and
fɪ if t > TB
DUt= <!
0 else
к.
Equation (9) considers an exogenous break in the intercept, (10) an exogenous break in the
trend, and (ɪɪ) considers a break in both trend and intercept. To account for the possible serial
autocorrelation, lagged values of the dependent variables can be included in the regression.
The problem with the Perron test is that the breakpoint must be known a priori which is a
seriously restrictive assumption. Zivot and Andrews (1992) modified the Perron test, to
endogenously search for the breakpoints. That is achieved by computing the t-statistics for all
breakpoints, then choosing the breakpoint selected by the smallest t-statistic, that being the
least favourable one for the null hypothesis.
3.3. Cointegration analysis
The two most widely used cointegration tests are the Engle-Granger (Engle and Granger,
1987) two-step method and Johansen’s multivariate approach (Johansen, 1988). Engle and
Granger base their analysis on testing the stationarity of the error term in the cointegrating
relationship. An OLS regression is run with the studied variables, and the residuals are tested
for unit roots. If the null of non-stationarity can be rejected the variables are considered to be
cointegrated.
The Johansen testing procedure has the advantage that allows for the existence of more than
one cointegrating relationship (vector) and the speed of adjustment towards the long-term
equilibrium is easily computed. The procedure is a Maximum Likelihood (ML) approach in a
multivariate autoregressive framework with enough lags introduced to have a well-behaved
disturbance term. It is based on the estimation of the Vector Error Correction Model (VECM)
of the form:
∆Zt = Γι∆Zt-ι + .. + Γk-ι∆Zt-k+ι + TIZ + ΨD + ut (12)
where Zt = [ PRt, PPt]’ a (2 x 1) vector containing the farm and retail price, both I(1), Γ1
,..Γk+1 are (2x2) vectors of the short run parameters, Π is (2x2) matrix of the long-run
parameters, Ψ is a (2x11) matrix of parameters , D are 11 centred seasonal dummies and ut is
the white noise stochastic term.
Π = αβ' , where matrix α represents the speed of adjustment to disequilibrium and β is a
matrix which represents up to (n - 1) cointegrating relationships between the non-stationary
variables. There are several realistically possible models in (12) depending on the intercepts
and linear trends. Following Harris (1995) these models defined as models 2-4, are: (M2) the
intercept is restricted to the cointegration space ; (M3) unrestricted intercept no trends - the