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A Note on Identification of Match Fixed Effects as Interpretable Unobserved Match Affinity

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  • Suguru Otani
  • Tohya Sugano

Abstract

We highlight that match fixed effects, represented by the coefficients of interaction terms involving dummy variables for two elements, lack identification without specific restrictions on parameters. Consequently, the coefficients typically reported as relative match fixed effects by statistical software are not interpretable. To address this, we establish normalization conditions that enable identification of match fixed effect parameters as interpretable indicators of unobserved match affinity, facilitating comparisons among observed matches. Using data from middle school students in the 2007 Trends in International Mathematics and Science Study (TIMSS), we highlight the distribution of comparable match fixed effects within a specific school.

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  • Suguru Otani & Tohya Sugano, 2024. "A Note on Identification of Match Fixed Effects as Interpretable Unobserved Match Affinity," Papers 2406.18913, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2406.18913
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    References listed on IDEAS

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    1. Eleanor Wiske Dillon & Jeffrey Andrew Smith, 2020. "The Consequences of Academic Match between Students and Colleges," Journal of Human Resources, University of Wisconsin Press, vol. 55(3), pages 767-808.
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    3. Ferreira, Priscila & Taylor, Mark, 2011. "Measuring match quality using subjective data," Economics Letters, Elsevier, vol. 113(3), pages 304-306.
    4. Atsushi Inoue & Ryuichi Tanaka, 2023. "Do teachers’ college majors affect students’ academic achievement in the sciences? A cross-subfields analysis with student-teacher fixed effects," Education Economics, Taylor & Francis Journals, vol. 31(5), pages 617-631, September.
    5. Mittag, Nikolas, 2019. "A simple method to estimate large fixed effects models applied to wage determinants," Labour Economics, Elsevier, vol. 61(C).
    6. Christopher Biolsi & Brian Goff & Dennis Wilson, 2022. "Task-level match effects and worker productivity: evidence from pitchers and catchers," Applied Economics, Taylor & Francis Journals, vol. 54(25), pages 2888-2899, May.
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