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Limit theorems for factor models

Publikace na Fakulta sociálních věd, Matematicko-fyzikální fakulta, Centrum pro ekonomický výzkum a doktorské studium |
2021

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

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.