This misunderstands who would actually gain from the measure. The vast bulk of the money goes to those earning more than £10,000. It is a very expensive tax cut, very poorly targeted on the working poor. (src)However, he misses the point. Danny studied economics, so one might hope he can appreciate the importance of numerate thinking on tax policy. Of course it is a tax cut for everyone, but it has the greatest proportionate effect on poorer workers: specifically, if one calculates the change in net income due to the tax change and divides it by the gross income, one finds that workers just at the cusp of the new threshold feel the greatest benefit. Workers just into the tax system on the old thresholds feel very little benefit, but then, they had barely any tax to pay anyway, so tweaking the tax system is never going to help them.So sure, the millionaire gets a benefit, but that is limited to a certain maximum, which must be at most a couple of thousand pounds. And maximum benefits are very socialist, right? To a millionaire, that extra money makes little difference, but to a worker on £13,000, it makes a lot of difference.Let us suppose, though, that Danny's point is taken by the Lib Dems. Can this problem be fixed? If we add another variable to our system, like the basic rate, then we can start to do clever things. For example, increasing the basic rate means we are able to claw back some of the tax reduction workers above the new threshold receive: then workers around the threshold get a double whammy, because they have the highest tax reduction and the highest felt effect.In fact, it should be possible (ignoring for a moment the existence of higher income tax bands) to specify a salary at which the net effect of taxation changes is zero, by increasing the basic rate appropriately. With a lower threshold of £12,000, if we decided to make the effect on the median salary zero (so that half the workforce felt a benefit and half, a loss), then we would increase the basic rate to about 29p in the pound. The change to the higher rate then 'freezes in' the effect on the worker, unless the higher rate is increased by the same amount. If, instead, we decided that no-one should lose out but higher-rate taxpayers should not have any benefit, then the basic rate should be raised to the more reasonable-sounding 24p in the pound.I do not know the budgetary effects of all this, but it is in principle possible to produce a policy which raises the threshold and the basic rate in such a way that a certain income level is unaffected and the budget is kept neutral, at least for a certain range of gross salaries. (Yes, it surprised me, too.) [EDIT: Later playing with a spreadsheet suggests that my initial instinct to be surprised was correct, as this probably isn't true; or at least if it is, it's only true for a range so limited as to be practically useless.] The only cost is that the party proposing this would be certain to earn headlines screaming about 'Liberal Democrat tax bombshell', even if the whole package were tailored to make the majority of people better off.A couple of notes for mathematicians: I'm working from a mental model of tax policy which supposes that the equations linking the 'tax policy' space of (change in threshold, change in basic rate) and the 'effect' space of (worker neutrality point, static budgetary effect) are linear. My quick tests suggest that works fine, although the static assumption is obviously a problem. I don't know what distribution is best to assume for incomes, but it should be possible to provide a very rough estimate if a suitable distribution can be found. Poisson, maybe?
Monday, January 18, 2010
The best tax policy on the market
The Lib Dems propose to raise the threshold at which workers start to pay tax from the current £6,500 or so to around £12,000, which is roughly in line with the minimum wage for a full-time worker. By the way, it is very clever politics: it implicitly accuses Labour of a double standard. Having decided that people need a certain amount of money to live on, Labour decides they can make do with less and taxes them.Danny Finkelstein, however, is unimpressed: