# An exercise for the reader

Here\’s how we should be measuring the top marginal tax rate in a US sense:

For the U.S. economy, the current top income marginal tax rate on earnings
is about 42.5 percent, combining the top federal marginal income tax bracket of
35 percent with the Medicare tax and average state taxes on income and sales.

Note that there is no inclusion of social security taxation because that is capped at below the level of income we are talking about (the top 1%).

In more detail, the calculation is:

The top tax rate ? is 42.5 percent for ordinary labor income when combining the top federal individual
tax rate of 35 percent, uncapped Medicare taxes of 2.9 percent, and an average combined state top
income tax rate of 5.86 percent and average sales tax rate of 2.32 percent. The average across states is
computed using state weights equal to the fraction of fi lers with adjusted gross income above \$200,000
that reside in the state as of 2007 (IRS, 2009a). The 2.32 percent average sales tax rate is estimated as
40 percent of the average nominal sales tax rate across states (as the average sales tax base is about
40 percent of total personal consumption.) As the 1.45 percent employer Medicare tax is deductible for
both federal and state income taxes, and state income taxes are deductible for federal income taxes, we
have ((1 – .35) × (1 – .0586) – .0145)/(1.0145 × 1.0232) = .575, and hence ? = 42.5 percent.

Excellent.

In the same paper we have the finding that this marginal tax rate should be much higher than it is:

the optimal top tax rate using the current taxable income base
(and ignoring tax externalities) would be ? * = 1/(1 + 1.5 × 0.57) = 54 percent,
while the optimal top tax rate using a broader income base with no deductions
would be ? * = 1/(1 + 1.5 × 0.17) = 80 percent.

Lovely.

Now, here\’s the thing. That 54% or 80% top marginal tax rate is not the marginal income tax rate. It is the marginal total tax rate. And what would be interesting is to find out whether we in the UK are under, at or above that recommended rate. This recommended rate being the peak of the Laffer Curve by the way. Tax the top 1% until trying totax them any more reduces tax revenues (and it also ignores long term effects but we\’ll ignore that too here).

So, given the US taxes that they include in their calculation of the best top marginal rate, what UK taxes do we have to include?

Well, firstly, obviously the 50% tax band for income tax. Then we\’ve got to add the uncapped part of employees\’ national insurance. 1% isn\’t it? Or did they raise it to 2%?

So already we can see that we\’re very close to that peak of the Laffer Curve given the current tax base of 54%. But how clo9se do we get to that 80%?

That I think is the more interesting question. We need to add the uncapped employers\’ NI of 13.8%. Because yes they are assuming that the incidence of such \”employer paid\” taxes is on the worker\’s wages. And, of course, we\’ve got to add the effect of 20% VAT (for they include sales taxes). ONS I think publishes tables of how much each decile pays in VAT as a protion of income, don\’t they? That would be a good starting point.

Now, someone better with numbers than I am could actually work this out: what is the current UK top marginal tax rate calculated the same way that Diamond and Saetz have calculated their one.

And I am certain that we\’ll find that the current rate is above the Laffer Curve peak rate given the current method of determining the tax base. And I wouldn\’t be at all surprised to find out that it\’s above the higher one they give as well, or perhaps just approacing it.

BTW, do note that the UK cannot actually get to that much wider tax base that the US can: because UKites can just bugger off across the channel to dodge taxes, something Americans cannot do. So the UK Laffer peaks could well be lower than the US ones anyway.

1. JustAnotherTaxpayer says:

Yes, top rate employee NI is 2% now.

0.50 + 0.02 + (0.138 / 1.138) = 0.641

top marginal income rate is hence 64.1%

if you presume that is spent on full-rated VAT stuff,

(1 – 0.358 ) * 0.8 = 0.287

so top marginal tax take is 71.3%.

Someone should audit my maths, though. Haven’t done the tricks with working how what % of top income is spent on VATted goods.

2. If you’re going to treat employers’ NI as part of the gross salary, then that makes the income tax and employees’ NI rates lower. The calculation is:
(0.5 + 0.02 + 0.138)/1.138 = 57.82%

It seems to me that sales taxes should not be included in marginal tax rates. We need to know not what % of top income goes to VAT, but what % of marginal top income does. My guess is that that’s very close to zero.

3. Alex says:

PaulB, you say that almost zero % of marginal top income goes to VAT. That surprises me, any data on this?

4. Richard says:

(and ignoring tax externalities)

Doesn’t that mean “ignoring the major determinants of the optimal top tax rate”?

5. JustAnotherTaxpayer says:

Good point, thanks PaulB. Why do you think there is no marginal propensity to spend on VAT rated goods for high earners? Don’t tell me the stories about bankers and champagne aren’t true!

6. I’m just guessing, based on my own spending habits.

7. John77 says:

WTF The highest marginal tax rates are on those struggling and simultaneously paying income tax and receiving tax credits. Excuse while I use my head to dent the nearest wall.
There is comprehensive data published but not produced by ONS – the drawback is that ONS does not believe it – and UK data is not perfectly comparable to the USA, so the only data I *really* trust is the Geoffrey Howe effect.
I read recently that both Jenson Button and Lewis Hamilton have moved to Switzerland, like Nat Rothschild
I DO NOT believe that consumption taxes have a significant effect on the incentive to work although they may have a significant effect on the willingness of consumers to condone evasion of VAT (I have observed surprise when I told a workman that I should pay a higher price by cheque than the cash alternative).

8. Andy Cooke says:

Looks like we’re all having different results on marginal income tax due to employers NI.

From first principles: Employer puts £100 to pay employee at top marginal rates.

£13.80 goes in employers contributions.
£100-£13.80 left = £86.20

50% of £86.20 on tax = £43.10
2% of £86.20 on employees NI = £1.724

Total deductions = £13.80+£43.10+£1.724 =£58.624

Marginal effective tax rate (ignoring sales taxes) = 58.624%

9. Andy Cooke says:

If we accept that consupmtion taxes will affect behaviour on income (I’m not completely convinced), the IFS tables show that effects of changing VAT on expenditure decile are failry equivalent at the higher expenditure deciles, but have a lower effect as you go up income deciles.

So (wild figure in the air), let’s say half of the marginal increase is spent on VAT-able items; half saved (and include ranges from “none spent” to “all spent” on VAT)

Of £41.376 left of th £100, half (£20.688) is spent on VAT-able items, purchasing £17.24-worth of goods (£3.448 in VAT).

Thus effective rate is 62.072% +/-3.448%
(from 58.624% to 65.52%)

As an aside, I quoted (eyeballing it from graph in an IFS presentation) in an argument with someone elsewhere on the Laffer Peak in the UK that “about 44% looks right”. Using the “without VAT” figures, a rate of 44% top income tax would give 53.452% effective marginal rate.

-feels smug-

Using the figures without VAT effects (which I feel is more defensible, but can’t prove), top rate of tax should be 44.6% (call it 45%).

Using the figures with VAT effects, it should be 39.8% (central projection; between 34.0% (max spend on VAT) and 44.6% (min spend on VAT))

10. Andy Cooke says:

Chuntering merrily to myself on what is probably a dead thread anyway 🙂

Even using the Treasury figures on their ready reckoner (found here: http://www.hmrc.gov.uk/stats/tax_expenditures/menu.htm )

The effects of abolishing the 50% rate, increasing the higher rate to 44% and increasing the threshold for higher rate tax to a nice neat £50kpa to make up for that increase (inclusive of lower threshold, so an income of £50k is where you pay higher rate), the Treasury should be better off by £1.5bn per year, increasing to about £1.8bn per year by 2013.

If the authors of this report are right, the increase should be even greater.

11. Andy, the 13.8% employers’ NI is a percentage of the employees’ marginal notional pay. So for a £87.87 pay increase the employer would pay £12.13 additional NI. Hence in your calculation the employers’ NI should be 12.13% not 13.8%.

12. Andy Cooke says:

PaulB – thanks for that. I was always under the impression that the 13.8% was off of the total payroll bill (before the employee sees it).

If it’s £12.13, the effective rate is – as you say – 57.82%.

If we include VAT, it’s 57.82%-64.85%, with a central (50% spent on VATables) of 61.34%

Ignoring VAT, the Laffer peak for the higher rate tax would then be 45.6%
(inclusive of the VAT effects, 35.1%-45.6%; central projection 40.9%)

So we should (in my master plan) set higher rate tax to 45%. The Treasury should be better off by over £2bn.

13. diogenes says:

re VAT…the theory goes that “essentials” (such as raw foodstuffs) are zero-rated…so the “luxury” things you buy such as suits, ties, cufflinks, alcohol, smoked salmon, cleaners, gym fees, etc etc are all clobbered by VAT, which ought therefore to impinge disproportionately on the “rich”, however you define that term.