Tax-Gate: An Alternative With No Cliff-Edge

Nigel Williams, 25 May 2012

By Mervyn Stone

“Let the Dean and Canons lay their heads together and the thing will be done”

was Sidney Smith’s idea for how to lay a wooden pavement around St Paul’s.

It is a pity that the 2020 Tax Commission, the Taxpayers’ Alliance and the Institute of Directors did not put their heads together before the Commission came out with its flat-rate tax proposal (20 May, 2012)―one that, to a first and probably adequate approximation, can be regarded as a system based on just two numbers, a 30% flat-rate (absorbing National Insurance) and a personal allowance of £10k.

It is a pity because, with just one more number, you can get rid of the ‘cliff edge’ at £10k and obtain smoother ‘progressivity’.  That is done by defining the third number T (a threshold gross income well in excess of £10k) as the largest gross income to get any personal allowance― and then making the personal allowance bridge the gap smoothly between zero at T and the full allowance of £10k for a gross income of £10k.  If T is chosen wisely, these are the technical features that could ensure democratic acceptance.

In its present form, the Commission’s proposal has been met with predictable outrage, given that, at face value, it would appear to be blatantly regressive in cutting to 30% the top tax-rate on the income that the rich currently declare to HMRC, but with only a modest increase in personal allowance in the other balance pan.

The merits of a 3-number scheme (no cliff-edge and smooth progressivity) do not depend on their arithmetic values.  So, for simplicity of exposition and necessity of illustration, I will give two of the numbers the already-mooted values of 30%, £10k.  A degree of generality is useful, however, so the symbol T will be around until we get down to arithmetic illustration, when T will be rather arbitrarily set at £60k.

To have any chance of acceptance, new policies must start with a good acronym: GATE stands for the four element of the alternative scheme:

1. gross income G
2. variable personal allowance A
3. threshold gross income T
4. effective tax-rate E.

Under GATE, a gross income of G would be taxed at less than 30% by a fraction A/G.  In other ‘words’  E = 30 x (1 − A/G).  By allowing A to depend on G and making a smooth choice of that dependence, the ‘cliff-edge’ for G can be eliminated―and replaced by a smooth transition of the effective tax-rate E from the 0% rate for the poor (G below £10k) to the 30% rate for those with G in excess of T.

But how, precisely, should A be made to vary with G, to bridge the gap between those two levels?  Personal allowance A has to be made equal to G for G under £10k, and has to be zero for G in excess of T―in these respects, GATE agrees with the Commission proposal.  However, it is not the size of one’s personal allowance but one’s personal value of E that would be the talking point of this new taxation system (were it to be introduced).  So the choice of how the tax-man calculates the allowance A for any particular G has to be a consequence of how we would like the ‘bottom line’ percentage E to vary with G.  For T = £60k, this table shows how E would increase with G if we wanted it to do so linearly (from 0% when G is £10k to 30% when G equals T):

I think the simplicity of such a table makes the case for linearity.  But simplicity for E comes only at the cost of complexity for how personal allowance A has to vary with G (in the interval from £10k to T) in order to ensure the linearity for E.  The necessary algebra should not overwhelm the HMRC computer! :

A = G x (T − G)/(T − £10k) .

If it ever came to implementation of this 3-number scheme, there would have to be more than a public consultation about the choice of the three numbers―and more than just thinking of three multiples of ten.  The objective would be a democratic balance of conflicting interests.  Parliament would have to elicit a legally enforceable social consensus.  An informed national debate would require:

1. calculations of how total Treasury tax-take might be hypothetically affected―using ONS data on personal gross income (hypothetical because a rigorously implemented flat-rate tax at source would be a powerful anti-avoidance and anti-evasion measure);
2. Treasury estimates of the scale of avoidance and evasion under the present system;
3. independent estimates of the financial and other economic benefits of a simplified system.

Flat-rate reform of the tax system would have a number of easily identifiable benefits.  For all but masochists and tax-accountants, GATE would banish the annual misery of a baroque Tax Return, since tax-payers would simply declare any gross income not taxed at source―e.g. in the ‘black economy’ or in foreign investments.  Tax offices could be emptied except for a few ‘dark arts’ officers doing random checks on gross income declarations.  The ‘tax due’ is a simple mathematical function of the agreed gross income and the Collector of Taxes would demand the tax-due, less tax already paid at source at 30% (gracefully refunding any overpayment).  So simple, in fact, that tax-payers could be given (and those relying on small investments might welcome) the option of making several Tax Returns in a year rather than annually!

Mervyn Stone is Emeritus Professor of Statistics at UCL and author of the Civitas publication Failing to Figure.