IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v23y2022icp1-18.html
   My bibliography  Save this article

Testing for coefficient differences across nested linear regression specifications

Author

Listed:
  • Blackburn, McKinley L.

Abstract

Statistical applications often involve a comparison of coefficients across two different nested linear regression specifications. However, these comparisons are rarely accompanied by a hypothesis test for the coefficients being equal. Standard specification tests from econometrics, while easy to apply, are not useful in this case. Generalized versions of these tests can be seen as essentially applying the delta method to the omitted-variable-bias formula, but have a tendency to over-reject, especially in small samples when errors are heteroskedastic. Resampling procedures can be helpful in this case, with approaches associated with the jackknife performing particularly well in conducting this test.

Suggested Citation

  • Blackburn, McKinley L., 2022. "Testing for coefficient differences across nested linear regression specifications," Econometrics and Statistics, Elsevier, vol. 23(C), pages 1-18.
    • Handle: RePEc:eee:ecosta:v:23:y:2022:i:c:p:1-18
    DOI: 10.1016/j.ecosta.2021.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306221000496
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2021.03.007?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. Frangos, Chris C. & Schucany, William R., 1990. "Jackknife estimation of the bootstrap acceleration constant," Computational Statistics & Data Analysis, Elsevier, vol. 9(3), pages 271-281, May.
    2. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    3. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    4. Jonah B. Gelbach, 2016. "When Do Covariates Matter? And Which Ones, and How Much?," Journal of Labor Economics, University of Chicago Press, vol. 34(2), pages 509-543.
    5. Emily Oster, 2019. "Unobservable Selection and Coefficient Stability: Theory and Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 187-204, April.
    6. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    7. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    8. Kauermann G. & Carroll R.J., 2001. "A Note on the Efficiency of Sandwich Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1387-1396, December.
    9. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    10. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    11. J. A. Hausman & W. E. Taylor, 1980. "Comparing Specification Tests and Classical Tests," Working papers 266, Massachusetts Institute of Technology (MIT), Department of Economics.
    12. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    13. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    14. Gerald G. Brown & Herbert C. Rutemiller, 1977. "Means and Variances of Stochastic Vector Products with Applications to Random Linear Models," Management Science, INFORMS, vol. 24(2), pages 210-216, October.
    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. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Testing for the appropriate level of clustering in linear regression models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2027-2056.
    2. 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.
    3. Antoine A. Djogbenou & James G. MacKinnon & Morten Ø. Nielsen, 2017. "Validity Of Wild Bootstrap Inference With Clustered Errors," Working Paper 1383, Economics Department, Queen's University.
    4. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    5. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    6. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2023. "Fast and reliable jackknife and bootstrap methods for cluster‐robust inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 671-694, August.
    7. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    8. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 106, University of California, Davis, Department of Economics.
    9. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    10. Romano, Joseph P. & Wolf, Michael, 2017. "Resurrecting weighted least squares," Journal of Econometrics, Elsevier, vol. 197(1), pages 1-19.
    11. José Murteira & Esmeralda Ramalho & Joaquim Ramalho, 2013. "Heteroskedasticity testing through a comparison of Wald statistics," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 12(2), pages 131-160, August.
    12. Godfrey, L.G., 2006. "Tests for regression models with heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2715-2733, June.
    13. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Size-corrected Bootstrap Test after Pretesting for Exogeneity with Heteroskedastic or Clustered Data," MPRA Paper 110899, University Library of Munich, Germany.
    14. Yang He & Otávio Bartalotti, 2020. "Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals [Using Maimonides’ rule to estimate the effect of class size on scholastic achievemen," The Econometrics Journal, Royal Economic Society, vol. 23(2), pages 211-231.
    15. 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.
    16. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    17. Jeffrey D. Michler & Anna Josephson, 2022. "Recent developments in inference: practicalities for applied economics," Chapters, in: A Modern Guide to Food Economics, chapter 11, pages 235-268, Edward Elgar Publishing.
    18. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.
    19. Aleksey Oshchepkov & Anna Shirokanova, 2020. "Multilevel Modeling For Economists: Why, When And How," HSE Working papers WP BRP 233/EC/2020, National Research University Higher School of Economics.
    20. Jongmoo Jay Choi & Hoje Jo & Jimi Kim & Moo Sung Kim, 2018. "Business Groups and Corporate Social Responsibility," Journal of Business Ethics, Springer, vol. 153(4), pages 931-954, December.

    More about this item

    Keywords

    Omitted variables; Hausman test; Sensitivity analysis; Resampling procedures;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:ecosta:v:23:y:2022:i:c:p:1-18. 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: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.