TY - CHAP AB - In this chapter 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 Appendix A along with the data. VL - 30 SN - 978-1-78190-309-4, 978-1-78190-310-0/0731-9053 DO - 10.1108/S0731-9053(2012)0000030008 UR - https://doi.org/10.1108/S0731-9053(2012)0000030008 AU - Lye Jenny N. AU - Hirschberg Joseph G. ED - Dek Terrell ED - Daniel Millimet PY - 2012 Y1 - 2012/01/01 TI - Inverse Test Confidence Intervals for Turning-Points: A Demonstration with Higher Order Polynomials T2 - 30th Anniversary Edition T3 - Advances in Econometrics PB - Emerald Group Publishing Limited SP - 59 EP - 95 Y2 - 2024/03/29 ER -