  Policy evaluation is central to economic data analysis, but economists mostly
work with observational data in view of limited opportunities to carry out
controlled experiments. In the potential outcome framework, the panel data
approach (Hsiao, Ching and Wan, 2012) constructs the counterfactual by
exploiting the correlation between cross-sectional units in panel data. The
choice of cross-sectional control units, a key step in its implementation, is
nevertheless unresolved in data-rich environment when many possible controls
are at the researcher's disposal. We propose the forward selection method to
choose control units, and establish validity of the post-selection inference.
Our asymptotic framework allows the number of possible controls to grow much
faster than the time dimension. The easy-to-implement algorithms and their
theoretical guarantee extend the panel data approach to big data settings.
