IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v36y2017i6-9p667-698.html
   My bibliography  Save this article

The asymptotic behaviour of the residual sum of squares in models with multiple break points

Author

Listed:
  • Alastair R. Hall
  • Denise R. Osborn
  • Nikolaos Sakkas

Abstract

Models with multiple discrete breaks in parameters are usually estimated via least squares. This paper, first, derives the asymptotic expectation of the residual sum of squares and shows that the number of estimated break points and the number of regression parameters affect the expectation differently. Second, we propose a statistic for testing the joint hypothesis that the breaks occur at specified points in the sample. Our analytical results cover models estimated by the ordinary, nonlinear, and two-stage least squares. An application to U.S. monetary policy rejects the assumption that breaks are associated with changes in the chair of the Fed.

Suggested Citation

  • Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2017. "The asymptotic behaviour of the residual sum of squares in models with multiple break points," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 667-698, October.
  • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:667-698
    DOI: 10.1080/07474938.2017.1307523
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2017.1307523
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/07474938.2017.1307523?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Otilia Boldea & Alastair Hall & Sanggohn Han, 2012. "Asymptotic Distribution Theory for Break Point Estimators in Models Estimated via 2SLS," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 1-33.
    2. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    3. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 115(1), pages 147-180.
    4. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    5. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    6. Martin Ellison & Thomas J. Sargent, 2012. "A Defense Of The Fomc," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(4), pages 1047-1065, November.
    7. Glenn D. 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.
    8. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    9. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    10. Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2013. "Inference on Structural Breaks using Information Criteria," Manchester School, University of Manchester, vol. 81, pages 54-81, October.
    11. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    12. Orphanides, Athanasios, 2004. "Monetary Policy Rules, Macroeconomic Stability, and Inflation: A View from the Trenches," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(2), pages 151-175, April.
    13. Neil Kellard & Denise Osborn & Jerry Coakley & Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2015. "Structural Break Inference Using Information Criteria in Models Estimated by Two-Stage Least Squares," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 741-762, September.
    14. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    15. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    16. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    17. Ninomiya, Yoshiyuki, 2005. "Information criterion for Gaussian change-point model," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 237-247, May.
    18. Duffy, John & Engle-Warnick, Jim, 2006. "Multiple Regimes in U.S. Monetary Policy? A Nonparametric Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1363-1377, August.
    19. Shaghil Ahmed & Andrew Levin & Beth Anne Wilson, 2004. "Recent U.S. Macroeconomic Stability: Good Policies, Good Practices, or Good Luck?," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 824-832, August.
    20. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    21. Pesaran, M Hashem & Smith, Richard J, 1994. "A Generalized R[superscript]2 Criterion for Regression Models Estimated by the Instrumental Variables Method," Econometrica, Econometric Society, vol. 62(3), pages 705-710, May.
    22. Bertille Antoine & Otilia Boldea, 2015. "Efficient Inference with Time-Varying Information and the New Keynesian Phillips Curve," Discussion Papers dp15-04, Department of Economics, Simon Fraser University, revised 25 Aug 2016.
    23. Seong Yeon Chang & Pierre Perron, 2018. "A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(6), pages 577-601, July.
    24. Tore Ellingsen & Ulf Soderstrom, 2001. "Monetary Policy and Market Interest Rates," American Economic Review, American Economic Association, vol. 91(5), pages 1594-1607, December.
    25. Jean Boivin & Marc P. Giannoni, 2006. "Has Monetary Policy Become More Effective?," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 445-462, August.
    26. Stryhn, Henrik, 1996. "The location of the maximum of asymmetric two-sided Brownian motion with triangular drift," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 279-284, 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. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.

    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. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Boston University - Department of Economics - Working Papers Series WP2019-02, Boston University - Department of Economics.
    2. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    3. Casini, Alessandro & Perron, Pierre, 2021. "Continuous record Laplace-based inference about the break date in structural change models," Journal of Econometrics, Elsevier, vol. 224(1), pages 3-21.
    4. Otilia Boldea & Alastair R. Hall, 2013. "Testing structural stability in macroeconometric models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 9, pages 206-228, Edward Elgar Publishing.
    5. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    6. Eiji Kurozumi & Yohei Yamamoto, 2015. "Confidence sets for the break date based on optimal tests," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 412-435, October.
    7. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    8. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    9. Shimizu, Kenichi, 2023. "Asymptotic properties of Bayesian inference in linear regression with a structural break," Journal of Econometrics, Elsevier, vol. 235(1), pages 202-219.
    10. Seong Yeon Chang & Pierre Perron, 2018. "A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(6), pages 577-601, July.
    11. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany.
    12. Komlan, Fiodendji, 2013. "The asymmetric reaction of monetary policy to inflation and the output gap: Evidence from Canada," Economic Modelling, Elsevier, vol. 30(C), pages 911-923.
    13. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    14. Bertille Antoine & Otilia Boldea, 2015. "Efficient Inference with Time-Varying Information and the New Keynesian Phillips Curve," Discussion Papers dp15-04, Department of Economics, Simon Fraser University, revised 25 Aug 2016.
    15. Kurozumi, Eiji & Tuvaandorj, Purevdorj, 2011. "Model selection criteria in multivariate models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 164(2), pages 218-238, October.
    16. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    17. Neil Kellard & Denise Osborn & Jerry Coakley & Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2015. "Structural Break Inference Using Information Criteria in Models Estimated by Two-Stage Least Squares," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 741-762, September.
    18. Pierre Perron & Yohei Yamamoto, 2008. "Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors," Boston University - Department of Economics - Working Papers Series wp2008-017, Boston University - Department of Economics.
    19. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
    20. Perron, Pierre & Yamamoto, Yohei, 2014. "A Note On Estimating And Testing For Multiple Structural Changes In Models With Endogenous Regressors Via 2sls," Econometric Theory, Cambridge University Press, vol. 30(2), pages 491-507, April.

    More about this item

    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:taf:emetrv:v:36:y:2017:i:6-9:p:667-698. 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: http://www.tandfonline.com/LECR20 .

    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.