The meaning of mean
Ed Balls says today is Black Wednesday for British families: the day when tax and benefit changes will come into force which will cost the average household about £200 a year. But the Treasury says that for most households, today will actually be slightly brighter than yesterday, because, on average, the changes that are coming into force will leave households in the lower 80% of the income scale better off.
Who is right? Unfortunately, they both are. Fittingly enough, it all depends on the meaning of the word mean.
First things first. The opposition are right that, on average, British households will lose over £200 a year as a result of the mass of changes that come into force today - or about 0.7% of household income. Among other things, there'll be a significant rise in the personal tax allowance which will benefit around 23 million basic rate taxpayers, a 1% increase in National Insurance contributions, the removal of child tax credits for better-off families, and a move to uprate benefits and credits in line with the CPI instead of the RPI.
The Treasury doesn't dispute the £200 a year figure. But they say the average does not do justice to the highly progressive nature of the changes. The losses are heavily concentrated in the top 20% of the income distribution - so concentrated, in fact, that on average, households in the other 80% of the income distribution actually gain from the changes - albeit very marginally.
Figures from the IFS back up the Treasury analysis, at least on that point. The IFS says households in the top 10% will see an average 2.7% cut in their net income from the changes coming in today, whereas a household in the middle, in the 5th or 6th decile, will see their income go up by about 0.3%. A household in the bottom 10% will get an average increase of just 0.1%, and the average boost for households in the 2nd and 3rd deciles is even smaller than that, However, it's enough to allow ministers to claim that the bottom 80%, on average, will gain.
But then it's the opposition's turn to point out that an average can hide a multitude of sins. In fact, many families within each of those segments will lose out - in some cases, quite significantly - from the changes, even if the net impact on households in their income group is positive.
That's no surprise: the benefit changes generally hit families with children, because that's who generally gets the benefits in the first place. Whereas basic rate taxpayers will gain from the increase in the personal allowance, whether they have children or not.
In the IFS example, a single earner household with 2 children starts losing money from today's changes the moment their income goes above £18,000. By and large, the "winning" examples that the Treasury point to involve households with two earners, with both able to benefit from a higher personal allowance.
By their nature, all of these estimates also leave out the much bigger hit to household incomes from the rise in VAT. When that tax change is added to the others for the new financial year, the average household will be losing about 1.9% of their income, with the top and bottom tenth of the population losing most.
And of course, that's on top of all the price rises and real wage cuts that are also hitting households, which are not due to the government but are hitting family budgets all the same.
Depending on what you mean by mean, it might not be such a "Black Wednesday" for British households. But it's shaping up to be a pretty dark year.
It's no surprise that Ed Balls and Danny Alexander have been trading statistics all day on today's tax and benefit changes. To add further light to this murky topic, I've pulled together more numbers to clarify exactly what's happened to household incomes as a result of today's tax and benefit changes, and the VAT rise earlier this year.
It turns out the average loss to households from today's changes is just under £225 a year: that's the 0.7% hit to net incomes that I mentioned earlier.
Within that, the average loss for the top tenth of households will be in the region of £2,415 a year, while the average gain to households in the 5th and 6th deciles - in the middle - will be about £74 a year. The gain to households in the bottom tenth will be about £15 a year, on average, and households in the 2nd decile, one up from the bottom, will enjoy a princely gain of £1.42 a year. No wonder Labour has found it easy to find lower to middle income families who lose out.
As I described earlier, when you add in January's VAT changes, the numbers get much bigger, and they are all negative. The average loss for 2011 goes up to £600 per household.
Within that, the average total loss to households in the top 10% will be just over 3.6%: in cash terms, just over £3,200. The average total loss for households in the bottom 10% will be £190, but that's the equivalent of 1.8% of their net income, making them the second biggest losers, in percentage terms. On average, families in the 5th and 6th deciles will be about 1% worse off as a result of all these changes. That's the equivalent of about £272 a year.
So now you know. But all the same caveats apply. There'll be plenty of families in these income brackets who will lose more than the average figures suggest - and many others who will lose less. That's why they call it an average.