Testing Hypotheses of Functional Structure: Some Rules for Determining Flexibility of Restricted Production Models

Rules are proposed to help determine whether a production function maintains flexibility under parametric restrictions required to impose homogeneity, homotheticity, and forms of separability. After imposing restrictions and applying the rules, many second-order "flexible " forms are found to be more inflexible than formerly believed. Key words: flexible functional forms, hypothesis testing. The catalogue of flexible functional forms avail-able for modeling technologies is vast and growing. Although a subset of these forms are appealing because of their interpretation as a se-ries expansion (Blackorby, Primont, and Rus-sell 1978), it is the flexibility property, common to all of them, which first interested economists and helped motivate their development. Flexi-bility refers to a model's capacity to provide in-dependent measures of the function value, gra-dient vector, and hessian of some underlying function at an arbitrary point. As Diewert, Lau, Chambers, and others have shown, the model must contain a minimal number of parameters to achieve such flexibility. Just as it is possible to determine the minimal number of parameters required for adequate flexibility in an unconstrained production model, it is also possible to determine the minimal number of parameters required for adequate flexibility of homogenous, homothetic, and sep-arable models. Why bother? The reason is that parametric restrictions needed to impose ho-mogeneity or separability can sometimes render the model homogeneity inflexible or separabil-ity inflexible (Blackorby, Primont, and Russell 1977; hereafter BPR refers to the 1977 paper). That is, after imposing restrictions, insufficien