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Non-parametric Panel Data Models with Interactive Fixed Effects

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  • Joachim Freyberger

Abstract

This article studies non-parametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed. I focus on models where the unobservables have a factor structure and enter an unknown structural function non-additively. The setup allows the individual effects to impact outcomes differently in different time periods and it allows for heterogeneous marginal effects. I provide sufficient conditions for point identification of all parameters of the model. Furthermore, I present a non-parametric sieve maximum likelihood estimator as well as flexible semiparametric and parametric estimators. Monte Carlo experiments demonstrate that the estimators perform well in finite samples. Finally, in an empirical application, I use these estimators to investigate the relationship between teaching practice and student achievement. The results differ considerably from those obtained with commonly used panel data methods.

Suggested Citation

  • Joachim Freyberger, 2018. "Non-parametric Panel Data Models with Interactive Fixed Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1824-1851.
    • Handle: RePEc:oup:restud:v:85:y:2018:i:3:p:1824-1851.
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    File URL: http://hdl.handle.net/10.1093/restud/rdx052
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    Citations

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    Cited by:

    1. Romuald Meango & Esther Mirjam Girsberger, 2023. "Identification of Ex ante Returns Using Elicited Choice Probabilities: an Application to Preferences for Public-sector Jobs," Papers 2303.03009, arXiv.org, revised Jun 2024.
    2. Botosaru, Irene & Muris, Chris & Pendakur, Krishna, 2023. "Identification of time-varying transformation models with fixed effects, with an application to unobserved heterogeneity in resource shares," Journal of Econometrics, Elsevier, vol. 232(2), pages 576-597.
    3. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    4. Ben Deaner, 2018. "Proxy Controls and Panel Data," Papers 1810.00283, arXiv.org, revised Nov 2023.
    5. Qian Sun, 2023. "SOE wage premium in China: new evidence," Empirical Economics, Springer, vol. 64(3), pages 1121-1147, March.
    6. Chang, Huibin & Indra, Debarshi & Maiti, Abhradeep, 2023. "Metropolitan area heterogeneity and the impact of road infrastructure improvements on VMT," Transportation Research Part A: Policy and Practice, Elsevier, vol. 175(C).
    7. Kenichi Nagasawa, 2018. "Treatment Effect Estimation with Noisy Conditioning Variables," Papers 1811.00667, arXiv.org, revised Sep 2022.
    8. Alain-Philippe Fortin & Patrick Gagliardini & Olivier Scaillet, 2023. "Latent Factor Analysis in Short Panels," Swiss Finance Institute Research Paper Series 23-44, Swiss Finance Institute.
    9. Okui, Ryo & Yanagi, Takahide, 2019. "Panel data analysis with heterogeneous dynamics," Journal of Econometrics, Elsevier, vol. 212(2), pages 451-475.
    10. Nagasawa, Kenichi, 2020. "Identification and Estimation of Group-Level Partial Effects," The Warwick Economics Research Paper Series (TWERPS) 1243, University of Warwick, Department of Economics.
    11. Irene Botosaru & Chris Muris & Senay Sokullu, 2022. "Time-Varying Linear Transformation Models with Fixed Effects and Endogeneity for Short Panels," Department of Economics Working Papers 2022-01, McMaster University.
    12. Dmitry Arkhangelsky & Aleksei Samkov, 2024. "Sequential Synthetic Difference in Differences," Papers 2404.00164, arXiv.org.
    13. Irene Botosaru & Chris Muris & Krishna Pendakur, 2020. "Intertemporal Collective Household Models: Identification in Short Panels with Unobserved Heterogeneity in Resource Shares," Department of Economics Working Papers 2020-09, McMaster University.
    14. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    15. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    16. Loh, Isaac, 2023. "Genericity of the completeness condition with constrained instruments," Economics Letters, Elsevier, vol. 224(C).
    17. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    18. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    19. Joachim Freyberger, 2021. "Normalizations and misspecification in skill formation models," Papers 2104.00473, arXiv.org, revised Jul 2022.

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