Forecasting with Deep Pooled Panel Neural Networks

In this paper, we propose a deep pooled estimator, motivated by the universal approximation property of neural networks, to capture nonlinear relationships between predictors and targets when modeling and forecasting with panel data. The approach is flexible, accommodating different penalty functions and potentially high-dimensional predictors. It allows for nonlinear cross-sectional dependencies. To evidence the utility of the proposed estimator when forecasting, we apply it in two different applications. First, we forecast the progression of new COVID-19 cases across G7 countries. Second, we forecast inflation in the G7. In both applications, our method delivers significant forecasting gains over both linear panel and nonlinear time-series (unit-specific) models that do not pool data across countries. These results highlight the importance when forecasting of pooling cross-country information via a flexible nonlinear model. Examining partial derivatives from our model provides interpretable insights: school closures and workplace restrictions show declining effectiveness as COVID-19 immunity strengthened, while the inflation-unemployment relationship proves highly unstable across both countries and time periods, particularly during the post-pandemic inflation surge.