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Ridge Estimation of High Dimensional Two-Way Fixed Effect Regression

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  • Junnan He
  • Jean-Marc Robin

Abstract

We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size, the bias, and the variance-covariance matrix of the vector of estimated fixed effects converge to deterministic equivalents that depend only on the expected network. We provide simulations and an application using administrative data on wages for worker-firm matches.

Suggested Citation

  • Junnan He & Jean-Marc Robin, 2026. "Ridge Estimation of High Dimensional Two-Way Fixed Effect Regression," Papers 2601.04101, arXiv.org.
    • Handle: RePEc:arx:papers:2601.04101
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    References listed on IDEAS

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    1. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
    2. M. J. Andrews & L. Gill & T. Schank & R. Upward, 2008. "High wage workers and low wage firms: negative assortative matching or limited mobility bias?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(3), pages 673-697, June.
    3. Miren Azkarate-Askasua & Miguel Zerecero, 2022. "Correcting Small Sample Bias in Linear Models With Many Covariates," CRC TR 224 Discussion Paper Series crctr224_2022_376, University of Bonn and University of Mannheim, Germany.
    4. John M. Abowd & Francis Kramarz & David N. Margolis, 1999. "High Wage Workers and High Wage Firms," Econometrica, Econometric Society, vol. 67(2), pages 251-334, March.
    5. Stéphane Bonhomme & Thibaut Lamadon & Elena Manresa, 2019. "A Distributional Framework for Matched Employer Employee Data," Econometrica, Econometric Society, vol. 87(3), pages 699-739, May.
    6. Rasmus Lentz & Suphanit Piyapromdee & Jean-Marc Robin, 2022. "The Anatomy of Sorting - Evidence from Danish Data," Working Papers hal-03869383, HAL.
    7. Rasmus Lentz & Suphanit Piyapromdee & Jean‐Marc Robin, 2023. "The Anatomy of Sorting—Evidence From Danish Data," Econometrica, Econometric Society, vol. 91(6), pages 2409-2455, November.
    8. John M. Abowd & Kevin L. McKinney & Ian M. Schmutte, 2019. "Modeling Endogenous Mobility in Earnings Determination," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 405-418, July.
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