IDEAS home Printed from https://ideas.repec.org/p/man/cgbcrp/174.html
   My bibliography  Save this paper

Estimation and Inference in Unstable Nonlinear Least Squares Models

Author

Listed:
  • Otilia Boldea
  • Alastair R. Hall

Abstract

There is compelling evidence that many macroeconomic and financial variables are not generated by linear models. This evidence is based on testing linearity against either smooth nonlinearity or piece-wise linearity, but there is no framework that encompasses both. This paper provides an econometric framework that allows for both breaks and smooth nonlinearity in-between breaks. We estimate the unknown break-dates simultaneously with other parameters via nonlinear least-squares. Using new central limit results for nonlinear processes, we provide inference methods on break-dates and parameter estimates and several instability tests. We illustrate our methods via simulated and empirical smooth transition models with breaks.

Suggested Citation

  • 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 University of Manchester.
    • Handle: RePEc:man:cgbcrp:174
    as

    Download full text from publisher

    File URL: http://hummedia.manchester.ac.uk/schools/soss/cgbcr/discussionpapers/dpcgbcr174.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ghysels, Eric & Hall, Alastair, 1990. "A Test for Structural Stability of Euler Conditions Parameters Estimated via the Generalized Method of Moments Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 355-364, May.
    2. Dolado Juan & Pedrero Ramón María-Dolores & Ruge-Murcia Francisco J., 2004. "Nonlinear Monetary Policy Rules: Some New Evidence for the U.S," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-34, September.
    3. 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.
    4. 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.
    5. Rossi, Barbara, 2006. "Are Exchange Rates Really Random Walks? Some Evidence Robust To Parameter Instability," Macroeconomic Dynamics, Cambridge University Press, vol. 10(1), pages 20-38, February.
    6. Florio, Anna, 2006. "Asymmetric interest rate smoothing: The Fed approach," Economics Letters, Elsevier, vol. 93(2), pages 190-195, November.
    7. D. W. K. Andrews, 2003. "End-of-Sample Instability Tests," Econometrica, Econometric Society, vol. 71(6), pages 1661-1694, November.
    8. Caner, Mehmet, 2007. "Boundedly pivotal structural change tests in continuous updating GMM with strong, weak identification and completely unidentified cases," Journal of Econometrics, Elsevier, vol. 137(1), pages 28-67, March.
    9. 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.
    10. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    11. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-337, July.
    12. Luca Benati & Paolo Surico, 2008. "Evolving U.S. Monetary Policy and The Decline of Inflation Predictability," Journal of the European Economic Association, MIT Press, vol. 6(2-3), pages 634-646, 04-05.
    13. 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.
    14. Marc Lavielle & Eric Moulines, 2000. "Least‐squares Estimation of an Unknown Number of Shifts in a Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 33-59, January.
    15. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    16. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    17. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230, National Bureau of Economic Research, Inc.
    18. 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.
    19. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    20. 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.
    21. Mehtap Kesriyeli & Denise R. Osborn & Marianne Sensier, 2006. "Nonlinearity and Structural Change in Interest Rate Reaction Functions for the US, UK and Germany," Contributions to Economic Analysis, in: Nonlinear Time Series Analysis of Business Cycles, pages 283-310, Emerald Group Publishing Limited.
    22. Denise R. Osborn & Dong Heon Kim & Marianne Sensier, 2005. "Nonlinearity in the Fed's monetary policy rule," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 621-639.
    23. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234, January.
    24. 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.
    25. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    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 335-348, July.
    27. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    28. Chengsi Zhang & Denise R. Osborn & Dong Heon Kim, 2008. "The New Keynesian Phillips Curve: From Sticky Inflation to Sticky Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(4), pages 667-699, June.
    29. 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.
    30. Jushan Bai & Pierre Perron, 2003. "Critical values for multiple structural change tests," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 72-78, June.
    31. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    32. Brunner, Karl & Meltzer, Allan H., 1976. "The Phillips curve," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 1-18, January.
    33. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    34. Richard A. Meese & Andrew K. Rose, 1991. "An Empirical Assessment of Non-Linearities in Models of Exchange Rate Determination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 603-619.
    35. 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 1254-1275, December.
    36. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    37. Teräsvirta, Timo, 1996. "Smooth Transition Models," SSE/EFI Working Paper Series in Economics and Finance 132, Stockholm School of Economics.
    38. 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 361-386, June.
    39. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    40. 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.
    41. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    42. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    43. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    44. 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.
    45. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(3), pages 403-436, June.
    46. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    47. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
    48. 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.
    49. 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.
    50. 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.
    51. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    52. Donald W. K. Andrews & Ray C. Fair, 1988. "Inference in Nonlinear Econometric Models with Structural Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 615-640.
    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. 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.
    2. Giraitis, Liudas & Kapetanios, George & Marcellino, Massimiliano, 2021. "Time-varying instrumental variable estimation," Journal of Econometrics, Elsevier, vol. 224(2), pages 394-415.
    3. Val鲩e Chouard & Daniel Fuentes Castro & Delphine Irac & Matthieu Lemoine, 2014. "Assessing the losses in euro area potential productivity due to the financial crisis," Applied Economics, Taylor & Francis Journals, vol. 46(23), pages 2711-2720, August.
    4. 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.
    5. 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.
    6. Gabriela Ciuperca & Zahraa Salloum, 2015. "Empirical likelihood test in a posteriori change-point nonlinear model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 919-952, November.
    7. 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.
    8. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    9. Hall Alastair & Sakkas Nikolaos, 2013. "Approximate p-Values of Certain Tests Involving Hypotheses About Multiple Breaks," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 53-67, July.
    10. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    11. Pavel Yaskov, 2010. "Testing for predictive ability in the presence of structural breaks (in Russian)," Quantile, Quantile, issue 8, pages 127-135, 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. 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.
    2. 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.
    3. 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.
    4. Somayeh Mardaneh, 2012. "How Do Oil Shocks A¤ect the Structural Stability of Hybrid New Keynesian Phillips Curve?," Discussion Papers in Economics 12/20, Division of Economics, School of Business, University of Leicester.
    5. 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.
    6. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    7. 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.
    8. Jouini, Jamel & Boutahar, Mohamed, 2005. "Evidence on structural changes in U.S. time series," Economic Modelling, Elsevier, vol. 22(3), pages 391-422, May.
    9. 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.
    10. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    11. Mohitosh Kejriwal, 2020. "A Robust Sequential Procedure for Estimating the Number of Structural Changes in Persistence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(3), pages 669-685, June.
    12. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2008. "Inference regarding multiple structural changes in linear models estimated via two stage least squares," MPRA Paper 9251, University Library of Munich, Germany, revised 20 Jun 2008.
    13. 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.
    14. 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.
    15. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    16. 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.
    17. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    18. Strikholm, Birgit, 2006. "Determining the number of breaks in a piecewise linear regression model," SSE/EFI Working Paper Series in Economics and Finance 648, Stockholm School of Economics.
    19. Alaa Abi Morshed & Elena Andreou & Otilia Boldea, 2018. "Structural Break Tests Robust to Regression Misspecification," Econometrics, MDPI, vol. 6(2), pages 1-39, May.
    20. 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.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:man:cgbcrp:174. 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: Marianne Sensier (email available below). General contact details of provider: https://edirc.repec.org/data/semanuk.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.