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Estimation and inference in unstable nonlinear least squares models

  • Boldea, Otilia
  • Hall, Alastair R.

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.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 172 (2013)
Issue (Month): 1 ()
Pages: 158-167

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Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:158-167
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Mehmet Caner, 2005. "Boundedly Pivotal Structural Change Tests in Continuous Updating GMM with Strong, Weak Identification and Completely Unidentified Cases," Econometrics 0509016, EconWPA.
  2. 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.
  3. Barbara Rossi, 2005. "Are Exchange Rates Really Random Walks? Some Evidence Robust to Parameter Instability," International Finance 0503006, EconWPA.
  4. Richard A. Meese & Andrew K. Rose, 1991. "An Empirical Assessment of Non-Linearities in Models of Exchange Rate Determination," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 603-619.
  5. 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.
  6. 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.
  7. Elena Andreou & Eric Ghysels, 2001. "Detecting Mutiple Breaks in Financial Market Volatility Dynamics," CIRANO Working Papers 2001s-65, CIRANO.
  8. Donald W.K. Andrews, 2002. "End-of-Sample Instability Tests," Cowles Foundation Discussion Papers 1369, Cowles Foundation for Research in Economics, Yale University.
  9. Florio, Anna, 2006. "Asymmetric interest rate smoothing: The Fed approach," Economics Letters, Elsevier, vol. 93(2), pages 190-195, November.
  10. 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.
  11. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
  12. Zhongjun Qu & Pierre Perron, 2005. "Estimating and testing structural changes in multivariate regressions," Boston University - Department of Economics - Working Papers Series WP2005-012, Boston University - Department of Economics.
  13. 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.
  14. 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, 06.
  15. 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.
  16. 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.
  17. James H. Stock & Mark W. Watson, 2002. "Has the Business Cycle Changed and Why?," NBER Working Papers 9127, National Bureau of Economic Research, Inc.
  18. 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.
  19. 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.
  20. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  21. 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 355-64, May.
  22. 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.
  23. Elliott, Graham & Muller, Ulrich K., 2004. "Confidence Sets for the Date of a Single Break in Linear Time Series Regressions," University of California at San Diego, Economics Working Paper Series qt9hf4j4c2, Department of Economics, UC San Diego.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(03), pages 403-436, June.
  30. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  31. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  32. Boldea, O. & Hall, A.R. & Han, S., 2012. "Asymptotic distribution theory for break point estimators in models estimated via 2SLS," Other publications TiSEM 2e2fbb75-c4ff-4279-8243-e, Tilburg University, School of Economics and Management.
  33. 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.
  34. 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.
  35. Lucas, Robert Jr, 1976. "Econometric policy evaluation: A critique," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 1(1), pages 19-46, January.
  36. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
  37. Jushan Bai & Pierre Perron, 2003. "Critical values for multiple structural change tests," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 72-78, 06.
  38. 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.
  39. 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.
  40. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  41. 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.
  42. 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.
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