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Sequentially Testing Polynomial Model Hypotheses using Power Transforms of Regressors

Author

Listed:
  • 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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    Cited by:

    1. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    2. 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.
    3. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?," Papers 2009.02262, arXiv.org, revised Dec 2021.
    4. Hu, Zhishui & Phillips, Peter C.B. & Wang, Qiying, 2021. "Nonlinear Cointegrating Power Function Regression With Endogeneity," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1173-1213, December.
    5. 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.
    6. 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.
    7. Jin Seo Cho & Matthew Greenwood‐Nimmo & Yongcheol Shin, 2023. "Recent developments of the autoregressive distributed lag modelling framework," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 7-32, February.
    8. Choi, Jaedo & Moon, Hyungsik Roger & Cho, Jin Seo, 2024. "Sequentially Estimating The Structural Equation By Power Transformation," Econometric Theory, Cambridge University Press, vol. 40(1), pages 98-161, February.
    9. 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.
    10. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.

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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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