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.