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Confidence bounds for the extremum determined by a quadratic regression

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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

Suggested Citation

  • Jenny Lye & Joe Hirschberg, 2004. "Confidence bounds for the extremum determined by a quadratic regression," Econometric Society 2004 Australasian Meetings 217, Econometric Society.
    • Handle: RePEc:ecm:ausm04:217
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    1. William A. Barnett, 2000. "New Indices of Money Supply and the Flexible Laurent Demand System," Contributions to Economic Analysis, in: The Theory of Monetary Aggregation, pages 325-359, Emerald Group Publishing Limited.
    2. Murphy, Kevin M & Welch, Finis, 1990. "Empirical Age-Earnings Profiles," Journal of Labor Economics, University of Chicago Press, vol. 8(2), pages 202-229, April.
    3. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    4. 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.
    5. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
    6. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-170, February.
    7. Hsing, Yu, 1996. "Estimating the laffer curve and policy implications," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 25(3), pages 395-401.
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    More about this item

    Keywords

    Turning Point; Fieller interval; U-shaped;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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