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«Testing Market Equilibrium: Is Cointegration Informative? Kevin McNew and Paul L. Fackler Cointegration methods are increasingly used to test for ...»

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Journal of Agricultural and Resource Economics 22(2):191-207

Copyright 1997 Western Agricultural Economics Association

Testing Market Equilibrium:

Is Cointegration Informative?

Kevin McNew and Paul L. Fackler

Cointegration methods are increasingly used to test for market efficiency and integration. The economic rationale for these tests, however, is generally unclear. Using

a simple spatial equilibrium model to simulate equilibrium price behavior, it is shown that prices in a well-integrated, efficient market need not be cointegrated. Furthermore, the number of cointegrating relationships among prices is not a good indicator of the degree to which a market is integrated.

market integration, spatial markets, time-series analysis

Key words:

Introduction It has become common to apply cointegration techniques to the analysis of spatial price relationships, both to test the law of one price (LOP) and to examine the degree to which different regions are mutually integrated. Cointegration models presuppose that observable variables exhibiting nonstationary behavior will nonetheless maintain long-run relationships. These long-run relationships are conceptually interpreted as stochastic (longrun) economic equilibria. In this view an economy is described as a multivariable dynamic system, equilibria as the attractors of the system (the set of points towards which the system tends to move), and error-correction mechanisms as the forces that move prices toward the attractor.

Among the most common examples of an error-correcting mechanism is arbitrage in a spatial market; this is the example that Engle and Granger use in their introduction to a volume of readings on cointegration. The essence of the argument is that prices of a homogenous good from two different regions should tend to be equal in the long run.

More specifically, an extended period with no exogenous shocks would move the two prices towards equality. The error-correction mechanism is the arbitrage process. Profit opportunities arise when the economy is away from the attractor and arbitrage forces prices back towards the attractor defined by the relationship p, = P2. This is essentially a statement of the LOP.

A number of studies have used this idea to test the LOP (Ardeni; Goodwin 1992a;

Goodwin and Grennes; Michael, Nobay, and Peel).1 Some studies simply test for cointegration; others contend that not only should cointegration be present but a specific linear price relationship should be stationary. Baffes argues that price movements in one The authors are, respectively, an assistant professor in the Department of Agricultural and Resource Economics at the University of Maryland and associate professor in the Department of Agricultural and Resource Economics at North Carolina State University.

I Cointegration has also been used to test forward market efficiency (Corbae, Lim, and Ouliaris) and the rationality of the term structure of interest rates (Hall, Anderson, and Granger). Like the LOP, these involve arbitrage relationships defined by complementarity conditions. The results of this study, therefore, also extend to these concepts.

192 December 1997 Journal of Agricultural and Resource Economics location should be matched, in the long run, with one-for-one price movements in another location; this is equivalent to the stationarity of price spreads.

A corollary to the above assertion is that the absence of trade between regions (either direct or indirect) should result in prices that are not cointegrated. This has led some researchers to use cointegration as an indicator for the strength of regional connections.

For example, Goodwin (1992b) and Goodwin and Grennes suggest that a system of n spatial prices should have at least one cointegrating relationship, and the number of cointegrating relationships among prices can indicate the extent of market integration.

Thus, full market integration requires n - 1 cointegrating vectors and any number of cointegrating vectors less than n - 1 implies markets which are not fully integrated.

Similar suggestions are made in Benson et al. (1994a) and Silvapulle and Jayasuriya.

Also, some studies perform bivariate tests on price pairs, associating the degree of integration for a given location with the number of other locations exhibiting cointegration (Alexander and White).

The purpose of this study is to suggest caution in the application and interpretation of cointegration models in analyzing spatial price behavior. To demonstrate that such caution is warranted, we develop an equilibrium spatial market model that is used to simulate prices. The simulations allow us to explore the hypothesis that cointegration in prices should occur because the forces of market integration and efficiency tend to result in linearly related prices.

Unlike many studies, we sharply distinguish between the concepts of efficiency and integration. In our treatment, the concepts of efficiency and the LOP are synonymous and taken to mean that arbitrage opportunities are quickly eliminated and therefore negligible in observed variables, including prices. This feature is a necessary condition for market equilibrium and, therefore, is a distinguishing feature of price behavior. Market integration, on the other hand, we define as the extent to which shocks arising in one location are passed on to other locations, a meaning that is consistent with the work of Harriss and Ravallion. The specific definition (stated in a later section) will arise naturally out of the equilibrium model used here.

The analysis indicates that neither efficiency nor market integration necessarily leads to linearly related prices. Our demonstration centers around the arbitrage mechanism, which is shown to be an insufficient force to ensure a simple linear relationship among spatial prices. There are two parts to this demonstration. First we show that if the underlying forces affecting supply and demand in different regions are not cointegrated, arbitrage alone will not guarantee that prices exhibit cointegration, especially as transport rates increase in size and volatility. Second, if the demand and supply forces are themselves cointegrated across regions, an analyst may conclude that prices are cointegrated regardless of whether there are interregional flows of commodities and associated binding arbitrage conditions. Examples of cointegrated economic shocks include weather variability in agricultural production, public policies that have similar impacts across regions, or income and inflation factors. In these instances, the presence of cointegration does not indicate that arbitrage is the source of the error correction mechanism. It therefore follows that the degree of cointegration among prices is not a useful measure of the strength of the interregional market integration.

The suggestion that statistical measures do not always have simple economic interpretations is not new. Harriss and Ravallion argue that high price correlations do not necessarily indicate a high degree of market integration. Transaction costs are also known Market Equilibrium and Cointegration 193 McNew and Fackler to influence cointegration tests. For example, Davutyan and Pippenger show that one is less likely to find cointegrated prices or stationary price spreads when transaction costs are large. Goodwin (1992a) suggests that the lack of cointegration for international wheat prices may be due to nonstationarity in ocean freight rates; Hsu and Goodwin provide further evidence on this point. Indeed, Granger also suggests that nonstationary risk premia may explain the lack of cointegrated treasury bond prices in the early 1980s.

In spite of these cautions, the number of studies that pay no attention to the problem greatly outweigh those that even mention it. Furthermore, the issue has not been explored systematically within the context of an economic model of spatial price determination.

A novel feature of the current article is that an explicit spatial equilibrium model is used to generate simulated prices with known economic properties. This represents a kind of controlled experiment that allows us to explore whether the interpretations placed on cointegration tests are justified.

To focus attention on the potential problems in applying cointegration to the analysis of spatial prices, we first discuss spatial models of price behavior and their implications for cointegration. Later we discuss a very simple spatial equilibrium model and an associated measure of market integration are developed. The model is used to generate simulated price data to illustrate some of the problems discussed above.

Spatial Equilibrium Models and Price Spreads

A number of spatial equilibrium models currently exist, although many (if not most) can be classified into two groups. The first, originating with Hotelling and Smithies, is a network framework with markets or firms located at network nodes and consumers or commodity producers located continuously along network links. Agents located along the links will choose to transact at the node offering the best price net of transport costs.

Such models, which we call agents-on-links models, are often, although not exclusively, used to model spatial oligopoly situations where firms exert some local monopoly or monopsony power but may gain or lose market share to firms located at other nodes.

Benson et al. (1994a,b) study the cointegration of spatial prices in the context of such a model, but provide no formal link between the model and cointegration methods. The application of cointegration methods in the analysis of market power has been criticized by Werden and Froeb.

The second group of models is also based on a network structure but the network links serve only for commodity transportation flows. Such point-location models originated with Enke and Samuelson and were popularized by Takayama and Judge. They have mainly been used to model perfectly competitive markets characterized by distinct regions or centers of activity.

Which of these two classes of models is appropriate depends on the nature of the market. For example, agricultural products are often produced in rural areas around isolated processing plants. The plants have local monopsony power, but are constrained by the possibility that producers can ship to competitors' plants. In a study of the prices paid to producers at the plant, the first model would therefore be appropriate. On the other hand, many bulk goods are collected or processed at a small number of points and then transported to a small number of major distribution centers; grain, coal, and gasoline markets are examples. In such cases, as well as in many international trade situations, 194 December 1997 Journal of Agricultural and Resource Economics especially those involving ocean freight or tariffs imposed at the border, point-location models are appropriate.

The issue of whether a perfect competition assumption is appropriate is conceptually different from that of the choice of a spatial structure. An agents-on-links model with a competitive assumption might be appropriate in a situation in which several firms are located at each of the major distribution centers.

In the point-location model each pair of nodes is either linked by trade or it isn't. If the nodes are linked by trade (either directly or indirectly) then prices will differ by an amount that depends only on transport rates. To illustrate, suppose region 1 ships to region 2, so there is a direct trade link. The appropriate arbitrage condition is P2 - pA = r1, where Pi is the price in region i and rij is the cost of shipping from region i to j.

The regions may also be indirectly linked. For example, suppose regions 1 and 2 both ship to 3; prices must satisfy P2 = p 3 - r23 and p, = p 3 - r13, implying that P2 - P1 = r13 - r 23. An immediate implication for dynamic price behavior is that price spread stationarity requires transport rate stationarity.2 This is an empirical question, and indeed, there is some evidence to suggest that ocean freight rates, at least, behave like many other prices in exhibiting nonstationarity (Hsu and Goodwin). 3 With an agents-on-links model the relationship between the nodal prices is even more complicated. Between each node a boundary exists at which an agent is indifferent between transacting with one node or the other. Thus, the prices at the nodes will generally not differ by the cost of transporting the goods between them, and hence, arbitrage between the two nodal points cannot be the mechanism generating cointegrated prices.

If there is a role for arbitrage as an error correcting mechanism in the agents-on-links model, it must be the arbitrage that occurs in determining the boundary. For example, suppose that regions 1 and 2 are d miles apart and there is a constant per mile transport cost, r, between them. The indifference boundary, B, measured in miles from region 1, satisfies the arbitrage condition p1 - rB = P2 - r(d - B); equilibrium prices are therefore related according to (1) P2 - P = r(d - 2B).

In this case the stationarity of the price differentials depends on the stationarity not only of the transport rates but also of the market boundary times the transport rate. The location of the boundary will shift over time as demand, supply, and transportation costs change; thus it is determined in a complex way by all the relevant factors affecting the market. As these are the same factors causing the apparent price nonstationarity, arbitrage alone cannot account for price spread stationarity. 4 2More precisely, for all price spreads to be stationary, all transport rates must be stationary. It is possible, however, for some spreads to be stationary and not others. For example, suppose that r13 and r2 are nonstationary but that r 3 - r2 is 3 stationary. Consider a market in which locations 1 and 2 consistently ship to location 3, so = p -3 r3 and P2 = P3 - r.

= 23 This implies that P2 - Pl is stationary but P2 - p and Pl - p are not.

3If transport rate data were available, cointegration among the prices and the transport rates could be analyzed. Such data are generally difficult to obtain and even when transport rates are available, other important transaction costs that affect price relationships may not be.

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