  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.
