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An Exact Test For The Choice Of The Combination Of First Differences And Percentage Changes In Linear Models

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  • Wai Cheung Ip

    (The Hong Kong Polytechnic University)

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    Abstract

    Econometric models are often formulated in terms of the first difference or the percentage change, both of which may be generalized by the Box-Cox difference transformation. Unfortunately, economic theory typically provides little guidance to the proper functional forms appropriate to the specification of the economic relationships. The choice of suitable functional forms thus relies heavily upon established statistical procedures. Existing procedures adopt primarily the classical likelihood approach and mainly confine to a single transformation parameter only, thus seriously limiting the use of more appropriate models. When multi-parameter transformation is allowed, these procedures would require to search over a multidimensional grid of values, rendering them extremely expensive, if not impossible, to find the optimal solution.We have derived an exact test for the parameter vector of transformation in linear models. By utilizing Taylor series approximations this reduces to a choice between two regression equations. The test statistic which has an exact F-distribution can be easily calculated from these two regression equations by least squares estimation, which algorithm is available from the very handy to the sophisticated statistical packages. It is therefore a simple and ready statistical procedure for assessing the suitable choice of the functional forms of the variables, thereby allowing more flexible and appropriate economic relations be formulated and their validity be tested.

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    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 31.

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    Date of creation: 05 Jul 2000
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    Handle: RePEc:sce:scecf0:31

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    Postal: CEF 2000, Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas, 25,27, 08005, Barcelona, Spain
    Fax: +34 93 542 17 46
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    Web page: http://enginy.upf.es/SCE/
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    1. Colclough, William G. & Lange, Mark D., 1982. "Empirical evidence of causality from consumer to wholesale prices," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 379-384, August.
    2. Layson, Stephen K & Seaks, Terry G, 1984. "Estimation and Testing for Functional Form in First Difference Models," The Review of Economics and Statistics, MIT Press, vol. 66(2), pages 338-43, May.
    3. Coulson, N Edward & Robins, Russell P, 1985. "A Comment on the Testing of Functional Form in First Difference Models," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 710-12, November.
    4. Leonall C. Andersen & Keith M. Carlson, 1970. "A monetarist model for economic stabilization," Review, Federal Reserve Bank of St. Louis, issue Apr, pages 7-25.
    5. R. W. Hafer & Scott E. Hein, 1980. "The dynamics and estimation of short-run money demand," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 26-35.
    6. Thornton, James R & Agnello, Richard J & Link, Charles R, 1978. "Poverty and Economic Growth: Trickle Down Peters Out," Economic Inquiry, Western Economic Association International, vol. 16(3), pages 385-94, July.
    7. Park, Timothy, 1991. "Double Length Regressions for Testing the Box-Cox Difference Transformation," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 181-85, February.
    8. Seaks, Terry G & Vines, Donna P, 1990. "A Monte Carlo Evaluation of the Box-Cox Difference Transformation," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 506-10, August.
    9. Godfrey, Lesley G & Wickens, Michael R, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," Review of Economic Studies, Wiley Blackwell, vol. 48(3), pages 487-96, July.
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