IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v1y2013i3p236-248d30523.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/1/3/236/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2225-1146/1/3/236/
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    2. Esther Stroe-Kunold & Joachim Werner, 2009. "A drunk and her dog: a spurious relation? Cointegration tests as instruments to detect spurious correlations between integrated time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(6), pages 913-940, November.
    3. Lee, Young-Sook & Kim, Tae-Hwan & Newbold, Paul, 2005. "Spurious nonlinear regressions in econometrics," Economics Letters, Elsevier, vol. 87(3), pages 301-306, June.
    4. Imad A. Moosa, 2017. "Blaming suicide on NASA and divorce on margarine: the hazard of using cointegration to derive inference on spurious correlation," Applied Economics, Taylor & Francis Journals, vol. 49(15), pages 1483-1490, March.
    5. Lee, Chien-Chiang & Lee, Jun-De, 2009. "Income and CO2 emissions: Evidence from panel unit root and cointegration tests," Energy Policy, Elsevier, vol. 37(2), pages 413-423, February.
    6. Martin Wagner, 2023. "Residual-based cointegration and non-cointegration tests for cointegrating polynomial regressions," Empirical Economics, Springer, vol. 65(1), pages 1-31, July.
    7. Stypka, Oliver & Wagner, Martin, 2019. "The Phillips unit root tests for polynomials of integrated processes revisited," Economics Letters, Elsevier, vol. 176(C), pages 109-113.
    8. Yap, Wei Yim & Lam, Jasmine S.L., 2006. "Competition dynamics between container ports in East Asia," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(1), pages 35-51, January.
    9. Md. Sharif Hossain & Md. Thasinul Abedin, 2016. "Multivariate Dynamic Co-integration and Causality Analysis between Inflation and its Determinants," Journal of Economics and Behavioral Studies, AMH International, vol. 8(5), pages 240-250.
    10. Valérie Mignon & Christophe Hurlin, 2007. "Une synthèse des tests de cointégration sur données de panel," Économie et Prévision, Programme National Persée, vol. 180(4), pages 241-265.
    11. Mr. Jacques Bouhga-Hagbe, 2004. "A Theory of Workers' Remittances with An Application to Morocco," IMF Working Papers 2004/194, International Monetary Fund.
    12. Bühler, Wolfgang & Korn, Olaf, 1998. "Hedging langfristiger Lieferverpflichtungen mit kurzfristigen Futures: möglich oder unmöglich?," ZEW Discussion Papers 98-20, ZEW - Leibniz Centre for European Economic Research.
    13. Becker, Sascha O & Boll, P. David & Voth, Hans-Joachim, 2025. "Spatial Unit Roots in Regressions : A Practitioner’s Guide and a Stata Package," The Warwick Economics Research Paper Series (TWERPS) 1541, University of Warwick, Department of Economics.
    14. Jacob Gyntelberg & Mico Loretan & Tientip Subhanij & Eric Chan, 2010. "Private information, stock markets, and exchange rates," BIS Papers chapters, in: Bank for International Settlements (ed.), The international financial crisis and policy challenges in Asia and the Pacific, volume 52, pages 186-210, Bank for International Settlements.
    15. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
    16. Pär Österholm, 2005. "The Taylor Rule: A Spurious Regression?," Bulletin of Economic Research, Wiley Blackwell, vol. 57(3), pages 217-247, July.
    17. Alvaro Pereira & João Jalles & Martin Andresen, 2012. "Structural change and foreign direct investment: globalization and regional economic integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(1), pages 35-82, April.
    18. Chowdhury, Rosen & Cook, Steve & Watson, Duncan, 2023. "Reconsidering the relationship between health and income in the UK," Social Science & Medicine, Elsevier, vol. 332(C).
    19. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    20. Chi-Young Choi & Ling Hu & Masao Ogaki, 2005. "Structural Spurious Regressions and A Hausman-type Cointegration Test," RCER Working Papers 517, University of Rochester - Center for Economic Research (RCER).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jecnmx:v:1:y:2013:i:3:p:236-248:d:30523. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.