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  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 . Monte Carlo simulations are conducted to demonstrate the finite sample performance of our proposal, and an empirical example illustrates the usefulness of our procedure when many controls are available in reality .
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 .
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. Monte Carlo simulations are conducted to demonstrate the finite sample performance of our proposal, and an empirical example illustrates the usefulness of our procedure when many controls are available in reality