IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v220y2021i2p532-543.html
   My bibliography  Save this article

An econometric approach to the estimation of multi-level models

Author

Listed:
  • Yang, Yimin
  • Schmidt, Peter

Abstract

In this paper we consider “multidimensional” or “hierarchical” or “multilevel” models that are popular in the educational and economics literatures. Instead of two levels (individuals over time in the standard panel data model), we now have multiple levels (e.g. students in classrooms in schools in districts). We apply standard methods of analysis for econometric panel data to multilevel models. Specifically, we generalize the results of Hausman and Taylor and the subsequent literature to these models. This is a non-trivial extension because we now have more than one kind of time-invariant effect and more than one kind of “between” regression. We discuss estimation by GMM both with and without the assumption of no conditional heteroskedasticity. We also discuss endogeneity and dynamic models, and we generalize the concept of testing the exogeneity assumptions using a variable addition test.

Suggested Citation

  • Yang, Yimin & Schmidt, Peter, 2021. "An econometric approach to the estimation of multi-level models," Journal of Econometrics, Elsevier, vol. 220(2), pages 532-543.
    • Handle: RePEc:eee:econom:v:220:y:2021:i:2:p:532-543
    DOI: 10.1016/j.jeconom.2020.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407620301317
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2020.04.012?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. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    2. Laszlo Balazsi & Laszlo Matyas & Tom Wansbeek, 2018. "The estimation of multidimensional fixed effects panel data models," Econometric Reviews, Taylor & Francis Journals, vol. 37(3), pages 212-227, March.
    3. Hausman, Jerry A & Taylor, William E, 1981. "Panel Data and Unobservable Individual Effects," Econometrica, Econometric Society, vol. 49(6), pages 1377-1398, November.
    4. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    5. Laszlo Matyas, 1997. "Proper Econometric Specification of the Gravity Model," The World Economy, Wiley Blackwell, vol. 20(3), pages 363-368, May.
    6. Jee-Seon Kim & Edward Frees, 2007. "Multilevel Modeling with Correlated Effects," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 505-533, December.
    7. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    8. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-1395, November.
    9. 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.
    10. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
    11. Laszlo Matyas (ed.), 2017. "The Econometrics of Multi-dimensional Panels," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-319-60783-2.
    12. Baltagi, Badi H., 2015. "The Oxford Handbook of Panel Data," OUP Catalogue, Oxford University Press, number 9780199940042.
    13. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    14. Amemiya, Takeshi & MaCurdy, Thomas E, 1986. "Instrumental-Variable Estimation of an Error-Components Model," Econometrica, Econometric Society, vol. 54(4), pages 869-880, July.
    15. Breusch, Trevor S & Mizon, Grayham E & Schmidt, Peter, 1989. "Efficient Estimation Using Panel Data," Econometrica, Econometric Society, vol. 57(3), pages 695-700, May.
    16. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    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. Albert Okunade & Ahmad Reshad Osmani & Toluwalope Ayangbayi & Adeyinka Kevin Okunade, 2021. "Children’s Health Capital Investment: Effects of U.S. Infant Breastfeeding on Teenage Obesity," Econometrics, MDPI, vol. 9(4), pages 1-15, November.
    2. Yang, Yimin, 2022. "A correlated random effects approach to the estimation of models with multiple fixed effects," Economics Letters, Elsevier, vol. 213(C).
    3. Leslie E. Papke & Jeffrey M. Wooldridge, 2023. "A simple, robust test for choosing the level of fixed effects in linear panel data models," Empirical Economics, Springer, vol. 64(6), pages 2683-2701, June.
    4. Guohua Feng & Jiti Gao & Bin Peng, 2021. "Productivity Convergence in Manufacturing: A Hierarchical Panel Data Approach," Papers 2111.00449, arXiv.org.

    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. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    2. Donald W.K. Andrews & Biao Lu, 1999. "Consistent Model and Moment Selection Criteria for GMM Estimation with Applications to Dynamic Panel Data Models," Cowles Foundation Discussion Papers 1233, Cowles Foundation for Research in Economics, Yale University.
    3. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
    4. Sebastian Kripfganz & Claudia Schwarz, 2019. "Estimation of linear dynamic panel data models with time‐invariant regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(4), pages 526-546, June.
    5. Mayer, Alexander, 2022. "On the local power of some tests of strict exogeneity in linear fixed effects models," Econometrics and Statistics, Elsevier, vol. 24(C), pages 49-74.
    6. Doug J. Chung & Byungyeon Kim & Byoung G. Park, 2019. "How Do Sales Efforts Pay Off? Dynamic Panel Data Analysis in the Nerlove–Arrow Framework," Management Science, INFORMS, vol. 65(11), pages 5197-5218, November.
    7. Mitze, Timo & Alecke, Björn & Untiedt, Gerhard, 2008. "Trade, FDI and Cross-Variable Linkages: A German (Macro-)Regional Perspective," MPRA Paper 12245, University Library of Munich, Germany.
    8. Vasilis Sarafidis & Tom Wansbeek, 2020. "Celebrating 40 Years of Panel Data Analysis: Past, Present and Future," Monash Econometrics and Business Statistics Working Papers 6/20, Monash University, Department of Econometrics and Business Statistics.
    9. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    10. Jing Jia & Zhongtian Li, 2022. "Corporate Environmental Performance and Financial Distress: Evidence from Australia," Australian Accounting Review, CPA Australia, vol. 32(2), pages 188-200, June.
    11. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    12. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    13. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
    14. Maria Elena Bontempi & Jan Ditzen, 2023. "GMM-lev estimation and individual heterogeneity: Monte Carlo evidence and empirical applications," Papers 2312.00399, arXiv.org, revised Dec 2023.
    15. Kyuho Jin, 2022. "Can Business Groups Survive Institutional Advancements? Examining the Role of Internal Market for Non-Tradable, Intangible Assets," Sustainability, MDPI, vol. 14(17), pages 1-17, September.
    16. Sarafidis, Vasilis & Yamagata, Takashi & Robertson, Donald, 2009. "A test of cross section dependence for a linear dynamic panel model with regressors," Journal of Econometrics, Elsevier, vol. 148(2), pages 149-161, February.
    17. Osvaldo Lagares, 2016. "Capital, Economic Growth and Relative Income Differences in Latin America," Discussion Papers 16/03, Department of Economics, University of York.
    18. Güzin Bayar, 2018. "Estimating export equations: a survey of the literature," Empirical Economics, Springer, vol. 54(2), pages 629-672, March.
    19. Ahn, Seung C. & Schmidt, Peter, 1997. "Efficient estimation of dynamic panel data models: Alternative assumptions and simplified estimation," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 309-321.
    20. Kitazawa, Yoshitsugu, 2001. "Exponential regression of dynamic panel data models," Economics Letters, Elsevier, vol. 73(1), pages 7-13, October.

    More about this item

    Keywords

    Panel data; Hierarchical model; Multi-level model; Hausman and Taylor; Exogeneity tests;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

    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:220:y:2021:i:2:p:532-543. 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.