Assumptions:
1- We know about the points of structural change
U1t N (0, ϭ
2
)
U2t N (0, ϭ
2
)
U1t = before change, U2t = after change
2- No auto-correlation
Steps To Apply Chow Test:
1- before structural change
Yt = β1 + β2Xt + U1t
RSS1 » dfn-k
2- after structural change
Yt = ɣ1 + ɣ2Xt+ U2t
RSS2 » dfn-k
3- fit the regression model for combine period (under regression parameter stability)
Yt = ꭤ1 + ꭤ2X2 + U3t
df >> n1+n2-k
4- since the first two samples are demand independent so the ∑ equal to,
RSSur = RSS1 + RSS2
5- set up the hypothesis
Ho; there is structural stability
Hi; there is structural change
6- compute the test – statistic
𝐹 =
RSSr−RSSur/k
RSSur(n1+n2−2k)
7- set the level of significance i.e., = 0.05
find fꭤ:
D.o.f for nominator(k)
D.o.f for denominator(n1+n2-2k)
8- compare the Fcal with Ftab
if
Fcal ≥ Ftab
Then reject Ho (structural change)
The Chow test is just an ordinary F test where the null hypothesis being tested is
that the coefficients are equal in the two samples. So the null hypothesis sum of
squares comes from the pooled regression with no dummies. … The key point is that
this is really no different from any other hypothesis test

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