Swinney: Confused or Aiming to Confuse?

From the archive — published in 2015 on the original Chokkablog, kept as it was written.

Last night (16/12/2015) on the BBC's Scotland 2015 programme John Swinney was asked why he had chosen not to use the Scottish Rate of Income Tax (SRIT) to mitigate the pressure on public spending driven by Westminster's austerity policies.


If you watch from 13 minutes in, you'll see he's pressed as to why he didn't increase the SRIT by even just 1p in the pound. The following is a verbatim transcript:
"Well what that would have done would've put a disproportionate impact, and had a disproportionate impact on the incomes of people in low income households. It would have in fact been about double the effect on the taxable income of individuals at the lower income thresholds rather than people at higher income thresholds and I don't judge that to be the right way to deploy any tax raising changes"
Similar statements are now being parroted around social media. By seeding this misunderstanding Swinney shows that he either doesn't understand the effect of Personal Allowances on effective tax rates or that he is consciously trying to deceive the Scottish electorate.

Let me explain.

If all income was subject to tax then the statement above would make sense. If for example low earners paid 20% on all income and higher earners 40% then adding a flat 1% additional tax to both would indeed be "disproportionate". The lower earners' tax burden would rise by 1/20 = 5.0% whereas higher earners would rise by 1/40 = 2.5%.  I think this is how most people intuitively think about tax; it's an intuitive misconception that Swinney either shares or wishes to exploit.

Maybe Swinney is unaware of this thing called the Personal Allowance, the threshold above which tax has to be paid?

To illustrate with realistic (but rounded) numbers: say the Personal Allowance (PA) is £10k and we look at a low earner on £20k and a higher earner on £40k.  The 1% additional tax is only paid on income above the Personal Allowance, so

So the lower earner is seeing a further £100/£20k = 0.5% of their total income being lost but the higher earner sees a further £300/£40k = 0.75% of theirs.

The simplest explanations is this: The Personal Allowance means that the higher an individual's earnings, the larger the proportion of their income that is subject to the additional 1%.


I've used round numbers here to try and make the illustration clear, but they're pretty close to the actual figures. For those who like to see the actual numbers (and a graph) I include them at the end of this post.


But this is about more than arguing over how to interpret percentages. These additional taxes would be directly available to the Scottish Government to alleviate spending cuts, to protect the public services on which the most needy in society depend.

Let's take our worked example further: what does the Scottish Government do with the extra £400 they've raised from our two tax payers? Even if they couldn't find a way of spending it to disproportionately help the lower earner (as they surely could), both the earners in our scenario could benefit from £200 of additional public spending (their "population share" of the additional £400 raised).

The net effect would therefore be that our lower earner would be £100 better off (because they pay £100 more tax but they benefit from £200 more public spending). This would have been achieved by our higher earner making a net contribution of £100 more (paying £300 more in tax but only receiving back £200 by way of public spending).

Of course there are non-earners who could benefit from those additional taxes, which would be even more redistributive than the example above.

SRIT may be a blunt instrument, but it undeniably has the potential to redistribute wealth from the richer to the poorer.

So now let's return to Swinney's statement:
"It would have in fact been about double the effect on the taxable income of individuals at the lower income thresholds rather than people at higher income thresholds"
It appears to me that this statement is demonstrably untrue. If I'm right then Swinney is either an incompetent Finance Minister or a liar.


***** Clarification / Correction *****
When I first published this post I offered that if anybody could demonstrate that I'm wrong - that his statement could be justified with reference to robust factual analysis - then I would of course post an appropriate correction and apology here. So here we go ...

It appears Swinney's figure comes from taking the %age increase in the %age effective tax rate (which is a bizarre way to interpret "proportionate impact" as the explanation above I hope proves - taking percentages of percentages nearly always leads to confusion).

In our worked example (see table below) the effective tax rates are 9% and 15% respectively. If we take the increase in effective rate and divide it by the effective rate, our £20k and £40k earners both see a 5% increase (the numbers are rounded in the table;  0.47/9.40 and 0.74/0.147 respectively). At £60k the increase by this measure becomes 3.69% (0.82/22.34), at the higher threshold (£150k) the figure becomes 2.8%. So 5.0/2.8 = "proportionately 1.8 times more" i.e. double in Mr Swinney's rhetoric (I'm not quibbling abut 1.8 vs 2.0).

If you've understood the worked example above, I hope you'll agree using this figure to argue that lower earners are disproportionately impacted is disingenuous at best.

I'm happy to apologise for suggesting Swinney might have been lying. I maintain however that he either doesn't really understand what the figures mean or he is trying to confuse people

**** Clarification Ends *****


The Smith Commission powers being delivered through the Scotland Act 2015 will give the Scottish Government the ability to flex all income tax thresholds and rates. Let's hope that by the time those powers are delivered our SNP overlords have managed to understand how taxes work and/or start being honest about the choices they are making.

Is that too much to ask?






The following graph shows the effect of the personal allowance (note the personal allowance gets phased out between £100k and £121k) and changing tax rates at different thresholds. Note how the red line (adding 1% to SRIT) subtly diverges from the blue line - this is the graphical representation of the dynamics this blog describes.



I'm indebted to Andy Wightman for pointing out the existence of this incredibly misleading graphic (which simply ignores the Personal Allowances diluting impact for lower rate tax payers). I'm genuinely shocked to find it comes from this Scottish Parliament Information Centre (SPICe) briefing paper. Holyrood: we have a problem.





All archive posts · What I'm writing now