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Summary We consider peer effect estimation in social network models where some network links are incorrectly measured. We show that if the number or magnitude of mismeasured links does not grow too quickly with the sample size, then standard instrumental variables estimators that ignore these measurement errors remain consistent, and standard asymptotic inference methods remain valid. These results hold even when the link measurement errors are correlated with regressors or with structural errors in the model. Simulations and real data experiments confirm our results in finite samples. These findings imply that researchers can ignore small numbers of mismeasured links in networks.
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This content will become publicly available on January 1, 2026
With random regressors, least squares inference is robust to correlated errors with unknown correlation structure
Abstract Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the errors. We depart from existing literature by showing that with random regressors, linear regression inference is robust to correlated errors with unknown correlation structure. The existing theoretical analyses for linear regression are no longer valid because even the asymptotic normality of the least squares coefficients breaks down in this regime. We first prove the asymptotic normality of the t statistics by establishing their Berry–Esseen bounds based on a novel probabilistic analysis of self-normalized statistics. We then study the local power of the corresponding t tests and show that, perhaps surprisingly, error correlation can even enhance power in the regime of weak signals. Overall, our results show that linear regression is applicable more broadly than the conventional theory suggests, and they further demonstrate the value of randomization for ensuring robustness of inference.
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- Award ID(s):
- 1945136
- PAR ID:
- 10625613
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 112
- Issue:
- 1
- ISSN:
- 1464-3510
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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