[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/17772.html
   My bibliography  Save this paper

Identification and Estimation of Gaussian Affine Term Structure Models

Author

Listed:
  • James D. Hamilton
  • Jing Cynthia Wu
Abstract
This paper develops new results for identification and estimation of Gaussian affine term structure models. We establish that three popular canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate contribution of the paper is the proposal of minimum-chi-square estimation as an alternative to MLE. We show that, although it is asymptotically equivalent to MLE, it can be much easier to compute. In some cases, MCSE allows researchers to recognize with certainty whether a given estimate represents a global maximum of the likelihood function and makes feasible the computation of small-sample standard errors.

Suggested Citation

  • James D. Hamilton & Jing Cynthia Wu, 2012. "Identification and Estimation of Gaussian Affine Term Structure Models," NBER Working Papers 17772, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:17772
    Note: AP ME
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w17772.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Geert Bekaert & Seonghoon Cho & Antonio Moreno, 2010. "New Keynesian Macroeconomics and the Term Structure," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(1), pages 33-62, February.
    3. 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.
    4. Pierre Collin‐Dufresne & Robert S. Goldstein & Christopher S. Jones, 2008. "Identification of Maximal Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 63(2), pages 743-795, April.
    5. GlennD. Rudebusch & Tao Wu, 2008. "A Macro-Finance Model of the Term Structure, Monetary Policy and the Economy," Economic Journal, Royal Economic Society, vol. 118(530), pages 906-926, July.
    6. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    8. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    9. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    10. Aït-Sahalia, Yacine & Kimmel, Robert L., 2010. "Estimating affine multifactor term structure models using closed-form likelihood expansions," Journal of Financial Economics, Elsevier, vol. 98(1), pages 113-144, October.
    11. Andrew Ang & Sen Dong & Monika Piazzesi, 2005. "No-arbitrage Taylor rules," Proceedings, Federal Reserve Bank of San Francisco.
    12. Hordahl, Peter & Tristani, Oreste & Vestin, David, 2006. "A joint econometric model of macroeconomic and term-structure dynamics," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 405-444.
    13. Kim, Don H. & Orphanides, Athanasios, 2012. "Term Structure Estimation with Survey Data on Interest Rate Forecasts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(1), pages 241-272, February.
    14. Don H. Kim, 2008. "Challenges in macro-finance modeling," Finance and Economics Discussion Series 2008-06, Board of Governors of the Federal Reserve System (U.S.).
    15. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    16. Greg Duffee, 2011. "Forecasting with the term structure: The role of no-arbitrage restrictions," Economics Working Paper Archive 576, The Johns Hopkins University,Department of Economics.
    17. Beechey, Meredith J. & Wright, Jonathan H., 2009. "The high-frequency impact of news on long-term yields and forward rates: Is it real?," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 535-544, May.
    18. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2010. "Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 143-178, September.
    19. Don H. Kim & Jonathan H. Wright, 2005. "An arbitrage-free three-factor term structure model and the recent behavior of long-term yields and distant-horizon forward rates," Finance and Economics Discussion Series 2005-33, Board of Governors of the Federal Reserve System (U.S.).
    20. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    21. Glenn D. Rudebusch & Eric T. Swanson & Tao Wu, 2006. "The Bond Yield "Conundrum" from a Macro-Finance Perspective," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 24(S1), pages 83-109, December.
    22. Marcello Pericoli & Marco Taboga, 2008. "Canonical Term-Structure Models with Observable Factors and the Dynamics of Bond Risk Premia," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(7), pages 1471-1488, October.
    23. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
    24. Ang, Andrew & Piazzesi, Monika & Wei, Min, 2006. "What does the yield curve tell us about GDP growth?," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 359-403.
    25. 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.
    26. James D. Hamilton & Jing Cynthia Wu, 2012. "The Effectiveness of Alternative Monetary Policy Tools in a Zero Lower Bound Environment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(s1), pages 3-46, February.
    27. Monika Piazzesi & John Cochrane, 2009. "Decomposing the Yield Curve," 2009 Meeting Papers 18, Society for Economic Dynamics.
    28. 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.
    29. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    30. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    31. Gregory R. Duffee, 2008. "Evidence on Simulation Inference for Near Unit-Root Processes with Implications for Term Structure Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 108-142, Winter.
    32. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
    33. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    34. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2014. "Do Central Bank Liquidity Facilities Affect Interbank Lending Rates?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 136-151, January.
    35. Newey, Whitney K., 1987. "Efficient estimation of limited dependent variable models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 36(3), pages 231-250, November.
    36. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    37. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    38. Marcello Pericoli & Marco Taboga, 2008. "Canonical Term-Structure Models with Observable Factors and the Dynamics of Bond Risk Premia," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(7), pages 1471-1488, October.
    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. Hamilton, James D. & Wu, Jing Cynthia, 2014. "Testable implications of affine term structure models," Journal of Econometrics, Elsevier, vol. 178(P2), pages 231-242.
    2. Argyropoulos, Efthymios & Tzavalis, Elias, 2021. "The influence of real interest rates and risk premium effects on the ability of the nominal term structure to forecast inflation," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 785-796.
    3. Leo Krippner, 2009. "A theoretical foundation for the Nelson and Siegel class of yield curve models," Reserve Bank of New Zealand Discussion Paper Series DP2009/10, Reserve Bank of New Zealand.
    4. Zbynek Stork, 2016. "Term Structure of Interest Rates: Macro-Finance Approach," EcoMod2016 9566, EcoMod.
    5. Taboga, Marco, 2009. "Macro-finance VARs and bond risk premia: A caveat," Review of Financial Economics, Elsevier, vol. 18(4), pages 163-171, October.
    6. Doshi, Hitesh & Jacobs, Kris & Liu, Rui, 2018. "Macroeconomic determinants of the term structure: Long-run and short-run dynamics," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 99-122.
    7. Duffee, Gregory R., 2013. "Bond Pricing and the Macroeconomy," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 907-967, Elsevier.
    8. Felix Geiger, 2009. "International Interest-Rate Risk Premia in Affine Term Structure Models," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 316/2009, Department of Economics, University of Hohenheim, Germany.
    9. Pericoli, Marcello & Taboga, Marco, 2012. "Bond risk premia, macroeconomic fundamentals and the exchange rate," International Review of Economics & Finance, Elsevier, vol. 22(1), pages 42-65.
    10. Byrne, Joseph & Cao, Shuo & Korobilis, Dimitris, 2015. "Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty," MPRA Paper 63844, University Library of Munich, Germany.
    11. Glenn D. Rudebusch, 2010. "Macro‐Finance Models Of Interest Rates And The Economy," Manchester School, University of Manchester, vol. 78(s1), pages 25-52, September.
    12. P. Byrne, Joseph & Cao, Shuo & Korobilis, Dimitris, 2015. "Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-71, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Refet S. Gürkaynak & Jonathan H. Wright, 2012. "Macroeconomics and the Term Structure," Journal of Economic Literature, American Economic Association, vol. 50(2), pages 331-367, June.
    14. Nikolaos Karouzakis, 2021. "The role of time‐varying risk premia in international interbank markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5720-5745, October.
    15. 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.
    16. De Pooter, Michiel & Ravazzolo, Francesco & van Dijk, Dick, 2006. "Predicting the term structure of interest rates incorporating parameter uncertainty, model uncertainty and macroeconomic information," MPRA Paper 2512, University Library of Munich, Germany, revised 03 Mar 2007.
    17. Renne, J-P., 2009. "Frequency-domain analysis of debt service in a macro-finance model for the euro area," Working papers 261, Banque de France.
    18. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    19. 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.
    20. Carlo A. Favero & Arie E. Gozluklu & Haoxi Yang, 2016. "Demographics and the Behavior of Interest Rates," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 64(4), pages 732-776, November.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • 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:nbr:nberwo:17772. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.