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An econometric approach to the estimation of multi-level models. (English) Zbl 1464.62524

Summary: 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.

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
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