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Inverse Test Confidence Intervals for Turning points: A

  • J. N. Lye and J. G. Hirschberg

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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Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 1160.

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Length: 41 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:mlb:wpaper:1160
Contact details of provider: Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia
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