Distribution of Agricultural Research Impacts

When there is a correspondence between two logical systems, duality can be used to derive a correspondence between results in one system and results in another system (Russell and Wilkinson, 1978). Under appropriate regularity conditions, dual functions such as normalized profit functions in production economics embody the same information on technology as the more familiar primal production functions. The technology can be examined directly using the primal approach or indirectly using the dual approach. It is often easier to estimate product supply and input demand relationships using a dual approach, because only endogenous variables appear on the left-hand side of equations and only exogenous variables appear on the right-hand side of equations (Shumway, 1983). Duality concepts allow the estimation of output supply and input demand functions that are consistent with underlying economic theory (Shumway, 1986). Estimation generally requires that the equations be estimated as a system in order to account for relevant cross-equation restrictions. Regularity conditions related to homogeneity, symmetry, and curvature properties required to ensure that a profit-maximizing solution exists can be maintained through appropriate restrictions or tested. Considering the versatility and power of the duality approach, one would conclude that empirical estimates using this approach might be better in some sense than estimates from other models that were not consistent with economic theory. The purpose of this paper is to review empirical estimates related to technological change in U.S. agriculture that have been obtained using the duality approach. Both static and dynamic duality models will be considered, although there is only limited empirical evidence on technological change using the dynamic duality approach.