  Structural Equation/Causal Models (SEMs/SCMs) are widely used in epidemiology
and social sciences to identify and analyze the average causal effect (ACE) and
conditional ACE (CACE). Traditional causal effect estimation methods such as
Inverse Probability Weighting (IPW) and more recently Regression-With-Residuals
(RWR) are widely used - as they avoid the challenging task of identifying the
SCM parameters - to estimate ACE and CACE. However, much work remains before
traditional estimation methods can be used for counterfactual inference, and
for the benefit of Personalized Public Policy Analysis (P$^3$A) in the social
sciences. While doctors rely on personalized medicine to tailor treatments to
patients in laboratory settings (relatively closed systems), P$^3$A draws
inspiration from such tailoring but adapts it for open social systems. In this
article, we develop a method for counterfactual inference that we name
causal-Graphical Normalizing Flow (c-GNF), facilitating P$^3$A. First, we show
how c-GNF captures the underlying SCM without making any assumption about
functional forms. Second, we propose a novel dequantization trick to deal with
discrete variables, which is a limitation of normalizing flows in general.
Third, we demonstrate in experiments that c-GNF performs on-par with IPW and
RWR in terms of bias and variance for estimating the ATE, when the true
functional forms are known, and better when they are unknown. Fourth and most
importantly, we conduct counterfactual inference with c-GNFs, demonstrating
promising empirical performance. Because IPW and RWR, like other traditional
methods, lack the capability of counterfactual inference, c-GNFs will likely
play a major role in tailoring personalized treatment, facilitating P$^3$A,
optimizing social interventions - in contrast to the current
`one-size-fits-all' approach of existing methods.
