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Discretizing Unobserved Heterogeneity
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Discretizing Unobserved Heterogeneity

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  • Stéphane Bonhomme
  • Thibaut Lamadon
  • Elena Manresa

Abstract

We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on two‐step grouped fixed‐effects (GFE) estimators, where individuals are first classified into groups using kmeans clustering, and the model is then estimated allowing for group‐specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function—possibly nonlinear and time‐varying—of a low‐dimensional continuous latent type, and informative moments are available for classification. We illustrate the method in a model of wages and labor market participation, and in a probit model with time‐varying heterogeneity. We derive asymptotic expansions of two‐step GFE estimators as the number of groups grows with the two dimensions of the panel. We propose a data‐driven rule for the number of groups, and discuss bias reduction and inference.

Suggested Citation

  • Stéphane Bonhomme & Thibaut Lamadon & Elena Manresa, 2022. "Discretizing Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 90(2), pages 625-643, March.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:2:p:625-643
    DOI: 10.3982/ECTA15238
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    References listed on IDEAS

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    9. Iris Kesternich & Bettina Siflinger & James P. Smith & Franziska Valder, 2022. "Relationship Stability: Evidence from Labor and Marriage Markets," CEBI working paper series 22-20, University of Copenhagen. Department of Economics. The Center for Economic Behavior and Inequality (CEBI).
    10. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2023. "Specification testing with grouped fixed effects," Papers 2310.01950, arXiv.org.
    11. Romuald Meango, 2023. "Using Probabilistic Stated Preference Analyses to Understand Actual Choices," Papers 2307.13966, arXiv.org.
    12. Igor Custodio João & Julia Schaumburg & André Lucas & Bernd Schwaab, 2024. "Dynamic Nonparametric Clustering of Multivariate Panel Data," Journal of Financial Econometrics, Oxford University Press, vol. 22(2), pages 335-374.
    13. Jose Garcia-Louzao & Alessandro Ruggieri, 2023. "Labor Market Competition and Inequality," CESifo Working Paper Series 10829, CESifo.
    14. Leknes, Stefan & Rattsø, Jørn & Stokke, Hildegunn E., 2022. "Assortative labor matching, city size, and the education level of workers," Regional Science and Urban Economics, Elsevier, vol. 96(C).
    15. Boyuan Zhang, 2022. "Incorporating Prior Knowledge of Latent Group Structure in Panel Data Models," Papers 2211.16714, arXiv.org, revised Oct 2023.
    16. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    17. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    18. Øystein Daljord, 2022. "Durable Goods Adoption and the Consumer Discount Factor: A Case Study of the Norwegian Book Market," Management Science, INFORMS, vol. 68(9), pages 6783-6796, September.
    19. Guy Aridor, 2022. "Measuring Substitution Patterns in the Attention Economy: An Experimental Approach," CESifo Working Paper Series 10190, CESifo.
    20. Geert Dhaene & Martin Weidner, 2023. "Approximate Functional Differencing," Papers 2301.13736, arXiv.org, revised May 2023.
    21. Langevin, R.;, 2024. "Consistent Estimation of Finite Mixtures: An Application to Latent Group Panel Structures," Health, Econometrics and Data Group (HEDG) Working Papers 24/16, HEDG, c/o Department of Economics, University of York.

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