Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models

This paper studies the task of estimating heterogeneous treatment effects in causal panel data models with covariate effects. We propose a novel **Co**variate-Adjusted **DE**ep C**A**usal **L**earning (**CoDEAL**) framework, that cohesively deal with the underlying heterogeneity and nonlinearity of both panel units and covariate effects. CoDEAL integrates nonlinear covariate effect components (parameterized by a feed-forward neural network) with nonlinear factor structures (modeled by a multi-output autoencoder) to form a heterogeneous causal panel model. The nonlinear covariate component flexibly captures complex covariate influences on outcomes, and the nonlinear factor decomposition enables CoDEAL to effectively capture both cross-sectional and temporal dependencies inherent in the data panel. This latent structural information is subsequently integrated into a customized matrix completion algorithm, thereby facilitating more accurate counterfactual imputation. Moreover, the use of a multi-output autoencoder explicitly accounts for heterogeneity across units and enhances the model interpretability of the latent factors. We establish theoretical guarantees on the convergence of the estimated counterfactuals and demonstrate the compelling performance of the proposed method using extensive simulation studies and real-world data applications.