Can you trust the wage gap data?

Last week Dr Jackie Blue, the Equal Employment Opportunity Commissioner at the Human Rights Commission, came out with a report which included the finding that "Women in the public service are paid on average 14 per cent [14.3% to be precise] less than men". The gap was also a bit wider than the wage gap in the workplace as a whole (12.8%). As you can imagine, the finding got widespread coverage, with (just as one example) the Pay Equity Challenge Coalition saying that "It is simply unacceptable for there to be such a difference in pay based on gender".

Trouble is, the pay gap statistic is pretty much hopeless as any guide to what's actually going on. Here's a worked example showing why.

A medical facility hires two types of employee -  psychotherapists (highly skilled, empathetic, predominantly women, well paid) and orderlies (semi-skilled, burly, predominantly male, lower paid). There are three orderlies per psychotherapist, and psychotherapists are paid five times what the orderlies get.

Unfortunately the manager of this facility is a bad employer who discriminates heavily against women, both in terms of hiring and what they are paid. Although male psychotherapists make up only 10% of the workforce at large, they make up 20% of this facility's roster of psychotherapists. Male orderlies make up 70% of the general workforce, but 80% here.

Men are also heavily favoured when it comes to pay. The psychotherapist/orderly wage differential is maintained at five to one, but in a discriminatory fashion. Male psychotherapists are paid five times what male orderlies get and female psychotherapists are paid five time what female orderlies get, but male pay rates are higher for each occupation. Male psychotherapists are paid 25% more than female psychotherapists, and male orderlies are paid 25% more than female orderlies.

So: what's the wage gap for this blatantly discriminatory outfit?

It's a large one - in favour of women. The average income for the women in this facility is just over twice the average income of the men (the reason being that the high proportion of women in the highly paid psychotherapy role dominates everything else that is going on in the data).

The large measured wage gap is, in other words, totally useless on its own as a diagnostic tool, as it is capable of throwing up both Type 1 and Type 2 errors. In this case, it suggests discrimination in favour of women (which isn't happening) and fails to flag the discrimination in favour of men (which is).

To be fair, the Commissioner is aware of these data limitation issues. Her report notes that the explanation provided by the State Services Commission for the New Zealand public sector wage gap is that “A higher than average proportion of women work in lower paid occupation groups and a higher than average proportion of men work in the higher paid occupation groups", which is exactly what drove the result in the worked example above. And she goes on to say that "This begs the questions – why are women less likely to be in higher paid occupation groups? Is the work women do considered to be of less value because it is women’s work? Are there barriers to women accessing higher paid occupations?", which are eminently reasonable lines of enquiry.

I'm highly sympathetic to those lines of enquiry, and in general to efforts to detect and tackle discrimination. All I'm saying here is that the statistic that people have seized on as evidence that discrimination is happening is deeply inadequate in that role.