How do HMRC overstate the cost of the basic personal allowance by more than £20 billion?

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I have come across a curious anomaly in HMRC’s statistics. I am publishing this commentary in the hope that an explanation is available that I have missed.

Amongst the statistics that HMRC publish is data on the cost of tax reliefs. This is available here and here. I am, in particular, looking at the cost of the basic personal allowance, which according to HMRC’s data has changed as follows over the last few years:

I will look at 2015/16 as we have reasonably reliable data on the number of tax payers in that year and data is not distorted by additional reliefs. The last reliable estimate of the number of taxpayers is that there are about 30.7 million taxpayers (table 3.5).

Dividing the cost of the personal allowance is not a statistically accurate thing to do for reason I will note below, but is still a useful heuristic exercise. If done the £93.8 billion cost comes down to £3,055 for each taxpayer. HMRC says in note 30 to the table that:

The costs of the personal income tax allowances do not cover individuals who are not on HMRC records because their income is below the tax threshold

In other words, it seems that the cost is only that attributable to people who actually pay tax: they do not attribute a cost to those who are economically active but who do not pay tax, which in my estimate (I’ll be publishing more on this soon) might be about 6.4 million people in that year. If these people were included the cost would reduce to £2,528 a head.

It’s important to note that the personal allowance was £10,600 in 2015/16.

The basic rate of tax was 20%.

This means that for the basic rate tax payer the tax relief was worth £2,160.

For those earning over £100,000 (near enough for these purposes) the personal allowance was withdrawn. It appears that this impacted approximately 779,000 taxpayers (table 3.4). This meant 3,849,000 taxpayers effectively got two personal allowances compared to the basic rate taxpayer (same source).

The net effect of this is that to estimate the impact of all this the value of the personal allowance at basic rate should be multiplied by 33.77 million (30.7 — .779 + 3.849). That comes to £72.9 billion.

But HMRC claim the cost was £93.8 billion. That is an additional cost they have found of £20.9 billion. That is a personal allowance for an additional 9.7 million people if they all had income to use the whole allowance, which is extraordinarily unlikely. It is also very definitely more than the number of economically active people who do not pay tax.

Now, I stress, there may be something glaringly obvious that I have got wrong here, so I put it put for discussion and comment. But if I am right then the quality of these estimates has to be questioned.