# Paul B tells us

1) The Diamond and Saez paper does not tell us what the revenue-maximizing tax rate is. It gives us a formula which (subject to their assumptions) allows us to calculate such a rate (the marginal rate on high earners), if we know the elasticity of taxable income and a parameter describing the shape of the high-end tail of income distributions. The 54% Tim quotes is just a number he likes.

Looking at the Diamond and Saetz paper we get:

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. Taking as fixed state and payroll tax rates, such rates
correspond to top federal income tax rates equal to 48 and 76 percent, respectively.

Note that the \”payroll taxes\” which they include would very much include employers\’ NI in our UK case.

Further, there\’s good reason to think that the territorial nature of the UK tax system, as opposed to the citizenship based US one, would mean that the optimal top UK rate will be lower.

And I certainly think that they telling us the actual top optimal rate there, not just providing a formula.

#### 4 comments on “Paul B tells us”

1. PaulB says:

Tim, it says “as an illustration”. Later in the same paragraph it describes the elasticity of 0.57 as a “conservative upper bound”. Furtherm0re, the Pareto parameter of 1.5 there comes from US data: the appropriate value in the UK seems to be lower. I wrote about all this here.

Tim adds: My real point is that this is the paper and calculation that Ritchie and others use to “prove” that the optimal top tax rate is 75% and above.

When this paper shows in fact that in our position it’s more like 54%. Almost exactly where we are at present.

2. Ian B says:

For me, the baffling part of all this is that so many apparently intelligent people believe that such formulae can actually be discovered.

3. Surreptitious Evil says:

Ian,

I’m sure that the formula is reasonably approximable. I’m less sure that the parameters could be estimated with any degree of accuracy.

4. Andy Cooke says:

I think PaulB’s in the right here:

Richie et al have been quoting the numerical result of the formula for the US without adjusting for the different payroll and consumption taxes in the UK (as Tim points out). However, to adjust for those differences but not the different elasticity and Pareto parameter is to make an exactly analogous mistake.

The elasticity was recently estimated as 0.46 by the OBR (justifying the cut to 45% rate); this was very close to the figure estimated by the IFS. So to plug in an elasticity of 0.57 just because that’s the US figure would be incorrect as well.

Just because Richie quotes figures from formulae without adjusting for the differences between UK and US doesn’t mean it’s right to do so with picking out others. We should use UK payroll taxes, UK consumption taxes, UK elasticity and UK Pareto value or we won’t get the UK result.