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Polynomial Regressions and Nonsense Inference

Author

Listed:
  • Daniel Ventosa-Santaulària

    (Centro de Investigación y Docencia Económicas (CIDE), División de Economía, Carretera México-Toluca 3655 Col. Lomas de Santa Fe, Delegación Álvaro Obregón, México 01210, Mexico)

  • Carlos Vladimir Rodríguez-Caballero

    (Center for Research in Econometric Analysis of Time Series (CREATES) and Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, Building 2622 (203), Aarhus V 8210, Denmark)

Abstract

Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis and psychology, just to mention a few examples. In many cases, the data employed to estimate such specifications are time series that may exhibit stochastic nonstationary behavior. We extend Phillips’ results (Phillips, P. Understanding spurious regressions in econometrics. J. Econom. 1986, 33, 311–340.) by proving that an inference drawn from polynomial specifications, under stochastic nonstationarity, is misleading unless the variables cointegrate. We use a generalized polynomial specification as a vehicle to study its asymptotic and finite-sample properties. Our results, therefore, lead to a call to be cautious whenever practitioners estimate polynomial regressions.

Suggested Citation

  • Daniel Ventosa-Santaulària & Carlos Vladimir Rodríguez-Caballero, 2013. "Polynomial Regressions and Nonsense Inference," Econometrics, MDPI, vol. 1(3), pages 1-13, November.
    • Handle: RePEc:gam:jecnmx:v:1:y:2013:i:3:p:236-248:d:30523
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    References listed on IDEAS

    as
    1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    2. Marco Leonardi & Giovanni Pica, 2013. "Who Pays for it? The Heterogeneous Wage Effects of Employment Protection Legislation," Economic Journal, Royal Economic Society, vol. 123(12), pages 1236-1278, December.
    3. Zsolt Darvas, 2008. "Estimation Bias and Inference in Overlapping Autoregressions: Implications for the Target‐Zone Literature," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(1), pages 1-22, February.
    4. Chandrajit Chatterjee & Ram Rup Sarkar, 2009. "Multi-Step Polynomial Regression Method to Model and Forecast Malaria Incidence," PLOS ONE, Public Library of Science, vol. 4(3), pages 1-11, March.
    5. Labson B. Stephen & Crompton Paul L., 1993. "Common Trends in Economic Activity and Metals Demand: Cointegration and the Intensity of Use Debate," Journal of Environmental Economics and Management, Elsevier, vol. 25(2), pages 147-161, September.
    6. Lee, Young-Sook & Kim, Tae-Hwan & Newbold, Paul, 2005. "Spurious nonlinear regressions in econometrics," Economics Letters, Elsevier, vol. 87(3), pages 301-306, June.
    7. Pena, Daniel & Rodriguez, Julio, 2005. "Detecting nonlinearity in time series by model selection criteria," International Journal of Forecasting, Elsevier, vol. 21(4), pages 731-748.
    8. O'Brien, Edward J., 2008. "A note on spurious nonlinear regression," Economics Letters, Elsevier, vol. 100(3), pages 366-368, September.
    9. de Jong, Robert M., 2003. "Logarithmic spurious regressions," Economics Letters, Elsevier, vol. 81(1), pages 13-21, October.
    10. Wagner, Martin, 2012. "The Phillips unit root tests for polynomials of integrated processes," Economics Letters, Elsevier, vol. 114(3), pages 299-303.
    11. Maximilian Auffhammer & Ryan Kellogg, 2011. "Clearing the Air? The Effects of Gasoline Content Regulation on Air Quality," American Economic Review, American Economic Association, vol. 101(6), pages 2687-2722, October.
    12. Christos Ioannidis & David A. Peel & Michael J. Peel, 2003. "The Time Series Properties of Financial Ratios: Lev Revisited," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(5‐6), pages 699-714, June.
    13. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    14. Kellenberg, Derek, 2012. "Trading wastes," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 68-87.
    15. Green, Donald P. & Leong, Terence Y. & Kern, Holger L. & Gerber, Alan S. & Larimer, Christopher W., 2009. "Testing the Accuracy of Regression Discontinuity Analysis Using Experimental Benchmarks," Political Analysis, Cambridge University Press, vol. 17(4), pages 400-417.
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    More about this item

    Keywords

    polynomial regression; misleading inference; integrated processes;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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