Causal Analysis in Theory and Practice

December 20, 2014

A new book out, Morgan and Winship, 2nd Edition

Filed under: Announcement,Book (J Pearl),General,Opinion — judea @ 2:49 pm

Here is my book recommendation for the month:
Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research) Paperback – November 17, 2014
by Stephen L. Morgan (Author), Christopher Winship (Author)
ISBN-13: 978-1107694163 ISBN-10: 1107694167 Edition: 2nd

My book-cover blurb reads:
“This improved edition of Morgan and Winship’s book elevates traditional social sciences, including economics, education and political science, from a hopeless flirtation with regression to a solid science of causal interpretation, based on two foundational pillars: counterfactuals and causal graphs. A must for anyone seeking an understanding of the modern tools of causal analysis, and a must for anyone expecting science to secure explanations, not merely descriptions.”

But Gary King puts it in a more compelling historical perspective:
“More has been learned about causal inference in the last few decades than the sum total of everything that had been learned about it in all prior recorded history. The first comprehensive survey of the modern causal inference literature was the first edition of Morgan and Winship. Now with the second edition of this successful book comes the most up-to-date treatment.” Gary King, Harvard University

King’s statement is worth repeating here to remind us that we are indeed participating in an unprecedented historical revolution:

“More has been learned about causal inference in the last few decades than the sum total of everything that had been learned about it in all prior recorded history.”

It is the same revolution that Miquel Porta noted to be transforming the discourse in Epidemiology (link).

Social science and Epidemiology have been spear-heading this revolution, but I don’t think other disciplines will sit idle for too long.

In a recent survey (here), I attributed the revolution to “a fruitful symbiosis between graphs and counterfactuals that has unified the potential outcome framework of Neyman, Rubin, and Robins with the econometric tradition of Haavelmo, Marschak, and Heckman. In this symbiosis, counterfactuals emerge as natural byproducts of structural equations and serve to formally articulate research questions of interest. Graphical models, on the other hand, are used to encode scientific assumptions in a qualitative (i.e. nonparametric) and transparent language and to identify the logical ramifications of these assumptions, in particular their testable implications.”

Other researchers may wish to explain the revolution in other ways; still, Morgan and Winship’s book is a perfect example of how the symbiosis can work when taken seriously.

A new review of Causality

Filed under: Book (J Pearl),General,Opinion — eb @ 2:46 pm

A new review of Causality (2nd Edition, 2013 printing) has appeared in Acta Sociologica 2014, Vol. 57(4) 369-375.
Reviewed by Felix Elwert, University of Wisconsin-Madison, USA.

Elwert highlights specific sections of Causality that can empower social scientists with new insights or new tools for applying modern methods of causal inference in their research. Coming from a practical social science perspective, this review is a welcome addition to the list of 33 other reviews of Causality, which tend to be more philosophical. see

I am particularly gratified by Elwert’s final remarks:
“Pearl’s language empowers social scientists to communicate causal models with each other across sub-disciplines…and enables social scientists to communicate more effectively with statistical methodologists.”

September 2, 2014

In Defense of Unification (Comments on West and Koch’s review of *Causality*)

Filed under: Discussion,General,Opinion — moderator @ 3:05 am

A new review of my book *Causality* (Pearl, 2009) has appeared in the Journal of Structural Equation Modeling (SEM), authored by Stephen West and Tobias Koch (W-K). See

I find the main body of the review quite informative, and I thank the reviewers for taking the time to give SEM readers an accurate summary of each chapter, as well as a lucid description of the key ideas that tie the chapters together. However, when it comes to accepting the logical conclusions of the book, the reviewers seem reluctant, and tend to cling to traditions that lack the language, tools and unifying perspective to benefit from the chapters reviewed.

The reluctance culminates in the following paragraph:
“We value Pearl’s framework and his efforts to show that other frameworks can be translated into his approach. Nevertheless we believe that there is much to be gained by also considering the other major approaches to causal inference.”

W-K seem to value my “efforts” toward unification, but not the unification itself, and we are not told whether they doubt the validity of the unification, or whether they doubt its merits.
Or do they accept the merits and still see “much to be gained” by pre-unification traditions? If so, what is it that can be gained by those traditions and why can’t these gains be achieved within the unified framework presented in *Causality*?

To read more, click here.

July 31, 2012

Follow-up note posted by Elias Bareinboim

Filed under: Discussion,General,Identification,Opinion — eb @ 4:15 pm

Andrew Gelman and his blog readers followed-up with the previous discussion (link here) on his methods to address issues about causal inference and transportability of causal effects based on his “hierarchical modeling” framework, and I just posted my answer.

This is the general link for the discussion:

Here is my answer:


July 19, 2012

A note posted by Elias Bareinboim

In the past week, I have been engaged in a discussion with Andrew Gelman and his blog readers regarding causal inference, selection bias, confounding, and generalizability. I was trying to understand how his method which he calls “hierarchical modelling” would handle these issues and what guarantees it provides. Unfortunately, I could not reach an understanding of Gelman’s method (probably because no examples were provided).

Still, I think that this discussion having touched core issues of scientific methodology would be of interest to readers of this blog, the link follows:

Previous discussions took place regarding Rubin and Pearl’s dispute, here are some interesting links:

If anyone understands how “hierarchical modeling” can solve a simple toy problem (e.g., M-bias, control of confounding, mediation, generalizability), please share with us.


September 4, 2011

Comments on an article by Grice, Shlimgen and Barrett (GSB): “Regarding Causation and Judea Pearl’s Mediation Formula”

Filed under: Discussion,Mediated Effects,Opinion — moderator @ 3:00 pm

Stan Mulaik called my attention to a recent article by Grice, Shlimgen and Barrett (GSB) (linked here ) which is highly critical of structural equation modeling (SEM) in general, and of the philosophy and tools that I presented in “The Causal Foundation of SEM” (Pearl 2011) (  In particular, GSB disagree with the conclusions of the Mediation Formula — a tool for assessing what portion of a given effect is mediated through a specific pathway.

I responded with a detailed account of the disagreements between us (copied below), which can be summarized as follows:


1. The “OOM” analysis used by GSB is based strictly on frequency tables (or “multi-grams”) and, as such, cannot assess cause-effect relations without committing to some causal assumptions. Those assumptions are missing from GSB account, possibly due to their rejection of SEM.

2. I define precisely what is meant by “the extent to which the effect of X on Y is mediated by a third variable, say Z,” and demonstrate both, why such questions are important in decision making and model building and why they cannot be captured by observation-oriented methods such as OOM.

3. Using the same data and a slightly different design, I challenge GSB to answer a simple cause-effect question with their method (OOM), or with any method that dismisses SEM or causal algebra as unnecessary.

4. I further challenge GSB to present us with ONE RESEARCH QUESTION that they can answer and that is not answered swiftly, formally and transparently by the SEM methodology presented in Pearl (2011). (starting of course with the same assumptions and same data.)

5. I explain what gives me the assurance that no such research question will ever be found, and why even the late David Friedman, whom GSB lionize for his staunch critics of SEM, has converted to SEM thinking at the end of his life.

6. I alert GSB to two systematic omissions from their writings and posted arguments, without which no comparison can be made to other methodologies:
(a) A clear statement of the research question that the investigator attempts to answer, and
(b) A clear statement of the assumptions that the investigator is willing to make about reality.

Click here for the full response.


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 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

September 23, 2009

Differences Induced by Adding Covariates

Filed under: Opinion — moderator @ 3:00 am

Donald Klein writes:

Unfortunately, much of this is over my head. As a practicing trialist the apparent disagreements re managements of # of covariates in ANCOVA seems important but I can’t find a reference to an actual trial where these alternative analyses produced different results. Even a model trial would be helpful to show the import of these theoretical differences.

Similarly with regard to missing data , which turns the experimental randomization towards a naturalistic study.


Don Klein

July 22, 2009

Resolution of a Debate on Covariate Selection in Causal Inference

Filed under: Discussion,Opinion — judea @ 6:00 pm

Judea Pearl writes:

Recently, there have been several articles and many blog entries concerning the question of what measurements should be incorporated in various methods of causal analysis.The statement below is offered by way of a resolution that (1) summarizes the discussion thus far, (2) settles differences of opinion and  (3) remains faithful to logic and facts as we know them today.

The resolution is reached by separating the discussion into three parts:  1.  Propensity score matching  2. Bayes analysis 3. Other techniques

1. Propensity score matching. Everyone is in the opinion that one should screen variables before including them as predictors in the propensity-score function.We know that, theoretically, some variables are capable of increasing bias (over and above what it would be without their inclusion,) and some are even guaranteed to increase such bias.

1.1 The identity of those bias-raising variables is hard to ascertain in practice. However, their
general features can be described in either graphical terms or in terms of the "assignment mechanism", P(W|X, Y0,Y1),if such is assumed.

1.2 In light of 1.1, it is recommend that the practice of adjusting for as many measurements as possible should be approached with great caution. While most available measurements are bias-reducing, some are bias-increasing.The criterion of producing "balanced population" for
matching, should not be the only one in deciding whether a measurement should enter the propensity score function.

2. Bayes analysis. If the science behind the problem, is properly formulated as constraints over the prior distribution of the "assignment mechanism" P(W|X, Y, Y0,Y1), then one need not exclude any measurement in advance; sequential updating will properly narrow the posteriors to reflect both the science and the available data.

2.1 If one can deduce from the "science" that certain covariates are "irrelevant" to the problem at hand,there is no harm in excluding them from the Bayesian analysis. Such deductions can be derived either analytically, from the algebraic description of the constraints, or graphically, from the diagramatical description of those constraints.

2.2 The inclusion of irrelevant variables in the Bayesian analysis may be advantageous from certain perspectives (e.g., provide evidence for missing data) and dis-advantageous from others (e.g, slow convergence, increase in problem dimensionality, sensitivity to misspecification).

2.3 The status of intermediate variables (and M-Bias) fall under these considerations. For example, if the chain Smoking ->Tar-> Cancer represents the correct specification of the problem, there are advantages (e.g., reduced variance (Cox, 1960?)) to including Tar in the analysis even though the causal effect (of smoking on cancer) is identifiable without measuring Tar, if Smoking is randomized. However, misspecification of the role of Tar, may lead to bias.

3. Other methods. Instrumental variables, intermediate variables and confounders can be identified, and harnessed to facilitate effective causal inference using other methods, not involving propensity score matching or Bayes analysis. For example, the measurement of Tar in the example above, can facilitate a consistent estimate of the causal effect (of Smoking on Cancer) even in the presence of unmeasured confounding factors, affecting both smoking and cancer. Such analysis can be done by either graphical methods (Causality, page 81-88) or counterfactual algebra (Causality, page 231-234).

Thus far, I have not heard any objection to any of these conclusions, so I consider it a resolution of what seemed to be a major disagreement among experts. And this supports what Aristotle said (or should have said): Causality is simple.


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