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Inferences for the Extremum of Quadratic Regression Models

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Author Info
Joseph G. Hirschberg
Jenny N. Lye

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Abstract

Quadratic functions are often used in regression to infer the existence of an extremum in a relationship although tests of the location of the extremum are rarely performed. We investigate the construction of the following confidence intervals: Delta, Fieller, estimated first derivative, bootstrapping, Bayesian and likelihood ratio. We propose interpretations for the unbounded intervals that may be generated by some of these methods. The coverage of the confidence intervals is assessed by Monte Carlo; the Delta and studentized bootstrap can perform quite poorly. Of all the methods, the first derivative method is easiest to implement.

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File URL: http://www.economics.unimelb.edu.au/SITE/research/workingpapers/wp04/906.pdf
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Publisher Info
Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 906.

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Length: 24 pages
Date of creation: 2004
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Handle: RePEc:mlb:wpaper:906

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Related research
Keywords: Inverted U-Shaped; turning point; Fieller method; Delta method; 1st derivative function; Bayesian; Likelihood ratio; Bootstrap.;

Find related papers by JEL classification:
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Herbert G. Thompson, Jr. & Lynda L. Wolf, 1993. "Regional Differences in Nuclear and Fossil-Fuel Generation of Electricity," Land Economics, University of Wisconsin Press, vol. 69(3), pages 234-248. [Downloadable!] (restricted)
  2. 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.
  3. Jenny N. Lye & Joe Hirschberg, 2004. "Alcohol consumption, smoking and wages," Applied Economics, Taylor and Francis Journals, vol. 36(16), pages 1807-1817, September. [Downloadable!] (restricted)
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  4. Hsing, Yu, 1996. "Estimating the laffer curve and policy implications," The Journal of Socio-Economics, Elsevier, vol. 25(3), pages 395-401. [Downloadable!] (restricted)
  5. Zellner, Arnold, 1978. "Estimation of functions of population means and regression coefficients including structural coefficients : A minimum expected loss (MELO) approach," Journal of Econometrics, Elsevier, vol. 8(2), pages 127-158, October. [Downloadable!] (restricted)
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  1. J. G. Hirschberg, J. N. Lye & D. J. Slottje, 2008. "Confidence Intervals for Estimates of Elasticities," Department of Economics - Working Papers Series 1053, The University of Melbourne. [Downloadable!]
  2. J.G. Hirschberg & J. N. Lye, 2007. "Providing Intuition to the Fieller Method with Two Geometric Representations using STATA and Eviews," Department of Economics - Working Papers Series 992, The University of Melbourne. [Downloadable!]
Statistics
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