Mechanisms and Counterfactuals
This week we review the counterfactual theory of causation and the kinds of causal inferences it licenses. We’ll compare and contrast two complementary views of a causal mechanism: as a directed acyclic graph (DAG) that connects variables and implies statistical independence relations between them, and as independence relations that connect the potential outcome (PO) for each of these variables that individual cases can realize.
It is often helpful to think of POs as the individual level implications of a DAG, where some implications are about what did not happen but could have done had things gone differently.
In the background of each way of thinking about causation is the idea that there is a set of specific functions that realize the arrows in the DAG and are the reason that the POs have whatever structure they do. Since we seldom have strong ideas about what these functions look like, it is often useful to ask whether summaries of a functional relationship at particular values of the variables can be identified from data without knowing the functional forms in advance. This is the question of non-parametric causal identification, for which DAGs were designed. We can also ask about the minimal assumptions about functional form required, for example that some relationship is monotonically increasing. For this, switching to POs becomes necessary.
WhatIf ch. 1, 2, 3, 6, and 10
G. W. Imbens (2020) Potential Outcome and Directed Acyclic GraphApproaches to Causality: Relevance for Empirical Practice in Economics Arxiv 1907.07271v2 (A graph skeptical overview of this week’s topics from an economist)
Steiner et al. 2017 Graphical models for quasi-experimental designs Sociological Methods and Research.