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Abstract
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.