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The Global Properties of the Minflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms

William A. Barnett
Yul W. Lee

Abstract

Caves and Christensen [16] have provided a procedure for displaying the regular regions of a flexible functional form in the 2-good homothetic and nonhomothetic cases and in the 3-good homothetic case. We extend the procedure to the nonhomothetic 3-good case, and we apply the extended procedure to the translog, generalized Leontief, and minflex Laurent flexible functional form. In addition, we acquire the regular regions for the minflex Laurent model in the 2-good nonhomothetic case and superimpose the resulting regions on those already found by Caves and Christensen for the translog and generalized Leontief models. We find that the new minflex Laurent model generally has the largest regular regions of the three flexible functional forms. In addition, the regular region of the minflex Laurent model is found to expand as real income increases. As a result, that model is particularly well suited for use with time series data, which typically is characterized by positive long term growth trends in real income. In such applications, all recent data and future forecasts can be expected to lie within the regular region of the minflex Laurent model. Although it is possible for some of the earliest data to fall outside that regular region, the model's regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets. The regular region of each of three models moves when the model's parameters are changed. With the generalized Leontief or translog model, the regular region's shape, location, and size are unpredictable without prior knowledge of the model's parameters. With either of those two models, the intersection of the model's regular regions, as the parameters are changed, is contained within a very small neighborhood of the one point at which we require the model to be regular. With the minflex Laurent model, the primary properties of the regular regions are invariant to the values of the parameters, and the intersection of the displayed regular regions is a very large unbounded set. The width of that intersection increases without limit as real income increases.