Combining cross-section and time series data is a long and well established
practice in empirical economics. We develop a central limit theory that
explicitly accounts for possible dependence between the two data sets. We focus
on common factors as the mechanism behind this dependence. Using our central
limit theorem (CLT) we establish the asymptotic properties of parameter
estimates of a general class of models based on a combination of
cross-sectional and time series data, recognizing the interdependence between
the two data sources in the presence of aggregate shocks. Despite the
complicated nature of the analysis required to formulate the joint CLT, it is
straightforward to implement the resulting parameter limiting distributions due
to a formal similarity of our approximations with the standard Murphy and
Topel's (1985) formula.Comment: arXiv admin note: substantial text overlap with arXiv:1507.0441
