Wage distributions – mean, median and economically inactive
Wage distributions – mean, median and economically inactive

Wage distributions – mean, median and economically inactive

Suppose we want to compare the average hourly wages of full-time workers living in the different areas of Leicestershire. How should we judge average?

It is strongly recommended to compare using the median wage. This is the amount earned by the person ‘in the middle of the income distribution’. For instance, as you can see in the table below, the median hourly wage for a full-time work in Blaby was estimated at £16.97 in March 2020. This means that 50% of workers earned a wage below £16.97 and 50% a wage above. The alternative to the median, which is not recommended, is to look at the mean wage. The mean wage is the ‘average amount earned’ using the common everyday interpretation of average. As you can see the mean wage is typically considerably more than the median.

MedianMean
Blaby£16.97£19.34
Charnwood£14.01£16.02
Harborough£17.96£20.27
Leicester£11.63£14.07
Melton£12.69£14.75
North West Leicester£14.77£18.71
Oadby and Wigston£15.97£19.31
Estimated hourly wage of full-time worker.

Why not use the mean? Let us give an example to illustrate the pitfalls. The numbers for Leicester are estimated from around 75,000 residents (that are full-time employees). Suppose that Leicester City Football Club sign up Cristiano Ronaldo and pay him £30 million a year (and he goes to live on the Narborough Road). What will this do to the median wage in Leicester? Nothing, because one extra resident is not going to make any difference to the wage in the middle of the distribution. What will it do to the mean? It will increase it by £0.23 to £14.30 (based on their being 1730 hours in a working year.)

This increase in the average wage is potentially misleading. Suppose, for instance, Leicester City Council wants to boost wages in the city and judges progress relative to changes in the mean wage. Signing Ronaldo would have generated a 1.6% increase in the mean wage but done absolutely nothing to benefit other workers or address the issues that probably prompted the desire for an increase in wages. The problem with the mean, as we see with the Ronaldo example, is that it is biased by high earners, who have an over-sized influence on the mean.

The median wage also, though, has its problems in interpretation. The key thing to keep in mind is that the median is a calculated relative to a particular subset of the population. For example, the number of Leicester in the table above is based on around 75,000 residents in full time employment (fitting the specifications of the ASHE) but there are around 235,000 people in Leicester aged 16-64. Care is, therefore, needed in drawing conclusions from this restricted subset of the population.

To see why this matters, suppose that a new initiative from the City Council results in 5,000 unemployed residents getting a job that pays £9 per hour. This would generally be judged a good thing. It would, however, push down the median wage because there are 5,000 more people at the bottom end of the distribution. The mean wage also drops by £0.32 to £13.75. Thus, the policy, while it seems beneficial, ends up making the numbers look worse. It is important, therefore, to put any discussion of wages in a context of measuring overall employment and economic activity.

This could be crucial in measuring the effect of Covid. If Covid reduces employment in lower skilled, lower wage sectors, such as hospitality, then average wages may go up. This, though, would not be good news. It would just be a reflection of increased unemployment of lower skilled workers.

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