Clearly, this approach has its limi

Clearly, this approach has its limitations. Since spatial price differentials become more aggregated, it produces inferential difficulties when investigating the linkage location of any revealed impediment to trade. Indeed, if there is a large number of local market linkages, then (depending on what other local non-price variables are relevant) it may become impossible to identify even the indirect radial linkage. As always, the merits of the model need to be judged in its specific applications.
Since the main aim in estimating the model is to test alternative hypotheses to do with market integration, its econometric specification should not prejudice the outcome. This is most easily assured if the alternative hypotheses can be nested within a more general model and so tested as restricted forms. For estimation, it is also convenient to assume that the functions f (i = 1,…,N) can be given a linear representation by introducing an appropriate stochastic term.
The econometric version of equations (1) and (2) should also embody a suitable dynamic structure; as is well known, dynamic effects can arise from a number of conditions in the underlying behavioral relations including expectations formation and adjustment costs (for a survey of the possibilities see Hendry, Pagan, and Sargan).
Combining these considerations, the following econometric model of a T-period series of prices for N regions is assumed: