Inverse Test Confidence Intervals for Turning points: A
In this paper we demonstrate the construction of inverse test confidence intervals for the turning points in estimated nonlinear relationships by the use of the marginal or first derivative function. First, we outline the inverse test confidence interval approach. Then we examine the relationship between the traditional confidence intervals based on the Wald test for the turning-points for a cubic, a quartic and fractional polynomials estimated via regression analysis and the inverse test intervals. We show that the confidence interval plots of the marginal function can be used to estimate confidence intervals for the turning points that are equivalent to the inverse test. We also provide a method for the interpretation of the confidence intervals for the second derivative function to draw inferences for the characteristics of the turning-point. This method is applied to the examination of the turning points found when estimating a quartic and a fractional polynomial from data used for the estimation of an Environmental Kuznets Curve. The Stata do files used to generate these examples are listed in the appendix along with the data.
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- repec:cup:cbooks:9780521785167 is not listed on IDEAS
- Ho-Chuan (River) Huang & Yi-Chen Lin & Chih-Chuan Yeh, 2012. "An appropriate test of the Kuznets hypothesis," Applied Economics Letters, Taylor & Francis Journals, vol. 19(1), pages 47-51, January.
- Bronwyn Coate & Tim R.L. Fry, 2012. "Better off Dead? Prices Realised for Australian Paintings Sold at Auction," ACEI Working Paper Series AWP-02-2012, Association for Cultural Economics International, revised Feb 2012.
- Vandaele, Walter, 1981. "Wald, likelihood ratio, and Lagrange multiplier tests as an F test," Economics Letters, Elsevier, vol. 8(4), pages 361-365.
- Stanley Winer & Michael Tofias & Bernard Grofman & John Aldrich, 2008. "Trending economic factors and the structure of Congress in the growth of government, 1930–2002," Public Choice, Springer, vol. 135(3), pages 415-448, June.
- Jeffrey M Wooldridge, 2010.
"Econometric Analysis of Cross Section and Panel Data,"
MIT Press Books,
The MIT Press,
edition 2, volume 1, number 0262232588, June.
- Jeffrey M. Wooldridge, 2001. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262232197, June.
- Hirschberg, J.G. & Lye, J.N., 2010. "Two geometric representations of confidence intervals for ratios of linear combinations of regression parameters: An application to the NAIRU," Economics Letters, Elsevier, vol. 108(1), pages 73-76, July.
- repec:cup:cbooks:9780521780506 is not listed on IDEAS
- Gang Liu & Terje Skjerpen & Kjetil Telle, 2009.
"Unit roots, polynomial transformations and the environmental Kuznets curve,"
Applied Economics Letters,
Taylor & Francis Journals, vol. 16(3), pages 285-288.
- Gang Liu & Terje Skjerpen & Anders Rygh Swensen & Kjetil Telle, 2006. "Unit Roots, Polynomial Transformations and the Environmental Kuznets Curve," Discussion Papers 443, Research Department of Statistics Norway.
- Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
- Hirschberg, J.G. & Lye, J.N. & Slottje, D.J., 2008. "Inferential methods for elasticity estimates," Journal of Econometrics, Elsevier, vol. 147(2), pages 299-315, December.
- Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
- Tamás Bartus, 2005. "Estimation of marginal effects using margeff," Stata Journal, StataCorp LP, vol. 5(3), pages 309-329, September.
- Clark, Andrew E. & Oswald, Andrew J. & Warr, Peter B., 1994. "Is job satisfaction u-shaped in age ?," CEPREMAP Working Papers (Couverture Orange) 9407, CEPREMAP.
- Florenz Plassmann & Neha Khanna, 2007. "Assessing the Precision of Turning Point Estimates in Polynomial Regression Functions," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 503-528.
- Richmond, Amy K. & Kaufmann, Robert K., 2006. "Is there a turning point in the relationship between income and energy use and/or carbon emissions?," Ecological Economics, Elsevier, vol. 56(2), pages 176-189, February.
- French, Michael T. & Zarkin, Gary A., 1995. "Is moderate alcohol use related to wages? Evidence from four worksites," Journal of Health Economics, Elsevier, vol. 14(3), pages 319-344, August.
- Lind, Jo Thori & Mehlum, Halvor, 2007.
"With or Without U? The appropriate test for a U shaped relationship,"
21/2007, Oslo University, Department of Economics.
- Jo Thori Lind & Halvor Mehlum, 2010. "With or Without U? The Appropriate Test for a U-Shaped Relationship," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(1), pages 109-118, 02.
- Lind, Jo Thori & Mehlum, Halvor, 2007. "With or Without U? - The appropriate test for a U shaped relationship," MPRA Paper 4823, University Library of Munich, Germany.
- Kearsley, Aaron & Riddel, Mary, 2010. "A further inquiry into the Pollution Haven Hypothesis and the Environmental Kuznets Curve," Ecological Economics, Elsevier, vol. 69(4), pages 905-919, February.
- Bagliani, Marco & Bravo, Giangiacomo & Dalmazzone, Silvana, 2008. "A consumption-based approach to environmental Kuznets curves using the ecological footprint indicator," Ecological Economics, Elsevier, vol. 65(3), pages 650-661, April.
- Kavi Kumar, K.S. & Viswanathan, Brinda, 2007. "Changing structure of income indoor air pollution relationship in India," Energy Policy, Elsevier, vol. 35(11), pages 5496-5504, November.
- Shahdad Naghshpour, 2005. "The cyclical nature of family income distribution in the united states: An empirical note," Journal of Economics and Finance, Springer, vol. 29(1), pages 138-143, March.
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