TESTING INTERNATIONAL PRICE TRANSMISSION UNDER ...

Empirical Tests for Spatial Price Analysis
defined as the situation within, at or outside the arbitrage condition. Market
efficiency is equivalent to the probability of the regime which satisfies the
arbitrage condition to be one and the others to be zero. Baulch (1997) extends this
model by adding explicit information on transaction costs and allowing trade flow
reversals to take place. The use of this approach (called the Parity Bound Model)
allows markets to be integrated in some periods but not in others (trade flows
discontinuity), transfer costs to vary between periods, and prices to be
contemporaneously determined.
Indicating with P1 t − P2
t the price differential, with C 12 the transfer cost, and
with u It and u Ot the additional error terms inside and outside the parity bounds
(assumed to be independently and half normally distributed), three regimes are
derived according to the size of price spreads and of transfer costs:
− P = C . Regime 1 – efficient arbitrage: the price differential is
− P1 t 2t
12
exactly at the parity bound; transfer costs equal the market price differential
and there are no impediments to trade between markets. Trade will cause
prices to move on a one-to one basis and the arbitrage conditions are
binding.
P P = C − u . Regime 2 – the price differential is inside the parity
− 1 t − 2t
12 It
bound. In this case, the interpretations of Baulch and Sexton et al. are
slightly different. For Baulch, when the price differential is inside the parity
bound, it is because transfer costs exceed the inter-market spread: trade will
not occur and the arbitrage conditions will not be binding (no profitable
trade flows). For Sexton et al., that assume unidirectional trade, if the price
spread is within the arbitrage band it is because too much trade has occurred
(“relative glut”).
P P = C + u . Regime 3 – the price differential is outside the parity
− 1 t − 2t
12 Ot
bound. In Baulch’s model, if spreads exceed transfer costs, the spatial
arbitrage conditions are violated whether or not trade occurs (non exploited
profitable trade opportunity). In the interpretation of Sexton et al., too little
trade occurs (“relative shortage” case).
In the switching regime models presented, the probability distribution
associated with the price spread is a mixture of three distributions, corresponding
to the three regimes. The logarithm of the likelihood function of the sample is
minimized and gives probability estimates for each of the three regimes 23 : the
extent of market integration is expressed in terms of a continuous frequency of
23 If transfer costs were known, testing for the efficiency of spatial arbitrage would reduce to arithmetically
calculate whether trade occurred or not whenever the inter-market price differential exceeded or not transfer
costs. But time series data on transfer costs are rarely available: either they must be estimated and inserted in
the model, or be an endogenous parameter (Sexton et al. 1991).
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