Limit Theorems for Factor Models

Stanislav Anatolyev and Anna Mikusheva

Papers from arXiv.org

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.

Date: 2018-07, Revised 2020-09
New Economics Papers: this item is included in nep-ecm and nep-ets
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Published in Econom. Theory 37 (2021) 1034-1074

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http://arxiv.org/pdf/1807.06338 Latest version (application/pdf)

Related works:
Journal Article: LIMIT THEOREMS FOR FACTOR MODELS (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1807.06338

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