The Future of Smallholder Farming in Eastern Africa - Uganda ...

where P t = P t -P t-1 , and P t-k = P t-k - P t-k-1; k = 2,3,4,…n; P t is price at time t;,,, and are
parameters to be estimated and t is the error term.
If the value of the ADF statistic is less than the critical values, it shows that P t is stationary. If
P t is non-stationary, it should be determined whether P t is stationary in the first difference by
repeating the above procedure. To test for co-integration, Engle and Granger (1987)
developed a two-step residual-based test. The first step is to conduct OLS regression of one
price series (P wit in this case) on another price series (P rit ) plus a constant and a time trend,
which is known as co-integration regression.
P
wit
= θ + λP
+ ψt
+ ν ………………………………………………………..(5.2)
rit
t
where P wit and P rit are the wholesale and retail prices of crop i at time t; ,, and are
parameters to be estimated and t is the error term.
The second step is to test whether the residuals (t) from the co-integration regression in
equation (2) are non-stationary by using the following test:
n
t− 1
+ ∑ω
k
Δν
t−k
+ μ
k = 2
Δν = ην
………………………………………………………(5.3)
t
where t = t - t-1 ; t-k = t-k - t-k-1 , t, t-1 , t-k-1 are, respectively, residuals at time t, t-1, t-k, and t-k-
1; and are parameters to be estimated and is the error term.
According to equation (3), if the t-statistic value of is less than the relevant critical value, then
the two price series are said to be co-integrated, and hence, the two markets are integrated.
The results of the stationary tests are presented in Table 5.8.
The results of the stationary test indicate that both wholesale and retail prices pass the test,
and we can further proceed to do integration test. For integration, we try to investigate or test
between wholesale and retail prices for the different crops. The results of the integration tests
are given in Table 5.9.