Limit Theorems for Factor Models

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.