IDEAS home Printed from https://ideas.repec.org/p/yor/yorken/19-05.html
   My bibliography  Save this paper

Estimating the term structure with linear regressions: Getting to the roots of the problem

Author

Listed:
  • Adam Golinski
  • Peter Spencer

Abstract

Linear estimators of the affine term structure model are inconsistent since they cannot reproduce the factors used in estimation. This is a serious handicap empirically,giving a worse fit than the conventional ML estimator that ensures consistency. We show that a simple self-consistent estimator can be constructed using the eigenvalue decomposition of a regression estimator. The remaining parameters of the model follow analytically. The fit of this model is virtually indistinguishable from that of the ML estimator. We apply the method to estimate various models of U.S. Treasury yields and a joint model of the U.S. and German yield curves.

Suggested Citation

  • Adam Golinski & Peter Spencer, 2019. "Estimating the term structure with linear regressions: Getting to the roots of the problem," Discussion Papers 19/05, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:19/05
    as

    Download full text from publisher

    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2019/1905.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Michael D. Bauer, 2018. "Restrictions on Risk Prices in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 196-211, April.
    2. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," The Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
    3. Scott Joslin & Marcel Priebsch & Kenneth J. Singleton, 2014. "Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks," Journal of Finance, American Finance Association, vol. 69(3), pages 1197-1233, June.
    4. Michael D. Bauer & Glenn D. Rudebusch & Jing Cynthia Wu, 2012. "Correcting Estimation Bias in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 454-467, April.
    5. David K. Backus & Jonathan H. Wright, 2007. "Cracking the Conundrum," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 38(1), pages 293-329.
    6. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2013. "Pricing the term structure with linear regressions," Journal of Financial Economics, Elsevier, vol. 110(1), pages 110-138.
    7. Mirko Abbritti & Luis A. Gil-Alana & Yuliya Lovcha & Antonio Moreno, 2016. "Term Structure Persistence," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 331-352.
    8. Anh Le & Kenneth J. Singleton & Qiang Dai, 2010. "Discrete-Time Affine-super-ℚ Term Structure Models with Generalized Market Prices of Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2184-2227.
    9. Abrahams, Michael & Adrian, Tobias & Crump, Richard K. & Moench, Emanuel & Yu, Rui, 2016. "Decomposing real and nominal yield curves," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 182-200.
    10. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    11. Scott Joslin & Anh Le & Kenneth J. Singleton, 2013. "JFEC Invited Paper: Gaussian Macro-Finance Term Structure Models with Lags," Journal of Financial Econometrics, Oxford University Press, vol. 11(4), pages 581-609, September.
    12. Meldrum, Andrew & Raczko, Marek & Spencer, Peter, 2016. "Overseas unspanned factors and domestic bond returns," Bank of England working papers 618, Bank of England.
    13. Hamilton, James D. & Wu, Jing Cynthia, 2012. "Identification and estimation of Gaussian affine term structure models," Journal of Econometrics, Elsevier, vol. 168(2), pages 315-331.
    14. Hamilton, James D. & Wu, Jing Cynthia, 2014. "Testable implications of affine term structure models," Journal of Econometrics, Elsevier, vol. 178(P2), pages 231-242.
    15. Goliński, Adam & Spencer, Peter, 2017. "The advantages of using excess returns to model the term structure," Journal of Financial Economics, Elsevier, vol. 125(1), pages 163-181.
    16. Michael D. Bauer & Glenn D. Rudebusch, 2014. "The Signaling Channel for Federal Reserve Bond Purchases," International Journal of Central Banking, International Journal of Central Banking, vol. 10(3), pages 233-289, September.
    17. Antonio Diez de Los Rios, 2015. "A New Linear Estimator for Gaussian Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 282-295, April.
    18. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    19. Joslin, Scott & Le, Anh & Singleton, Kenneth J., 2013. "Why Gaussian macro-finance term structure models are (nearly) unconstrained factor-VARs," Journal of Financial Economics, Elsevier, vol. 109(3), pages 604-622.
    20. Gregory R. Duffee, 2011. "Information in (and not in) the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 24(9), pages 2895-2934.
    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. Januj Amar Juneja, 2021. "How do invariant transformations affect the calibration and optimization of the Kalman filtering algorithm used in the estimation of continuous-time affine term structure models?," Computational Management Science, Springer, vol. 18(1), pages 73-97, January.
    2. Januj Amar Juneja, 2022. "A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 173-220, June.
    3. Meldrum, Andrew & Raczko, Marek & Spencer, Peter, 2023. "The information in joint term structures of bond yields," Journal of International Money and Finance, Elsevier, vol. 134(C).
    4. Antonio Diez de los Rios, 2017. "Optimal Estimation of Multi-Country Gaussian Dynamic Term Structure Models Using Linear Regressions," Staff Working Papers 17-33, Bank of Canada.

    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. Speck, Christian, 2023. "Pricing the Bund term structure with linear regressions – without an observable short rate," Discussion Papers 08/2023, Deutsche Bundesbank.
    2. Hlouskova, Jaroslava & Sögner, Leopold, 2020. "GMM estimation of affine term structure models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 2-15.
    3. Creal, Drew D. & Wu, Jing Cynthia, 2015. "Estimation of affine term structure models with spanned or unspanned stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 60-81.
    4. Meldrum, Andrew & Raczko, Marek & Spencer, Peter, 2023. "The information in joint term structures of bond yields," Journal of International Money and Finance, Elsevier, vol. 134(C).
    5. Antonio Diez de Los Rios, 2015. "A New Linear Estimator for Gaussian Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 282-295, April.
    6. Hitesh Doshi & Kris Jacobs & Rui Liu, 2021. "Information in the Term Structure: A Forecasting Perspective," Management Science, INFORMS, vol. 67(8), pages 5255-5277, August.
    7. Kaminska, Iryna & Mumtaz, Haroon & Šustek, Roman, 2021. "Monetary policy surprises and their transmission through term premia and expected interest rates," Journal of Monetary Economics, Elsevier, vol. 124(C), pages 48-65.
    8. Michael D. Bauer & Glenn D. Rudebusch, 2020. "Interest Rates under Falling Stars," American Economic Review, American Economic Association, vol. 110(5), pages 1316-1354, May.
    9. Christensen, Bent Jesper & van der Wel, Michel, 2019. "An asset pricing approach to testing general term structure models," Journal of Financial Economics, Elsevier, vol. 134(1), pages 165-191.
    10. Januj Juneja, 2018. "Empirical performance of Gaussian affine dynamic term structure models in the presence of autocorrelation misspecification bias," Review of Quantitative Finance and Accounting, Springer, vol. 50(3), pages 695-715, April.
    11. Michael D. Bauer, 2018. "Restrictions on Risk Prices in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 196-211, April.
    12. Schupp, Fabian & Geiger, Felix, 2018. "With a little help from my friends: Survey-based derivation of euro area short rate expectations at the effective lower bound," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181529, Verein für Socialpolitik / German Economic Association.
    13. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    14. Goliński, Adam & Spencer, Peter, 2017. "The advantages of using excess returns to model the term structure," Journal of Financial Economics, Elsevier, vol. 125(1), pages 163-181.
    15. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2021. "No‐arbitrage priors, drifting volatilities, and the term structure of interest rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 495-516, August.
    16. Goliński, Adam & Zaffaroni, Paolo, 2016. "Long memory affine term structure models," Journal of Econometrics, Elsevier, vol. 191(1), pages 33-56.
    17. Juneja, Januj, 2017. "Invariance, observational equivalence, and identification: Some implications for the empirical performance of affine term structure models," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 292-305.
    18. Bruno Feunou & Jean-Sébastien Fontaine, 2018. "Bond Risk Premia and Gaussian Term Structure Models," Management Science, INFORMS, vol. 64(3), pages 1413-1439, March.
    19. Liu, Yan & Wu, Jing Cynthia, 2021. "Reconstructing the yield curve," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1395-1425.
    20. Andreasen, Martin M. & Christensen, Bent Jesper, 2015. "The SR approach: A new estimation procedure for non-linear and non-Gaussian dynamic term structure models," Journal of Econometrics, Elsevier, vol. 184(2), pages 420-451.

    More about this item

    Keywords

    term structure; linear regression estimators; self-consistent model; estimation methods; two-country model.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:yor:yorken:19/05. 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: Paul Hodgson (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.html .

    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.