Fun with numbers: Falling unemployment vs falling median wages.

From the BBC:

UK unemployment fell in the three months to January but there was a sharp slowdown in wage growth.

The Office for National Statistics (ONS) said the unemployment rate fell to 4.7% - it has not been lower than that since the summer of 1975.

However, wage growth has slowed significantly to 2.2% from 2.6% in the previous three-month period. Wages are rising above the rate of inflation, which is currently 1.8%, but the gap has narrowed...

Chris Snowdon at the IEA reconciles this apparent contradiction:

A one per cent drop in median earnings, as shown in the FT graphic, does not mean that people have been slogging away in the same old job on lower wages than they received before the recession.

Nor should it be inferred that life is rosier in France and Spain where median earnings are slightly higher than they were in 2007. When it comes to wage data, you only count if you have a job. The unemployment rate in France is twice as high as it is in Britain. In Spain, it is four times higher.

Understanding changes in the labour market helps us to explain the counter-intuitive finding that median incomes have risen since 2007 while median wages have fallen. Part of the reason is that people who were previously on benefits have found work, thereby raising their own incomes, but have disproportionately taken jobs that pay less than average, thereby lowering the median.

In general, this has made people better off. If, on the other hand, the economy had shed large numbers of low-skilled jobs, the median income would have risen mathematically without benefiting anyone.
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His article also mentions this:

But whilst there is no evidence that wages are falling, it is true that they have fallen and that whilst median earnings are rising they have still not returned to the levels seen in 2007. 

That is what the Financial Times chart actually shows and the FT offers several reasons for this, including the relatively high inflation rate between 2008 and 2011, but averages can be misleading and there is one statistical explanation that is so important that the ONS dedicated a whole webpage to it in 2015.

There is another obvious explanation for that. Let's assume our employer has been allocating £100 of pre-tax profit ('value added') to wage costs since 2007.

Back in 2007, the maximum he could pay out was £100 less 17.5% VAT less 12.8% Employer's NIC:

£100/1.175 x 1/1.128 = £75.49

Fast forward to 2017, the maximum he can pay out is £100 less 20% VAT less 13.8% Employer's NIC less 3% Workplace Pension contributions (assuming the median employee has opted in, which is questionable but let's run with it):

£100/1.20 x 1/1.138 * 1/1.03 = £71.10.

Those tax changes would cause a +/- 6% decline in reported total wages over the period, or 0.6% a year on average.