In this text we exposited the potential outcomes approach to causality, also known as the Rubin Causal Model, and hope to have convinced the reader of its usefulness. In this final chapter we briefly summarize this approach and discuss other topics in causal inference where this approach may be useful. Many of these are areas of ongoing research, and we hope to discuss them in more detail in a second volume.

The starting point of our approach is the notion of potential outcomes. For each unit in a population, and for each level of a treatment, there is a potential outcome. Comparisons of these potential outcomes define the causal effects; we view these as well-defined irrespective of the assignment mechanism, and thus irrespective of what we actually are able to observe. We often place restrictions on these potential outcomes. Most important in the current text is the stability assumption, or SUTVA, that rules out differences between potential outcomes corresponding to different levels of the treatment for units other than the unit under consideration, and rules out unrepresented levels of treatments

We can observe at most one of the potential outcomes for each unit. Causal inference is therefore intrinsically a missing data problem. Given the potential outcomes, there is a key role in our approach for the assignment mechanism, which defines which potential outcomes are observed and which are missing. The current text is largely organized by different types of assignment mechanisms. The simplest is that of a classical randomized experiment where the researcher knows the assignment mechanism entirely. Such assignment mechanisms are discussed in Part II of the text. Then, in the main part of the text, Parts III and IV, we discuss regular assignment mechanisms where we know part but not all of the assignment mechanism. We discuss the importance of the design stage of a study for causal effects where the outcome data are not yet used. At this stage a researcher can carry out preliminary analyses that make the final analyses that do involve the outcome data more credible and robust.