Threshold effects in price transmission: the case of Brazilian wheat, maize, and soya prices.

Economists often view a close association between prices of similar goods in spatially or vertically separated markets, a concept closely associated with the Law of One Price (LOP), as being a sign of competition and the efficient functioning of markets. Observing closely related prices might, however, also reflect oligopolistic, collusive, or price fixing behavior. An extensive literature has developed on evaluating spatial market integration to assess the degree to which shocks in one market are transmitted into spatially separate markets. The interest for the economist is often, as noted by Barrett and Li (2002), concerned with the concept of Pareto efficiency since prices form the appropriate signaling mechanism of relative scarcity which ensures that producers appropriately specialize and that resources are optimally used. The question of price transmission also has important distributional implications, with the pass-through of policy and nonpolicy changes determining the extent to which different constituencies gain or lose.

The issues of integration and efficiency, in the context of spatially separated markets, has attracted much attention in the literature and are often linked to concerns over the impact of market liberalization across developed, less developed, and transition country economies alike (Baulch 1997). Early work in this area used cross-market price correlation or simple regression-based tests to assess the degree of market integration. More recently the recognition that price series are often nonstationary has led to widespread use of cointegration techniques following Ardeni (1989). However, these relatively simple Granger causality and cointegration approaches to the problem have been criticized on the grounds that they ignore the potentially important role played by transfer costs, such as transport and transactions costs (McNew and Fackler 1997; Fackler and Goodwin 2001; Barrett 2001; Barrett and Li 2002), they assume a linear relationship between prices which is inconsistent with discontinuous trade (Baulch 1997), and possess only weak power to discriminate between integrated and independent markets.

The LOP states that the price of identical goods in spatially separated markets should be the same after conversion to a common currency. The mechanism by which the LOP is maintained is that of spatial arbitrage. Should the prices of identical products differ in two markets then, in the absence of transport and transaction costs, rents to arbitrage exist which ensure that traders move product from surplus, low price, markets toward deficit, high price, markets until such rents are exhausted and the LOP holds once more. Nevertheless, in the majority of the literature, asymmetries in adjustment, poor spatial transmission of prices and deviation from the LOP have often been linked to high transport or transaction costs, protection, market barriers or some other form of imperfect competition (e.g., Kinnucan and Forker 1987; Ward 1982; Pick, Karrenbrock, and Carman 1990). Such imperfections, however, require that the spatial arbitrage conditions be modified to take explicit account of these costs since they drive a wedge between prices observed in different locations. Consider two spatially separated markets, A and B, that trade a single homogeneous good. Denote the transfer costs in time t between market A and B as [k.sup.AB.sub.t] and contemporaneous prices, expressed in a common currency, in each respective market as [P.sup.A.sub.t] and [P.sup.B.sub.t]. Rents to arbitrage are present, and trade occurs from markets A to B, for example, for as long as [P.sup.A.sub.t] + [k.sup.AB.sub.t] [less than or equal to] [P.sup.B.sub.t]. (1) Arbitrage rents disappear and trade ceases when [P.sup.A.sub.t] + [k.sup.AB.sub.t] > [P.sup.B.sub.t], however, only when [P.sup.A.sub.t] + [k.sup.AB.sub.t] [greater than or equal to] [P.sup.B.sub.t] can these two markets be said to be integrated since [P.sup.A.sub.t] + [k.sup.AB.sub.t] < [P.sup.B.sub.t] can only hold in the long term in the absence of trade or if trade fails to address the relative abundance of goods in either market because of the relative size of each market.

It can be seen from these arguments that the transmission of price signals between spatially segregated markets may, if it occurs, exhibit a nonlinear form. Price comovement might, under these arbitrage conditions, be "equilibrium restoring" when price differentials exceed transfer costs to traders while when the price differentials fall short of transfer costs, prices are not equilibrium restoring. This case could lead to a switch in regime between periods of trade and nontrade. However, if some proportions of traders' transfer costs are fixed then it is possible that some form of, somewhat slower, equilibrium restoring process may still be expected within the "threshold," or "neutral," band defined by k. The insight that there may be bands and asymmetries in price adjustment means there is a need for new approaches.

The most common approach used in the recent literature makes use of threshold effects, as one manifestation of poor transmission, to take account of transactions costs, asymmetries and nonlinearities (e.g., Abdulai 2000). One strand of the threshold literature has focused on asymmetric adjustment, whereby prices might adjust differently depending on whether they are above or below equilibrium (see, e.g., Granger and Lee 1989; Kinnucan and Forker 1987; Mohanty, Peterson, and Kruse 1996). Threshold behavior and asymmetric adjustment are distinct concepts. However, Abdulai (2000) also distinguishes between threshold models of an asymmetric and a symmetric type, the former being where the reaction to positive price shocks differs from that to a negative shock, but both types allow for asymmetric within- and out-of-threshold adjustment. It is the latter case that interests us here. Under such circumstances, and within a range, markets may be effectively separated, in that trade does not occur, although still integrated according to the modified LOP definition. Only when prices are outside of a threshold, will price changes in one market be transmitted to another market. This type of threshold model corresponds closely to those introduced by Balke and Fomby (1997) and developed by Hansen and Seo (2002) and Seo (2003). These articles postulate that the existence of transaction costs prevents investors realizing an investment opportunity and apply threshold cointegration to the term structure of interest rates. Goodwin and Piggot (2001) and Sephton (2003) make use of similar models to these in the context of price transmission.

The threshold autoregressive (TAR) and momentum threshold autoregressive (MTAR) models in Granger and Lee (1999), Enders and Granger (1998), and Escribano and Pfann (1997) have been the most popular threshold models. These allow for negative shocks, or deviations from equilibrium, to have different effects from those that are positive. They are related to, but distinct from, the models suggested by Balke and Fomby (1997), Hansen and Seo (2002), and Seo (2003).

If data on transport and other transactions costs were available to the price analyst then it would, as Baulch (1997) states, be a relatively simple arithmetic exercise to determine the "threshold band" within which trade would not be profitable. However, such data are rarely available. Also, it may be that there exist some costs faced by traders that are fixed. The partitioning of the various costs in k into fixed and variable components is likely to be arbitrary. Furthermore, as noted by Barrett and Li (2002), the potential for transfer costs to be nonstationary places important restrictions on this type of approach. However, typical estimates of such cost from "Structure, Conduct and Performance" studies are rarely available for the frequency and duration of available price series to enable the analyst to investigate the potential relationship further. The attractiveness, therefore, of employing models that allow the readily available price data to "speak for themselves" is evident.

This article introduces and implements a generalization of the symmetric version of the Hansen and Seo (2002) threshold autoregression model (TAR), which embodies both the Equilibrium-TAR (Eq-TAR) and Band-TAR models discussed in Balke and Fomby (1997). (2) While the Eq-TAR model follows conventional practice and assumes that it is the center of the threshold interval that forms the point of attraction from both outside and inside the interval, the Band-TAR allows the outer boundary of the threshold band to be that point of attraction from without. This distinction is important for inference and for subsequent analysis. If the data support the Band-TAR model, then price analysts would do better to look for mechanisms other than notional "long-run equilibrium" between two prices with which forecast price movements in a given series when that series lies within the threshold band.