IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Estimation and inference in unstable nonlinear least squares models

  • Boldea, Otilia
  • Hall, Alastair R.

In this paper, we extend Bai and Perron's (1998, Econometrica, pp. 47-78) method for detecting multiple breaks to nonlinear models. To that end, we consider a nonlinear model that can be estimated via nonlinear least squares (NLS) and features a limited number of parameter shifts occurring at unknown dates. In our framework, the break-dates are estimated simultaneously with the parameters via minimization of the residual sum of squares. Using new uniform convergence results for partial sums, we derive the asymptotic distributions of both break-point and parameter estimates and propose several instability tests. We provide simulations that indicate good finite sample properties of our procedure. Additionally, we use our methods to test for misspecification of smooth-transition models in the context of an asymmetric US federal funds rate reaction function and conclude that there is strong evidence of sudden change as well as smooth behavior.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://mpra.ub.uni-muenchen.de/23150/1/MPRA_paper_23150.pdf
File Function: original version
Download Restriction: no

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23150.

as
in new window

Length:
Date of creation: 20 May 2010
Date of revision:
Handle: RePEc:pra:mprapa:23150
Contact details of provider: Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  2. Elena Andreou & Eric Ghysels, 2001. "Detecting Multiple Breaks in Financial Market Volatility Dynamics," University of Cyprus Working Papers in Economics 0202, University of Cyprus Department of Economics.
  3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  4. DOLADO, J.J. & MARIA-DOLORES, R. & RUGE-MURCIA, Francisco J., 2003. "Nonlinear Monetary Policy Rules: Some New Evidence for the U.S," Cahiers de recherche 2003-24, Universite de Montreal, Departement de sciences economiques.
  5. Mehmet Caner, 2005. "Boundedly Pivotal Structural Change Tests in Continuous Updating GMM with Strong, Weak Identification and Completely Unidentified Cases," Econometrics 0509016, EconWPA.
  6. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, 03.
  7. Meese, Richard A & Rose, Andrew K, 1991. "An Empirical Assessment of Non-linearities in Models of Exchange Rate Determination," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 603-19, May.
  8. Ghysels, E & Hall, A., 1988. "A Test For Structural Stability Of Euler Conditions Parameters Estimated Via The Generalized Methods Of Moments Estimators," Cahiers de recherche 8837, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Otilia Boldea & Alastair R. Hall, 2012. "Estimation and Inference in Unstable Nonlinear Least Squares Models," Centre for Growth and Business Cycle Research Discussion Paper Series 174, Economics, The Univeristy of Manchester.
  10. Sowell, Fallaw, 1996. "Optimal Tests for Parameter Instability in the Generalized Method of Moments Framework," Econometrica, Econometric Society, vol. 64(5), pages 1085-1107, September.
  11. D. W. K. Andrews, 2003. "End-of-Sample Instability Tests," Econometrica, Econometric Society, vol. 71(6), pages 1661-1694, November.
  12. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  13. D H Kim & D R Osborn & M Sensier, 2002. "Nonlinearity in the Fed's Monetary Policy Rule," The School of Economics Discussion Paper Series 0205, Economics, The University of Manchester.
  14. Benati, Luca & Surico, Paolo, 2007. "Evolving U.S. monetary policy and the decline of inflation predictability," Working Paper Series 0824, European Central Bank.
  15. Chengsi Zhang & Denise R. Osborn & Dong Heon Kim, 2006. "The New Keynesian Phillips Curve: from Sticky Inflation to Sticky Prices," The School of Economics Discussion Paper Series 0631, Economics, The University of Manchester.
  16. Barbara Rossi, 2005. "Are Exchange Rates Really Random Walks? Some Evidence Robust to Parameter Instability," Data 0503001, EconWPA.
  17. Mehtap Kesriyeli & Denise R. Osborn & Marianne Sensier, 2004. "Nonlinearity and Structural Change in Interest Rate Reaction Functions for the US, UK and Germany," Working Papers 0414, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
  18. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
  19. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  20. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  21. repec:cup:cbooks:9780521770415 is not listed on IDEAS
  22. Michael McAller & Marcelo C. Medeiros, 2007. "A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries," Textos para discussão 544, Department of Economics PUC-Rio (Brazil).
  23. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
  24. Alastair R. Hall & Sanggohn Han & Otilia Boldea, 2009. "Inference regarding multiple structural changes in linear models with endogenous regressors," Centre for Growth and Business Cycle Research Discussion Paper Series 125, Economics, The Univeristy of Manchester.
  25. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc.
  26. Hall, Alastair R & Sen, Amit, 1999. "Structural Stability Testing in Models Estimated by Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 335-48, July.
  27. Kang Kyu Ho & Kim Chang-Jin & Morley James, 2009. "Changes in U.S. Inflation Persistence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(4), pages 1-23, September.
  28. repec:cup:cbooks:9780521779654 is not listed on IDEAS
  29. Jushan Bai & Pierre Perron, 2003. "Critical values for multiple structural change tests," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 72-78, 06.
  30. Schaling, Eric, 2004. "The Nonlinear Phillips Curve and Inflation Forecast Targeting: Symmetric versus Asymmetric Monetary Policy Rules," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(3), pages 361-86, June.
  31. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
  32. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2008. "Asymptotic Distribution Theory for Break Point Estimators in Models Estimated via 2SLS," MPRA Paper 9472, University Library of Munich, Germany.
  33. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
  34. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
  35. Florio, Anna, 2006. "Asymmetric interest rate smoothing: The Fed approach," Economics Letters, Elsevier, vol. 93(2), pages 190-195, November.
  36. Alogoskoufis, George S & Smith, Ron, 1991. "The Phillips Curve, the Persistence of Inflation, and the Lucas Critique: Evidence from Exchange-Rate Regimes," American Economic Review, American Economic Association, vol. 81(5), pages 1254-75, December.
  37. Andrews, Donald W K & Fair, Ray C, 1988. "Inference in Nonlinear Econometric Models with Structural Change," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 615-39, October.
  38. 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.
  39. Eitrheim, Øyvind & Teräsvirta, Timo, 1995. "Testing the Adequacy of Smooth Transition Autoregressive Models," SSE/EFI Working Paper Series in Economics and Finance 56, Stockholm School of Economics.
  40. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  41. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
  42. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(03), pages 403-436, June.
  43. Dufour, Jean-Marie & Ghysels, Eric, 1996. "Editors' introduction recent developments in the econometrics of structural change," Journal of Econometrics, Elsevier, vol. 70(1), pages 1-8, January.
  44. Bec Frédérique & Ben Salem Mélika & Collard Fabrice, 2002. "Asymmetries in Monetary Policy Reaction Function: Evidence for U.S. French and German Central Banks," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(2), pages 1-22, July.
  45. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:23150. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.