TESTING INTERNATIONAL PRICE TRANSMISSION UNDER ...

Empirical Tests for Spatial Price Analysis
3.3.2.2 Asymmetric adjustment models
The concept of “asymmetry” refers to the fact that adjustment coefficients are
allowed to vary depending on the sign of price differentials. A very intuitive
explanation of why this might be the case is that agents holding market power will
pass-through only (or mostly) positive input changes (Ghoshray 2002).
In dynamic applications, the short-run adjustment term is then substituted by
two separate coefficients indicating the response, respectively, to negative and
positive deviations from the long run equilibrium.
Prakash et al. (2001 cited Conforti 2004, p.9), look at the significance of a
dummy variable accounting for positive residuals in the static regression between
the two price series involved. If this variable is significantly different from zero,
and has a positive sign, transmission is asymmetric, since positive shocks are
passed through faster than the negative ones (Conforti 2004, p.9).
In more sophisticated models, the speed of adjustment is expected to vary
according to either the sign or the variations of price differentials. We start from
the autoregressive model of the VECM error correction term, which we have
indicated as zt. In equation 3.37, rejecting the null hypothesis of no cointegration
(H0: γ = 0) implies that the residuals ωt, are stationary (Ghoshray 2002, p. 304),
Δz = γ z −1 + ω
(3.37)
t
t
t
The Threshold Autoregressive Model (TAR model) can be represented as
Δ t = I t 1 zt
−1 + 1−
I t ) γ 2 zt
−1
z γ ( + ω
(3.38)
where I is the Heaviside indicator, which takes the following form:
I
t
1
=
0
if
if
z
z
t−1
t−1
≥ 0
< 0
t
(3.39)
In this model, the adjustment coefficients are then allowed to vary according to
the sign of the long-term residuals of the cointegration relationship. If the
residuals are positive, the adjustment coefficient will be γ1; if they are negative, it
will be γ2.
The sufficient conditions for the stationarity of zt are γ1 , γ2 < 0.
If for example, -1 < γ1 < γ2 < 0, this means that the negative phase of zt will
tend to be more persistent than the positive phase.
In the Momentum Threshold Autoregressive Model (M-TAR model), the
adjustment coefficients can vary according to the sign of the variations of price
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