Summary
A quadratic Box-Cox methodology is presented for choice of flexible functional form that includes consistent computation of variance estimates. Empirical viability of the procedure is investigated by specifying a dual profit function using highly aggregated U.S. agricultural data. Conditional and unconditional variance estimates for the parameters are compared and contrasted. Like-lihood ratio tests are utilized to discriminate among the generalized Leontief, normalized quadratic, translog, and square-rooted quadratic functional forms. Statistical results indicate that the squarerooted quadratic is the preferred choice of functional form for these data, followed by the normalized quadratic.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Appelbaum E (1979) On the choice of functional forms. International Economic Review 20:449–57
Ball VE (1988) Modelling supply response in a multiproduct framework. American Journal of Agricultural Economics 70:813–25
Berndt ER, Khaled MS (1979) Parametric productivity measurement and choice among flexible functional forms. Journal of Political Economy 87:1221–45
Blackley P, Follain JR, Ondrich J (1984) Box-Cox estimation of hedonic models: how serious is the iterative OLS variance bias? The Review of Economics and Statistics 66:348–53
Dagenais MG, Gaudry MJI, Liem TC (1987) Urban travel demand: the impact of Box-Cox transformations with nonspherical residual errors. Transportation Research 21B:443–47
Despotakis KA (1986) Economic performance of flexible functional forms. European Economic Review 30:1107–43
Rasmussen DW, Zuehlke TW (1990) On the choice of functional form for hedonic price functions. Applied Economics 22:431–38
Seaks TG, Layson SK (1983) Box-Cox estimation with standard econometric problems. The Review of Economics and Statistics 65:160–64
Spitzer JJ (1982a) A primer on the Box-Cox estimation. The Review of Economics and Statistics 64:307–13
Spitzer JJ (1982b) A fast and efficient algorithm for the estimation of parameters in models with the Box-Cox transformation. Journal of the American Statistical Association 77:760–66
Spitzer JJ (1984) Variance estimates in models with the Box-Cox transformation: implications for estimation and hypothesis testing. Review of Economics and Statistics 66:645–52
Zarembka P (1974) Frontiers in econometrics. New York Academic Press
Author information
Authors and Affiliations
Additional information
Fermin S. Ornelas is an econometrician, American Express Travel Co., Phoenix, Arizona. C. Richard Shumway is a professor and Teofilo Ozuna, Jr. is an associate professor in the Department of Agricultural Economics, Texas A & M University, College Station, Texas.
Appreciation is extended to Eldon Ball for access to his data set for U.S. agriculture and to Carl Shafer and Steve Fuller for helpful comments on an earlier draft.
Texas Agricultural Experiment Station Technical Article No. 25892. This material is based on work partially supported by the U.S. Department of Agriculture under Agreement No. 58-3AEM-8-00104.
Rights and permissions
About this article
Cite this article
Ornelas, F.S., Shumway, C.R. & Ozuna, T. Using the quadratic Box-Cox for flexible functional form selection and unconditional variance computation. Empirical Economics 19, 639–645 (1994). https://doi.org/10.1007/BF01205820
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01205820