Farm prices, retail prices, and directed graphs: Results for pork and beef

Gardner studies the consequences of the competitive model in factor and product markets. He is able to show, within the context of this model, how various shifts in the demand and supply for food will affect the retail-to-farm price ratio and the farmer's share of retail food expenditures. Hein and others have taken the deductive model described by Gardner as a blueprint in studying prices measured at different levels of the marketing chain with time-ordered observational data (nonexperimental data). This work relies heavily on lagged relationships to infer the direction of information flows in linear models. Given an information set (Ω(t-1) - X(t-1)), a nonzero partial correlation between prices at two different levels of the marketing chain, say, Y(t) and X(t-1), can be interpreted as indicating that X(t-1) causes Y(t), assuming that Ω(t-1) is the universal information set. In applications, of course, we never have the universal information set, so Ω(t-1) is defined as some set of important concomitant variables, Z(t-1), in addition to past values of X and Y. The reduction from the universal information set to a particular set of concomitant variables makes all such inference prima facie. Thus, researchers studying X and Y on information set Z might conclude that X causes Y, whereas those studying a slightly different set of conditioning information, say, Z', might conclude that X does not cause Y. Such studies say little about contemporaneous relationships among the variables X, Y, and Z. If one models data on X, Y, and Z as a vector autoregression, some assumption about contemporaneous correlation between innovations must be made. Early work applied the Choleski factorization, which is a recursive ordering between X, Y, and Z: X→ Y→ Z. A more recent approach to dealing with the contemporaneous correlation problem is the so-called structural factorization, following the similar approaches of Bernanke and Sims. A problem with the former (Choleski) is that the world might not be recursive (Cooley and LeRoy, Sims). A problem with the latter is that correct structural information might be unknown outside of a particular deductive model. This paper investigates the use of directed graphs in providing help in the standard practice of both assuming that Ω(t-1) is causally sufficient and providing data-based evidence on ordering in contemporaneous time. First, we review what is now a vast literature on directed graphs. Then we present results from the application of the method to modeling pork and beef prices at the farm and retail levels over recent time. Finally, we provide a conclusion.