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An econometric approach to the estimation of multi-level models

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  • 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
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    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.

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    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

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