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LIMIT THEOREMS FOR FACTOR MODELS

Published online by Cambridge University Press:  09 November 2020

Stanislav Anatolyev  and
Anna Mikusheva
Stanislav Anatolyev*
Affiliation:
CERGE-EI New Economic School
Anna Mikusheva
Affiliation:
Massachusetts Institute of Technology
*
Address correspondence to Stanislav Anatolyev, CERGE-EI, Politickych vězňů 7, 11121 Prague 1, Czech Republic; e-mail: stanislav.anatolyev@cerge-ei.cz.
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Abstract

This paper establishes central limit theorems (CLTs) 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 microparameters estimated separately for each entity. The CLT applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. This 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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 5 , October 2021 , pp. 1034 - 1074
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

We thank the Editor Peter C.B. Phillips, Co-Editor Guido Kuersteiner, and three anonymous referees for guidance and helpful suggestions that have greatly improved this paper. Support for Stanislav Anatolyev by Czech Science Foundation under grants 17-26535S and 20-28055S is gratefully acknowledged. Support for Anna Mikusheva by National Science Foundation under grant 1757199 is gratefully acknowledged.

References

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