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Branching Fixed Effects: A Proposal for Communicating Uncertainty

Patrick Kline

arXiv 8 Dec 2025 · Econometrics

arXiv:2512.08101 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Economists often rely on estimates of linear fixed effects models produced by other teams of researchers. Assessing the uncertainty in these estimates can be challenging. I propose a form of sample splitting for networks that partitions the data into statistically independent branches, each of which can be used to compute an unbiased estimate of the parameters of interest in two-way fixed effects models. These branches facilitate uncertainty quantification, moment estimation, and shrinkage. Drawing on results from the graph theory literature on tree packing, I develop algorithms to efficiently extract branches from large networks. I illustrate these techniques using a benchmark dataset from Veneto, Italy that has been widely used to study firm wage effects.

Citation extraction

47
references
72
in-text mentions
47
distinct cited
3
self-citations
15,651
main-text words

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Kline, Patrick (2024) Firm wage effects self1.000105100%
2Kline, Patrick and Saggio, Raffaele and Sølvsten, Mikkel (2020) Leave-out estimation of variance components self0.87452100%
3Walters, Christopher R (2024) Empirical Bayes Methods in Labor Economics0.84333100%
4Ignatiadis, Nikolaos and Saha, Sujayam and Sun, Dennis L and Muralid… (2023) Empirical Bayes mean estimation with nonparametric errors via order statistic regression on replicated data0.73732100%
5Abowd, John M and Kramarz, Francis and Margolis, David N (1999) High wage workers and high wage firms0.64422100%
6Abowd, John M and Creecy, Robert H and Kramarz, Francis (2002) Computing person and firm effects using linked longitudinal employer-employee data0.64422100%
7Jochmans, Koen and Weidner, Martin (2019) Fixed-effect regressions on network data0.64422100%
8Krutchkoff, Richard G (1967) A supplementary sample non-parametric empirical Bayes approach to some statistical decision problems0.64422100%
9Nash-Williams, C.\ St.\ J.\ A (1961) Edge-Disjoint Spanning Trees of Finite Graphs0.64422100%
10Roskind, James and Tarjan, Robert E (1985) A Note on Finding Minimum-Cost Edge-Disjoint Spanning Trees0.64422100%

Showing the top 10 of 47 scored citations.