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Limit Theorems for Factor Models
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Limit Theorems for Factor Models

Author

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  • Stanislav Anatolyev
  • Anna Mikusheva

Abstract

The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous micro-parameters estimated separately for each entity. The central limit theorem applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. The paper studies the conditions when one can consistently estimate the asymptotic variance, and proposes a bootstrap scheme for cases when one cannot. A small simulation study illustrates performance of the asymptotic and bootstrap procedures. The results are useful for making inferences in two-step estimation procedures related to factor models, as well as in other related contexts. Our treatment avoids structural modeling of cross-sectional dependence but imposes time-series independence.

Suggested Citation

  • Stanislav Anatolyev & Anna Mikusheva, 2018. "Limit Theorems for Factor Models," Papers 1807.06338, arXiv.org, revised Sep 2020.
    • Handle: RePEc:arx:papers:1807.06338
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    References listed on IDEAS

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    1. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
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    8. Anatolyev, Stanislav & Mikusheva, Anna, 2022. "Factor models with many assets: Strong factors, weak factors, and the two-pass procedure," Journal of Econometrics, Elsevier, vol. 229(1), pages 103-126.
    9. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
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    11. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    12. Kleibergen, Frank & Zhan, Zhaoguo, 2015. "Unexplained factors and their effects on second pass R-squared’s," Journal of Econometrics, Elsevier, vol. 189(1), pages 101-116.
    13. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, July.
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    Cited by:

    1. Anatolyev, Stanislav & Mikusheva, Anna, 2022. "Factor models with many assets: Strong factors, weak factors, and the two-pass procedure," Journal of Econometrics, Elsevier, vol. 229(1), pages 103-126.
    2. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.

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