Wednesday, July 18, 2012

Causality

This way of describing causality seems wrong to me:
Causality is a useful shorthand for describing “usefulness as a predictor” and it has, as far as I can see, no other useful meaning.
Certainly, Landsburg means to say that you can't single out one cause for what happens to you in your life.  There are lots of other influences, of course.  But, settling on "usefulness as a predictor" as a definition of causality runs contrary to what is taught in introductory econometrics.  After all, we instructors of econometrics go through great pains to distinguish between predictive relationships and causal ones.

Here's the econometrics lesson in short: X is useful for predicting Y if the two are correlated, but as you learned in your first statistics course, correlation is not causation.  If X and Y are correlated, it could be because Y causes X, X causes Y, or some confounding variable Z causes both of them.

Back to Landsburg's contention that causality should be defined as "usefulness as a predictor," there are two problems as I see it with this definition:
  1. You can have a completely wrong notion for how the world works, and still have a model can still be "useful as a predictor" because it describes the correlations that matter to you.
  2. Alternatively, you might observe no relationship between choice and outcome, but ultimately, there is an underlying causal relationship ... and we just don't have enough data to see it.
Landsburg might argue that "usefulness as a predictor" aspires to more than merely describing correlations.  He might say that a description of the world is useful as a predictor only if it is robust to changing the confounding variables (or alternatively, only if you have and use infinite data on everything that matters).  If this is what Landsburg means, it feels like he's using the wrong language to describe it because he is insisting on something much stronger than the ability to predict.

In closing, here's an example that should help make the point.  If you know is that a person is a minority living in a city, that information is useful to predict the person's life outcomes, but it is much harder (and largely false) to argue the fact the person is a minority causes those life outcomes.