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Sequentially Testing Polynomial Model Hypotheses using Power Transforms of Regressors

Author

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  • JIN SEO CHO

    (Yonsei University)

  • PETER C.B. PHILLIPS

    (Yale University University of Auckland, Singapore Management University & University of Southampton)

Abstract

We provide a methodology for testing a polynomial model hypothesis by extending the approach and results of Baek, Cho, and Phillips (2015; BCP) that tests for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We examine and generalize the BCP quasi-likelihood ratio test dealing with the multifold identification problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful in the application of sieve approximations. Simulations show good performance in the sequential test procedure in identifying and estimating unknown polynomial order. The approach, which can be used empirically to test for misspecification, is applied to a Mincer (1958, 1974) equation using data from Card (1995). The results confirm that Mincer¡¯s log earnings equation is easily shown to be misspecified by including nonlinear effects of experience and schooling on earnings, with some flexibility required in the respective polynomial degrees.

Suggested Citation

  • Jin Seo Cho & Peter C.B. Phillips, 2016. "Sequentially Testing Polynomial Model Hypotheses using Power Transforms of Regressors," Working papers 2016rwp-90, Yonsei University, Yonsei Economics Research Institute.
  • Handle: RePEc:yon:wpaper:2016rwp-90
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    References listed on IDEAS

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    1. Jin Seo Cho & Isao Ishida & Halbert White, 2013. "Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions (published in: Essays in Nonlinear Time Series Econometrics, Festschrift in Honor of Timo Teras," Working papers 2013rwp-55, Yonsei University, Yonsei Economics Research Institute.
    2. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    3. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    4. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    6. Cho, Jin Seo & Ishida, Isao, 2012. "Testing for the effects of omitted power transformations," Economics Letters, Elsevier, vol. 117(1), pages 287-290.
    7. Jacob A. Mincer, 1974. "Introduction to "Schooling, Experience, and Earnings"," NBER Chapters, in: Schooling, Experience, and Earnings, pages 1-4, National Bureau of Economic Research, Inc.
    8. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(4), pages 557-614, August.
    9. Jacob Mincer, 1958. "Investment in Human Capital and Personal Income Distribution," Journal of Political Economy, University of Chicago Press, vol. 66, pages 281-281.
    10. Jacob A. Mincer, 1974. "Schooling, Experience, and Earnings," NBER Books, National Bureau of Economic Research, Inc, number minc74-1, March.
    11. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
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    Citations

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    Cited by:

    1. Jin Seo Cho & Jin Seok Park & Sang Woo Park, 2018. "Testing for the Conditional Geometric Mixture Distribution," Working papers 2018rwp-123, Yonsei University, Yonsei Economics Research Institute.
    2. Peter C. B. Phillips & Zhentao Shi, 2019. "Boosting: Why You Can Use the HP Filter," Papers 1905.00175, arXiv.org, revised Nov 2020.
    3. Mohitosh Kejriwal & Xiaoxiao Li & Evan Totty, 2020. "Multidimensional skills and the returns to schooling: Evidence from an interactive fixed‐effects approach and a linked survey‐administrative data set," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 548-566, August.
    4. Mohitosh Kejriwal & Xiaoxiao Li & Evan Totty, 2019. "Multidemsional Skills and Returns to Schooling: Evidence from an Interactive Fixed Effects Aproach and a Linked Survey-Administrative Dataset," Purdue University Economics Working Papers 1316, Purdue University, Department of Economics.
    5. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: A New Angle on the Environmental Kuznets Curve," Papers 2009.02262, arXiv.org.
    6. Jaedo Choi & Jin Seo Cho & Hyungsik Roger Moon, 2020. "Sequentially Estimating the Structural Equation by Power Transformation," Working papers 2020rwp-162, Yonsei University, Yonsei Economics Research Institute.
    7. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Jan 2021.
    8. Dakyung Seong & Jin Seo Cho & Timo Terasvirta, 2019. "Comprehensive Testing of Linearity against the Smooth Transition Autoregressive Model," Working papers 2019rwp-151, Yonsei University, Yonsei Economics Research Institute.
    9. Zhishui Hu & Peter C.B. Phillips & Qiying Wang, 2019. "Nonlinear Cointegrating Power Function Regression with Endogeneity," Cowles Foundation Discussion Papers 2211, Cowles Foundation for Research in Economics, Yale University.

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    More about this item

    Keywords

    QLR test; Asymptotic null distribution; Misspecification; Mincer equation; Nonlinearity; Polynomial model; Power Gaussian process; Sequential testing.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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