Assessing the Precision of Turning Point Estimates in Polynomial Regression Functions

Florenz Plassmann and Neha Khanna

Econometric Reviews, 2007, vol. 26, issue 5, 503-528

Abstract: Researchers often report point estimates of turning point(s) obtained in polynomial regression models but rarely assess the precision of these estimates. We discuss three methods to assess the precision of such turning point estimates. The first is the delta method that leads to a normal approximation of the distribution of the turning point estimator. The second method uses the exact distribution of the turning point estimator of quadratic regression functions. The third method relies on Markov chain Monte Carlo methods to provide a finite sample approximation of the exact distribution of the turning point estimator. We argue that the delta method may lead to misleading inference and that the other two methods are more reliable. We compare the three methods using two data sets from the environmental Kuznets curve literature, where the presence and location of a turning point in the income-pollution relationship is the focus of much empirical work.

Keywords: Asymmetric confidence interval; Environmental Kuznets curve hypothesis; MCMC; Quantiles (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (18)

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DOI: 10.1080/07474930701512105

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