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.

In this article, we use a deep quantile estimator, based on neural networks and their universal approximation property to examine a non-linear association between the conditional quantiles of a dependent variable and predictors. This methodology is versatile and allows both the use of different penalty functions, as well as high dimensional covariates. We present a Monte Carlo exercise where we examine the finite sample properties of the deep quantile estimator and show that it delivers good finite sample performance. We use the deep quantile estimator to forecast value-at-risk and find significant gains over linear quantile regression alternatives and other models, which are supported by various testing schemes. Further, we consider also an alternative architecture that allows the use of mixed frequency data in neural networks. This article also contributes to the interpretability of neural network output by making comparisons between the commonly used Shapley Additive Explanation values and an alternative method based on partial derivatives.

In this short paper we provide time-series approaches, to forecast the rate of growth of confirmed cases of the novel CoViD-19 pandemic in the most severely affected countries. We examine the performance of non-linear curve fitting models, including logistic and spline functions, and more elaborate parametric neural network models.