# Calculating the optimal progessive income tax

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calculating-the-optimal-progessive-income-tax

An interesting new paper from Peter Diamond and Emmanuel Saez, trying to calculate what would be the optimal top tax rate to have in a progressive income tax system. Worth taking seriously as one has a Nobel and the second is tipped to be an obvious choice in years to come.

The things that need to be balanced are that the poor like an extra £ of redistribution more than the rich hate losing an extra £ to taxation and there will be behavioural changes as a result of changes in taxation rates. So, the calculation is really, what's the top rate at which we can snaffle as much as we can off the rich to give to the poor without killing that rich goose that lays those golden eggs?

As an illustration using the different elasticity estimates of Gruber and Saez (2002) for high income earners mentioned above, the optimal top tax rate using the current taxable income base (and ignoring tax externalities) would be *=1/(1+1.5 x 0.57)=54 percent while the optimal top tax rate using a broader income base with no deductions would be *=1/(1+1.5 x 0.17)=80 percent.

You can just see it now, can't you? Whoopee! Tax the rich more!

Well, actually, this research was done for the US but let's apply it to the UK. This is the top tax rate for the top 1% as well: roughly those who currently pay the 50% income tax rate in the UK situation. It's also not the income tax rate. It's the total marginal tax rate: so we must include national insurance as well, that 13.8% that employers nominally but workers actually pay at such income levels.

So, we've firstly got evidence that the 50 % income tax rate in the UK is above the optimal level for that with the NI takes us well over our calculated to be optimal level of 54%. We'd need to have a top income tax rate of some 42, 43%, for the total marginal rate to be at that optimal 54%.

So, this is good, isn't it? Cut taxes now!

There's also a much more important difference that we should note between the US and UK tax systems. A US citizen is taxed on global income in the US. If they leave the country they still pay US taxes (with a large tax free allowance, with credits for foreign taxes paid). So the only possible behavioural response for a US citizen to such high tax rates is to just earn less money.

For a UK citizen of course this is not true. We can work less, take more leisure, if we think the Treasury is taking too much off us, just as can the American. But we can also leave. In fact, we're signed up to the EU which guarantees that we can move. Also, it guarantees that you cannot discriminate between EU citizens on the basis of national origin. So a Brit living in France would pay tax just like anyone else living in France: it would not be possible for the UK Treasury to insist that income made outside the UK were to be taxed at some special UK citizen only rate.

This escape hatch means that the optimal top rates decline: by quite how much no one as yet knows but it is obvious that they do decline.

So this is even better. We need to really cut taxes now!

And as to that mooted 80% top marginal rate? If we had a broader tax base and no deductions? That ability to bugger off and thumb ones' nose at the Treasury still applies. Meaning that the up to date research from two of the world's finer economists tells us that UK income tax rates are too high.

As, of course, we here at the ASI have been telling you for decades.