Three analytical frameworks of causal inference and their applications

Causality is a generic relationship between an effect and a cause that produces it. The causal relationship among things has been a research hotspot; however, the complexity of causality is sometimes far beyond our imagination. Although some causality problems seem easy to analyze, finding an exact answer may not be easy. Nevertheless, through the continuous innovation and development of empirical research methods in recent decades, we have had several clear analytical frameworks and effective methods on how to define and estimate causality. Exploring the causal effects among things is a promising research topic in many fields, such as statistics, computer science, and econometrics. With Joshua D. Angrist and Guido W. Imbens winning the Nobel Prize in economics for their methodological contributions to the analysis of causality in 2021, causal inference is expected to thrive in these fields. This paper briefly introduces the basic concepts involved in causal inference and its three analytical frameworks, namely, counterfactual framework (CF), potential outcome framework (POF), and structural causal model (SCM). Firstly, we introduce the origin of causal effects according to CF. Secondly, based on the counterfactual theory, two analysis frameworks are considered (POF and SCM), and we introduce the associated key theories and methods. The SCM explains the causal theory through mathematics and computable language, and it is a calculation model that clearly expresses hypotheses, propositions, and conclusions. It quantitatively analyzes the pair of cause variables under the premise that the cause and effect variables are known. The POF makes up for the missing potential results, such that the effect of the observational research is close to experimental research. The SCM is a causal inference method based on graph theory. It divides events into three levels: observation, intervention, and counterfactual. Through the “do” operation, the causal relationship at the intervention and counterfactual levels could be reduced to low-dimensional problems, which can be solved via statistical methods. Finally, the current application scenarios of causal inference in many fields are discussed in this paper, and the three analysis frameworks are compared.