Casual inference

From the NZ Herald:

“The survey found almost 65 per cent of women believed they were paid less because of their gender. Just under 43 per cent of men agreed but 47 per cent didn’t.”

Unfortunately the Herald doesn’t tell us what the actual question was. Were people asked whether they, personally, were paid differently because of their gender, or whether women, on average, were paid less because of their gender?   In either case, my sympathies are with Women’s Affairs Minister Hekia Parata, who refused to offer her own answer to the “simplistic” poll question.

There are two statistical problems here. The first is what we mean by “because of their gender”.  After that’s settled, we have the problem of finding data to answer the question.  Inference about cause and effect from non-experimental data will always be hard because of both problems, but that’s what we’re here for.

Usually, when we say that income or health is worse because of some factor, we mean that if you could experimentally change the factor you would change health or income. We say high blood pressure causes strokes, and we mean that if you lower the blood pressure of a bunch of people, fewer of them will get strokes.  This isn’t possible for gender — not only can we not assign gender at random, we can’t even say what it would mean to do that.  Would a female Dan Carter be his sister Sarah, or Irene van Dyk?

In one sense the answer to “Are women paid less because they are women?” is “Well, duh”.  That is, women are paid less, and it’s not because of any factor external to gender.  There isn’t something that makes people more likely to be women and also makes them earn less money.   For tuataras this would be possible — tuatara gender is determined (in part) by temperature during incubation, and temperature could easily affect their success in life — but not for humans.

If you ask “Are people with long hair paid less because they have long hair?” the situation is different.  People who have long hair are paid less on average than those with short hair (or those who are bald), but this is because of a prior cause — gender affects preferences for hair length, and also affects income.

The interesting questions are about the mechanism by which women are paid less: how to fix it, and how much it is someone’s fault.  Is it because employers discriminate in pay, or because women are less likely to negotiate promotions and raises? Is it because women are more likely to leave the workforce or work part-time for part of their career? Is it because jobs with more women in them get paid less, even within the same industry?  Is it because a predominance of men in senior positions makes networking easier for men? Or something else?   The answers here do make a difference for policy: some of these differences can be targeted by making information about pay available, some by discrimination law, some by education, and some only by major social changes.   The data we need is hard to find, and it’s certainly not in opinion polls.  The Herald does have another very sensible article discussing these issues.

One thing the poll certainly doesn’t give us is the conclusion drawn by Green MP Catherine Delahunty: “It shows that my bill and the Alasdair Thompson debacle has actually raised an issue that needs addressing so that’s a good thing.”   This is an issue that needs discussing, but that would be equally true regardless of the results of the poll.