations, and Period II, say nor-
mal, having n
2
observations. Here, the objective is to find out
whether there is any structural change or shift in the yield pat-
tern between the drought and normal periods. Let there be two
variables Y = productivity and X = area under cultivation and
data were collected at two periods of time and given as follows:
Period I
Period II
Productivity
Area
Productivity
Area
1
2
1
2
2
4
3
4
2
6
3
6
4
10
5
8
6
13
6
10
6
12
7
14
9
16
9
18
11
20
To investigate this, the following models are defined:
Period I: Y = α
1
+ β
1
X + u (Drought)
Period II: Y = α
2
+ β
2
X + u (Normal)
Here, the aim is to test α
1
= α
2
and β
1
= β
2
.
Test statistic
Let the number of restrictions be s. The test statistic is as
follows:
(
RSS SS /s
RSS/np
−
)
F
=
r
u
(
−
)
u
which follows the F distribution with (s, n − p) d.f. RSS
r
is the
residual sum of squares under null hypothesis and RSS
u
is the
residual sum of squares under usual model (Waterman 1974).
