Counterfactually-Equivalent Structural Causal Modelling Using Causal Graphical Normalizing Flows

Abstract

Recent research has highlighted the properties that deep-learning inspired causal models such as Deep-Structural Causal Model (Deep-SCM), Causal Autoregressive Flow (CAREFL) and Causal-Graphical Normalizing Flow (c-GNF) should exhibit to guarantee observational and interventional distribution equivalence with the true underlying causal data generating process (DGP), making them suitable for estimating average causal effect (ACE) or conditional ACE (CACE). However, for accurate individual-level causal effect (ICE) estimation and personalized treatment/public-policy formulation, it is crucial to ensure counterfactual equivalence between these models and the DGP. Firstly, we demonstrate that c-GNFs provide counterfactual equivalence under certain monotonicity assumption of the DGP, enabling precise ICE estimation and personalized treatment/public-policy analysis. Secondly, using this counterfactual equivalence of c-GNFs, we perform a counterfactual analysis and personalized public-policy analysis of the impact of International Monetary Fund (IMF) programs on child poverty using large-scale real-world observational data. Our results indicate a reduction in child poverty due to the IMF program at different personalization granularities. Our study also performs sensitivity analyses to assess potential threats to the unconfoundedness assumption and estimates ACE bounds and the E-value. This illustrates the potential of c-GNFs for causal and counterfactual inference in fields such as social, natural, and medical sciences.