IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v172y2013i2p205-221.html
   My bibliography  Save this article

Heavy tails of OLS

Author

Listed:
  • Mikosch, Thomas
  • de Vries, Casper G.

Abstract

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions.

Suggested Citation

  • Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:205-221
    DOI: 10.1016/j.jeconom.2012.08.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612001996
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2012.08.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marc Hallin & Yves-Caoimhin Swan & Thomas Verdebout & David Veredas, 2013. "R-estimation in linear models with stable errors," ULB Institutional Repository 2013/136281, ULB -- Universite Libre de Bruxelles.
    2. Lewis, Karen K., 1995. "Puzzles in international financial markets," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 37, pages 1913-1971, Elsevier.
    3. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    4. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    5. Chow, Gregory C., 1984. "Random and changing coefficient models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 21, pages 1213-1245, Elsevier.
    6. Robert Blattberg & Thomas Sargent, 2010. "Regression With Non-Gaussian Stable Disturbances: Some Sampling Results," World Scientific Book Chapters, in: Greg M Allenby (ed.), Perspectives On Promotion And Database Marketing The Collected Works of Robert C Blattberg, chapter 1, pages 7-16, World Scientific Publishing Co. Pte. Ltd..
    7. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    8. Feige, Edgar L & Swamy, P A V B, 1974. "A Random Coefficient Model of the Demand for Liquid Assets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 6(2), pages 241-252, May.
    9. Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
    10. Jurecková, Jana & Koenker, Roger & Portnoy, Stephen, 2001. "Tail behavior of the least-squares estimator," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 377-384, December.
    11. Fama, Eugene F., 1976. "Forward rates as predictors of future spot rates," Journal of Financial Economics, Elsevier, vol. 3(4), pages 361-377, October.
    12. Sack, Brian, 2000. "Does the fed act gradually? A VAR analysis," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 229-256, August.
    13. N. Gregory Mankiw & Jeffrey A. Miron, 1986. "The Changing Behavior of the Term Structure of Interest Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(2), pages 211-228.
    14. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
    15. Andrews, Beth & Davis, Richard A., 2013. "Model identification for infinite variance autoregressive processes," Journal of Econometrics, Elsevier, vol. 172(2), pages 222-234.
    16. Martin Lettau & Sydney Ludvigson, 2001. "Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1238-1287, December.
    17. John Y. Campbell & Robert J. Shiller, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 495-514.
    18. Nolan, John P. & Ojeda-Revah, Diana, 2013. "Linear and nonlinear regression with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 186-194.
    19. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-692, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guus Balkema & Paul Embrechts, 2018. "Linear Regression for Heavy Tails," Risks, MDPI, vol. 6(3), pages 1-70, September.
    2. Maarten R C van Oordt & Chen Zhou, 2019. "Estimating Systematic Risk under Extremely Adverse Market Conditions," Journal of Financial Econometrics, Oxford University Press, vol. 17(3), pages 432-461.
    3. Kanishka Misra & Paolo Surico, 2014. "Consumption, Income Changes, and Heterogeneity: Evidence from Two Fiscal Stimulus Programs," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(4), pages 84-106, October.
    4. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    5. Maarten van Oordt & Chen Zhou, 2015. "Systemic risk of European banks: Regulators and markets," DNB Working Papers 478, Netherlands Central Bank, Research Department.
    6. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.
    7. Chen, Wang & Zhang, Zhiwen & Hamori, Shigeyuki & Kinkyo, Takuji, 2021. "Not all bank systemic risks are alike: Deposit insurance and bank risk revisited," International Review of Financial Analysis, Elsevier, vol. 77(C).

    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. Thomas Mikosch & Casper G. de Vries, 2006. "Tail Probabilities for Regression Estimators," Tinbergen Institute Discussion Papers 06-085/2, Tinbergen Institute.
    2. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    3. Guidolin, Massimo & Thornton, Daniel L., 2018. "Predictions of short-term rates and the expectations hypothesis," International Journal of Forecasting, Elsevier, vol. 34(4), pages 636-664.
    4. Iichiro Uesugi & Guy M. Yamashiro, 2003. "On the Relationship Between the Very Short Forward and the Spot Interest Rate," Discussion papers 03013, Research Institute of Economy, Trade and Industry (RIETI).
    5. Lekkos, Ilias & Milas, Costas, 2004. "Time-varying excess returns on UK government bonds: A non-linear approach," Journal of Banking & Finance, Elsevier, vol. 28(1), pages 45-62, January.
    6. Tom Engsted & Stig V. Møller & Magnus Sander, 2013. "Bond return predictability in expansions and recessions," CREATES Research Papers 2013-13, Department of Economics and Business Economics, Aarhus University.
    7. Stephen A. Buser & G. Andrew Karolyi & Anthony B. Sanders, "undated". "Adjusted Forward Rates as Predictors of Future Spot Rates," Research in Financial Economics 9605, Ohio State University.
    8. G. Boero & C. Torricelli, 1999. "The Information in the Term of Structure: further Results for Germany," Working Paper CRENoS 199912, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    9. Gianna Boero & Costanza Torricelli, 2002. "The information in the term structure of German interest rates," The European Journal of Finance, Taylor & Francis Journals, vol. 8(1), pages 21-45.
    10. Bulkley, George & Harris, Richard D.F. & Nawosah, Vivekanand, 2011. "Revisiting the expectations hypothesis of the term structure of interest rates," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1202-1212, May.
    11. repec:hal:spmain:info:hdl:2441/5221 is not listed on IDEAS
    12. Buraschi, Andrea & Jiltsov, Alexei, 2005. "Inflation risk premia and the expectations hypothesis," Journal of Financial Economics, Elsevier, vol. 75(2), pages 429-490, February.
    13. repec:adr:anecst:y:1998:i:52:p:01 is not listed on IDEAS
    14. Schmeling, Maik & Schrimpf, Andreas & Steffensen, Sigurd A.M., 2022. "Monetary policy expectation errors," Journal of Financial Economics, Elsevier, vol. 146(3), pages 841-858.
    15. Rudebusch, Glenn D., 1995. "Federal Reserve interest rate targeting, rational expectations, and the term structure," Journal of Monetary Economics, Elsevier, vol. 35(2), pages 245-274, April.
    16. Jondeau, E. & Ricart, R., 1996. "The Expectation Theory: Tests on French, German, and American Euro-Rates," Working papers 35, Banque de France.
    17. Hans Patrick Bidias-Menik & Simplice Gaël Tonmo, 2020. "Interest Rate Predictability In Some Selected African Countries," Copernican Journal of Finance & Accounting, Uniwersytet Mikolaja Kopernika, vol. 9(3), pages 45-60.
    18. Han, Bing & Hirshleifer, David & Wang, Tracy Yue, 2005. "Investor Overconfidence and the Forward Discount Puzzle," Working Paper Series 2005-21, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    19. Vides, José Carlos & Golpe, Antonio A. & Iglesias, Jesús, 2021. "The impact of the term spread in US monetary policy from 1870 to 2013," Journal of Policy Modeling, Elsevier, vol. 43(1), pages 230-251.
    20. repec:spo:wpmain:info:hdl:2441/5221 is not listed on IDEAS
    21. Sophocles N. Brissimis & Evangelia A. Georgiou, 2022. "The effects of Federal Reserve's quantitative easing and balance sheet normalization policies on long-term interest rates," Working Papers 299, Bank of Greece.
    22. Luis Ceballos & Alberto Naudon & Damián Romero, 2016. "Nominal term structure and term premia: evidence from Chile," Applied Economics, Taylor & Francis Journals, vol. 48(29), pages 2721-2735, June.
    23. Alfonso Novales & Emilio Domínguez, 2002. "Can forward rates be used to improve interest rate forecasts?"," Documentos de Trabajo del ICAE 0225, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

    More about this item

    Keywords

    Heavy tails; OLS estimator distribution; Small sample inference;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

    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:eee:econom:v:172:y:2013:i:2:p:205-221. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.