EconBase
← All papers

Cluster-Robust Inference for Quadratic Forms

Michal Kolesár, Pengjin Min, Wenjie Wang, Yichong Zhang

arXiv 14 Feb 2026 · Econometrics

arXiv:2602.13537 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and controls, inference on variance components, and testing multiple restrictions in a linear regression. Naïve plug-in estimators are known to be biased. We study a leave-one-cluster-out estimator that is unbiased, and provide sufficient conditions for its asymptotic normality. For inference, we establish the consistency of a leave-three-cluster-out variance estimator under primitive conditions. In addition, we develop a novel leave-two-cluster-out variance estimator that is computationally simpler and guaranteed to be conservative under weaker conditions. Our analysis allows cluster sizes to diverge with the sample size, accommodates strong within-cluster dependence, and permits the dimension of the covariates to diverge with the sample size, potentially at the same rate.

Citation extraction

40
references
98
in-text mentions
40
distinct cited
1
self-citations
13,784
main-text words

appendix boundary found by appendix_command · 22% of the source is main text. Read the extracted text to check this.

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 M., Saggio, Raffaele (2020) Leave-Out Estimation of Variance Components1.000124100%
2Yap, Luther (2025) Inference with Many Weak Instruments and Heterogeneity1.00074100%
3Chao, John C., Swanson, Norman R., Woutersen, Tiemen (2023) Jackknife Estimation of a Cluster-Sample IV Regression Model with Many Weak Instruments1.00073100%
4Anatolyev, Stanislav (2023) Testing Many Restrictions under Heteroskedasticity1.00064100%
5Cattaneo, Matias D., Jansson, Michael, Newey, Whitney K (2018) Inference in Linear Regression Models with Many Covariates and Heteroscedasticity0.92843100%
6Evdokimov, Kirill S, Kolesr, Michal (2018) Inference in Instrumental Variables Analysis with Heterogeneous Treatment Effects0.92843100%
7Jochmans, Koen (2022) Heteroscedasticity-Robust Inference in Linear Regression Models With Many Covariates0.84333100%
8Abowd, John M., Kramarz, Francis, Margolis, David N (1999) High Wage Workers and High Wage Firms0.73732100%
9Jung, Hyunseok, Liu, Xiaodong (2026) Testing for Peer Effects without Specifying the Network Structure0.73732100%
10Kolesr, Michal (2013) Estimation in an instrumental variables model with treatment effect heterogeneity0.73732100%

Showing the top 10 of 40 scored citations.