arXiv 27 Dec 2025 · Econometrics
arXiv:2512.22697 · PDF · DOI · OpenAlex · Extracted main text
We study instrumental variable regression in data rich environments. The goal is to estimate a linear model from many noisy covariates and many noisy instruments. Our key assumption is that true covariates and true instruments are repetitive, though possibly different in nature; they each reflect a few underlying factors, however those underlying factors may be misaligned. We analyze a family of estimators based on two stage least squares with spectral regularization: canonical correlations between covariates and instruments are learned in the first stage, which are used as regressors in the second stage. As a theoretical contribution, we derive upper and lower bounds on estimation error, proving optimality of the method with noisy data. As a practical contribution, we provide guidance on which types of spectral regularization to use in different regimes.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bao, Z., Hu, J., Pan, G., and Zhou, W (2019) Canonical correlation coefficients of high-dimensional gaussian vectors: Finite rank case | 0.644 | 2 | 2 | 100% |
| 2 | Benaych-Georges, F. and Nadakuditi, R. R (2012) The singular values and vectors of low rank perturbations of large rectangular random matrices | 0.644 | 2 | 2 | 100% |
| 3 | Andrews, I (2016) Conditional linear combination tests for weakly identified models | 0.405 | 1 | 1 | 100% |
| 4 | Andrews, I (2018) Valid two-step identification-robust confidence sets for GMM | 0.405 | 1 | 1 | 100% |
| 5 | Bai, J. and Ng, S (2006) Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions | 0.405 | 1 | 1 | 100% |
| 6 | Bai, J. and Ng, S (2010) Instrumental variable estimation in a data rich environment | 0.405 | 1 | 1 | 100% |
| 7 | Bai, J. and Wang, P (2016) Econometric analysis of large factor models | 0.405 | 1 | 1 | 100% |
| 8 | Baik, J., Ben Arous, G., and Péché, S (2005) Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices | 0.405 | 1 | 1 | 100% |
| 9 | Carrasco, M (2012) A regularization approach to the many instruments problem | 0.405 | 1 | 1 | 100% |
| 10 | Carrasco, M. and Tchuente, G (2016) Regularization based Anderson–Rubin tests for many instruments | 0.405 | 1 | 1 | 100% |
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