by In a recent issue of Real World Economics Review there was a rather interesting, if somewhat dense, article by Judea Pearl and Bryant Chen entitled Regression and Causation: A Critical Examination of Six Econometrics Textbooks … The paper appears to turn on a single dichotomy. The authors point out that there is a substantial difference between what they refer to as the “conditional-based expectation” and “interventionist-based expectation”. The first is given the notation: E[Y|X] While the second is given the notation: E[Y|do(X)] The difference between these two relationships is enormous. The first notation — that is, the “conditional-based expectation” — basically means that the value Y is statistically dependent on the value X … The second notation — that is, the “interventionist-based expectation” — refers to something else entirely. It means that the value Y is causally dependent on the value X … Now, if we simply go out and take a statistical measure of earnings and expected performance we will find a certain relationship — this will be the conditional-based expectation and it will be purely a statistical relationship. If, however, we take a group of employees and raise their earnings, X, by a given amount will we see the same increase in performance, Y, as we would expect from a study of the past statistics? Obviously not.
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In a recent issue of Real World Economics Review there was a rather interesting, if somewhat dense, article by Judea Pearl and Bryant Chen entitled Regression and Causation: A Critical Examination of Six Econometrics Textbooks …
The paper appears to turn on a single dichotomy. The authors point out that there is a substantial difference between what they refer to as the “conditional-based expectation” and “interventionist-based expectation”. The first is given the notation:
E[Y|X]
While the second is given the notation:
E[Y|do(X)]
The difference between these two relationships is enormous. The first notation — that is, the “conditional-based expectation” — basically means that the value Y is statistically dependent on the value X …
The second notation — that is, the “interventionist-based expectation” — refers to something else entirely. It means that the value Y is causally dependent on the value X …
Now, if we simply go out and take a statistical measure of earnings and expected performance we will find a certain relationship — this will be the conditional-based expectation and it will be purely a statistical relationship.
If, however, we take a group of employees and raise their earnings, X, by a given amount will we see the same increase in performance, Y, as we would expect from a study of the past statistics? Obviously not. This example, of course, is the interventionist-based expectation and is indicative of a causal relationship between the variables …
In economics we are mainly interested in causal rather than statistical relationships. If we want to estimate, for example, the multiplier, it is from a causal rather than a statistical point-of-view. Yet the training that many students receive leads to confusion in this regard. Indeed, we may go one further and ask whether such a confusion also sits in the mind of the textbook writers themselves.
This confusion between statistical relationships and causal ones has long been a problem in econometrics. Keynes, for example, writing his criticism of the econometric method in his seminal paper Professor Tinbergen’s Method noted that Tinbergen had made precisely this error …
The question then arises: why, after over 70 years, are econometrics textbooks engaged in the same oversights and vaguenesses as some of the pioneering studies in the field? I think there is a simple explanation for this. Namely, that if econometricians were to be clear about the distinction between statistical and causal relations it would become obvious rather quickly that the discipline holds far less worth for economists than it is currently thought to possess.
For my own take on the issues raised by Pearl and Chen see here.