TESTING INTERNATIONAL PRICE TRANSMISSION UNDER ...

Empirical Tests for Spatial Price Analysis
cointegrated and the model is equivalent to a VAR in first differences; if rank(Π)
= n, the variables are stationary and the model is equivalent to a VAR in levels; if
0 < rank(Π) = r < n, the variables are cointegrated. Π can be decomposed as
Π = αβ' , where α is the (n X r) matrix of the speed of adjustment coefficients and
β is the (n X r) matrix of the cointegration vectors. The basic assumption is that
β′pt = zt, representing the long run disequilibrium error, is stationary. All variables
of an error correction model (ECM) exhibit the property of stationarity under the
conditions that the levels of the individual variables are integrated of order one
and a cointegration relationship between the variables exists. Statistical
significance of the error correction parameter implies in turn the existence of a
cointegrating relationship (Thompson et al. 2002, p.1044).
There is also an alternative way to derive an ECM model which includes
responses from a one-lagged long run disequilibrium term (Lucchetti 2008).
Starting from the general VAR
p = A p − + ε
(3.29)
t
1
t 1
t
subtracting pt-1 on both sides, we have that
∆p = Πp − + ε
(3.30)
t
t 1
t
where Π = A1-I = αβ′, whose rank allows to determine the presence of
cointegration amongst the variables (see above). An autoregressive term can be
added to remove the short run persistence in the error tem; like in equation 3.26,
in the following VECM
'
t = αβ pt
1 + ∑ Γ
− k 1
− i=
1 i
∆p ∆p + ε
t−i
t
(3.31)
where pt is a vector containing the prices, β is the cointegration matrix which
contains the long-run coefficients (the degree of price transmission, Prakash 1999
cited Conforti 2004, p.3), α is the loading matrix which contains the adjustments
parameters (a measure of the speed of price transmission, Prakash 1999 cited
Conforti 2004, p.3), Γi are matrixes containing coefficients that account for shortrun
relations, and εt are white noise errors. Since the long run relation is the LOP,
and being prices written in logarithmic form, the assumption is that price spreads
(that is, all components which account for price spreads) are a stationary
proportion of prices.
When prices are expressed in logs, the coefficients included in β can be read as
price transmission elasticities. In fact, if pt contains only two log-prices, say p1t,
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