Causal Analysis in Theory and Practice

May 31, 2010

An Open Letter from Judea Pearl to Nancy Cartwright concerning “Causal Pluralism”

Filed under: Discussion,Nancy Cartwright,Opinion,structural equations — moderator @ 1:40 pm

Dear Nancy,

This letter concerns the issue of “causal plurality” which came up in my review of your book “Hunting Causes and Using Them” (Cambridge 2007) and in your recent reply to my review, both in recent issue of Economics and Philosophy (26:69-77, 2010).

My review:

Cartwright Reply:

I have difficulties understanding causal pluralism because I am a devout mono-theist by nature, especially when it comes to causation and, although I recognize that causes come in various shades, including total, direct, and indirect causes, necessary and sufficient causes, actual and generic causes, I have seen them all defined, analyzed and understood within a single formal framework of Structural Causal Models (SCM) as described in Causality (Chapter 7).

So, here I am, a mono-theist claiming that every query related to cause-effect relations can be formulated and answered in the SCM framework, and here you are, a pluralist, claiming exactly the opposite. Quoting:

“There are a variety of different kinds of causal systems; methods for discovering causes differ across different kinds of systems as do the inferences that can be made from causal knowledge once discovered. As to causal models, these must have different forms depending on what they are to be used for and on what kinds of systems are under study.

If causal pluralism is right, Pearl’s demand to tell economists how they ought to think about causation is misplaced; and his own are not the methods to use. They work for special kinds of problems and for special kinds of systems – those whose causal laws can be represented as Pearl represents them. HC&UT argues these are not the only kinds there are, nor uncontroversially the most typical.

I am very interested in finding out if, by committing to SCM I have not overlooked important problem areas that are not captured in SCM. But for this we need an example; i.e., an example of ONE problem that cannot be formulated and answered in SCM.

The trouble I have with the examples sited in your reply is that they are based on other examples and concepts that are scattered on many pages in your book and, thus, makes it hard to follow. Can we perhaps see one such example, hopefully with no more than 10 variables, described in the following format:

Example: An agent is facing a decision or a question.

Given: The agent assumes the following about the world: 1. 2. 3. ….
The agent has data about …., taken under the following conditions.
Needed: The agent wishes to find out whether…..

Why use this dry format, you may ask, when your book is full with dozens of imaginative examples, from physics to econometrics? Because if you succeed in showing ONE example in this concise format you will convert one heathen to pluralism, and this heathen will be grateful to you for the rest of his spiritual life.

And if he is converted, he will try and help you convert others (I promise) and, then, who knows? life on this God given earth would become so much more enlightened.

And, as Aristotle used to say (or should have) May clarity shine on causality land.


Judea Pearl

May 15, 2010

On the Causal Hierarchy and Robins and Richardson’s MCM

Filed under: General — moderator @ 2:00 am

Judea Pearl writes:

Thomas’ latest posting triggered my curiosity to re-examine the causal hierarchy. Originally (see Causality chapter 1), I have characterized causal sentences into three categories:

1. probabilistic (i.e., non-causal, or what we can estimate from observational studies)
2. experimental (i.e., do-expressions, or what we can estimate from controlled, randomized experiments)
3. counterfactuals (i.e., subscripted sentences, or everything that can be computed from a fully specified structural model that is, a collection of functions with probabilities on the exogenous variables)

Click here for the full post.

As always, we welcome your views on this topic. To continue the discussion, please use the comment link below to add your thoughts. You can also suggest a new topic of discussion using our submission form by clicking here.

May 3, 2010

On Mediation, counterfactuals and manipulations

Filed under: Discussion,Opinion — moderator @ 9:00 pm

Opening remarks

A few days ago, Dan Sharfstein posed a question regarding the “well-defineness” of “direct effects” in situations where the mediating variables cannot be manipulated. Dan’s question triggered a private email discussion that has culminated in a posting by Thomas Richardson and Jamie Robins (below) followed by Judea Pearl’s reply.

We urge more people to join this important discussion.

Thomas Richardson and James Robins’ discussion:


There has recently been some discussion of mediation and direct effects.

There are at least two issues here:

(1) Which counterfactuals are well defined.

(2) Even when counterfactuals are well defined, should we include assumptions that identify effects (ie the natural direct effect) that could never be confirmed even in principle by a Randomized Controlled Trial (RCT).

As to (1) it is clear to most that all counterfactuals are vague to a certain extent and can be made more precise by carefully describing the (quite possibly only hypothetical) intervention you want the counterfactual to represent. For this reason,  whether you take manipulation or causality as ontologically primary, we need to relate causation to manipulation to clarify and make more precise which counterfactual world we are considering.

On (2) we have just finished a long paper on the issue, fleshing out considerably an argument I (Jamie) made at the American Statistical Association (in 2005) discussing a talk by Judea on natural (pure and total) direct effects.

“Alternative Graphical Causal Models and the Identification of Direct Effects”

It is available at

Here is a brief summary:

Click here for the full post.

Best wishes,

Jamie Robins  and Thomas Richardson

Judea Pearl’s reply:

As to the which counterfactuals are “well defined”, my position is that counterfactuals attain their “definition” from the laws of physics and, therefore, they are “well defined” before one even contemplates any specific intervention. Newton concluded that tides are DUE to lunar attraction without thinking about manipulating the moon’s position; he merely envisioned how water would react to gravitaional force in general.

In fact, counterfactuals (e.g., f=ma) earn their usefulness precisely because they are not tide to specific manipulation, but can serve a vast variety of future inteventions, whose details we do not know in advance; it is the duty of the intervenor to make precise how each anticipated manipulation fits into our store of counterfactual knowledge, also known as “scientific theories”.

Regarding identifiability of mediation, I have two comments to make; ‘ one related to your Minimal Causal Models (MCM) and one related to the role of structural equations models (SEM) as the logical basis of counterfactual basis of counterfactual analysis.

Click here for Judea’s reply.

Best regards,

Judea Pearl

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