This paper establishes some asymptotic results such as central limit theorems and consistency of variance estimation in factor models. We consider a setting common to modern macroeconomic and financial models where many counties/regions/ macro-variables/ 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. We establish a central limit theorem  for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. We also study sufficient conditions when one can consistently estimate the asymptotic variance . These results are useful for making inferences in two-step estimation procedures related to factor models . We avoid structural modeling of cross-sectional dependence but impose time-series independence.
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.
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