Michal Kolesár, Pengjin Min, Wenjie Wang, Yichong Zhang
arXiv 14 Feb 2026 · Econometrics
arXiv:2602.13537 · PDF · DOI · OpenAlex · Extracted main text
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.
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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 | Kline, Patrick M., Saggio, Raffaele (2020) Leave-Out Estimation of Variance Components | 1.000 | 12 | 4 | 100% |
| 2 | Yap, Luther (2025) Inference with Many Weak Instruments and Heterogeneity | 1.000 | 7 | 4 | 100% |
| 3 | Chao, John C., Swanson, Norman R., Woutersen, Tiemen (2023) Jackknife Estimation of a Cluster-Sample IV Regression Model with Many Weak Instruments | 1.000 | 7 | 3 | 100% |
| 4 | Anatolyev, Stanislav (2023) Testing Many Restrictions under Heteroskedasticity | 1.000 | 6 | 4 | 100% |
| 5 | Cattaneo, Matias D., Jansson, Michael, Newey, Whitney K (2018) Inference in Linear Regression Models with Many Covariates and Heteroscedasticity | 0.928 | 4 | 3 | 100% |
| 6 | Evdokimov, Kirill S, Kolesr, Michal (2018) Inference in Instrumental Variables Analysis with Heterogeneous Treatment Effects | 0.928 | 4 | 3 | 100% |
| 7 | Jochmans, Koen (2022) Heteroscedasticity-Robust Inference in Linear Regression Models With Many Covariates | 0.843 | 3 | 3 | 100% |
| 8 | Abowd, John M., Kramarz, Francis, Margolis, David N (1999) High Wage Workers and High Wage Firms | 0.737 | 3 | 2 | 100% |
| 9 | Jung, Hyunseok, Liu, Xiaodong (2026) Testing for Peer Effects without Specifying the Network Structure | 0.737 | 3 | 2 | 100% |
| 10 | Kolesr, Michal (2013) Estimation in an instrumental variables model with treatment effect heterogeneity | 0.737 | 3 | 2 | 100% |
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