Pushing Against the Glass Ceiling
With the 8th March marking International Women’s Day, it’s a time to consider and celebrate all that women have done for the world.
Names, but some amongst many, are called to the fore. From science with Marie Curie. To matters of state with Angela Merkel, Condoleezza Rice, Hillary Rodham Clinton, Janet Yellen, Madeleine Albright, Margaret Thatcher, and Queen Elizabeth II. To business and industry with Sara Blakely and Gina Rinehart. To those who’ve done their best to make the word a better place, such as Florence Nightingale and Mother Teresa. To those that entertain us, such as Oprah, Ellen, Meryl Streep, and Julianne Moore.
The list of women who have achieved both greatness and public recognition in their respective fields is not a small one by any means. And any such listing must ultimately be incomplete.
Equally though, we should also acknowledge those whose stories are no less remarkable, but often remain unmentioned. Those outside of the limelight and maybe only know to the precious few. The mothers, the sisters, the daughters. From the single mother who overcomes adversity to raise her child as best she can, to the woman who educated herself in a country where females are prevented from going to school. All will matter in their own way.
Yet it was the recent words of actress Patricia Arquette which has added, or perhaps reaffirmed, a question and issue. Her Oscar acceptance speech with the ending comment on gender equality (read the transcript) has again stirred words on a thorny subject.
Equality. A word which can be as suggestively hopeful as it can be hopelessly problematic.
Commentary has been rife. Some believe she was sincere and opened up a dialogue. Criticism has naturally been there as well.
In a subsequent interview in Time, Patricia herself stated:
“I guess I don’t think people really understood what I meant by that. I don’t think they understood what I was talking about, exactly. This is a huge discrimination issue affecting women across America. It affects whole lives — the impact of this.”
Numbers Don’t Lie…
Focusing initially on some simplified numerical examples, consider what may be required to achieve the notion of equality thereby closing the gender income gap.
Assume that this particularly small world’s population is an even split between males and females. Half of the world is male and the other half is female.
Now to simplify things further, assume that initially in Year 0 there are only 100 jobs, of which 75 males and 25 females are currently employed.
Assume for simplicity that both males and females earn exactly the same wage.
Also assume that the people decry this employment mix is unfair, and that the company must employ an equal mix of male and females.
Instantly firing 25 of the currently employed males and hiring 25 new females is reasonably viewed as unfeasible, considering unfair dismissal laws, amongst many other things.
So instead, the company suggests that because it grows at an annual rate of 2 percent, then always rounding down to the nearest whole person for each year, will mean that in Year 1 the company can create two additional new jobs (with a workforce of 102 people in total).
Being a grossly simplified example, also assume that once hired, no-one leaves the employ of company.
Because it’s all about equal employment opportunity, it is also enforced that the company must follow the policy of hiring equally males and females for new employees. With the exception that if it is an odd number of new employees to be hired for the year, then one more female will be hired than the number of males hired. (For example if three new employees were to be hired, two would be female and one would be male). This is done to help close the gap quicker, which is where the interests of being fair are focused at present.
Therefore setting the target employment at equal halves of male and females gives the following:
Year 0, has 75 males and 25 females, and 100 employees overall.
Year 1, hires 1 new male and 1 new female, to give 76 males and 26 females, and 102 employees overall.
Year 2, hires 1 new male and 1 new female, to give 77 males and 27 females, and 104 employees overall.
Year 3, hires 1 new male and 1 new female, to give 78 males and 28 females, and 106 employees overall.
This continues, and in the interests of space for omitting all the steps, the numbers of male and female employees are equalised in:
Year 116, hires 7 new males and 8 new females, to give 396 males and 396 females, and 792 employees overall.
Let that sink in for awhile. Under an apparently fair policy, and (admittedly) overtly simplified circumstances (where the people have very long lifespans indeed), it effectively takes 116 years to equalise the numbers of male and female employees in the company.
The people, including the erudite modellers and even some of the bureaucrats, upon running the numbers decide that this is far too long to be fair.
Instead, for a second scenario, it is then wondered what if under the same assumptions of growth, only females were hired as new employees until the ratio of males to females employed was one to one. Therefore:
Year 0, has 75 males and 25 females, and 100 employees overall.
Year 1, hires no new males and 2 new females, to give 75 males and 27 females, and 102 employees overall.
Year 2, hires no new males and 2 new females, to give 75 males and 29 females, and 104 employees overall.
Year 3, hires no new males and 2 new females, to give 75 males and 31 females, and 106 employees overall.
This continues, and again in the interests of space omitting the extra steps, the numbers of male and female employees are equalised in:
Year 25, hires no new males and 2 new females, to give 75 males and 75 females, and 150 employees overall.
Given the requirement of 25 years to change things, effectively an entire generation, and that people want change now, a third scenario is suggested.
What if, instead the company hired extra people? Make all the new hires again females to expedite the process, and hire at a rate of 4 percent per annum rounding down to the nearest whole number of new employees. Continue this each year until male and female employees are equal in number.
Management of the company protests that the rate of growth at 4 percent per annum in new hires is over and above the 2 percent per annum that the company realistically grows at, and it cannot be sustained.
Jobs and the aggregate numbers of the male to female employee ratio being equalised though are the concerns of the people and their Government. So the number are worked through again:
Year 0, has 75 males and 25 females, and 100 employees overall.
Year 1, hires no new males and 4 new females, to give 75 males and 29 females, and 104 employees overall.
Year 2, hires no new males and 4 new females, to give 75 males and 33 females, and 108 employees overall.
Year 3, hires no new males and 4 new females, to give 75 males and 37 females, and 112 employees overall.
This continues, more rapidly this time with fewer steps needed (and again omitted to save space).
Year 11, hires no new males and 5 new females, to give 75 males and 73 females, and 148 employees overall.
Meaning that for Year 12, the policy would have to be altered. Otherwise in that year, there’d be 75 males and 78 males, and 153 employees overall should the policy continue without revision. (Note this kind of overshooting effect is not uncommon amongst such policies.)
The issue in this third scenario, whilst it rapidly achieves its goal of equal employment for males and females by numbers in the workforce, is at what cost is this achieved. The jobs created were surplus to those required, suggesting perhaps waste and excess capacity, even if the aggregate employment figures appeared as desired.
This is not to any way belittle either sex, or gender. The purpose was to look logically and mathematically, using very simple examples how long it can take to bring about change. That for one group to catch up to another is seldom instant.
Starting Socioeconomics (and Hidden Markov Chains)
What was omitted were the many facets of the reality of careers and nuances of the workplace. Retirement, maternity (and paternity) leave, changing jobs, even taking holidays, all spring to mind. The many qualitative factors of life in general, which may be too innumerable list.
Therein is the rub. Details. Choices made and the environment in which they are made, all tend to suggest that income earned is very much path dependent. Where one ends up is a consequence of the path they took to get there. It may be through active volition. It may also be part of the circumstances of birth and lucky genes, and whether one was born into wealth or poverty.
An individual can of course rise or fall themselves; though some can find that left alone to circumstance, in aggregate they’ll probably end up about where they started. Not always, but one born with a silver spoon is more likely to find the silver spoon still there on their deathbed than one who never had the silver spoon to begin with. Similarly so for the wooden spoon. A few exceptional cases though, may start with no spoon and have a golden one at the end. Or vice versa.
This is part of what makes discussion of the gender pay gap and gender equality (at least regarding work) nowhere near as simple as some seem to suggest. As was raised in this article, and citing related figures, the numbers regarding the earnings of men and women tend to lack sufficient details to make proper comparisons.
Noting that apparent gender income gaps tend to become more pronounced as age increases.
Further, that it is not in question that incomes are different between the genders; rather exactly why are they different and what accounts for this?
That things are being concealed within the aggregate numbers, and obscured by them. Before making claims about any gender pay gaps, if the claims are to be valid, then they should control for factors such as age and the number of contiguous years spent working in the same job as well as being in same the industry.
Consider just how different the following two examples are likely to be:
Male, aged 30 years, has spent the past decade working fulltime in the mining industry.
Female, aged 30 years, spent two years in the retail industry, the next four years raising her child, then studied for three years earning a university degree, and has spent the past year working part-time in the finance industry.
Or, if you’d prefer:
Female, aged 30 years, has spent the past decade working fulltime in the mining industry.
Male, aged 30 years, spent two years in the retail industry, the next four years raising his child, then studied for three years earning a university degree, and has spent the past year working part-time in the finance industry.
These are quite simply not comparing like with alike.
They are qualitatively very different. Consequently they are also likely to be quantitatively very different as well.
So it’s ultimately misleading to claim that the male earned one amount and the female earned another, and state the gap is thus.
In many industries, employment can also be a LIFO (last in, first out) situation. Meaning that newer employees are more likely to be made redundant, and more senior employees are more likely to retain their jobs. Overall this situation is actually quite economically and psychologically complex. (Including within the business itself, as there can be a benefit to retaining those with experience and fully trained for their roles; it may also lead to stagnation and complacency.) It may be doing it a disservice to oversimplify it in a toy example. The toy example, can however, give insight into the logic of the matter regardless.
In a business, who generally earns the most and where are they placed in the organisation’s hierarchy? Typically it is the boss who earns the most in the business. (There are exceptions to this. Being paid money as income versus things such as stock ownership and options make things again more complicated than necessary for the discussion here.) Unless brought in from an external position, the boss may also have typically been at the company a rather long time. Generally the top position goes to an in-house employee who worked their way up (most of) the ranks as opposed to a new hire. (Again exceptions do apply here, such as new CEOs brought in as “agents of change” to turn an ailing companying around for example.)
The effect of compounding on wage percentage increases can also have a very big impact.
Then factor in the skewness of wealth distributions. Whilst the distribution of wealth isn’t necessarily an all or nothing situation, it does have a very long right tail. (And is probably more accurately represented by a power-law distribution.)
Average, What Does it Mean?
There are 10 people in the room. Eight woman and two men.
Each of the eight women earns an income of $100,000 per annum. Their average (mean) annual income is therefore, $100,000.
One of the men, earns $25,000 annually. The other man, however, is Bill Gates whose annual income is $1 billion. (This is not an accurate assumption; at the time of writing he was worth approximately US$78.8 billion, based on his profile on Forbes).
Therefore, the average (mean) annual income of all the people in the room is $100.0825 million, and the average (mean) annual income a male earns is $500.0125 million.
So all the women in the room now each earn less than the average (mean) annual income overall, and, also less than the average (mean) annual income of a male.
In the above example, because of Bill Gates’ disproportionately large income, using the mean as the average is severely skewing the results. Giving the apparent gender pay gap.
Within reason, using the median can better reflect what is the average, because it is less sensitive to large outliers and their resultant skewness. In the example, the median wage would be $100,000 and the gender pay gap has disappeared.
However, if the aggregate data itself is flawed, then so will be the median and any decisions made from it. The median wage in the example was influenced by the number of women in the hypothetical workforce in the room.
Beyond the example (and Bill Gate represents an extreme example), if in the real world there are more men in the workforce than women, and they’ve tended to work more and earn more (perhaps simply because they have been in the same job or within the same company longer; and are probably also older), then they are going to skew even the median wage. Which again gives rise to a gender pay gap.
Unless the data is analysed in much greater and finer detail, the average wages of male and females based on aggregated figures can be extremely misleading.
Economist Thomas Sowell has analysed this is detail, and argues that after controlling for the relevant factors (to compare those things which are then essentially the same) the gender pay gap is nowhere near as large or even significant as it is claimed to be. Sowell contends that overall, income equality is more of a myth than anything else, brought about by making invalid and unqualified comparisons. Especially that care is needed when comparing the differences between aggregates (and income brackets) to individuals.
In each of the numerical examples above, things were deliberately and grossly oversimplified, and dynamics and uncertainty ignored. To paraphrase things far more eloquent and insightful: It is trying to hit a moving target with a crooked aim. Suggesting not only the unintended consequences should things go amiss, but that policies aimed at closing gaps without the full awareness of the circumstances and implications at hand are often hopelessly naïve.
The hiring of any demographic purely to target represented number proportions is not empowering to people in that demographic subset. It is tokenism. Granted there should be equal employment opportunity and access to apply for the job, but ultimately the person hired should be the best person for the job. Regardless of what their gender, age, ethnicity, religion, or otherwise may be.
However, hiring someone simply to fill something like a quota of, say, having 50 percent of all employees as female (or male), seems equally as anachronistic as not hiring someone purely because they’re a woman (or a man).
It might make the numbers look better from a bean counter’s perspective. It may even be helpful for the individual who gets a job they otherwise wouldn’t have. Although if at the core of it, it is hollow and people know this, then a papered over shell that looks good from the outside but doesn’t stand up on its own to more detailed scrutiny is bound to collapse at some point.
Furthermore, if save for decree or subsidies, the jobs are not needed, aren’t the jobs then in and off themselves also products of wasteful tokenism. Akin to two people taking turns of one person digging a hole and then the other filling it in. They may both be employed but they are not truly producing anything or providing a useful service. Just shifting things back and forth without progress.
The Fallacy of Aggregation
Intellectually, in aggregate, there is no meaningful difference between the level of overall intelligence between males and females. Where there is an apparent, and well accepted difference, is in physicality. Which is to suggest, some jobs, reliant upon strength may be easier in general for males than females.
Whether more physical jobs pay more than less physical jobs (or the corollary) is open to debate, provided that the actual conditions and circumstances of the jobs are properly taken into account. What may be true of one country, or even region, may not necessarily be true of another.
Also for consideration: Which do people tend to gravitate towards, what they are good at, or what they are not good at? Add to that personal interests, peer groups, and even nepotism such as it may be. Then the dynamics of one size fits all begin to become all the more questionable.
The simplified numerical examples have shown the gender income numbers have not only gaps in them, but also lots of holes in the logic of such comparisons. To reiterate, it not that income differences exist between the genders, but to accurately account for why they do exist.
Another thing to consider, is whether creating (apparently unnecessary) jobs benefits both the individual and the whole. The more hard-lined may argue in aggregate this is a waste, and maybe at best, a redistribution of resources via subsidisations.
Yet for all the suggestion of job creation, is the job actually wanted? The state of the economy and the availability of employment (and welfare) at the time may influence an individual’s decision. Similarly, some may not want to work in a given job. Others still, may be happy to take any employment they can get.
Connecting the dots between the individuals and their behaviours to the overall macro-level of the aggregates is seldom straightforward. As is attempting to go in reverse. Especially given path dependence.
The Equations Don’t Balance
On one hand, there is now the rising acknowledgement of gender and gender-like qualities being a spectrum and words such as cisgender and zhe, amongst others, are entering the language where diversity and difference is being accepted. On the other hand, in other areas there’s another ultimately false attempt to homogenise male and females into being exactly the same.
Whilst it may be good to rattle a few chains and make some noise, if issues in gender inequality are truly to be addressed, then the line of enquiry needs to be driven by the data. And the data currently used in the gender pay gap debate seems to lump too much together as though we are all the same.
We may all be people, but we are also each a person with different skillsets.
Equal pay for equal work is both fair and equitable. An admirable goal which should be reached for regardless of the side of the debate one may find themselves.
What do you think? Anything (almost) a man can do, a woman can do? Or, anything a man or woman can do, pick the best person for the job and pay them accordingly?
Feature Image Credit: Glabb