Monday, September 27, 2010

Gender Pay Gaps - Myths

Myths about the Gender Pay Gap

Warning: this post contains mathematics. I apologise to those of you who find this intimidating but I make statements that follow mathematically from the definition of the gender pay gap and it is important that I give my reasoning so that those who are not put off by a bit of straightforward algebra can check it. If you can not read the equations and want to, try this link.

The important conclusion is that an institutional gender pay gap is an incomplete and ambiguous measure of inequality. It is incomplete because the gender pay gap can be small or zero even when the overall proportion of women in the workplace is low. We therefore need to know the proportion of women in the workplace as well as the gender pay gap. It is ambiguous because while if the proportion of women in each salary interval falls as the salary increases then the pay gap is non-zero it is possible for the pay gap to be small or zero and the proportion of women by salary interval to still have undesirable features such as a lack of women at the highest levels. In addition, because the gender pay gap compounds structural factors that are common to both men and women, namely, the salary scale and the number of people in each salary interval, with an inequality factor, namely, how the proportion of women varies with salary, it is difficult to compare different workplaces unless the structural factors are similar.

For these reasons the minimum information required to make sense of a gender pay gap is

  • the number of women and the number of men (number rather than proportion since the proportion can be calculated from the numbers and the numbers give an idea of whether the measured gap reflects underlying inequality or just a fluctuation or contingency)
  • the average salary for women
  • the average salary for men
  • the proportion of women by grade or salary

Myth 1: The gender pay gap measures the extent to which women are paid less than men for doing the same job.

There are three contributions to the gender pay gap:
1. Occupational segregation: there are more women in low paid occupations and occupations in which women predominate attract lower pay.
2. Vertical segregation: within an occupation there are more women at lower levels.
3. In some cases women are paid less than men for doing the same job or for work of equivalent value, which is illegal.

There are numerous causes of the gender pay gap, for example, research commissioned by the Government Equalities Office in the UK identifies several factors including differences in years of full time work and the negative effect on wages of having worked part time or taken time out of the labour market to care for a family.

Myth 2: The gender pay gap is a useful indicator of inequality.

The gender pay gap is defined by:

gap = (average pay for men - average pay for women)/(average pay for men)

The average pay for women can be written as:

S_A^W = \frac{\sum_{i=1}^{n}{p_iN_iS_i} }{\sum_{i=1}^{n}{p_iN_i} }

and the average pay for men as

S_A^M = \frac{\sum_{i=1}^{n}{(1-p_i)N_iS_i} }{\sum_{i=1}^{n}{(1-p_i)N_i}}

where N_i is the number of people with salary S_i and p_i is the proportion of them who are women. The number of different salaries (or salary categories) is n. The symbol \sum_{i=1}^{n}{} means add all the terms from 1 to n together. These formulas work when people are paid on a salary scale or when there are enough people that it makes sense to make a histogram of the number of people in each salary interval.
The total number of people is N_T = \sum_{i=1}^{n}{N_i} . The total number of women is N_W = \sum_{i=1}^{n}{p_iN_i} , the total number of men is N_M = \sum_{i=1}^{n}{(1-p_i)N_i} and the overall proportion of women is p=\frac{N_W}{N_T} . This implies that the difference between the average pay for men and the average pay for women can be written as

S_A^M-S_A^W=\frac{1}{p(1-p)} \sum_{i=1}^{n}{(p-p_i)(\frac{N_i}{N_T})S_i }

and the gender pay gap as

g = \frac{S_A^M-S_A^W}{S_A^M} =\frac{\sum_{i=1}^{n}{(1-p_i/p)N_iS_i} }{\sum_{i=1}^{n}{(1-p_i)N_iS_i} } .

So, the difference between average pay for men and average pay for women depends on two structural factors, namely, the salary scale and the proportion of jobs at each salary scale point, and an inequality factor, namely, the way in which the proportion of women at each scale point varies with scale point. One implication is that the pay gap will be zero whenever the proportion of women is constant with scale point regardless of what that proportion is. Hence, the pay gap is an incomplete measure of inequality. A workplace with a zero pay gap that has only 10% women is hardly a shining example of gender equality.

From a mathematical point of view we have two equations

p=\frac{\sum_{i=1}^{n}{p_iN_i} }{\sum_{i=1}^{n}{N_i} } , which defines p, and

g = \frac{S_A^M-S_A^W}{S_A^M} =\frac{\sum_{i=1}^{n}{(1-p_i/p)N_iS_i} }{\sum_{i=1}^{n}{(1-p_i)N_iS_i} }

which defines the gap. If we want g=0 then we have two equations in n unknowns. This is an under-determined system, unless there are only two steps on the salary scale, so there is the possibility of finding other solutions that give a zero gap besides p_i=p for all i. This means that while if p_i is constant then the gap is zero and if p_i falls systematically as i increases then the gap will be non-zero there could be solutions which have a small or zero gap that nevertheless have undesirable features such as a lack of women at the highest salary levels. The figure below shows an example, which has 220 men and 180 women (45% women among a staff of 400) on an eleven point scale where each point is has a salary 5% greater than the one below starting from £20,000. The average salary for men is £24,923.41 and the average salary for women is £24,901.72, which is a gap of 0.09%. Nevertheless, only 35% of the posts in the top three grades are held by women and only 20% of the posts in the highest grade are held by women. Click here to view the spreadsheet I used to create this figure. The spreadsheet itself is available at this link.

So, as a measure of inequality the gender pay gap is both incomplete and ambiguous.

Myth 3: The overall national pay gap will be eliminated if each workplace eliminates its own pay gap.

Suppose Employer A has a largely female, largely relatively unskilled workforce while Employer B has a largely male, largely skilled or professional workforce. Both employers could eliminate their pay gaps but Employer A would still be paying their predominantly female workforce less on average than Employer B was paying their predominantly male workforce.

Myth 4: The gender pay gap provides a means of comparing inequality across workplaces

As noted in under Myth 2, the gender pay gap depends on two structural factors and an inequality factor. Unless the workplaces have the same salary scale and the same proportion of jobs at each salary scale point it is very difficult to draw conclusions about differences in equality in different workplaces. It would also be helpful if there was agreement on whether to divide by the average salary for men or the average salary for women in the expression for the pay gap. It could also be the case that in the example discussed under Myth 3 that Employer B has a gender pay gap that is hard to eliminate due to a shortage of women with the necessary professional qualifications, for example, in engineering, while Employer A is able to eliminate their gap despite the fact that women working for Employer B have higher average salaries than women working for employer B.

Thursday, September 23, 2010

Uk Equality Legislation: Specific Duties Consultation

In a previous post I wrote about different approaches to equality under Teresa Rees’s headings: Tinkering, Tailoring, Transforming. Recent equality legislation in the UK has the potential to be a framework for transforming both workplaces and service delivery to incorporate genuine equality. It also has the potential to create self-sustaining bureaucracies that achieve very little. Which happens depends not on the competence of organisations’ equality and diversity personnel but on the extent to which women, and other groups, avail themselves of the opportunities presented. The consultation on the specific duties is one such opportunity. While responding to consultations can seem like a waste of time, if you do not even attempt to make your views known your voice certainly will not be heard. So, if you live in the UK, download the consultation document from the Government Equalities Office website and respond.

The Equality Act 2010 integrates the former general equality duties that applied to disability, race and sex and extends them to apply to other characteristics such as sexual orientation. The general equality duty requires public authorities, which include universities and research councils, to eliminate discrimination and harassment, advance equality of opportunity and foster good relations between members of different groups. In the context of gender, the Act makes it explicit that advancing equality of opportunity includes removing or minimising disadvantages experienced by women (or men) but not by men (or women), taking steps to meet the needs of women (or men) that are different from those of men (or women), and encouraging women (or men) to participate in public life or any other activity in which participation by women (or men) is disproportionately low. (Note: the Act frames these duties in a way that applies to all characteristics. I have used gender as an example to avoid using the jargon that is required for a more general formulation.)

The specific duties are set by regulation and are intended to provide a framework that ensures that something actually happens. Under previous legislation the specific duties varied. For example, the Race Equality Duty had a detailed prescription for data collection in Higher Education. The Gender Equality Duty required public authorities to gather and use information but had no specific requirements for data collection, other than that the requirement ‘to consider the need to include objectives to address the causes of any gender pay gap’ implies that you actually know what your pay gap is.

The previous specific duties for gender were:
  •      To prepare and publish a gender equality scheme, showing how it will meet its general and specific duties and setting out its gender equality objectives.
  •       In formulating its overall objectives, to consider the need to include objectives to address the causes of any gender pay gap. 
  •       To gather and use information on how the public authority's policies and practices affect gender equality in the workforce and in the delivery of services.
  •       To consult stakeholders (i.e. employees, service users and others, including trade unions) and take account of relevant information in order to determine its gender equality objectives.
  •       To assess the impact of its current and proposed policies and practices on gender equality.
  •       To implement the actions set out in its scheme within three years, unless it is unreasonable or impracticable to do so.
  •       To report against the scheme every year and review the scheme at least every three years.
[Source: Gender Equality Duty Code of Practice Gender Equality Duty Code of Practice England and Wales EOC 2006]. It was the responsibility of the Equality and Human Rights Commission (EHRC) to enforce the legislation by issuing guidance and, if necessary, through compliance orders or court orders.

The focus of the proposed new specific duties is on accountability through transparency. Public authorities will be required to publish data that will enable citizens and concerned groups to hold public authorities to account. The EHRC will determine what data should be published though the consultation document mentions the gender pay gap, the proportion of staff from ethnic minority communities and the distribution of disabled employees throughout an organisation’s structure.

Differences from the old specific duty for gender are
  • Public authorities will no longer be required to have an equality scheme. Consequently there will no longer be requirements to implement the scheme, to report against the scheme or to review the scheme.
  • There will no longer be a specific requirement for consultation but public bodies will be expected to be open about how they have engaged with people.
  • There will not be a specific duty requiring equality impact assessments as it is expected that equality impact assessment would form part of normal decision-making. However, the annual publication of equality information will include impact assessments.
  • Equality objectives should be reviewed every four years.

Differences from the proposals put forward under the previous government are:
  • There will be no national priorities set by the Secretary of State.
  • There will be no special focus on procurement as the general and specific duties already apply to all the functions of a public body.
  • Public bodies will no longer be required to set out the steps they propose to take in order to achieve equality objectives.

The proposed specific duties are
  • Workforce Transparency: Public bodies with 150 or more employees will be required to publish data, to be specified by the EHRC, on equality in their workforces. This is expected to include data on their gender pay gap, the proportion of staff from ethnic minorities and the distribution of disabled employees throughout the organisation’s structure. The data will have to be published at least annually.
  • Service Provision: Public bodies will be required to publish data, at least annually, that will enable people to judge how effectively they are eliminating discrimination, advancing equality and fostering good relations through the services they provide.
  • Setting objectives: Public bodies will be required, as part of their normal business planning process to set equality outcome objectives that are informed by evidence and that are specific, relevant and measurable. This will enable meaningful scrutiny by citizens and other interested groups. The objectives should be reviewed at least every four years.

The focus on outcomes is welcome. Far too much time and effort has gone into producing plans and then writing reports against those plans in which whatever did happen is presented as though it were what was planned. Trying to minimise the work involved in demonstrating compliance is also welcome. Partly because resources should be directed to achieving aims not demonstrating compliance and partly because equality should be embedded within normal procedures and practices not treated as an optional or externally imposed extra.

My concerns are:
  1. Will this ‘meaningful scrutiny by citizens and other interested groups’ actually occur? Are there enough people with the time and resources to carry out this scrutiny? How is it envisaged that such people will hold an institution such as a large, research-intensive university accountable?
  2. What data will be required? From a mathematical point of view the institutional gender pay gap is a flawed measure of inequality. However, a lot of people have invested a lot of time and effort into promoting it as a measure of inequality so we are probably stuck with it. The minimum amount of information required to make sense of a gender pay gap is the number of men, the number of women, the average salary of the men, the average salary of the women, and the proportion of women by salary band. It would also be helpful to know if women are disproportionately represented in some occupational groups and, in the context of research and academic staff in universities, whether there are differences by discipline. For workplaces that are large enough for such an exercise to be meaningful, it would be useful to know the proportion of women by salary band and age. This would help distinguish between situations where women are hard done by and something should be done and situations where women were hard done by and something has been done. There is no point in devoting time and resources to fixing something that is not broken. The Equality Challenge Unit, which provides guidance on equality for the higher education sector, has suggestions for the data that higher education institutions should use to inform setting equality objectives in their briefing ‘Revising Gender Equality Schemes’  (January 2010) and the ECU Gender Equality Scheme Self-Assessment Tool.
  3. If there is a conflict between presenting data and maintaining the privacy of individuals then privacy should be paramount.
  4. Objectives should be realistic and achievable as well as measurable. There is no point aiming for some arbitrary percentage of women among some particular group if that cannot be attained within a reasonable timeframe. It is often forgotten that the most important constraint on how fast the proportion of women among academics can change is the rate at which vacancies occur for them to be appointed to, unless new positions are created. Similarly there is no point aiming to train some proportion of your staff in something-or-other if the resources to deliver the training are not available.
  5. What do we mean by measurable? For example, in 2004 women made up 49% of acceptances to Natural Sciences at Cambridge. Five years later in 2009 women made up 40% of acceptances to Natural Sciences at Cambridge (Source: Cambridge University Reporter Undergraduate Admissions Statistics Special Issue, No. 15 2009-2010 and 21 February 2005). Is this a worrying decline or a random fluctuation? Having looked at the numbers, I am inclined to the latter view, though the former is tenable depending on how much the data are tortured. It could also reflect a change in the proportion of acceptances to biological Natural Sciences. Suppose the numbers had been the other way around (i.e. 49% in 2009 and 40% in 2004). Would this be evidence that the University was meeting equality objectives?
  6. It is hard to see how an institution could set or achieve equality objectives without consulting with relevant groups. It is very important that institutions should be required to state with whom and how they consulted.
  7. Institutions should also be required to state what steps they took to achieve their equality objectives. This would aid the ‘citizens and other interested groups’ to assess whether an institution is building a genuinely equal environment or whether it is just managing the numbers. For example, suppose an institution has reduced its gender pay gap. It would be of interest to know if this had been achieved by making lots of catering assistants and clerical workers redundant or by waiting for other institutions to develop the careers of their female staff and then poaching them. In addition it would be useful to other institutions to help them assess what actions are effective.

The proposed specific duties should enable institutions to embed equality within their organisations. If you have a view on whether or not the proposed specific duties make it more or less likely that this will happen then you should respond to the consultation.

Sunday, September 19, 2010

Christchurch Earthquake 2

More on the Christchurch earthquake, also known as the Canterbury earthquake or  the Darfield earthquake...

After much emailing on my husband's part, he and I travelled to Christchurch on Wednesday 8 September to help install sensors to measure accelerations caused by earthquakes in the aftershock sequence following the 7.1 earthquake on 4 September. The project is part of the Quake Catcher Network run from Stanford ( the Rapid Aftershock Mobilization Program in New Zealand ( A Ph.D. Student from Stanford had arrived in Christchurch that morning with 200 sensors in her luggage.

People volunteer to have a sensor in their home for a period of 4-6 weeks. The picture shows one of the sensors. It is secured to the floor using duct tape and glue for a hard floor and duct tape and Velcro for carpet. The cable plugs into a USB port on a computer which has to have BOINC (Berkeley Open Infrastructure for Network Computing)  installed to manage data transfers to the server. Between 8 September and 14 September up to five teams of people from GNS Science, Stanford and the Universities of Auckland and Wellington installed nearly all of the 200 sensors around Christchurch and the surrounding region.

Different parts of the city were affected differently by the shaking. Driving in from the south, we saw very little damage until we reached the central city area where a number of older brick or masonry buildings had been badly damaged. In fact, the three main types of damage were chimneys that either collapsed or became unsafe, older brick or masonry buildings that partially collapsed and problems due to soil liquefaction. When we arrived on 8 September many streets in the central city area were cordoned off. In fact, the serviced apartments where we were staying were inside a cordoned area and we had to be escorted to reception by a soldier. By the time we arrived, water and power had been restored over most of the affected area, though not in some of the most badly affected neighbourhoods and in rural areas. The biggest inconveniences for us were that for the first few days we were not allowed to use the lifts and the internet connections to the rooms were not working properly, possibly because aftershocks were loosening the ethernet cables. By Monday 13 September much of the city was  functioning normally, though a few streets were still closed due to unsafe buildings or continuing demolition.

The response of Christchurch residents to the call for volunteers to host a sensor was amazing. Even those whose houses were undamaged had still had an extraordinarily stressful experience, plus the additional stress of on-going aftershocks, including one of magnitude 5.1 on the morning of 8 September (before we arrived) that caused additional damage.

The GeoNet website has more information about the earthquake, including a video montage of the fault trace reconnaissance and some more on aftershocks. The GNS Science website has more information as well. There is an animation of the aftershock sequence at

We also recommend the Nobanno Bengali restaurant on the corner of Armagh and Colombo Streets in Christchurch. The food is excellent.

Saturday, September 4, 2010

Christchurch Earthquake

The major earthquake near Christchurch , around 350km north of here, woke us at 4.35 this morning. It was strong enough here for me to be concerned about objects falling, though none did. The timing was fortunate, in that not many people were out on the streets. Had they been, there would have been many more casualties. As it is, some people had some amazing escapes. For news stories see TVNZ or BBC.