The government’s decision to reject the recommended 1% rise in NHS salaries has been met with “contempt” by the unions.

The issue of public sector pay has become highly contentious, with each side arguing the other is better off: TUC general secretary Frances O'Grady points out “public sector workers now earn less than equivalent staff in the private sector”, whereas the opposition includes everyone from employers organisations like the CBI to former Apprentice contestant Katie Hopkins. Even the BBC’s business reporter claims that “however you measure average hourly earnings, either by calculating the mean or the median figure, public sector staff are paid more.”

So who is right?

It it easy to see why the view that the public sector pays better is commonly held. The figure below, using data from the Annual Survey of Hours and Earnings published by the Office for National Statistics (ONS), illustrates this – an overall gap of 17%, or £83.50 per week.

Source: ONS Annual Survey of Hours and Earnings

Statistics? D'oh!

But using simple averages to compare the pay gap between public and private can be misleading because it attributes the difference in earnings to the sector rather than the individual characteristics of the employees. The differences in skills, age and background are all much greater within each sector than between the two.

There is a danger here of falling into what statisticians refer to as Simpson’s Paradox. This is where the overall findings are reversed when broken down into smaller samples, and is a common problem when data sets that should be analysed separately are instead bundled together.

The most famous example of this problem is the Berkeley gender bias case. Here, 44% of male applicants were accepted to graduate school compared to 35% of women. A clear example of pro-male bias? Not quite.

When the data were examined department by department the bias disappeared, and if anything showed a marginal bias in favour of women. The result was caused by women being more likely to apply to highly competitive programmes (such as English) and men to less competitive programmes (such as Chemistry).

To avoid this danger, we need to identify the factors lurking beneath the headline figures that may explain wage differentials, and which may also be unevenly distributed across the two sectors.

Other factors

Occupation is an obvious example. Earnings tend to increase with skill level which may be captured by the employee’s occupation. According to the ONS, 61% of the public sector workforce are in high or upper middle skill level occupations, compared to 48% of the private sector. This divide has been exacerbated by the outsourcing in recent years of many lower skilled public sector jobs such as cleaning.

Occupation is also important because public sector employees are better qualified. For example, 45% of public sector employees have degrees compared to 27% of the private sector.

Age is another factor as it’s a proxy for experience, which in turn partly determines pay. As many jobs in the public sector require qualifications this means employees enter the workforce at an older age, and they tend to retire at an older age. Therefore, on average, the public sector workforce is older.

Source: ONS Annual Survey of Hours and Earnings

The pay differential between men and women is well documented. However this gap is lower in the public sector because there is a higher proportion of women employed in higher paying, professional jobs such as teaching and nursing. In comparison, in the private sector women are more likely to be found in lower paid jobs such as cleaning and catering.

Pay also varies across the country due to differing costs of living and varying local labour markets. As a greater proportion of public sector jobs are based in the high wage South East of England, this may also generate paradoxical findings.

Numerous studies have established that employees of large organisations earn more, on average, than those in small organisations, although lots of competing explanations have been offered to explain this finding. Almost all of the public sector (92%) is concentrated in large organisations with 500 or more employees compared to roughly half (49%) of the private sector.

The nature of employment also affects earnings. Full-time employees earn more per hour than part-time employees (by £4.63 per hour on average), while permanent staff also earn more than those on temporary contracts (by £2.14 per hour on average). The effect is expected to partly offset the previously mentioned factors as the public sector employs a higher percentage of part time workers (because promoting flexible working is more common) and more temporary workers.

Regression

Rather than relying on simple averages such as the median or mean wage, a more appropriate method to understand the role of the two sectors on wages is to use a sophisticated statistical model known as regression analysis. This allows us to measure the relationship between the (public/private) sector and earnings whilst controlling for all of these other factors.

A recent study by the ONS has done just this, and the figure below presents the average difference in mean hourly pay between the public and private sector as a percentage of the private sector wage.

Source: Annual Survey of Hours and Earnings and Monthly Wages and Salaries Survey

Two aspects of the findings are interesting. First, when controlling for all of these factors the pay gap last year was -1.9% – i.e. the public sector pays less than the private sector – and it has been negative for the past decade.

However, more striking is the importance of organisation size. Excluding it would result in an estimate that public sector employees are paid 2.7% more, on average, in 2013 than their private sector counterparts.

The distribution of earnings from the highest to the lowest earners is more compressed in the public sector. The pay gap at the top of the income distribution is larger (-10.8%) than at the bottom of the distribution (+8.4%) using the 95th and 5th percentile of the distribution to make the comparison. Senior managers therefore receive much higher wages in the private sector, while lower paid workers earn more in the public sector.

So who earns more? What is clear is that personal and job characteristics are far more important than whether you work in the public or private sector. Yet having controlled for all of these factors, the evidence points towards a small pay gap in favour of the private sector.

Hard Evidence is a series of articles in which academics use research evidence to tackle the trickiest public policy questions.