Distribution of Agricultural Research Impacts

When there is a correspondence between two logical systems, duality can be used to derivea correspondence between results in one system and results in another system (Russell andWilkinson, 1978). Under appropriate regularity conditions, dual functions such as normalizedprofit functions in production economics embody the same information on technology as the morefamiliar primal production functions. The technology can be examined directly using theprimal approach or indirectly using the dual approach. It is often easier to estimate productsupply and input demand relationships using a dual approach, because only endogenous variablesappear on the left-hand side of equations and only exogenous variables appear on the right-handside of equations (Shumway, 1983).Duality concepts allow the estimation of output supply and input demand functions thatare consistent with underlying economic theory (Shumway, 1986). Estimation generally requiresthat the equations be estimated as a system in order to account for relevant cross-equationrestrictions. Regularity conditions related to homogeneity, symmetry, and curvatureproperties required to ensure that a profit-maximizing solution exists can be maintainedthrough appropriate restrictions or tested.Considering the versatility and power of the duality approach, one would conclude thatempirical estimates using this approach might be better in some sense than estimates fromother models that were not consistent with economic theory. The purpose of this paper is toreview empirical estimates related to technological change in U.S. agriculture that have beenobtained using the duality approach. Both static and dynamic duality models will be considered,although there is only limited empirical evidence on technological change using thedynamic duality approach.