Just Instrument It

(With apologies to macro-economists.)

The amount of time you spend in education predicts your earnings quite strongly, and it's generally agreed (Simon Cowell aside) that if you want to do well in life, staying in education for longer is a good idea.

But how much effect does it have?  We could look at a survey of people's incomes and group them by education level, but this doesn't give a causal effect.  It might tell us that people who have a masters degree earn more during their lifetime, on average, than those who don't.  This could be because people from wealthy backgrounds can afford the tuition for a masters degree, and also have pals in the city who can help them get a big salary afterwards.  Or perhaps people who do masters degrees work harder than the rest.  We can't easily tell the difference: this problem is called confounding.

We can't tell whether time spent in education level causes earnings
to increase, or there's a third factor which affects both.

But is it causal? Defining causality

As I alluded to in my last post, defining what it means for $X$ to cause $Y$ is no simple task.  It is not an idea that can be defined in purely probabilistic terms, because it says something about the mechanisms underlying the system we are studying, and what will happen if we interfere with that system in some way.

Consider the example given at the end of the last post.  The headline was:

How a short nap can raise the risk of diabetes

The implication of this is that the risk of diabetes increases because of the nap.  But what does this mean?

If correlation isn't causation, then what is?

I've started to get a little tired of writing entirely about media shenanigans, and in all likelihood so, dear readers, have you tired of reading about them.  So today I'm going to provide one of the 'educational pieces' alluded to in this blog's description; specifically I'm going to start talking about causal inference, which is the driving force behind the research I'm lucky enough to be paid to do.

We hear a lot in statistics classes (if you're inclined to go to them) and places like this blog, that "correlation is not causation."  Packaged within this pithy but stern warning is some very sound advice: just because you observe a relationship between two things doesn't tell you anything about the mechanism (if any) which creates that relationship.