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Identification of Non-Additive Fixed Effects Models: Is the Return to Teacher Quality Homogeneous?

Author

Listed:
  • Jinyong Hahn
  • John D. Singleton
  • Neşe Yildiz

Abstract

Panel or grouped data are often used to allow for unobserved individual heterogeneity in econometric models via fixed effects. In this paper, we discuss identification of a panel data model in which the unobserved heterogeneity both enters additively and interacts with treatment variables. We present identification and estimation methods for parameters of interest in this model under both strict and weak exogeneity assumptions. The key identification insight is that other periods' treatment variables are instruments for the unobserved fixed effects. We apply our proposed estimator to matched student-teacher data used to estimate value-added models of teacher quality. We show that the common assumption that the return to unobserved teacher quality is the same for all students is rejected by the data. We also present evidence that No Child Left Behind-era school accountability increased the effectiveness of teacher quality for lower performing students.

Suggested Citation

  • Jinyong Hahn & John D. Singleton & Neşe Yildiz, 2023. "Identification of Non-Additive Fixed Effects Models: Is the Return to Teacher Quality Homogeneous?," NBER Working Papers 31384, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:31384
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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • H75 - Public Economics - - State and Local Government; Intergovernmental Relations - - - State and Local Government: Health, Education, and Welfare
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • I24 - Health, Education, and Welfare - - Education - - - Education and Inequality

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