SEM-DNN: New Neural Method Learns Bidirectional Causal Effects Without Instruments

Masahiro Tanaka’s new paper introduces SEM-DNN, a neural network framework designed to estimate bidirectional causal interactions from observational data. Traditional approaches struggle with this task because each outcome affects the other, creating endogeneity that flexible regressions often fail to disentangle. SEM-DNN overcomes this by leveraging heteroscedasticity—non-constant variance in structural shocks—to identify causal coefficients without relying on external instruments. The key identification trick is conditional covariance diagonalization: when structural shocks have zero conditional means, are conditionally uncorrelated given covariates, and exhibit nonproportional variances, only the true interaction coefficients can diagonalize the residual covariance across the feature space. The model jointly approximates nonlinear structural mean functions and feature-dependent variances using a diagonal Gaussian quasi-likelihood that incorporates the simultaneous-system Jacobian, ensuring consistency even with non-unique network parameterizations.

In Monte Carlo simulations with nonlinear, high-dimensional nuisance functions and non-Gaussian shocks, SEM-DNN consistently recovers structural effects more reliably than parametric, kernel-based, or separate-equation neural alternatives—though at greater computational cost. Tanaka also demonstrates the method on ready-to-eat cereal scanner data, analyzing contemporaneous price-sales feedback. This application showcases how SEM-DNN can assess identification strength, residual diagonalization, variance calibration, and optimization sensitivity in real-world settings. The paper establishes theoretical guarantees including unique identification and positive-definite local curvature of the profiled population criterion. While the computational overhead is higher, SEM-DNN’s ability to learn bidirectional causality from observational data alone could transform fields like econometrics, marketing science, and epidemiology where controlled experiments are infeasible.