Sunday, 28 August 2011

As Usual, Average Nonsense in JEP

THE average salary in Jersey increased by just 2.5 per cent during the last year - the second-lowest rise since 1995. According to figures released yesterday, a full-time worker now earns an average of £650 per week, or £33,800 per year. Although the rise is higher than the 1.1 per cent increase seen in 2009/10, it is significantly lower than the increases seen during the previous 15 years. Economic Development Minister Alan Maclean said: 'The earnings growth rate does remain low in historic terms, but that is not unexpected given that we have a weak labour market and a challenging economic climate.'

The regular report of misinformation is in the JEP again. All across the world, the measurement of national earnings have moved from the arithmetic mean, commonly known as the "average" to the median. The arithmetic mean is obtained by adding all the items up, and dividing by the number of items. The median is a statistical measure obtained by looking at the middle item in a distribution. See "Mean Versus Median" below.

For wages, the distribution is not a balanced one - the normal distribution or "bell curve" - but a highly skewed one, with a few higher wages grossly outbalancing the majority, which is why the median is a much better measure.

The States survey even mentions this - a warning not heeded by the JEP:

The level of average earnings derived from this survey is an informative indicator, particularly when comparing sub-sectors. It should be noted when interpreting these results that as a consequence of the earnings distribution being asymmetric (i.e. skewed towards higher values) the mean statistic provides a numerically greater measure of "average" earnings than the median. There are two surveys, and the 2009/10 Jersey Income Distribution Survey gives a median, so that:

the mean average weekly earnings of full-time equivalent employees (FTE) in Jersey in June 2011 was £650 per week
the median average weekly earnings of full-time equivalent employees (FTE) in Jersey in June 2011 was £520 per week

Now £520 gives a median yearly wage of £27,040, a fair bit smaller than £33,800.

The survey also notes:

The median average cannot be determined from the data collected for the Index of Average Earnings (IAE), since calculation of the median requires earnings at an individual level rather than at a company level. The Jersey Income Distribution Survey (IDS), which was carried out over the twelve-month period from May 2009 to May 2010, collected the necessary household and individual income information required to determine median income from earnings. The results derived from the IDS data, and presented below, include an up-rate from the survey period to June 2011 using the Jersey Index of Average Earnings.

But the main survey is terribly limited in scope:

Some 430 firms in the private sector were sent a survey questionnaire; 340 completed questionnaires were received back, representing a response rate of 79%.

Considering the number of small contractors, or individuals who run their own business, this seems like a very small number of businesses to survey, and one that itself will tend to reflect larger establishments.

I understand that Guernsey, on the other hand, can supply precise median figures for wages to a far higher degree of accuracy, although I have had trouble tracking it down. When I went to a recent talk at the Hotel de France, I was amazed to discover a figure being given for median wage. "Gobsmacked" would probably describe my reaction, having been told for years by the Jersey statistics department that it was not possible because of the nature of the survey (note they need a different survey to obtain the median which is also subject to sampling errors).

I asked the presenter from Guernsey how they managed a median, and Jersey didn't, and he told me they simply culled the information from the social security records. As far as I can remember, it was around £27,000 (figures on Guernsey's "open market"  - rental without property qualifications - are lower at a median of £18,000)

This is what he told me: there is no need for a survey, all the figures are available from Social Security on all Islander's earnings

In fact, it is massively more accurate. This works because although as in Jersey, there is an earnings ceiling, the median is the mid-point, so as long as it falls below the ceiling, it can be calculated.(see Mean versus Median below for an example). Now in Jersey:

There is an 'earning ceiling' this means that there is a cap on how much social security is paid by a person.  The earning ceiling this year is £3686 a month. So if you earn above this amount you will only pay Social Security on the first £3686 you earn, so the maximum you would pay would be £221.16 (6% of £3686). The maximum your employer would pay would be £239.59 (6.5% of £3686).

This means that the median (£520 per week = £2253 per month) is well below that, so it is quite possible to do as Guernsey does, and provide a median, not based on a survey, but based on the total workforce, with income gleaned from all the Social Security records, stripped to bare numbers, and easily number crunched in today's computers. All that is needed for median, in fact, is a sort from smallest to largest, and a count to find the mid-point.
Perhaps one day the JEP will have some real figures to report!

Mean versus Median

As an example, consider (as wages in thousands), the following cluster:


Now this results in Average = 25, Median = 25. (For the average - the mean - we sum, and divide by 8 in this case, for the median, we take the middle of the distribution when laid out in ascending order.)

Now let's change two of the numbers to 20.


Note that we now have Average = 23.75, Median = 25. The average has slipped down slightly.

Finally, let's just replace one of those 20s with a salary of a managing directors of a medium sized finance company (and I'm sure there are plenty with higher wages) at 120. We now have:


Average = 36.25, Median = 25

Note how rapidly the average wage has shifted. We

If we are calculating from Social Security, and there is a ceiling limit, say of 44, then the figures we work from show


But as long as the median - the middle of the list - falls below that (which it does), it can still be calculated at 25.



Anonymous said...

I am astounded that this is not already done. Something to hide? Everyone in Jersey should read this.

Anonymous said...

I get it. Using JEP reasoning, the average human being has less than 2 legs.

Simply add up all the legs in the world & divide by the number of people !

Even if you add in a certain number with prosthetic legs, the average is still less than 2.


I have 2 legs, more than average. Isn't living in Jersey wonderful?

Thank you JEP.

Anonymous said...

Well done Tony, I was part way through preparing a piece for my blog on this, but you have covered it very well, saving me the effort of finishing mine.

The 10 % reduction in average agricultural sector pay shows this up. When you consider how many are on minimum wage this mean value is disguising some much larger changes for a few people.

Nick Palmer said...

The point about getting the median wage from SS figures is good but, if one is going to use States data (anonymised, one hopes) like this, why not take the declared income amounts from the tax figures. Given these figures it wouldn't be too hard to publish actual graphs of income distribution, which would be far more informative than the simple, but profoundly deceptive, average wage we get presented with.

Nick Le Cornu said...

What is missing here is the will to collect and collate accurate statistical information. This is a deliberate policy decision to obscure the reality of poverty and wide disparities of income. Another example of concealment for political ends by the COM.