Slightly different analysis frameworks were adopted for
monthly an annual data. But in both cases the first step taken was the analysis
of the dynamic properties of the price series, aimed at understanding if price
pairs are integrated to the same order, by testing for the presence of unit
roots. For the monthly data, two different tests were applied: the Augmented
Dickey-Fuller (ADF) test, and the Phillip-Perron (PP)
test.^{[5]} These were run with and without a time
trend and a constant term^{[6]}, for a number of
lags varying from two to twelve, both on the log-level series and the series in
first differences.

On the basis of the properties, the test for unit roots was applied also to the residuals of the static regression between each pair of prices, in order to test for co-integration following the Engle and Granger (1987) procedure. Where co-integration arose, a set of Auto Regressive Distributed Lag (ARDL) models were specified and estimated as follows:

(1) |

where *pd* are the countries’ (logarithm of the)
import unit values in time *t*, *pw* is the (log) world reference
price, *a* is an intercept, *T* is a time trend, *e* is the error
term, and *t* is the period index.

A key issue in estimating this type of model is the
identification of the correct number of lags to be included, given that both
under- and over-parametrization can create problems, respectively of
misspecification and of unnecessary reduction in the degrees of freedom. The
relevant *J* and *K* were chosen here through the minimization of the
Akaike information criterion, supplemented by the Schwartz-Bayesian, the
Hannan-Quinn, and Log-Likelihood tests mainly to check for the consistency of
the results.

Given the lag structure, the presence of a long run relationship between *pd*
and *pw* can be tested by considering the parameters of the relation
in which, under the assumptions that
and it is

and |

Where the null of absence of co-integration is rejected in the Engle and Granger (1987) procedure, the adjustment taking place around the long run equilibrium can be modelled through an Error Correction (ECM) specification, such as:

(2) |

in which the coefficient
usually named “ECM coefficient”, indicates the short run adjustment
of prices toward the long run equilibrium, and l_{1}.is
the same as the one calculated from the ARDL model in (1).

Results reported here include for each commodity the
parameters and the *t* statistics for the long run equilibrium, together
with the results of the estimation of the corresponding ECM
specifications.

In order to test for Granger non-causality between the pairs of prices, model (1) and its reverse form have been estimated by dropping the contemporaneous coefficients, according to

and |

(3) |

Both equations were tested for g_{k} *b _{j}* g

Moreover, on these same price pairs the symmetry of
transmission is tested drawing on Prakash, Oliver and Balcombe (2002). A dummy
variable is added to the ARDL model (1), assigning a value of 1 to the
observations showing positive residuals in the static regression between each
pair of prices. Rejection of the *t* test on this variable allows the
series between which transmission is not symmetric to be identified When this is
the case, comparison of the short and the long run parameters of the ECM
specifications with and without the dummy, allows it to be understood if
positive price shocks are passed on the other price series to a greater or
smaller extent. In other words, if the model that includes the dummy variable
shows a higher speed and a higher degree of price transmission, this means that
positive shocks are transmitted more and faster than negative ones. This
procedure for testing asymmetry was applied only to those pairs of prices for
which the results indicate the presence of co-integration and of a significant
long run equilibrium, thereby precluding non-spurious cases, together with a
meaningful result of the Granger tests for non-causality.

Concerning annual data, they were also analyzed by testing for co-integration with the Engle and Granger (1987) procedure - after running the Unit Root tests - and for long run equilibrium; but in the specification of model (1) a simple structure including a maximum of two lags, without selection criteria, was assumed. The significance of the long parameter calculated from model (1) was tested while no evidence was reported for the ECM coefficients, which were considered less interesting, given that in annual data most of the short run variability is already averaged out. For this same reason, no tests were applied for causality and asymmetry on annual data.

^{[5]} As is known, the first is a
parametric test, based on the estimation of an AR(n) model, in which the
null hypothesis that the coefficients of the lagged dependent variables are
unitary is tested against a one sided alternative that they are strictly smaller
than one; where the former identifies a random walk, while a coefficient higher
than one would imply an explosive behaviour. The Phillips-Perron test is
conceptually similar to the ADF, but it is based on an AR(1) model, in
which the same test on the coefficient of the lagged variable is performed by
correcting the usual t-statistic with a (non parametric) estimate of the
spectrum of the error term.^{[6]} For brevity, only the tests
including the constant and the trend are reported in the tables. |