The support for the Band-TAR specification, with overshooting of
the threshold limit from out-of-threshold episodes, over the Eq-TAR
specification was unanimous in this study. However, this result was
curious in that the posterior mass of the parameter [theta] was weighted
toward unity even when adjustment was ostensibly symmetric in both
equations in the case for the Brazil-U.S. wheat and Brazil-Argentina
maize price pairs. While this finding is weakly indicative of a
threshold model it does raise the awkward question of what this result
means in these two cases? It is, of course, possible that there is some
other form of nonlinearity or structural break that is responsible for
the apparent existence of thresholds. This contention was supported by
the timing of movements inside and outside of the threshold in the case
of the Brazil-U.S. wheat price pair. In this case, the conclusion of
Mercosur, institutionalizing a free trade agreement among member states,
in 1995 may have reinforced the tendency for Brazil to obtain its wheat
imports more or less exclusively from Argentina, and weakened price
transmission from the United States. The ambiguous result for maize is
less easy to explain but may be either a result of the relatively small
volumes traded across Brazil's boarders or that the Mercosur
agreement was effective at reducing transactions costs between South
American countries at a time when Brazil switched from being a net
importer to a net exporter of this commodity.
We are grateful for the suggestions and helpful comments of two
anonymous referees and the constructive criticisms and encouragement of
the editor, Wade Brorsen, during the preparation of this article. Any
remaining errors are the authors'.
[Received April 2004; accepted May 2006.]
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(1) For the case of a trade flow from country B to country A,
rearrange the superscripts.
(2) Balke and Fomby (1997) also consider a further model, the
RD-TAR or returning drift threshold model, which has a unit root in each
regime and uses the drift parameters to restore "equilibrium."
From without, attraction is to the outer band rather than a central
equilibrium point. However, we do not consider this model here.
(3) The author has developed algorithms along the lines of those
suggested in Hansen and Seo (2002). However, Hansen and Seo's
methods are highly model specific and we have not been able to
generalize their methods to accommodate the more general TAR
specification of Model III.
(4) Deterministic trends, seasonality, etc., may play a role, but
we ignore these in the current exposition since they complicate but do
not undermine the points being made.
(5) From here on, we use the terms "symmetry" and
"asymmetry" to denote differential within and without
threshold response, rather than differential upward and downward price
adjustment, since our model is restricted to the symmetric case of the
latter.
(6) Details of all of these tests can be found in Maddala and Kim
(1998).
(7) These are nearly identical to a posterior mean from
nonthreshold models.
Kelvin Balcombe is lecturer in the Department of Agricultural and
Food Economics Department, in the School of Agriculture, Policy and
Development at the University of Reading, U.K. Alastair Bailey is
honorary senior lecturer and senior lecturer in Agricultural Economics
at Imperial College, London, Wye Campus & University of Kent, U.K.,
respectively, and Jonathan Brooks is senior economist at the OECD,
Paris, France.
Table 1. Unit Root Tests for Monthly Wheat, Maize and Soya Prices, by
Country, May 1988 to May 2001, August 1986 to May 2001, and May 1988
to April 2001, Respectively
With Time Trend
Commodity/Country ADF PP KPSS LMc
Wheat: Brazilian -2.78 -2.54 0.098 3.27 **
Argentine -2.55 -2.28 0.086 1.02 **
U.S. -1.89 2.04 0.097 1.73 **
Maize: Brazilian -2.33 -2.01 1.54 0.31 **
Argentine -2.96 -2.53 0.157 1.60 **
U.S. -2.25 -1.88 0.119 1.79 **
Soya: Brazilian -2.38 -2.19 0.08 9.07 **
U.S. -2.18 -1.73 0.08 1.56 **
Critical 5 % -3.41 0.463
Values 10% -3.12 0.347
Without Time Trend
Commodity/Country ADF PP KPSS LMc
Wheat: Brazilian -2.75 -2.52 0.108 0.68 **
Argentine -2.55 -2.3 0.078 1.05 **
U.S. -1.52 -1.41 0.224 ** 1.71 **
Maize: Brazilian -2.41 -2.12 0.145 * 0.25 **
Argentine -3.04 ** -2.12 * 0.134 * 1.15 **
U.S. -2.47 -2.02 0.144 * 1.79 **
Soya: Brazilian -2.38 -2.22 0.09 1.31 **
U.S. -2.07 -1.36 0.19 ** 8.78 **
Critical 5 % -2.86 0.119
Values 10% -2.57 0.146
Note: * and ** denote significance at the 5% and 10% levels,
respectively. Also note that the ADF and PP and the KPSS and LMc share
the same critical values, respectively.
Table 2. Johansen ML Tests for Cointegration between Commodity Price
Pairs
Number of
Commodity/ Cointegrating
Price Vectors Null
Pair versus Actual Eigenvalue
Wheat/Brazil 0 versus 1 21.58**
versus 1 versus 2 6.25
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