  In this paper we complement joint time series and cross-section convergence
results of Hahn, Kuersteiner and Mazzocco (2016) by allowing for serial
correlation in the time series sample. The implications of our analysis are
limiting distributions that have a well known form of long run variances for
the time series limit. We obtain these results at the cost of imposing strict
stationarity for the time series model and conditional independence between the
time series and cross-section samples. Our results can be applied to estimators
that combine time series and cross-section data in the presence of aggregate
uncertainty in models with rationally forward looking agents.
