Hugo Freeman, Dennis Kristensen
arXiv 7 May 2026 · Econometrics
arXiv:2605.06491 · PDF · DOI · OpenAlex · Extracted main text
We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step estimators of the nonparametric regression function and the fixed effects and relies on two key ingredients: First, we develop moment conditions for the common parameters that are Neyman orthogonal with respect to the nonparametric regression function. Second, we employ a novel adjustment of the nonparametric regression estimator so the estimated fixed effects do not generate incidental parameter biases. Together, these ensure that the resulting estimator of the common parameters is root-NT -- asymptotically normally distributed under weak conditions on the estimators of fixed effects and regression function. Next, we propose a novel two-step estimator of the nonparametric regression function and the fixed effects and verify that this particular estimator satisfies the conditions of our general theory. A numerical study shows that the proposed estimators perform well in finite samples.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Freeman, Hugo (2022) Multidimensional Interactive Fixed-Effects self | 1.000 | 6 | 4 | 100% |
| 2 | Freeman, Hugo and Weidner, Martin (2023) Linear panel regressions with two-way unobserved heterogeneity self | 0.977 | 15 | 6 | 93% |
| 3 | Beyhum, Jad and Mugnier, Martin (2025) Inference after discretizing unobserved heterogeneity | 0.937 | 17 | 4 | 82% |
| 4 | Deaner, Ben and Hsiang, Chen-Wei and Zeleneev, Andrei (2025) Inferring Treatment Effects in Large Panels by Uncovering Latent Similarities | 0.928 | 5 | 3 | 80% |
| 5 | Bai, Jushan (2009) Panel data models with interactive fixed effects | 0.894 | 7 | 5 | 71% |
| 6 | Bai, Jushan and Ng, Serena (2023) Approximate factor models with weaker loadings | 0.874 | 6 | 3 | 67% |
| 7 | Freeman, Hugo AND Kristensen, Dennis (2026) Nonparametric Identification and Estimation of Regressions with Two-Way Fixed Effects self | 0.843 | 3 | 3 | 100% |
| 8 | Zhang, Yuan and Levina, Elizaveta and Zhu, Ji (2017) Estimating network edge probabilities by neighbourhood smoothing | 0.794 | 8 | 3 | 50% |
| 9 | Opsomer, Jean D and Ruppert, David (1999) A root-n consistent backfitting estimator for semiparametric additive modeling | 0.794 | 6 | 3 | 50% |
| 10 | Andrews, Donald W. K (1994) Asymptotics for Semiparametric Econometric Models Via Stochastic Equicontinuity | 0.737 | 4 | 2 | 75% |
Showing the top 10 of 37 scored citations.