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A Note On Estimating And Testing For Multiple Structural Changes In Models With Endogenous Regressors Via 2sls

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  • Perron, Pierre
  • Yamamoto, Yohei

Abstract

This note provides a simple proof for the problem of estimating and testing for multiple breaks in a single equation framework with regressors that are endogenous. We show based on standard assumptions about the regressors, instruments, and errors that the second-stage regression of the instrumental variable procedure involves regressors and errors that satisfy all the assumptions in Perron and Qu (2006, Journal of Econometrics 134, 373–399) so that the results about consistency, rate of convergence and limit distributions of the estimates of the break dates, in addition to the limit distributions of the tests, are obtained as simple consequences. The results are obtained within a unified framework for various cases about the nature of the reduced form: stable, no structural changes but time variations in the parameters, structural changes at dates that are common to those of the structural form, and structural changes occurring at arbitrary dates.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:30:y:2014:i:02:p:491-507_00
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    References listed on IDEAS

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    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. 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.
    3. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    4. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    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. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    7. 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.
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    Cited by:

    1. Badi H. Baltagi & Qu Feng & Chihwa Kao, 2019. "Structural changes in heterogeneous panels with endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 883-892, September.
    2. Casini, Alessandro & Perron, Pierre, 2022. "Generalized Laplace Inference In Multiple Change-Points Models," Econometric Theory, Cambridge University Press, vol. 38(1), pages 35-65, February.
    3. Alessandro Casini & Pierre Perron, "undated". "Generalized Laplace Inference in Multiple Change-Points Models," Boston University - Department of Economics - Working Papers Series WP2018-012, Boston University - Department of Economics.
    4. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    6. 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.
    7. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    8. 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.
    9. Akiko Sakanishi, 2020. "Urban commuting behavior and time allocation among women: Evidence from US metropolitan areas," Regional Science Policy & Practice, Wiley Blackwell, vol. 12(2), pages 349-363, April.
    10. Elliott, Graham & Müller, Ulrich K., 2014. "Pre and post break parameter inference," Journal of Econometrics, Elsevier, vol. 180(2), pages 141-157.
    11. 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.
    12. 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.
    13. Alessandro Casini & Pierre Perron, 2018. "Continuous Record Asymptotics for Change-Points Models," Papers 1803.10881, arXiv.org, revised Nov 2021.
    14. Chen, Bin, 2015. "Modeling and testing smooth structural changes with endogenous regressors," Journal of Econometrics, Elsevier, vol. 185(1), pages 196-215.
    15. Yu, Ping, 2013. "Inconsistency of 2SLS estimators in threshold regression with endogeneity," Economics Letters, Elsevier, vol. 120(3), pages 532-536.
    16. Qian, Junhui & Su, Liangjun, 2014. "Structural change estimation in time series regressions with endogenous variables," Economics Letters, Elsevier, vol. 125(3), pages 415-421.
    17. Fu, Zhonghao & Hong, Yongmiao, 2019. "A model-free consistent test for structural change in regression possibly with endogeneity," Journal of Econometrics, Elsevier, vol. 211(1), pages 206-242.
    18. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    19. Alessandro Casini & Pierre Perron, 2015. "Continuous Record Asymptotics for Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2018-010, Boston University - Department of Economics, revised Nov 2017.
    20. Eckert, C. & J. Hohberger (Jan) & Franses, Ph.H.B.F., 2022. "Gaussian Copula Regression in the Presence of Thresholds," Econometric Institute Research Papers 2022-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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