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Abstract
A flexible functional form can provide a second-order approximation to an arbitrary
unknown function at a single point. Except in special cases, the parameters of flexible
forms will vary from one point of approximation to another. I use this property to
show that, in general, if an unknown function is homogeneous then i) Euler's Theorem
gives rise to linear equality constraints involving both the data and a set of
observation-varying flexible form parameters, ii) the common practice of imposing
homogeneity on flexible functional forms is unnecessarily restrictive, and iii) it is
possible to obtain estimates of the observation-varying parameters of approximating
flexible forms using a Singular Value Decomposition (SVD) estimator. Two
illustrations are provided: artificially-generated data is used to estimate the
characteristics of a generalised linear production function; and Canadian data is used
to estimate the characteristics of a consumer demand system.