Improving Causality Tests: Feed-forward Causality with Neural Networks and Machine Learning

Abstract

This paper develops a Feed-forward Neural Causality Test (FFNCT), a methodological improvement that addresses several limitations of causal inference for complex relationships between time series. Traditional causality tests often fail to capture nonlinear dynamics, regime-dependent relationships, and asymmetric responses. Drawing on recent advances in machine learning and neural networks, this paper improves several causality tests, increasing the ability to detect complex patterns in time series. This research provides both theoretical justification and empirical validation through a comparative analysis against traditional Granger causality and seven competing neural network–based alternatives, employing several performance metrics and cross-validation. To illustrate the proposed methodology, this paper analyzes the Phillips curve relationship using monthly U.S. data from 1948 to 2024. Empirical findings using FFNCT reveal statistically significant reverse causality between inflation and unemployment in the full sample, a result that challenges the prevailing belief. Moreover, the proposed regime-specific analysis reveals substantial heterogeneity in causal directionality across different periods, with some regimes exhibiting traditional Phillips curve causality (i.e., unemployment leading to inflation) and others exhibiting reverse or bidirectional causality. These empirical findings suggest more nuanced transmission channels between inflation and employment than conventional models. Therefore, this regime-dependent approach explains historical inconsistencies in Phillips curve analyses and demonstrates why flexible methodologies, such as FFNCT, are important for causal inference.