Confidence bounds for the extremum determined by a quadratic regression

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Confidence bounds for the extremum determined by a quadratic regression

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Jenny Lye
Joe Hirschberg

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Abstract

A quadratic function is frequently used in regression to infer the existence of an extremum in a relationship. Examples abound in fields such as economics, epidemiology and environmental science. However, most applications provide no formal test of the extremum. Here we compare the Delta method and the Fieller method in typical applications and perform a Monte Carlo study of the coverage of these confidence bounds. We find that unless the parameter on the squared term is estimated with great precision, the Fieller confidence interval may posses dramatically better coverage than the Delta method

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Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 217.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:217

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-10-30 (All new papers)
NEP-ECM-2004-10-30 (Econometrics)
NEP-IFN-2004-10-30 (International Finance)

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Berger, Mark C & Leigh, J Paul, 1988. "The Effect of Alcohol Use on Wages," Applied Economics, Taylor and Francis Journals, vol. 20(10), pages 1343-51, October.
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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.
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