The theory of causal effects (TCEs) is a mathematical theory providing a methodological foundation for design and analysis of experiments and quasi-experiments. TCE consists of two parts. In the first part, total, direct, and indirect effects are defined, the second part deals with causal inference, i.e., in the second part, it is shown how causal effects are identified by estimable quantities. In each part, there are two levels, a disaggregated and a reaggregated one.
In the definition part of TCE, the disaggregated level is called the atomic level. In this part, we translate J. St. Mill’s ceteris paribus clause into probabilistic concepts. For this purpose, we introduce temporal order between events and/or random variables using the concept of a filtration. Defining an atomic total-effect variable, we isolate the effects of \( X \) on \( Y \) , controlling for all variables that are prior or simultaneous to \( X \) , while ignoring.
