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

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Table 5.9: Results <strong>of</strong> <strong>in</strong>tegration tests<br />

Crop type Wholesale-retail market<br />

1. Teff<br />

Adda teff -6.04<br />

Wollenkomi teff -8.08<br />

Bechena teff -7.23<br />

2. Wheat<br />

Wheat first -5.43<br />

Wheat second -7.81<br />

Wheat third -6.54<br />

3. Maize<br />

White maize -5.98<br />

Maize mixed -6.96<br />

<strong>The</strong> results <strong>of</strong> the <strong>in</strong>tegration test show that the wholesale and retail markets are <strong>in</strong>tegrated. In<br />

other words, there a exists long-run and stable price relationship between the two markets for<br />

the sample gra<strong>in</strong> products. If there is <strong>in</strong>teraction between a pair <strong>of</strong> markets, then there must be<br />

Granger causality—that is, one series may cause another and vice versa. Thus, the next step is<br />

to conduct such a test <strong>in</strong> order to determ<strong>in</strong>e the direction <strong>of</strong> causality. <strong>The</strong>oretically, if a time<br />

series variable P wit <strong>in</strong>fluences another series variable P rit , then there exists a Granger<br />

causality relationship between these two variables <strong>in</strong> which P wit Granger causes P rit and<br />

vice versa. Formally, this test can be conducted based on the follow<strong>in</strong>g model.<br />

(i) Pwit<br />

= ψ<br />

11<br />

ΔP<br />

+ ... + ψ<br />

nΔP<br />

+ ψ ΔP<br />

+ + ψ<br />

nΔP<br />

−ζ<br />

[ P −αP<br />

−δ] + ε<br />

wit− 1 wit−n<br />

21<br />

...<br />

1<br />

rit−1<br />

2 wit−n<br />

1 wit−1<br />

rit−1<br />

it<br />

(5.4)<br />

(ii) Pr<br />

ψ<br />

31<br />

ΔP<br />

+ ... + ψ3<br />

nΔP<br />

+ ψ Pwit<br />

n<br />

P [ P P ]<br />

rit n 41Δ<br />

1<br />

+ ... + ψ4<br />

Δ −ζ2<br />

−α<br />

−δ<br />

+ ε<br />

− −<br />

−<br />

wit−1<br />

2t<br />

(5.5)<br />

=<br />

it rit 1<br />

wit−n<br />

rit−1<br />

<strong>The</strong> hypotheses to be tested to determ<strong>in</strong>e the Granger causality relationship between<br />

wholesale and retail prices are:<br />

(a)(P rit does not Granger Cause P wit ); and<br />

(b) (Pwit does not Granger Cause Prit)<br />

Based on the <strong>in</strong>tegration test, an attempt was made to perform a causality test for the two<br />

markets, and the results are given <strong>in</strong> Table 5.10.

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