TESTING INTERNATIONAL PRICE TRANSMISSION UNDER ...

Empirical Tests for Spatial Price Analysis
3.3.2.1 Threshold models
In threshold cointegration models, the basic assumption is that prices show a
tendency to return to their long run equilibrium only when price differentials
exceed a certain threshold 34 . In other words, when deviations in prices exceed this
“neutral band”, which accounts for transaction costs, a sort of regime switching is
triggered (Goodwin and Piggot 2001, p.303).
Some basic threshold cointegration models used in agricultural commodity
markets studies are the Eq-TAR representation and the Band-TAR representation
(see Balke and Fomby 1997; Brooks et al. 2005; Balcombe et al. 2007).
In the Eq-TAR representation (equation 3.34, where only the error correction
I
term, zt-1, and its adjustment coefficients, α z ) , are presented), when
i
( t−1
deviations from the long run equilibrium, zt, exceed the threshold’s width, λ,
prices are attracted towards the centre of the threshold interval. The subscripts I
and O denote the within and without π adjustment speed.
α (
I
z
i
−1
) t
= π
i,
O
i,
I
z
= π z
t−1
t−1
if
if
z
z
t−1
t−1
> λ
< λ
(3.34)
In general, the speed of adjustment is allowed to differ depending on prices to
be inside or outside the interval; if πi,I collapses to zero, this means that, inside the
band, the price spread will follow a random walk. In other words, this implies that
if the price differential is smaller than the transport costs the arbitrage
mechanisms will not be active and the two series will not be cointegrated; a price
differential smaller than the transport costs will not justify any shipment of the
commodities.
Differently from the Eq-TAR model, in the Band TAR model when prices are
outside the threshold they are attracted to the edge of the threshold band, rather
than to the middle of it. So, the Band -TAR representation is given by equation
(3.35):
34 Threshold models show the difference existing between cointegration and efficient arbitrage: if efficient
arbitrage takes place, unit root behaviour in price margins should be observed (this happens up to and right at
the parity bound); only when imperfect arbitrage takes place we should observe cointegration between the
prices (since cointegration implies GC in at least one direction, profits could be made predicting one with the
past values of the other; Dercon 1999, p.6; see also paragraph 3.3).
43