  In this paper we study neural networks and their approximating power in panel
data models. We provide asymptotic guarantees on deep feed-forward neural
network estimation of the conditional mean, building on the work of Farrell et
al. (2021), and explore latent patterns in the cross-section. We use the
proposed estimators to forecast the progression of new COVID-19 cases across
the G7 countries during the pandemic. We find significant forecasting gains
over both linear panel and nonlinear time series models. Containment or
lockdown policies, as instigated at the national-level by governments, are
found to have out-of-sample predictive power for new COVID-19 cases. We
illustrate how the use of partial derivatives can help open the "black-box" of
neural networks and facilitate semi-structural analysis: school and workplace
closures are found to have been effective policies at restricting the
progression of the pandemic across the G7 countries. But our methods illustrate
significant heterogeneity and time-variation in the effectiveness of specific
containment policies.
