IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v244y2024i1s0304407624001763.html
   My bibliography  Save this article

Fixed-b asymptotics for panel models with two-way clustering

Author

Listed:
  • Chen, Kaicheng
  • Vogelsang, Timothy J.

Abstract

This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2024) for linear panels. First, we show algebraically that this variance estimator (CHS estimator, hereafter) is a linear combination of three common variance estimators: the one-way unit cluster estimator, the “HAC of averages” estimator, and the “average of HACs” estimator. Based on this finding, we obtain a fixed-b asymptotic result for the CHS estimator and corresponding test statistics as the cross-section and time sample sizes jointly go to infinity. Furthermore, we propose two simple bias-corrected versions of the variance estimator and derive the fixed-b limits. In a simulation study, we find that the two bias-corrected variance estimators along with fixed-b critical values provide improvements in finite sample coverage probabilities. We illustrate the impact of bias-correction and use of the fixed-b critical values on inference in an empirical example on the relationship between industry profitability and market concentration.

Suggested Citation

  • Chen, Kaicheng & Vogelsang, Timothy J., 2024. "Fixed-b asymptotics for panel models with two-way clustering," Journal of Econometrics, Elsevier, vol. 244(1).
    • Handle: RePEc:eee:econom:v:244:y:2024:i:1:s0304407624001763
    DOI: 10.1016/j.jeconom.2024.105831
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407624001763
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2024.105831?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
    2. Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    3. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    4. Thompson, Samuel B., 2011. "Simple formulas for standard errors that cluster by both firm and time," Journal of Financial Economics, Elsevier, vol. 99(1), pages 1-10, January.
    5. Vogelsang, Timothy J., 2012. "Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects," Journal of Econometrics, Elsevier, vol. 166(2), pages 303-319.
    6. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 238-249, April.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    8. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    9. Mitchell A. Petersen, 2009. "Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches," The Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 435-480, January.
    10. John C. Driscoll & Aart C. Kraay, 1998. "Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 549-560, November.
    11. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    12. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    13. Sun, Yixiao, 2014. "Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference," Journal of Econometrics, Elsevier, vol. 178(P3), pages 659-677.
    14. 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.
    15. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    16. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
    17. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    18. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2018. "Asymptotic results under multiway clustering," Papers 1807.07925, arXiv.org, revised Aug 2018.
    19. Konrad Menzel, 2021. "Bootstrap With Cluster‐Dependence in Two or More Dimensions," Econometrica, Econometric Society, vol. 89(5), pages 2143-2188, September.
    20. Rho, Seung-Hwa & Vogelsang, Timothy J., 2019. "Heteroskedasticity Autocorrelation Robust Inference In Time Series Regressions With Missing Data," Econometric Theory, Cambridge University Press, vol. 35(3), pages 601-629, June.
    21. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B. & Vogelsang, Timothy J., 2016. "FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS," Econometric Theory, Cambridge University Press, vol. 32(1), pages 154-186, February.
    22. Eben Lazarus & Daniel J. Lewis & James H. Stock, 2021. "The Size‐Power Tradeoff in HAR Inference," Econometrica, Econometric Society, vol. 89(5), pages 2497-2516, September.
    23. Laurent Davezies & Xavier D’haultfœuille & Yannick Guyonvarch, 2021. "Empirical process results for exchangeable arrays," Post-Print hal-04430851, HAL.
    Full references (including those not matched with items on IDEAS)

    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. Kaicheng Chen & Timothy J. Vogelsang, 2023. "Fixed-b Asymptotics for Panel Models with Two-Way Clustering," Papers 2309.08707, arXiv.org, revised Aug 2024.
    2. 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.
    3. Sun, Yu & Yan, Karen X., 2019. "Inference on Difference-in-Differences average treatment effects: A fixed-b approach," Journal of Econometrics, Elsevier, vol. 211(2), pages 560-588.
    4. Timothy Conley & Silvia Gonçalves & Christian Hansen, 2018. "Inference with Dependent Data in Accounting and Finance Applications," Journal of Accounting Research, Wiley Blackwell, vol. 56(4), pages 1139-1203, September.
    5. Rho, Seunghwa & Vogelsang, Timothy J., 2021. "Inference in time series models using smoothed-clustered standard errors," Journal of Econometrics, Elsevier, vol. 224(1), pages 113-133.
    6. Vogelsang, Timothy J., 2012. "Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects," Journal of Econometrics, Elsevier, vol. 166(2), pages 303-319.
    7. Elif Guneren Genc & Ozlem Deniz Basar, 2017. "The Impact of OECD Countries¡¯ Macroeconomic Factors on Turkey¡¯s Foreign Trade," Research in World Economy, Research in World Economy, Sciedu Press, vol. 8(1), pages 24-36, June.
    8. Harold D Chiang & Bruce E Hansen & Yuya Sasaki, 2022. "Standard errors for two-way clustering with serially correlated time effects," Papers 2201.11304, arXiv.org, revised Dec 2023.
    9. 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.
    10. Bai, Jushan & Choi, Sung Hoon & Liao, Yuan, 2024. "Standard errors for panel data models with unknown clusters," Journal of Econometrics, Elsevier, vol. 240(2).
    11. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    12. Bruno Ferman, 2023. "Inference in difference‐in‐differences: How much should we trust in independent clusters?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 358-369, April.
    13. Liu, Cheng & Sun, Yixiao, 2019. "A simple and trustworthy asymptotic t test in difference-in-differences regressions," Journal of Econometrics, Elsevier, vol. 210(2), pages 327-362.
    14. Hwang, Jungbin & Sun, Yixiao, 2018. "Should we go one step further? An accurate comparison of one-step and two-step procedures in a generalized method of moments framework," Journal of Econometrics, Elsevier, vol. 207(2), pages 381-405.
    15. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
    16. Sequeira, Tiago & Morão, Hugo, 2020. "Growth accounting and regressions: New approach and results," International Economics, Elsevier, vol. 162(C), pages 67-79.
    17. Christian A. Vossler, 2013. "Analyzing repeated-game economics experiments: robust standard errors for panel data with serial correlation," Chapters, in: John A. List & Michael K. Price (ed.), Handbook on Experimental Economics and the Environment, chapter 3, pages 89-112, Edward Elgar Publishing.
    18. Jushan Bai & Sung Hoon Choi & Yuan Liao, 2021. "Feasible generalized least squares for panel data with cross-sectional and serial correlations," Empirical Economics, Springer, vol. 60(1), pages 309-326, January.
    19. Nan Liu & Yanbo Liu & Yuya Sasaki, 2024. "Estimation and Inference for Causal Functions with Multiway Clustered Data," Papers 2409.06654, arXiv.org.
    20. James G. MacKinnon & Morten {O}rregaard Nielsen & Matthew D. Webb, 2024. "Jackknife inference with two-way clustering," Papers 2406.08880, arXiv.org.

    More about this item

    Keywords

    Panel data; Clustering; Dependence; Standard errors; Fixed-b;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

    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:eee:econom:v:244:y:2024:i:1:s0304407624001763. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.