[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/max/cprwps/189.html
   My bibliography  Save this paper

Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model

Author

Listed:
Abstract
This paper studies the asymptotic power for the sphericity test in a fixed effect panel data model proposed by Baltagi, Feng and Kao (2011), (JBFK). This is done under the alternative hypotheses of weak and strong factors. By weak factors, we mean that the Euclidean norm of the vector of the factor loadings is O(1). By strong factors, we mean that the Euclidean norm of the vector of factor loadings is O(pn), where n is the number of individuals in the panel. To derive the limiting distribution of JBFK under the alternative, we first derive the limiting distribution of its raw data counterpart. Our results show that, when the factor is strong, the test statistic diverges in probability to infinity as fast as Op(nT). However, when the factor is weak, its limiting distribution is a rightward mean shift of the limit distribution under the null. Second, we derive the asymptotic behavior of the difference between JBFK and its raw data counterpart. Our results show that when the factor is strong this difference is as large as Op(n). In contrast, when the factor is weak, this difference converges in probability to a constant. Taken together, these results imply that when the factor is strong, JBFK is consistent, but when the factor is weak, JBFK is inconsistent even though its asymptotic power is nontrivial.

Suggested Citation

  • Badi Baltagi & Chihwa Kao & Fa wang, 2016. "Asymptotic Power of the Sphericity Test Under Weak and Strong Factors in a Fixed Effects Panel Data Model," Center for Policy Research Working Papers 189, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:189
    as

    Download full text from publisher

    File URL: https://surface.syr.edu/cpr/218/
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions," Journal of Econometrics, Elsevier, vol. 106(1), pages 143-170, January.
    2. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2012. "A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model," Journal of Econometrics, Elsevier, vol. 170(1), pages 164-177.
    3. Badi H. Baltagi & Esfandiar Maasoumi, 2013. "An Overview of Dependence in Cross-Section, Time-Series, and Panel Data," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 543-546, August.
    4. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    5. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    6. Badi H. Baltagi & Qu Feng & Chihwa Kao, 2011. "Testing for sphericity in a fixed effects panel data model," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 25-47, February.
    7. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    8. Alexander Chudik & M. Hashem Pesaran, 2013. "Large Panel Data Models with Cross-Sectional Dependence: A Survey," CESifo Working Paper Series 4371, CESifo.
    9. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    10. M. Hashem Pesaran & Aman Ullah & Takashi Yamagata, 2008. "A bias-adjusted LM test of error cross-section independence," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 105-127, March.
    11. M. Hashem Pesaran, 2021. "General diagnostic tests for cross-sectional dependence in panels," Empirical Economics, Springer, vol. 60(1), pages 13-50, January.
    12. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2012. "Signal Detection in High Dmension: The Multispiked Case," Working Papers ECARES ECARES 2012-036, ULB -- Universite Libre de Bruxelles.
    13. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2011. "Asymptotic Power of Sphericity Tests for High-Dimensional Data," Working Papers ECARES ECARES 2011-018, ULB -- Universite Libre de Bruxelles.
    14. Wang, Cheng, 2014. "Asymptotic power of likelihood ratio tests for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 184-189.
    15. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    16. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    17. M. Hashem Pesaran, 2015. "Testing Weak Cross-Sectional Dependence in Large Panels," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1089-1117, December.
    18. Frees, Edward W., 1995. "Assessing cross-sectional correlation in panel data," Journal of Econometrics, Elsevier, vol. 69(2), pages 393-414, October.
    19. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    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. Peng, Bin & Shen, Xinyuan & Ye, Jinqi, 2019. "Testing for sphericity in a fixed effects panel data model with time-varying variances," Economics Letters, Elsevier, vol. 181(C), pages 85-89.
    2. Zhaoyuan Li & Jianfeng Yao, 2021. "Extension of the Lagrange multiplier test for error cross-section independence to large panels with non normal errors," Papers 2103.06075, arXiv.org.
    3. Zhang, Yangchun & Zhou, Yirui & Liu, Xiaowei, 2023. "Applications on linear spectral statistics of high-dimensional sample covariance matrix with divergent spectrum," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

    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. Alexander Chudik & M. Hashem Pesaran, 2013. "Large panel data models with cross-sectional dependence: a survey," Globalization Institute Working Papers 153, Federal Reserve Bank of Dallas.
    2. Zhaoyuan Li & Jianfeng Yao, 2021. "Extension of the Lagrange multiplier test for error cross-section independence to large panels with non normal errors," Papers 2103.06075, arXiv.org.
    3. Zhenhong Huang & Zhaoyuan Li & Jianfeng Yao, 2023. "Unified and robust Lagrange multiplier type tests for cross-sectional independence in large panel data models," Papers 2302.14387, arXiv.org.
    4. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    5. Feng, Long & Zhao, Ping & Ding, Yanling & Liu, Binghui, 2021. "Rank-based tests of cross-sectional dependence in panel data models," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    6. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2012. "A Lagrange Multiplier test for cross-sectional dependence in a fixed effects panel data model," Journal of Econometrics, Elsevier, vol. 170(1), pages 164-177.
    7. Halunga, Andreea G. & Orme, Chris D. & Yamagata, Takashi, 2017. "A heteroskedasticity robust Breusch–Pagan test for Contemporaneous correlation in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 198(2), pages 209-230.
    8. Wang, Hongfei & Liu, Binghui & Feng, Long & Ma, Yanyuan, 2024. "Rank-based max-sum tests for mutual independence of high-dimensional random vectors," Journal of Econometrics, Elsevier, vol. 238(1).
    9. Hikmet Akyol & Selim Basar, 2024. "Empirical Analysis of Turkish Banking Sector Institutional and Macroeconomic Determinants of Risks," Istanbul Journal of Economics-Istanbul Iktisat Dergisi, Istanbul University, Faculty of Economics, vol. 73(74-1), pages 59-98, June.
    10. Schneider, Nicolas & Strielkowski, Wadim, 2023. "Modelling the unit root properties of electricity data—A general note on time-domain applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    11. Muhammad Shafiullah & Luke Emeka Okafor & Usman Khalid, 2019. "Determinants of international tourism demand: Evidence from Australian states and territories," Tourism Economics, , vol. 25(2), pages 274-296, March.
    12. M. Hashem Pesaran, 2015. "Testing Weak Cross-Sectional Dependence in Large Panels," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1089-1117, December.
    13. Badi H. Baltagi & Chihwa Kao & Bin Peng, 2016. "Testing Cross-Sectional Correlation in Large Panel Data Models with Serial Correlation," Econometrics, MDPI, vol. 4(4), pages 1-24, November.
    14. Auteri, Monica & Mele, Marco & Ruble, Isabella & Magazzino, Cosimo, 2024. "The double sustainability: The link between government debt and renewable energy," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    15. Michael Appiah & Bright Akwasi Gyamfi & Tomiwa Sunday Adebayo & Festus Victor Bekun, 2023. "Do financial development, foreign direct investment, and economic growth enhance industrial development? Fresh evidence from Sub-Sahara African countries," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 22(2), pages 203-227, May.
    16. Francesco Moscone & Elisa Tosetti, 2009. "A Review And Comparison Of Tests Of Cross‐Section Independence In Panels," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 528-561, July.
    17. Peng, Bin & Yu, Junqi & Zhu, Yi, 2021. "A heteroskedasticity robust test for cross-sectional correlation in a fixed effects panel data model," Economics Letters, Elsevier, vol. 201(C).
    18. Ioannis Kostakis & Sarantis Lolos, 2024. "Uncovering the impact of cultural heritage on economic growth: empirical evidence from Greek regions, 2000–2019," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 73(3), pages 1209-1239, October.
    19. Laeeq Razzak Janjua & Orhan Sanli & Mirela Panait & Mirela Cristea & Atteeq Razzak, 2024. "Impact of energy security and economic growth on poverty: sample of Sub-Saharan Africa," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(10), pages 25459-25484, October.
    20. Muhammad Shafiullah & Vassilios G. Papavassiliou & Muhammad Shahbaz, 2021. "Is There an Extended Education-Based Environmental Kuznets Curve? An Analysis of U.S. States," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 80(4), pages 795-819, December.

    More about this item

    Keywords

    Asymptotic power; Sphericity; John Test; Weak Factor; Strong Factor; High Dimensional Inference; Panel Data;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    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:max:cprwps:189. 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: Katrina Fiacchi (email available below). General contact details of provider: https://edirc.repec.org/data/cpsyrus.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.