Deep Learning for Individual Heterogeneity with Generated Regressors by Adversarial Training

Abstract

We propose a semiparametric framework that combines machine learning with generated regressors via control function to capture individual heterogeneity while addressing endogeneity and sample selection bias in complex econometric models. This approach models individual heterogeneity through high-dimensional observable characteristics, with generated regressors supporting the control function to manage endogeneity or sample selection bias flexibly across various economic structures. Leveraging a tailored deep learning architecture, our framework integrates control functions and parameter functions seamlessly, enabling its adaptation to diverse econometric models. Using adversarial training, we achieve sup-norm convergence rates of parameter functions and control function at the optimal min-max rate, which enhances robustness and yields valid inferences for inferential structural parameters in high-dimensional settings. Extending the Double Machine Learning (DML) approach, we incorporate endogenous components and establish a new influence function that directly includes generated regressors, broadening the framework’s applicability across econometric models. With automatic differentiation in PyTorch, the influence function applies directly to data, streamlining inference and supporting various structural parameters without additional calculations. This integration makes the framework particularly useful in applied settings where individual heterogeneity and endogeneity are critical, such as personalized policy-making, targeted economic interventions, and customized optimizations in technology. Our simulations demonstrate superior performance, validating this framework’s practical use in econometric analysis where heterogeneity and endogeneity are key considerations.