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Linear Regression with Weak Exogeneity

Anna Mikusheva, Mikkel Sølvsten

arXiv 17 Aug 2023 · Econometrics · publishedQuantitative Economics (2025) · 5 citations (OpenAlex)

arXiv:2308.08958 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies linear time series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given the present and past regressor values, allowing errors to correlate with future regressor realizations. We show that weak exogeneity in time series regressions with many controls may produce substantial biases and even render the least squares (OLS) estimator inconsistent. The bias arises in settings with many regressors because the normalized OLS design matrix remains asymptotically random and correlates with the regression error when only weak (but not strict) exogeneity holds. This bias's magnitude increases with the number of regressors and their average autocorrelation. To address this issue, we propose an innovative approach to bias correction that yields a new estimator with improved properties relative to OLS. We establish consistency and conditional asymptotic Gaussianity of this new estimator and provide a method for inference.

Citation extraction

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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
1Sawa, T (1978) The exact moments of the least squares estimator for the autoregressive model0.84333100%
2Stambaugh, R. F (1999) Predictive regressions0.84333100%
3Hansen, C., J. Hausman, and W. Newey (2008) Estimation with many instrumental variables0.73732100%
4Chao, J. C., N. R. Swanson, J. A. Hausman, W. K. Newey, and T. Woute… (2012) Asymptotic distribution of JIVE in a heteroskedastic IV regression with many instruments0.64422100%
5Kiviet, J. F., G. D. Phillips, and B. Schipp (1999) Alternative bias approximations in first-order dynamic reduced form models0.64422100%
6Kline, P., R. Saggio, and M. Slvsten (2020) Leave-out estimation of variance components0.64422100%
7Slvsten, M (2020) Robust estimation with many instruments0.5113233%
8Anatolyev, S (2019) Many instruments and/or regressors: A friendly guide0.51121100%
9Bao, Y. and A. Ullah (2007) The second-order bias and mean squared error of estimators in time-series models0.51121100%
10Hamilton, J. D (1994) Time series analysis0.51121100%

Showing the top 10 of 32 scored citations.

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