270 European Journal of Operational Research 30 (1987) 270-279 North-Holland The Laurent series approach to structural modeline William A. BARNETT and Yul W. LEE * Department of Economics, The University of Texas, Austin, TX 78712, U.S.A. Abstract: Caves and Christensen (1980) 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 forms. 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 the 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 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. Keywords: Modelling, consumption, demand 1. Introduction * William A. Bamett is the Stuart Professor of Economics and the Janey Briscoe Centennial Fellow of the IC* Research Institute at The University of Texas at Austin. Yul W. Lee. is a graduate student at The University of Texas at Austin. We are grateful to Sang Yong Han for his expert computing assistance and to Robert Basmann and Raymond Byron for their helpful comments. This research was partially sup- ported by NSF grant SOC 8305162. Received March 1985; revised September 1985 Many important hypotheses in consumption theory are equivalent to restrictions on first and second order derivatives. Hence the ability of a functional form to attain arbitrary first and sec- ond order derivatives, subject only to the restric- tions of maintained economic theory, is needed in testing such hypotheses. As a result, a literature has arisen on utility function specifications having the local capability of being able to attain arbi- 03X’-X17/87/%3.50 0 1987, Elsevier Science Publishers B.V. (North-Holland)