# Directed Acyclic Graphs and the no unrepresented prior common causes assumption

In Technical Point 6.1 of Hernán & Robins, the authors define a Directed Acyclic Graph (DAG) thus:

A causal DAG is a DAG in which:

1. the lack of an arrow from node $$V_j$$ to $$V_m$$ can be interpreted as the absence of a direct causal effect of $$V_j$$ on $$V_m$$ (relative to the other variables on the graph),
2. all common causes, even if unmeasured, of any pair of variables on the graph are themselves on the graph, and
3. any variable is a cause of its descendants.

I am interested in a nuanced interpretation of the meaning of #2. The counterfactual formal causal reasoning lit is full of DAGs with variables showing no prior cause, and no prior common cause.

My loose intuition is that all causes that are not truly randomized in the world of human experiences share prior causes:

• Going back to the "first causes" (big bang, genesis, etc. as your faith provides): had the universe not been created, contrary to fact, then these variables would have shaken out differently (prior common cause).
• Less cosmically: had the earth not formed, contrary to fact, then these variables would have shaken out differently (prior common cause).
• Less mythically: had the north and south Atlantic crossing and the institution of slavery not been a defining foundation of U.S. history, political economy, etc., contrary to fact, then these variables would have shaken out differently (prior common cause).
• Right up in the business involving common, if less historically proximate causes: had the individual not been born in a poor economy, contrary to fact, then the resources improving one's chances to become a firefighter, become physically fit, and have a long life expectancy might have shaken out differently.

The first DAG presented in Hernán & Robins (below) is below. One of the interpretations they give for this is risk of death ($$Y$$) is caused both by being a firefighter ($$A$$), and being physically fit ($$L$$) (which also causes $$A$$).

Obviously, prior causes—like the economic opportunity described in my last bullet point above—can be added to a DAG.

If there must be a prior common cause of all non-randomized variables in a DAG, given a long enough view, when do we stop drawing prior causes in practice?

Question: How to make the decision that for a variable there is no prior common cause shared with the other variables in an analysis?

I am not asking for a rationale preferring randomized designs over observational designs. I am also not asking (directly) about how to identify causal confounders. Rather, I am philosophically interested in what the meaning of no prior common causes given that everything shares prior common causes.

Pointing me to texts where these authors, or Pearl, Spirtes, or the other usual suspects have written deeply about this welcome.

Hernán, M. A. and Robins, J. M. (2018). Causal Inference. Chapman & Hall/CRC, Boca Raton, FL.

• Great question. I rarely find the assumptions people make in this area to be plausible. May 17, 2018 at 14:45

1) Included common causes often summarize the effects of more distant causes. In fact, this is behind the whole idea of instrumental variables: Some variables are causally far away from an outcome in the sense that they only affect one of its more proximate causes.

This is also quite natural when one is interested in human-subject research. Humans do not have endless memory, and use only information that is economically or psychologically relevant/available to them to inform their decision to take a certain treatment (e.g., become a firefighter). For example, many variables that measure socialization experiences affect $A$ and $Y$ in your firefighter example; but anything that relates to your great-grandparents will almost certainly be screened off by variables that relate to your grandparent and parents, because most people never interacted with their great-grandparents.

2) Very distant causes are in fact constant across units. E.g., the universe was, in fact, created, the earth was formed, and slavery is a defining foundation of the US. The outcomes of these variables are the same for every unit, so there is no variation across units that could induce confounding. I guess you could say that they are not proper "variables", and therefore do not have to be included in the DAG.

I am not aware of a thorough discussion of this question in the literature. This is unfortunate because many people don't see fairly obvious confounders, but also sometimes think that there may be a certain confounder where in fact should be none.

• Thank you for a great answer, Julian. I have taken the liberty of editing your answer to highlight these two really important points (and correct common usage for parent's parent's parent :). May 17, 2018 at 19:20