Review of Judea Pearl’s The Book of Why
A great number of life’s important questions are causal questions. Whether we are a parent trying to choose the best school for our child, a physician pondering the best approach for treating cancer in a patient, or a development economist seeking to understand the best way to facilitate growth in microenterprises, many of the pertinent questions we ask ourselves are about the effect of some choice X on an outcome Y.
If for no other reason than this, Judea Pearl’s The Book of Why: The New Science of Cause and Effect (with Dana Mackenzie) is an important book. This is partly because the topic it addresses in many ways subsumes virtually all popular books that focus on a particular causal question such as what is the best diet, the best path to success in business, or the best way to fight poverty. Instead, it takes us back to a more fundamental question: How do we identify any kind of causal relationship?
Like any good book that holds our attention, this book contains a villain. Pearl’s villain is Karl Pearson, whom many consider to be the founder of modern statistics. This is ironic because most of us who have studied statistics, whether we are aware of it or not, learned statistics from Pearson. But Pearl argues that in the early 20th century, Pearson took us down the wrong road. He did this by developing the field of statistics as an observational science rather than as a causal one. Juxtaposed to Pearson, the unsung hero of early statistics Pearl introduces us to is Seawall Wright, who when studying the breeding patters of Guinea Pigs, became the originator of causal diagrams.
Causal diagrams are the key to identifying causal relationships, Pearl argues, and throughout the book he doesn’t let more than a few pages go by without reminding us of this. A more formal term for these is Directed Acyclic Graphs (DAGs), and I will give an example from a recent paper of mine with Jeff Bloem, doctoral student at the University of Minnesota, in which we study the effect of a faith-based kindergarten in the Philippines called Jumpstart on subsequent academic performance. The DAG in Jeff’s and my paper would look like this:
As seen in the figure, a whole bunch of stuff affects a child’s academic performance, which is probably not news to anyone. Parental characteristics, Age, Gender, Sibling order, Socio-emotional skills (like patience, self-control, agreeableness, and grit), and even Jumpstart itself affect academic performance. And Jumpstart may affect Academic Performance directly, or potentially through the development of Socio-emotional Skills.
I find that one of the practical uses of DAGs like the one above is simply to clarify the set of relationships in a research study. In anything but the most simple and obvious set of causal relations, a DAG is immensely useful for clarifying the data-generating process one has in mind as a researcher. It is also helpful in spelling out our theory of change, such as from some kind of intervention.
But an even more important question is how do we isolate the causal effect of interventions like Jumpstart, and perhaps its effect as mediated through fostering of socio-emotional skills? Pearl shows us how.
Suppose X is a “treatment variable” of interest (like kindergarten, a health program, or microfinance), Y is an outcome variable (like academic performance, a body mass index, or enterprise profits), and Z is some other variable related to X and Y. Pearl gives us a few important definitions to work with: 1) Chains, 2) Forks, and 3) Colliders.
Now suppose X -> Z-> Y. Here we have a “Chain,” where the effect of X on Y is purely mediated through Z. Controlling for Z in our estimate of the causal relationship between X and Y will mask X,Y causality, but will reveal causality between Z and Y. In contrast if we have X <- Z -> Y, we have a “Fork,” where Z causes both X and Y. In trying to estimate the effect of X on Y, Pearl argues it is important to control for Forks, otherwise the relationship we estimate between X and Y will result in mere correlation and not the identification of a true causal relationship. Lastly, we may have X -> Z<- Y, or a “Collider.” The remedy for Colliders, Pearl points out, is exactly the opposite of Forks. If we control for the variables inside a collider, we introduce bias into our causal estimates. Ignoring them allows us to correctly estimate the casual X,Y relationship.
To identify the causal relationship between X and Y more generally, Pearl shows us that we need to statistically “block” all “backdoor paths” between the two variables. A backdoor path is an arrow in the diagram leading into X that can be traced through the diagram to Y. This can be done by controlling for Forks on backdoor paths and ignoring backdoor paths that contain colliders.
For example, in Jeff’s and my paper, to find the causal effect of Jumpstart on Academic Performance, we need to control for Parental Characteristics and Household Environment (which we do with a household fixed effect), which may have caused parents to put their kids in Jumpstart but also could have caused better performance in school. Notice that we also have a Fork at Socio-Emotional Skills. If we did not block the backdoor path through Parental Characteristics, and we did control for Socio-Emotional Skills, we would add a second bias in our estimate. By controlling for Socio-Emotional Skills, which may have a positive relationship with Jumpstart and Academic Performance, we introduce a spuriously negative relationship between the two variables.
The latter is easier to understand in another example. Suppose hard work + smarts = GPA, and hard work is independent of smarts. If we control for GPA (by say holding it constant at 3.5), a student who is a little smarter won’t have worked quite as hard to reach the same 3.5 GPA as a less smart student. So controlling for GPA creates a negative relationship between hard work and smarts where there is none.
As an economist, I found Pearl’s 370-page argument for the necessity of causal diagrams compelling. I also have found the attacks on this approach in social media and other places in response to the book to be interesting, but unconvincing: Why any researcher would want to leave a set of causal relationships less than clearly spelled out is unclear to me. And I also find it strange that other texts on estimating causal relationships, such as nearly any econometrics or psychometrics text, either leave out causal diagrams entirely or only briefly mention them. For example, Imbens and Rubin’s 2015 text on causal econometrics spends all of one paragraph on them. (Scott Cunningham’s new online econometrics text is a notable exception.)
Pearl’s chapter on mediation, a subject I am keenly interested in these days, falls short (along with everyone else) in cracking the biggest nut: how to deal with the problem of confoundedness in mediators, even (and perhaps especially) in randomized controlled trials. But he does offer a procedure that helps us to overcome the linear-relationship assumption so often used in identifying mediating variables. The formula he offers allows for estimating mediation, like the effects of Jumpstart working partially through the development of socio-emotional skills in our example, allows for varying effects.
Although I found the book immensely useful for thinking more clearly about causal relationships, I also found that Pearl himself, like most of the rest of us in academia, to be a little isolated from work that has occurred outside of his own applied discipline. (His is computer science.) There is a temptation to believe that all the important innovations in statistics have been captured in the techniques used in our own field, whether it be psychology, economics, math, political science, epidemiology or computer science, and Pearl does not escape his own biases in this regard. His grasp of what economists, for example, understand and don’t understand about causal relationships is incomplete, arising many times in the text, something that may drive empirical economists crazy at different points.
Some of the chapters, such as the final chapter on artificial intelligence, wander more into philosophy than provide us with new tools and insights. But in the larger scope of the book’s overall contribution and originality, these are relatively minor points. The Book of Why is a nicely accessible summary of his more rigorous treatment in his more formally academic treatise Causality (from Cambridge University Press, 2009). There are immensely useful ideas in this book that economists, psychologists, and many other researchers have never learned in their doctoral classes or been exposed to in seminars, and there is plenty of meat here to make it worth chewing on the statistical chicken while spitting out the bone. Pearl leaves readers with a compelling book, an excellent summary of his life’s work in the area, and one that will benefit the research of a wide array of empirically minded social scientists.
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