You may have seen the story in various media a few days ago about new work commissioned by Westpac suggesting that

New Zealand’s economy has a nearly $900 million annual economic hole because of low numbers of women in management roles, new research suggests.

But if there was an even split of men and women in management there would potentially be an $881m boost to the economy and a positive impact on businesses themselves.

I didn’t pay much attention to it, beyond noting to myself that $881 million is about 0.3 per cent of GDP –  not much of a “hole” in other words, even on Westpac’s (and the consultancy company they paid to do the research) own claims.

But I wondered quite how they’d come up with these estimates so last night –  while the resident woman in management was off at her office party –  I downloaded the document.

It begins with lots of puffery around the alleged economic and financial benefits of diversity –  our banks now apparently see themselves as “social justice warriors”.   I don’t claim any expertise in that particular literature, but I’d refer you to some of Eric Crampton’s reads or, indeed, to a paper I wrote about here a while ago, that leaves me pretty sceptical that there is anything much in the sorts of claims Westpac makes.

The bank is horrified that “60 per cent of businesses do not have a gender parity policy or strategy in place” –  as if picking the best person for the job, male, female, black, white or whatever –  isn’t any sort of legitimate approach to employment these days.   And seems to think that the mere existence of gaps between median earnings of mean and median earnings of women is somehow proof that employers are breaching laws “mandating equal pay for equal work”.  Perhaps Westpac’s crusading CEO could spend some time reading Claudia Goldin, for example.    In the Westpac world, there is apparently no recognition that more mothers than fathers prefer to take time out –  or work in less demanding roles –  to be actively involved in raising children (note the word “more” –  in this household, I’m the “primary caregiver”).  There are implausible claims (without proper documentation in the report) that raising the share of female managers raises rates of return on assets –  in New Zealand’s case they argue that reaching parity could raise returns on assets by 1.5 percentage points.     Not only are these huge numbers, but what sort of metric is return on assets anyway?  Some businesses require lots of fixed assets and other require not many at all.

But what I was really curious about was this alleged $881 million per annum that Westpac reckoned was being left on the table, simply because the share of female managers was less than the share of male managers.  How on earth, I wondered, did they get these estimates?

Fortunately, there is appendix to the report on the modelling.  They’ve attempted to come up with estimates of two separate effects:

• a “role model” effect in which a higher share of female managers encourages more women into the labour force, and
• an effect in which the availability of more (by number) flexible employment policies increases the number of women in the labour force.

Taking the “role model” effect first, the OECD has apparently been collecting data recently on the share of employed workers who are managers, by gender, for various countries (unfortunately for this study, there is no data for New Zealand).    But there is only data for four years (2011 to 2014), which even the authors concede make the subsequent model they estimate “statistically challenging”.    They model the labour force participation rate as a function of various things, including the share of women in managerial roles, and they find a statistically significant result.  Statistically significant, but very small.  On the assumption that the gap between the share of male employees who are managers and the share of female is the same in New Zealand as in Australia, if that gap was not there then, on this model, overall labour supply in New Zealand would rise by 0.15 per cent and –  according to a separate Deloittes model –  that would raise New Zealand GDP by 0.07 per cent.   Knocking off an hour earlier/later on Christmas Eve is probably worth about the same amount.

Even then, the results don’t really hold up to much scrutiny.  There is no underlying model of what determines the share of women in management roles (whether here –  for which they have no data –  or abroad), nothing that is robust across time (remember four years of data) and no insight as to what might be involved in achieving the sort of “parity” Westpac wants to see: closing the gap is treated (or so it seems) as something one can simply wave a wand and deliver.

If those estimates are both small and shaky, what follows is worse.   They attempt to estimate an effect on a company changing the number of flexible work policies of the proportion of women in management, and then translate that into an increase in overall labour supply.   Unfortunately all their data are Australian –  include a survey result on the number of working age people not in the labour force who claim that flexible working policies are very important consideration for them, and a count on the number of flexible working policies surveyed companies have in place.   In a simple model, they find that the number of flexible working policies (there is no sense of the empirical size/significance of any of them) is explained (statistically significantly) by the number of women in management in those companies, and thus conclude that if the proportion of women in management was raised to the same as men, there would be (in Australia) a 13 per cent increase in the number of flexible working policies.

The authors then take that 13 per cent increase, the 23 per cent of people not in the workforce who said flexible working practices mattered to them to get an estimate of how many more people would join the labour force through this channel if only the proportion of women in management was raised to parity with men.    They then adjust the result for the fact that many of the new entrants would only be part-time, and estimate that the overall labour supply in New Zealand would rise by 0.55 per cent.   Using the same Deloitte model as earlier this, it is estimated, would raise GDP by 0.26 per cent.

This is all incredibly ropey.  There is no attempt, for example, to assess how robust those answers to the survey were (probably many more people will say flexible working conditions really matter than actually mean it –  it is a socially desirable response).  There is no attempt to look at what the trade-offs for more –  by number –  flexible working policies might be: is there, for example, an offset in lower wages?  And there is no attempt to look for common third factors: maybe it isn’t women in management who  (causally) lead companies to offer more (by number) flexible working policies, but (say) a particular ethos among the owner and top managers of the particular business that drives both outcomes.  And there is no attempt to look at whether the presence of those flexible policies affects more strongly which firm a person (especially a woman) joins, rather than the choice to join the labour market at all.   And there is also no evidence for whether there are threshold effects –  eg perhaps having a lot of women managers lead to more –  by number – flexible work policies,  but the effects might be much smaller if the share of female managers moves from  say 35 per cent to 50 per cent, than if the share moves from 5 per cent to 20 per cent.

I’m not suggesting there is no effect, just that the case is not even remotely compellingly made on these numbers.  It might be fine for David McLean –  Westpac’s CEO –  to lead his firm’s “social justice warrior” campaign, but he really should be rather embarrassed to rely on numbers as shaky as these in support.  I do hope he does banking itself a bit better (then again, there were all those unapproved models where he found himself falling afoul of the Reserve Bank).

But to revert to my headline, did you notice the bottom line numbers for those two effects?  Here is my summary, just replicating their own numbers:

In each case, the increase in the labour supply (a cost to the individual concerned) exceeds the estimated increase in GDP.  In other words, on their own numbers nationwide productivity falls as a result (of increasing the proportion of female managers to that of males).

Do I believe the number?  No, I don’t.  I’m sure they are just an artefact of the CGE model of the New Zealand economy they assume –  perhaps something like adding labour, but with no change in productive capital or somesuch.  But Westpac published the numbers, and Westpac claimed the headlines, even though their own numbers suggest our nationwide would fall in the magic wand could be waved and their goal of parity achieved just like that.   It is a case of ropey inputs, ropey outputs, and not much more in the end than a left-liberal feel-good crusade.  Perhaps bankers should stick to banking.