IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2204.01373.html
   My bibliography  Save this paper

A Bootstrap-Assisted Self-Normalization Approach to Inference in Cointegrating Regressions

Author

Listed:
  • Karsten Reichold
  • Carsten Jentsch

Abstract

Traditional inference in cointegrating regressions requires tuning parameter choices to estimate a long-run variance parameter. Even in case these choices are "optimal", the tests are severely size distorted. We propose a novel self-normalization approach, which leads to a nuisance parameter free limiting distribution without estimating the long-run variance parameter directly. This makes our self-normalized test tuning parameter free and considerably less prone to size distortions at the cost of only small power losses. In combination with an asymptotically justified vector autoregressive sieve bootstrap to construct critical values, the self-normalization approach shows further improvement in small to medium samples when the level of error serial correlation or regressor endogeneity is large. We illustrate the usefulness of the bootstrap-assisted self-normalized test in empirical applications by analyzing the validity of the Fisher effect in Germany and the United States.

Suggested Citation

  • Karsten Reichold & Carsten Jentsch, 2022. "A Bootstrap-Assisted Self-Normalization Approach to Inference in Cointegrating Regressions," Papers 2204.01373, arXiv.org.
  • Handle: RePEc:arx:papers:2204.01373
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2204.01373
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vogelsang, Timothy J. & Wagner, Martin, 2014. "Integrated modified OLS estimation and fixed-b inference for cointegrating regressions," Journal of Econometrics, Elsevier, vol. 178(2), pages 741-760.
    2. Cai, Ye & Shintani, Mototsugu, 2006. "On The Alternative Long-Run Variance Ratio Test For A Unit Root," Econometric Theory, Cambridge University Press, vol. 22(3), pages 347-372, June.
    3. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 133(2), pages 703-739, August.
    6. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2015. "Bootstrap Testing of Hypotheses on Co‐Integration Relations in Vector Autoregressive Models," Econometrica, Econometric Society, vol. 83, pages 813-831, March.
    7. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2010. "A Sieve Bootstrap Test For Cointegration In A Conditional Error Correction Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 647-681, June.
      • Arnold Zellner & Franz C. Palm, 2000. "Correction," Econometrica, Econometric Society, vol. 68(5), pages 1293-1294, September.
    8. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    9. Nicholas M. Kiefer & Timothy J. Vogelsang, 2002. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation," Econometrica, Econometric Society, vol. 70(5), pages 2093-2095, September.
    10. Choi, In & Kurozumi, Eiji, 2012. "Model selection criteria for the leads-and-lags cointegrating regression," Journal of Econometrics, Elsevier, vol. 169(2), pages 224-238.
    11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    12. Xiaofeng Shao, 2015. "Self-Normalization for Time Series: A Review of Recent Developments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1797-1817, December.
    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. Jiti Gao & Bin Peng & Yayi Yan, 2022. "Higher-order Expansions and Inference for Panel Data Models," Papers 2205.00577, arXiv.org, revised Jun 2023.
    2. Karsten Reichold, 2022. "A Residuals-Based Nonparametric Variance Ratio Test for Cointegration," Papers 2211.06288, arXiv.org, revised Dec 2022.
    3. Jiti Gao & Bin Peng & Yayi Yan, 2022. "A Simple Bootstrap Method for Panel Data Inferences," Monash Econometrics and Business Statistics Working Papers 7/22, Monash University, Department of Econometrics and Business Statistics.
    4. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.

    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. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    2. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    3. Stephan Smeekes & Jean-Pierre Urbain, 2014. "On the Applicability of the Sieve Bootstrap in Time Series Panels," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 139-151, February.
    4. Casini, Alessandro, 2024. "The fixed-b limiting distribution and the ERP of HAR tests under nonstationarity," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Martin Wagner & Dominik Wied, 2017. "Consistent Monitoring of Cointegrating Relationships: The US Housing Market and the Subprime Crisis," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 960-980, November.
    6. Matei Demetrescu & Christoph Hanck & Robinson Kruse‐Becher, 2022. "Robust inference under time‐varying volatility: A real‐time evaluation of professional forecasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 1010-1030, August.
    7. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
    8. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    9. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.
    10. Pötscher, Benedikt M. & Preinerstorfer, David, 2017. "Further Results on Size and Power of Heteroskedasticity and Autocorrelation Robust Tests, with an Application to Trend Testing," MPRA Paper 81053, University Library of Munich, Germany.
    11. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2017. "A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data," Journal of Econometrics, Elsevier, vol. 197(2), pages 298-322.
    12. Hong, Yongmiao & Linton, Oliver & McCabe, Brendan & Sun, Jiajing & Wang, Shouyang, 2024. "Kolmogorov–Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Casini, Alessandro, 2023. "Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary models," Journal of Econometrics, Elsevier, vol. 235(2), pages 372-392.
    14. Shin‐Kun Peng & Takatoshi Tabuchi, 2007. "Spatial Competition in Variety and Number of Stores," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(1), pages 227-250, March.
    15. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    16. Kim, Min Seong & Sun, Yixiao, 2013. "Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 177(1), pages 85-108.
    17. Richard T. Baillie & Francis X. Diebold & George Kapetanios & Kun Ho Kim, 2022. "On Robust Inference in Time Series Regression," PIER Working Paper Archive 22-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    18. Vogelsang, Timothy J. & Franses, Philip Hans, 2005. "Testing for common deterministic trend slopes," Journal of Econometrics, Elsevier, vol. 126(1), pages 1-24, May.
    19. Kim, Bo Gyeong & Shin, Dong Wan, 2020. "A mean-difference test based on self-normalization for alternating regime index data sets," Economics Letters, Elsevier, vol. 193(C).
    20. Lee, Wei-Ming & Kuan, Chung-Ming & Hsu, Yu-Chin, 2014. "Testing over-identifying restrictions without consistent estimation of the asymptotic covariance matrix," Journal of Econometrics, Elsevier, vol. 181(2), pages 181-193.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2204.01373. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.