A model of spatial price differenti

A model of spatial price differentials for a tradable good is proposed which avoids the inferential dangers of received methods using static price correlations. The proposed method also extracts more information on the causes of price differentials from the same data. The method is illustrated using monthly rice price data for postindependence Bangladesh, including the very substantial regional price shocks during the 1974famine. Impediments to market integration are indicated.

Key words: Bangladesh, famine, market integration, modeling spatial price differentials.

Though much maligned, static price correlations remain the most common measure of spatial market integration in agriculture. By this method, bivariate correlation or regression coefficients are estimated between the time series of spot prices for an otherwise identical good or bundle of goods at different market locations?
There are a number of inferential dangers in bivariate modeling of this sort. The following example expands on an important point made elsewhere in the literature on market performance in agriculture (Blyn, Harriss). Suppose that trade is infinitely costly between two market locations but that the time series of prices at the two locations are synchronously, identically, and linearly affected by another variable. Possible examples include the price of a related third good traded in a common market or a shared dynamic seasonal structure in production. Then one can readily express price in one market as a linear function of price in the other market, with slope unity, even though the markets are segmented. Of course, any measurement errors or omitted variables would yield imprecision in a test equation based on the static bivariate model. But it remains that under these conditions the received method fails hopelessly as a test for market integration. The likelihood of serial dependence in the residuals obtained from a static model calibrated to nonstationary time series also leads one to be suspicious of the conclusions drawn from this method (Granger and Newbold).
However, with the same data, the static bivariate method can be readily extended into a dynamic model of spatial price differentials. By permitting each local price series to have its own dynamic structure (and allowing for any correlated local seasonality or other characteristics) as well as an interlinkage with other local markets, the main inferential dangers of the simpler bivariate model can be avoided." Most important, the alternative hypotheses of market integration and market segmentation can then be encompassed within a more general model and so tested as restricted forms.
A dynamic model also has the advantage that one can distinguish between the concepts of instantaneous market integration and the less restrictive idea of integration as a long-run target of the short-run dynamic adjustment process. This distinction seems important. In many settings it will be implausible that trade adjusts instantaneously to spatial price differentials, and so one would be reluctant to accept short-run market integration as an equilibrium concept. But given enough time, the short-run adjustments might exhibit a pattern which converges to such an equilibrium. If short-run integration is rejected, then it would be nice to know if there is any long-run tendency toward market integration. By permitting the investigator to answer this new question, a dynamic model can extract more information about markets from the same data used by the static model.
This paper offers an approach to testing agricultural market integration along these lines and illustrates it using data on the interregional price differentials for rice in Bangladesh during the turbulent postindependence period, 1972-1975. The period of analysis has been chosen to include the substantial regional price shocks which occurred during the 1974 famine (Seaman and Holt, Alamgir, Sen). Elsewhere I have examined the intertemporal performance of rice markets in Bangladesh during this period (Ravallion 1985b).

Why Study Market Integration?

It is well-known that, under regularly assumed restrictions on the continuity, slope, curvature, and domain of utility and production functions, a competitive equilibrium for a complete set of markets will exist and be efficient in the Paretian sense. In general, this will also hold for the spatial competitive equilibrium of an economy consisting of a set of regions among which trade occurs at fixed transport costs (Takayama and Judge). Such an equilibrium will have the property that, if trade takes place at all between any two regions, then price in the importing region equals price in the exporting region plus the unit transport cost incurred by moving between the two. If this holds then the markets can be said to be spatially integrated.
Market integration is by no means sufficient for the Pareto optimality of a competitive equilibrium. Even when based on a sound empirical methodology, the conclusion that markets are well integrated does not, of itself, imply an efficient spatial allocation (see, for example, Newbery and Stiglitz).
Nonetheless, one can be interested in empirically testing for spatial market integration without wishing to rest the case for or against Pareto optimality on the outcome. Measurement of market integration can be viewed as basic data for an understanding of how specific markets work.
For example, in the present setting, a study of the dynamics of market integration should throw some light on one of the oldest questions concerning famines in market economies: how long can an initially localized scarcity be expected to persist? Policies of nonintervention with markets during famines have often been advocated or defended along the following lines: given that the necessary transport infrastructure exists, the unaided response of grain traders to the induced spatial price differentials will quickly eliminate any localized scarcity. For example, this assumption was a cornerstone of the government of India's famine relief policy during much of the nineteenth and early twentieth centuries (Bhatia, Ambirajan). Against this view, it has often been argued that markets will be too slow to respond; for example, Ambirajan reports that during the severe famine of the mid1870s, the local government in Madras rebelled against the government of India's policy, arguing that "if time were given to the market, the necessary grain would eventually come, but time was what could not be given" (Ambirajan, p. 95). Since independence, governments of India and other countries in the subcontinent have tended to adopt highly interventionist policies concerning food grain markets (see, for example, Bhatia, chap. 12; George). An empirical assessment of the speed of market adjustment to spatial price differentials may help resolve this longstanding debate.

Modeling Spatial Market Structure

The specification of an econometric model of spatial price differentials will depend, in part, on assumptions about spatial market structure. Here I shall assume that there exists a group of local (rural) markets and a single central (urban) market. While there may be some trade among the local markets, it is trade with the central market which dominates local price formation. Depending on the number of local markets and their sizes, one can also posit that the central market price is influenced by various local prices.
Thus, the static pattern of price formation among N markets, where market 1 is the central market, may be summarized by a model of the form:

where Xi (i = 1, . . . , N) is a vector of other influences on local markets. The functions fi (i = 1,…, N) can be thought of as solutions of the appropriate conditions for market equilibrium, taking account of the main spatial choices and the costs of adjustment facing traders when deciding where to sell. The derivation of these functions does not seem to pose any new theoretical problems or insights, and so I shall take them as given.
At first sight, this model only seems well suited to a simple radial configuration of markets in which each local market is directly linked with the central market. In most applications a more plausible configuration is one in which some local markets only trade with the central market via other markets. However, provided one is willing to forgo identification of at least some of the non-radial linkages, the radial model given by equations (1) and (2) can often provide a useful characterization of more complex market structures. By subsuming linkages between intermediate local markets, an (implicit) binary relation can be obtained between each local market and the central market, and so the radial model is preserved.
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 formatio