## Apr 11 Gender Pay Gap

The UK government made all companies that have more than 250 employee's publish data on their gender pay gap. The average pay gap in across the country is 9.1% which is down from last years gap of 10.5 %. This has resulted in a flood of data and generated a lot of coverage in the press. These articles from the Sun (Pay gap 22%), Economist (29.5%%) and FT (Pay gap 19.4) and Independent (Dodged the requirement as it uses lots of freelancers so technically has less than 250 employees) give and idea of the coverage.

As is pointed out by the ALL CAPS comments at the bottom of many of these articles, the gender pay gap is not comparing like for like. The gender pay gap is not the same as equal pay, which means same money for the same role. What it does show is whether men are being paid on average more than women. This video by the Guardian (Pay gap 12.1%) gives a good explanation.

In this article, we will be looking at the data from a sector perspective. A sector is a broad class of businesses like Agriculture, Manufacturing, or Education. We will also be focusing more on where men and women sit in the pay hierarchy of a company.

## What is the overall picture?

The overall picture isn't great for pay parity. A total of 78% of companies have a median salary larger for men than women, 8% pay the same, and 14% pay women more. All industry sectors pay men more than women.

A major reason for this gap is that men occupy a disproportionate amount of the higher positions in companies. We know this because we can see the gender ratio's in each earning quartile. These quartiles represent whether an employee is in the bottom 25% of earners, the lower middle, upper middle or top 25% of earners within a company. We don't know what the company pays, but we do know where men and women sit in the quartile hierarchy. The bottom quartile is typically entry-level roles or unskilled labour. The top quartile is the senior management and the C-suite executives.

## Side effects of the Quartile representation

Using the quartiles can result in some strange looking results. As the widely seen tweet below shows.

The question in the tweet is entirely reasonable. As has been pointed out this is a result of the unequal amount of men and women in the company (It is also known as Simpson's Paradox).

To understand how this happens, look at the diagram below showing two balances. The balance on the right has an equal number of weights at either end, meaning its centre of mass is in the middle. The balance on the left has the weights placed unequally meaning the centre of mass has shifted. The fact that the balance on the left has fewer weights than the balance on the right does not affect where the centre of mass is.

The positioning of staff is the same as the weights. In Conde Nast's case, although there are lots of women at all levels of the organization, the men are disproportionately concentrated at the top mean they earn on average more than the women.

## The Male and Female Quartile center

If we find the centre of mass by gender across all companies, we can find the average centre of mass for the country. The average for men is 2.64, and the average for women is 2.34 (This difference is statistically significant). As some companies have 300 employees and others 30,000 we weighted the results by size of company. The figure below shows a histogram of how men and women are distributed across all companies. The figure shows the different peaks for male and female centre of mass.

In fact the male center of mass has 63% correlation with the median hourly pay difference.

## Underrepresentation

Quartile Mean Male Fract Median Male Fract
1 Lower 44.18 41.20
2 Lower Middle 47.09 43.80
3 Upper Middle 51.35 49.60
4 Top 58.64 60.00

At some point, everyone needs to enter the workforce, and eventually, everyone retires. This means that there is a constant flow of workers moving into up and out of the labour market.

Given that workforce is approximately gender balanced, it's intuitive to assume that all quartiles would be more or less balanced but they are not. The fraction of males making up each quartile increases as the quartiles increases as shown in the table.

We will use the relative representation equation shown below (A detailed derivation will be in the tech version) to understand the changes in gender representation between quartiles. In the Relative representation equation, x1 and x2 represent the fraction of females (or males) in two adjacent quartiles. When the fraction in both quartiles is the same the equation returns 0, this means there the expected representation the two quartiles. This doesn't mean that all companies should have a 50-50 gender split. However, if say the second highest quartile is 56% female it would be a surprise if the top quartile is only 5% female (Here's looking at you TUI). The equation finds these changes in relative representation

$$R=\frac{x_2(1-x_1)}{x_1(1-x_2)}-1$$

What we find is that 61% of companies have an under representation of women in the the lower middle quartile, this increases to 65% of companies in the upper middle quartile. In the top pay quartile 70% of companies have an under representation of women. IT should be noted that this under representation is only relative to adjacent quartile not the total fraction of women that make up the company. If this were the case the value would be much higher.

Finding the company average female representation score shows that UK companies have a median underrepresentation of women of 12%. The figure below shows that this distribution is right skewed meaning that the bulk of companies have underrepresentation but some companies have a large overrepresentation.

## Sector Summary

The below table sums up the different sectors covered by the analysis

Sector Relative Rep Male Center Female Center Diff Median Hourly % % Female % of total work force
activities of households 1.1 2.56 2.44 0.6 46.8 0
Health and Social work 1.1 2.54 2.49 0.1 79 7
International Bodies 1.18 2.54 2.47 0 56 0
Food and Hospitality 1.23 2.61 2.39 3 50.4 7
Arts and entertainment 1.26 2.6 2.4 2.7 50.4 2
Government 1.31 2.59 2.3 7.8 40.3 1
Water Utilities 1.34 2.55 2.33 7.5 20.7 1
administration and support 1.34 2.61 2.37 5.1 42.5 15
Wholesale and retail 1.34 2.61 2.41 4.4 53.1 19
transportation and storage 1.35 2.56 2.35 8.1 20.8 6
information and communication 1.36 2.6 2.26 16.2 31.1 4
other service activities 1.41 2.63 2.33 11.1 38.8 2
Science and Tech 1.48 2.64 2.3 14 41.2 9
education 1.49 2.77 2.39 23 73.6 8
manufacturing 1.5 2.58 2.25 10 22.6 10
Electric utilities 1.53 2.58 2.29 17.9 38.1 1
real estate 1.61 2.73 2.27 16 53.6 1
finance and insurance 1.68 2.74 2.25 24.4 49.4 4
construction 1.97 2.61 1.96 23.8 17.8 3

When we take the average difference in hourly wage and the average representation by sector, we see the figure below. This figure shows an a linear relationship between Promotion Bias and Hourly wage difference. This is not at all surprising and shows again that the best way of having a small gender pay gap is having a proportional representation of genders at all levels of the company.

## But we will never get absolute balance in all companies...

This is true but beside the point. In a balanced society all companies would have some over/under representation but the overall picture would be balanced. Pointing to a company like the Royal Mint (Pay gap -22%, i.e pays women more) as an example as anti-man bias doesn't make sense. In a balanced society we would in fact expect to see more companies like the Royal Mint and less companies like FujiFilm (Pay gap 38%). Unless you believe that women are inherently less able than men, the gender pay gap indicates that in many cases the best man for the job is in fact a woman. This is bad for the economy and bad for our claim to be a meritocracy.  If you think that women are inherently less able than men you need evidence to back up you claims that women are 9.1% less productive than men (It would also be helpful to explain how womens ability has increased dramatically over the last 50 years as indicated by a shrinking pay gap).

## Conclusions

Although equal pay for equal work is law. The gender pay gap data suggest that equal opportunities for jobs haven't yet occurred. Why not is an on going discussion (for a good overview see here). A good place to start fixing the income pay gap is to improve the relative representation of women in companies. This is done by developing talent and hiring senior managers who are more in line with the gender makeup of the company.

### ERM ACTUALLY...

The next steps are to provide a more detailed explanation of the process in the SSE tech section. Meanwhile if you think that I am a total libtard or a mansplaining idiot, please feel free to fork my code and provide a reproducible counter argument.

Git hub repo

### P.s

I would make a cool sortable table to lookup the relative representation of individual companies, but I am rubbish at html so can't sorry!