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Asymptotic Distribution Theory for Break Point Estimators in Models Estimated via 2SLS


  • Hall, Alastair R.
  • Han, Sanggohn
  • Boldea, Otilia


In this paper, we present a limiting distribution theory for the break point estimator in a linear regression model estimated via Two Stage Least Squares under two different scenarios regarding the magnitude of the parameter change between regimes. First, we consider the case where the parameter change is of fixed magnitude; in this case the resulting distribution depends on distribution of the data and is not of much practical use for inference. Second, we consider the case where the magnitude of the parameter change shrinks with the sample size; in this case, the resulting distribution can be used to construct approximate large sample confidence intervals for the break point. The finite sample performance of these intervals are analyzed in a small simulation study and the intervals are illustrated via an application to the New Keynesian Phillips curve.

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  • 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.
  • Handle: RePEc:pra:mprapa:9472

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    References listed on IDEAS

    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. 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.
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    4. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    5. 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.
    6. 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.
    7. 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.
    8. Donald W.K. Andrews & Ray C. Fair, 1987. "Inference in Econometric Models with Structural Change," Cowles Foundation Discussion Papers 832, Cowles Foundation for Research in Economics, Yale University.
    9. 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.
    10. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    11. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    12. Ghysels, Eric & Hall, Alastair, 1990. "Are consumption-based intertemporal capital asset pricing models structural?," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 121-139.
    13. Bhattacharya, P.K., 1987. "Maximum likelihood estimation of a change-point in the distribution of independent random variables: General multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 183-208, December.
    14. Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 309-336.
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    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. Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2015. "The Asymptotic Behaviour of the Residual Sum of Squares in Models with Multiple Break Points," The School of Economics Discussion Paper Series 1504, Economics, The University of Manchester.
    3. 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(02), pages 491-507, April.
    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. 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.
    6. 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.
    7. Pierre Perron & Yohei Yamamoto, 2015. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 119-144, January.
    8. Yu, Ping, 2013. "Inconsistency of 2SLS estimators in threshold regression with endogeneity," Economics Letters, Elsevier, vol. 120(3), pages 532-536.
    9. Otilia Boldea & Alastair R. Hall, 2013. "Testing structural stability in macroeconometric models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 9, pages 206-228 Edward Elgar Publishing.
    10. Qian, Junhui & Su, Liangjun, 2014. "Structural change estimation in time series regressions with endogenous variables," Economics Letters, Elsevier, vol. 125(3), pages 415-421.
    11. Ping Yu & Peter C.B. Phillips, 2014. "Threshold Regression with Endogeneity," Cowles Foundation Discussion Papers 1966, Cowles Foundation for Research in Economics, Yale University.
    12. 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.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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